chapter 4 conformal cooling channel generation

Transcription

THE HONG KONG POLYTECHNIC UNIVERSITY
DEPARTMENT OF INDUSTRIAL AND SYSTEMS ENGINEERING
Conformal Cooling Channels Design for
Rapid Plastic Injection Mould
AU Kin Man
A thesis submitted in partial fulfilment of the requirements for
the Degree of Doctor of Philosophy
July 2008
ABSTRACT
Cooling design in thermoplastic injection moulding (PIM) process is of
paramount importance to the performance of the mould, influencing both the quality
and productivity of the part being produced. However, cooling channel design and its
fabrication processes are limited to respectively simple configurations as well as
conventional machining processes, such as straight-line drilling, and milling, etc.
The advancement of rapid tooling (RT) technologies and solid freeform
fabrication (SFF) techniques have provided the capability to produce rapid tool or
injection mould with complex geometric design of cooling channel, which are
conformal to the contour of the mould core or cavity surfaces. The shape
conformance between the cooling channels and mould surface cavity can achieve a
nearer uniform cooling performance and thus with fewer defect formations. However,
method with sound theoretical base for the design and verification of cooling channel
corresponding to mould cavity (or core) surface in the PIM process is still lacking,
especially for the complex geometric design in conformal cooling channel (CCC.)
In this research, the cooling process of thermoplastic injection moulding is first
reviewed from the heat transfer viewpoint. The most effective heat transfer that can
be achieved in practice is then formulated in terms of visibility concepts of
computational geometry. Feasibility checks for both conventional straight-line drilled
-i-
cooling channels and conformal ones are then analyzed with light illumination.
Conformal cooling channel generation is re-examined and a more appropriate
equidistant cooling channel generation methodology is explained.
In addition, variable radius conformal cooling channel (VRCCC,) conformal
porous pocket cooling (CPPC,) and conformal pocket cooling (CPC) are proposed to
test their heat transferrabilities, and benchmarked against the straight-line drilled
cooling channel. The output results of industrial case studies are visualized by 3D
rendering using computer-aided industrial design (CAID) tool and validated with the
aid of meltflow analysis. It is found that further improvement in heat transferrability
between the cooling channel surface and the mould surface can be realized with
VRCCC and CPPC.
Finally, the limitations of the visibility based methodologies to rapid PIM of
zero defect parts are discussed and possible future works suggested.
- ii -
PUBLICATIONS ARISING FROM THE THESIS
Journal Paper
Au, K.M., Yu, K.M., and W.K. Chiu (2009), Visibility-based conformal cooling
channel generation for rapid tooling, (submitted to Computer-Aided Design: under
review).
Au, K.M. and Yu, K.M. (2006), Variable radius conformal cooling channel for rapid
tool, Material Science Forum, 532-533, 520-523.
Au, K.M. and Yu, K.M. (2005), A scaffolding architecture for conformal cooling
design in rapid plastic injection moulding, International Journal of Advanced
Manufacturing Technology, 34, 496-515.
Au, K.M. and Yu, K.M. (2004), Balanced Octree for tetrahedral mesh generation,
Material Science Forum, 471-472, 608-612.
- iii -
Conference Paper
Au, K.M. and Yu, K.M. (2005), Porous cooling passageway for rapid plastic
injection moulding, Proceedings of The 2nd International Conference on Advanced
Research in Virtual and Rapid Prototyping (VRAP2005), Leiria, Portugal, 28
September to 1 October, 2005, 595-600.
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ACKNOWLEDGEMENTS
I would like to express my sincere gratitude to my supervisor, Dr. K.M. Yu for
his continuous guidance, patience and support to me throughout all stages of the
postgraduate study at the Department of Industrial & Systems Engineering, The
Hong Kong Polytechnic University. His encouragement, invaluable suggestions and
countless discussions have made this research possible. His deep understanding and
wide knowledge have broadened my view on this research work.
The work presented here was supported by a grant from the Research grant
Council of the Hong Kong Special Administrative Region and the Hong Kong
Polytechnic University. Their financial supports have made this research to complete
successfully.
I would like to give my special thanks to Dr. W.K. Chiu for his advices of the
research work. Besides, I would like to convey my thanks to all the staff and
technician for their tremendous supports and suggestions. I would like to give my
great thanks to those people who gave me advices, ideas, information, and support
during my period of study.
Finally, I am genuinely thankful to my family and my dear friends. This
dissertation is especially dedicated to my parents for their encouragement and
support of the research work.
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TABLE OF CONTENTS
ABSTRACT
PUBLICATIONS ARISING FROM THE THESIS
ACKNOWLEDGEMENTS
TABLE OF CONTENTS
LIST OF FIGURES
LIST OF TABLES
NOTATIONS
i
iii
v
vi
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xxviii
xxx
CHAPTER 1 INTRODUCTION
1.1 Background of Plastic Injection Moulding Process (PIM)
1.1.1 Fundamental of PIM Process
1.1.2 Overview of PIM Cycle
1.1
1.3
1.4
1.2 Injection Moulded Cooling Process
1.5
1.3 Improper Design of Cooling System for PIM
1.8
1.4 Feasibility Verification of Cooling Channel Designs for Plastic
Injection Moulds
1.9
1.5 Contemporary Design Techniques for Conventional Plastic
Injection Mould Cooling Channel System
1.11
1.6 Contribution of the Research
1.15
1.7 Objectives of the Research
1.16
1.8 Outline of the Thesis
1.17
CHAPTER 2 LITERATURE SURVEY
2.1
2.1 Overview
- vi -
2.2 Heat Transfer in PIM Process
2.2.1 Theoretical issues on heat transfer for cooling in PIM process
2.2.2 Importance of conductive heat transfer in PIM process
2.2
2.3
2.5
2.3 Cooling Methods PIM
2.3.1 Straight-line drilled cooling channel
2.3.2 Devices for alternative cooling system
2.3.2.1 Baffle and bubbler systems
2.3.2.2 Thermal pin
2.3.2.3 Heat pipe system
2.6
2.8
2.11
2.12
2.13
2.14
2.4 Cooling Channel Design guidelines for PIM
2.4.1 Mould materials
2.4.2 Types of coolant flow
2.4.3 Location of cooling channel
2.4.4 Part thickness
2.4.5 Arrangement of cooling channel inside an injection mould
2.4.6 Geometric design of the cross-section of cooling channel
2.15
2.15
2.18
2.20
2.21
2.22
2.25
2.5 Computerized Cooling Design and Analysis in PIM
2.5.1 Cooling design using computational and mathematical
modellings
2.5.2 Computer-aided cooling channel design and analysis
2.28
2.28
2.6 Conformal Cooling Channel Design and Fabrication in Rapid
Plastic Injection Mould
2.6.1 Overview of RT for the potential of CCC integration
2.6.2 CCC by copper duct bending
2.6.3 CCC by laminated steel tooling (LST)
2.6.4 Existing direct fabrication process of CCC for rapid injection
mould or RT
2.6.5 Injection mould design with CCC integration by CAE
simulation
2.34
2.32
2.34
2.37
2.39
2.40
2.42
2.43
2.7 Chapter Summary
- vii -
CHAPTER 3 FEASIBILE COOLING CHANNEL
DESIGN FOR PIM
3.1 Overview
3.1
3.2 Problems for the Verification of Near Uniform Heat Transfer of
Cooling Channel Design for PIM
3.2.1 Heat Transfer Issues
3.2.1.1 Heat transferrable
3.2.1.2 Heat conductable
3.2.1.3 Heat convectable
3.2.1.4 Heat radiatable
3.2.1.5 Heat transferrability detection
3.2.2 Visibility techniques of computational geometry
3.2.2.1 Point visibility
3.2.2.2 Line visibility
3.2.2.3 Surface visibility
3.2.3 Relationship of heat transferrability, visibility, and light
illumination
3.2.4 Transformation between heat transferability, visibility, and
light illumination
3.2.5 Heat conduction and visibility
3.2.6 Normal vector for heat conduction and visibility
3.1
3.3
Shortest Distance Conduction Feasibility Check Algorithm for
Mould Surface for PIM
3.3.1 Outline of feasibility check algorithm
3.3.2 Feasible and infeasible of the cooling channel system
3.3.3 Uniform and non-uniform heat transfers
3.3.4 Problem of non-uniform heat transfer
3.3.5 Simplifications for the proposed algorithm
3.4 Mould Surface and Cooling Channel Design for the Inputs
3.4.1 Facet models of the mould surface as the input
3.4.2 Integration of the inputs for the mould surface and cooling
channel
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3.4
3.5
3.6
3.7
3.7
3.7
3.8
3.9
3.10
3.11
3.12
3.15
3.19
3.20
3.22
3.22
3.24
3.24
3.26
3.27
3.28
3.28
3.30
3.4.3 Cooling channel generation for the input
3.4.4 Orientation and position settings for the mould surface and
cooling channel design
3.4.5 Bounding box setting by negative offsetting process
3.32
3.33
3.5 Procedures of Feasibility Check Algorithm
3.5.1 Definitions and conditions of feasibility check algorithm
3.5.2 Feasibility check algorithm by visibility
3.5.3 Minimum number of point light source for feasibility check
algorithm
3.5.4 Transformation between point set from visibility and point
light source from light illumination for the feasibility check
algorithm
3.5.4.1 Point light source setting for the feasibility check
algorithm
3.5.4.2 Linear light source setting for the feasibility check
algorithm
3.5.4.3 Area light source setting for the feasibility check
algorithm
3.5.4.4 Linear and area light sources represented by a number
of point light sources
3.38
3.40
3.41
3.46
3.6 Intuitiveness of Feasibility Check by Light Illumination
3.6.1 3D model rendering after light illumination
3.6.2 Contributions of light illumination for feasibility check
algorithm
3.6.3 Cooling channel design verification by illuminance after 3D
rendering
3.6.4 Colour range determination for 3D rendering
3.6.5 RGB and monochromatic values of the output solution for the
feasibility check algorithm
3.6.6 Output solution illustrated via light illumination for feasibility
check algorithm
3.50
3.51
3.54
3.7 Chapter Summary
3.61
- ix -
3.33
3.47
3.47
3.48
3.49
3.50
3.54
3.56
3.58
3.58
CHAPTER 4 CONFORMAL COOLING
CHANNEL GENERATION
4.1
4.1 Overview
4.2 Issues on CCC
4.2.1 Straight-line cooling channel and CCC Generation
4.2.2 Simplification for the CCC generation in the feasibility check
algorithm
4.1
4.11
4.15
4.3 Relationship of CCC Generation and Light Illumination
4.16
4.4 Procedures of CCC Generation
4.4.1 Point light source setting for the CCC generation
4.4.1.1 Point light source setting for the cooling channel
design
4.4.1.2 Maximum visibility for point light source setting
4.4.1.3 Light Source Minimization
4.4.2 Connectivity of a set of point light sources by neighboring
point location
4.4.3 Topological representation for the connectivity of the point
light sources of CCC
4.4.3.1 Definitions of topological representation
4.4.3.2 Topological representation for single cooling channel
axis
4.4.3.3 Topological representation for multi-cooling channel
axes
4.4.3.4 Topological representation of cooling channel
designs for rapid tool injection mould with single
cavity (or core) or multi cavities (or cores)
4.4.4 Procedure of CCC generation
4.4.5 Output solution of the test model
4.4.6 Feasibility verification of the proposed CCC
4.4.7 File Export for further processing
4.17
4.20
4.21
4.21
4.26
4.30
4.32
4.34
4.37
4.38
4.39
4.41
4.44
4.45
4.47
4.48
4.5 Chapter Summary
-x-
CHAPTER 5
VARIABLE RADIUS
CONFORMAL COOLING
CHANNEL AND CONFORMAL
SURFACE COOLING
5.1 Problems of CCC
5.1
5.2 Variable Radius Conformal Cooling Channel for Uniform
Cooling Achievement in PIM Design
5.2.1 Design methodology for the VRCCC
5.2.2 Consideration of constraints in geometric design of VRCCC
5.2
5.8
5.11
5.3 Feasibility Check for VRCCC Design
5.3.1 Pre-processing of VRCCC generation in the feasibility check
algorithm
5.3.2 Point light source setting for VRCCC
5.3.3 Output result visualization for VRCCC
5.13
5.13
5.4 Conformal Surface Cooling Passageway
5.4.1 Conformal surface cooling design for ideal uniform heat
transfer
5.4.2 Conformal porous pocket cooling (CPPC) passageway for
rapid tool
5.4.3 Conformal scaffold pocket cooling (CSPC) passageway for
rapid tool
5.20
5.22
5.5 Feasibility Check for Conformal Surface Cooling
5.5.1 Pre-processing of conformal surface cooling passageway
generation in the feasibility check algorithm
5.29
5.30
- xi -
5.14
5.18
5.25
5.27
5.5.2 Point light source setting
5.5.3 Connectivity of conformal surface cooling passageway
5.5.4 Output result visualization for conformal surface cooling
passageway
5.31
5.33
5.34
5.37
5.6 Chapter Summary
CHAPTER 6 CASE STUDIES
6.1 Overview
6.1
6.2 Case Study for VRCCC Designs of a Soup Container
6.2.1 Position and orientation settings of the test model in virtual
environment
6.2.2 Point light source setting for the feasibility check algorithm
6.2.3 Output results visualization of the test model by 3D rendering
in virtual environment
6.2.4 Cooling channel design modification by maximum visibility
and Light Source Minimization of point light source setting
6.1
6.3
6.5
6.6
6.10
6.2.5 Melt flow analysis for CCC design verification in Case 1
6.17
6.3 Case study for CCC and Conformal Cooling Pocket Passageway
of a 3D Freeform Mouse Model
6.3.1 Input of 3D freeform mouse upper part model
6.3.2 Position and orientation settings of the test model in virtual
environment
6.3.3 Point light source setting for the cooling channel generation
6.3.4 Visualization of the output result of the test model by 3D
rendering in virtual environment
6.3.5 CCC design modification by maximum visibility and Light
source minimization on the mould surface
6.20
6.38
6.4 Chapter Summary
6.41
- xii -
6.20
6.21
6.23
6.24
6.29
CHAPTER 7 DISCUSSION & FUTURE WORK
7.1 Overview
7.1
7.2 Feasibility Check Algorithm
7.2.1 Light illumination in the feasibility check algorithm
7.2.2 Shortcomings of the feasibility check algorithm
7.2.2.1 Ignorance of internal structure or accessory obstruction
7.2.2.2 Lost of geometric data after file translation
7.2.2.3 Not a fully automatic generation
7.2.2.4 Performance of output solution by 3D rendering
between single and double point light sources
7.1
7.3
7.3
7.3
7.4
7.4
7.5
7.3 CCC Generation for the Feasibility Check Algorithm
7.3.1.1 Maximum visibility method
7.3.1.2 Light source minimization
7.3.2 Manual parameter settings in CCC generation
7.3.3 Cooling channel axis approximation
7.6
7.7
7.7
7.8
7.9
7.9
7.4 VRCCC for Rapid Tool or Injection Mould in PIM
7.4.1 Potential enhancement in VRCCC design
7.10
7.11
7.5 Conformal Surface Cooling for Rapid Tool or Injection Mould in
PIM
7.5.1 Difficulty in mould material for CPPC
7.5.2 Topological representation of conformal surface cooling
7.5.3 Ignore of process parameters in conformal surface cooling
passageway
7.5.4 Impossible of ideal uniform heat transfer
7.11
7.6 Future work
7.6.1 Internal accessories, types of mould and undercut inclusion
in the feasibility check algorithm
7.6.2 Integration of file format file
7.6.3 Implementation of commercial package
- xiii -
7.13
7.13
7.14
7.14
7.16
7.16
7.16
7.17
7.7 CCC generation
7.7.1 Fully automatic process in CCC generation
7.7.2 Cooling channel axis approximation in curve segments
7.7.3 CCC generation for other industrial manufacturing processes
7.17
7.17
7.17
7.18
7.8 Improvement in VRCCC
7.8.1 Process parameters in VRCCC consideration
7.18
7.18
7.9 Improvement in Conformal Surface Cooling
7.9.1 Mould material for the feasibility check
7.9.2 Pressure drop verification by CFD and CAE analysis
7.9.3 Connectivity of point light sources for CCPP via topological
representation
7.19
7.19
7.20
7.20
CHAPTER 8 CONCLUSION
8.1
Ref.1
REFERENCES
APPENDICES
A.1
Appendix A: Case 1
B.1
Appendix B: Case 2
- xiv -
LIST OF FIGURES
Figure 1-1 Injection moulding cycle [Rees 2002]
Figure 1-2 The difference of moulding cycle between a) slow
cooling, and b) effective cooling [Rees 2002]
Figure 1-3 Workflow of conventional injection mould and cooling
channel design
Figure 1-4 Workflow of CAIMD and cooling channel design
Figure 2-1 Schematic diagram of conductive heat transfer
Figure 2-2 Straight-line cooling channel design for the core plate [Pye
1989]
Figure 2-3 Stepped cooling channel design for the core plate [Pye
1989]
Figure 2-4 Angled cooling channel design for the core plate [Pye
1989]
Figure 2-5 Cooling channel design for a two-plate mould
Figure 2-6 Conventional cooling channel design of a part with
rectangular shape for the cavity plate [Pye 1989]
Figure 2-7 Position of a cooling channel from an injection mould
assembly at cross-sectional view [Cracknell 1993]
Figure 2-8 Baffle system [Shoemaker 2006]
Figure 2-9 Bubbler system [Shoemaker 2006]
Figure 2-10 Thermal pin system [Shoemaker 2006]
Figure 2-11 Heat pipe system [Pye 1989]
Figure 2-12 Laminar and turbulent flows [Shoemaker 2006]
Figure 2-13 Dimensions for cooling channel diameter (d), depth (D),
and pitch (P) [Shoemaker 2006]
Figure 2-14 Difference between a) mould surface, and b) mould
surface with part thickness
- xv -
1.4
1.6
1.10
1.14
2.4
2.7
2.8
2.8
2.9
2.10
2.11
2.12
2.13
2.13
2.14
2.18
2.21
2.22
Figure 2-15 Cooling channel generation by straight-line drilling
process [Menges 2001]
Figure 2-16 Spiral design of cooling channel [Menges 2001]
Figure 2-17 Difference between traditional straight-line drilling and
diffusion bonding methods for injection mould
fabrication [HKPC 2008]
Figure 2-18 Arrangement of cooling channel layout, a) in series and
b) in parallel [Rees 2002]
Figure 2-19 Geometry of the cooling channel design by
cross-sectional view [Hopkinson 2000b]
Figure 2-20 Incorporation of spiral cooling circuit for planar mould
plate [Cracknell 1993]
Figure 2-21 Geometry of the cooling channel design for deep core
[Rees 2002]
Figure 2-22 Distance traveled by heat energy from heat source to
heat sink for cooling channel, a) with circular
cross-section, and b) star-shaped cross-section
Figure 2-23 Computational model for cooling channel design
[Jacques 1982]
Figure 2-24 CCC design based on feature recognition algorithm
[Li 2000]
Figure 2-25 Design analysis of CAD model by Cosmos/Works
Figure 2-26 Workflow of injection mould cooling channel design by
MoldFlow analysis
Figure 2-27 Location of CCC of DTM RapidTool [Jacobs 1999]
Figure 2-28 AIMTM prototype tooling with CCC design CCC, a)
copper duct bending, and b) bending of cooling duct
evenly around the cavity wall (surrounding the ejector
pin) [Decelles 1999]
Figure 2-29 CCC design for soft RT mould by copper duct bending
method [Ferreira 2003]
Figure 2-30 Green parts of an injection mould with CCC design made
by MIT's 3DP [Xu 2001]
Figure 2-31 Comparison between conventional and CCC design for
cooling simulation [Schmidt 2000]
- xvi -
2.23
2.23
2.24
2.25
2.26
2.26
2.27
2.27
2.30
2.31
2.33
2.33
2.37
2.38
2.39
2.42
2.42
Figure 3-1 Relationship between heat transferrability, visibility, and
light illumination
Figure 3-2 Heat transferable between heat source and heat sink, a) no
insulation, and b) insulation
Figure 3-3 Heat flow with two heat sinks
Figure 3-4 Heat transferrability within an injection mould
Figure 3-5 Heat conduction from heat source to heat sink with
distance traveled l
Figure 3-6 Workflow of mould cooling design verification
G
Figure 3-7 Point visibility between a line segment from points p
G
and q , a) within a convex set, b) intersection point on the
boundary of a non-convex set, and c) within a non-convex
set
Figure 3-8 Line visibility in two-dimensional representation
Figure 3-9 Point visibility on a shallow convex 3D solid model a)
perspective view of CAD model, and b) 3D rendering
Figure 3-10 Line visibility on a shallow convex 3D solid model a)
Figure 3-11 Plane visibility on a shallow convex 3D solid model a)
Figure 3-12 Relationship between, a) heat transferrability, b)
visibility, and c) light illumination
Figure 3-13 Point to point bi-directional relationship for heat
transfer, visibility, and light illumination
Figure 3-14 Point to point set in visibility
Figure 3-15 Point set to point set visibility
Figure 3-16 Omi-direction of heat source to heat sink from mould
half surface to cooling channel surface
Figure 3-17 Justification of light illumination from heat conduction
in the feasibility check algorithm
Figure 3-18 Comparison between a) gazing point, and b) gazing
region by point-to-point visibility
Figure 3-19 Heat conduction between heat source and heat sink with
a) straight-line heat transfer media, and b) U-shaped heat
transfer media
- xvii -
3.4
3.5
3.5
3.6
3.7
3.8
3.10
3.10
3.12
3.12
3.12
3.16
3.16
3.17
3.17
3.18
3.18
3.19
3.20
Figure 3-20 Heat energy flow in omni-direction from a mould
surface point, a) convex, b) reflective/planar, c) convex,
d) concave (v-shaped)
Figure 3-21 Difference between the flow of heat energy, a) in
omni-direction, and b) in omni-direction
Figure 3-22 Shortest distance for heat transfer
Figure 3-23 Flowchart of feasibility check algorithm
Figure 3-24 Uniform heat transfer between mould surface and
cooling channel surface
Figure 3-25 Non-uniform heat transfer between mould surface and
Figure 3-26 Cooling channel and mould half surface as the input for
the feasibility check algorithm
Figure 3-27 Input of the faceted model
Figure 3-28 A 3D CAD model for the proposed algorithm
Figure 3-29 Injection mould assembly model
Figure 3-30 A faceted model of the injection mould, a) cavity plate,
and b) core plate
Figure 3-31 Removal of unnecessary facets for the feasibility check
algorithm
Figure 3-32 Cooling channel generation, a) geometric design of
straight-line drilled channel, and b) geometric design of
CCC
Figure 3-33 Bounding box creation by offsetting process
Figure 3-34 a) Negative offsetting process for bounding box
generation, and b) relationship of cooling channel
diameter ød and the distance d of bounding box from the
edge of mould cavity plate
Figure 3-35 Setting of cooling channel axis at different situations, a)
inside the bounding box, b) at the bounding box, and c)
outside the bounding box
Figure 3-36 a) Position and orientation of the inputs for the
feasibility check algorithm, and b) illustration of output
display of the input
Figure 3-37 Flowchart for the input of the test model for the
- xviii -
3.21
3.21
3.21
3.24
3.25
3.26
3.29
3.30
3.31
3.31
3.31
3.32
3.32
3.34
3.34
3.35
3.36
3.38
Figure 3-38 Feasibility check algorithm by visibility, a) a line set, b)
a point set, and c) two point sets
Figure 3-39 Feasibility check between a CCC design with its
corresponding mould surface, a) for visibility, and b) for
visibility and light illumination
Figure 3-40 A comparison of illumination on a curved surface, a) a
line, b) non-illuminable region by two point sets, and c)
complete illuminable by three point sets
Figure 3-41 Point light source setting with lower levels of resolution
at top view
Figure 3-42 Point light source setting with high levels of resolution at
top view
Figure 3-43 Minimization of the number of point light source along
the cooling channel axis by interpolation, a) cooling
channel axis, b) point light source setting, and c)
minimization of point light sources
Figure 3-44 Visibility and light illumination of a single point light
source set on a 3D sphere with a rectangular plane
intersection
Figure 3-45 A scene of point light source a) point light source
setting, and b) 3D rendering
Figure 3-46 A scene of linear light source, a) linear light source
setting, and b) 3D rendering
Figure 3-47 A scene of linear light source represented by point light
sources, a) setting of point light source, and b) 3D
rendering
Figure 3-48 A scene of area light source, a) area light source setting,
and b) 3D rendering
Figure 3-49 A scene of area light source projection represented by
point light sources, a) setting of point light source, and
b) 3D rendering
Figure 3-50 Surface normal vectors on 3D surface model a)
perspective view, and b) normal vectors on surface
boundary
- xix -
3.42
3.43
3.44
3.45
3.45
3.46
3.47
3.48
3.48
3.49
3.49
3.50
3.52
Figure 3-51 3D model rendering without point light source setting
Figure 3-52 A scene of incomplete light illumination a) point light
source setting, and b) 3D rendering
Figure 3-53 A scene of complete light illumination a) point light
sources setting, and b) 3D rendering
Figure 3-54 The range of colour spectrum by coloured visualization
processed by graphic design tool
Figure 3-55 Coloured output display visualization of surface
illumination after 3D rendering
Figure 3-56 RGB and monochromatic values for a 3D solid model of
pyramid
G
G
Figure 3-57 Visibility between two point sets pi and qi on object
surface
Figure 3-58 Light illumination on CAID software for 3D rendering
Figure 3-59 Display of image data of the test model
Figure 3-60 Image data point capturing at different positions
Figure 4-1 Solid models a) in single shell, and b) in multi-shell
Figure 4-2 An injection mould a) with side core [Fu 2008] and b)
without side core [Kong 2001]
Figure 4-3 CAD model of Injection mould with side core
Figure 4-4 a) Terrain polyhedron, and b) feature of Terrain
polyhedron [Berg 2000]
Figure 4-5 Terrain polyhedron formulated into injection mould half
surface model
Figure 4-6 A convex polyhedron
Figure 4-7 Workflow for the mould surface manipulation for CCC
generation
Figure 4-8 Taxonomy of similarity in conformal transformation
Figure 4-9 Uniform scaling of a 2D curved model
Figure 4-10 Unequal distances, d1 and d2 at different regions on the
boundaries between the original curved model and a
curve model
Figure 4-11 The problem of normal offsetting a) for a polygon, and b)
curved object
Figure 4-12 Difference of view in 3D between a) whole mould, and
b) mould half
- xx -
3.52
3.53
3.53
3.56
3.56
3.58
3.59
3.60
3.60
3.60
4.2
4.3
4.3
4.4
4.4
4.4
4.5
4.6
4.6
4.7
4.8
4.9
Figure 4-13 a) Offset wireframe above mould surface, b) complete
illuminatable achieved by two edges from offset
wireframe, and c) extra edge addition to form a single
circuit
Figure 4-14 Workflow of cooling channel generation process in CAD
Figure 4-15 The whole cooling channel generation in CAD, a)
smooth mould surface, b) polygonal mesh, c) simplified
polygonal mesh, d) offset surface, e) cooling channel in
wireframe, and e) cooling circuit in zig zag pattern
Figure 4-16 Normal offsetting of mould surface for CCC design
Figure 4-17 CCC design and generation, a) offset surface cut by
rectangular planes, b) cooling channel axis formed by
intersection, c) wireframe formation, and d) cooling
channel generation
Figure 4-18 Workflow of CCC generation in the feasibility check
algorithm
Figure 4-19 Relationship between CCC generation and light
illumination, a) a point, b) heat sink c) a straight-line
segment, d) cooling duct, e) geometric design of cooling
channel, f) straight-line drilled cooling channel
Figure 4-20 3D CAD model, a) a solid model, and b) a faceted model
Figure 4-21 Position and orientation settings (user view) of the test
product
Figure 4-22 Normal vectors display on the surface of the test model
Figure 4-23 Bounding box creation with a distance d (ø4mm) from
the edge of mould core plate
Figure 4-24 The workflow of CCC generation
Figure 4-25 Position setting of the first point light source at the
coolant inlet
Figure 4-26 Normal vector, a) on a 2D curve, and b) on a planar
circle
Figure 4-27 Normal vector on 3D a) relationship between normal
vector, tangent vector, and bi-normal vector, and b)
normal vector on a 3D triangular facet
- xxi -
4.11
4.12
4.13
4.14
4.14
4.15
4.16
4.19
4.19
4.19
4.20
4.20
4.21
4.22
4.23
Figure 4-28 Identification of maximum visibility of a single point
light source on a 2D polygonal surface a) partial
visibility, and b) maximum visibility
Figure 4-29 Maximum visibility of a cube, a) front view, b) top view,
c) perspective view, and d) 3D rendering at perspective
view
Figure 4-30 Maximum visibility of a hemi-sphere, a) front view, b)
top view, c) perspective view, and d) 3D rendering at
perspective view
Figure 4-31 Variation in number of point light sources for
non-convex model, a) single point light source, b)
rendering of single point light source, c) two point light
sources, d) rendering of two point light sources, e) three
point light sources, and f) rendering of three point light
sources
Figure 4-32 Light illumination of a 2D surface, a) fluorescent tube,
and b) two light bulbs
Figure 4-33 Variation in number of point light source on a 2D
circular mould surface, a) four point light sources, b)
five point light sources, and c) eight point light sources
Figure 4-34 Steps of point light source selection under neighboring
point location, a) tangent vector (by user specify)
towards the neighboring point at starting point, b) line
segment formation, and c) cooling channel axis
formation
Figure 4-35 Approximating a cooling channel axis in 3D, a) a
sequence of points before curve approximation, b)
cooling channel axis is approximated by a series of line
segments joining adjacent points along the cooling
channel axis, c) a cooling axis is interpolated from the
points
Figure 4-36 Approximation of the cooling channel axis via the point
light sources setting a) coordinates on point light
sources, and b) 3D geometric modeling of cooling
channel design with point light sources
- xxii -
4.23
4.24
4.25
4.27
4.29
4.30
4.31
4.33
4.34
Figure 4-37 Topological representation of a single cooling channel
axis
Figure 4-38 Topological representation of multi cooling channels
axes
Figure 4-39 Graphical representation of diverse CCC’s designs for a
mould cavity plate with multi-cavities in a rapid tool
Figure 4-40 The connectivity of diverse cooling channel designs for
the multi-cavities within a rapid tool
Figure 4-41 Point light source settings for the test model
Figure 4-42 Cooling channel axis by point light sources connectivity
Figure 4-43 Cooling channel axis generation for the CCC design in
relation to the mould surface
Figure 4-44 3D modelling of the CCC
Figure 4-45 3D rendering of test model after light illumination
Figure 4-46 3D rendering of the test model under colour display
Figure 4-47 Points picked up for cooling channel design verification
Figure 4-48 RGB and monochromatic values of image data at point
one
Figure 5-1 Geometric description of VRCCC with its central axis a)
top view, b) isometric view, c) front view, and d) side view
Figure 5-2 Rate of heat conduction at coolant inlet and outlet for
VRCCC
Figure 5-3 VRCCC design between mould cavity surface and cooling
channels, a) near the inlet portion, and b) near the outlet
portion
Figure 5-4 Surface normal offsetting process
Figure 5-5 Design methodology of VRCCC, a) offsetting of mould
cavity surface, b) cooling channel axis design along the
VRCCC c) variable diameter along the cooling channel
axis and d) 3D modelling of a rapid tool with VRCCC
design
Figure 5-6 Workflow of VRCCC generation for the feasibility check
algorithm
Figure 5-7 Relationship between coolant temperature, cooling
channel diameter and light source intensity, a) relationship
diagram and b) schematic drawing for the relationship
- xxiii -
4.37
4.38
4.40
4.41
4.42
4.43
4.43
4.44
4.44
4.45
4.46
4.46
5.4
5.5
5.6
5.9
5.10
5.13
5.15
Figure 5-8 Increase in light source intensity along the cooling channel
at different diameters (p1 = 200lx, p2 = 400lx, p3 = 600lx,
and p4 = 800lx)
Figure 5-9 Light illumination on a 3D plane with increasing light
source intensity
Figure 5-10 Point light source setting for a VRCCC in relation to a
mould surface
Figure 5-11 Geometric design of a VRCCC in relation to a mould
surface
Figure 5-12 3D rendering of the mould surface without point light
source setting
Figure 5-13 Coloured visualization output results of VRCCC in by
3D rendering in virtual environment of the mould
surface (isometric view)
Figure 5-14 Coloured visualization output results of VRCCC in by
3D rendering in virtual environment of the mould
surface (top view)
Figure 5-15 Gray scale visualization output results of VRCCC by 3D
rendering in virtual environment of the mould surface
(isometric view)
Figure 5-16 Gray scale visualization output results of VRCCC by 3D
rendering in virtual environment of the mould surface
(top view)
Figure 5-17 Variation of distance and rate of Heat conduction at
different region from mould surface to the VRCCC
surface
Figure 5-18 Conformal surface cooling for ideal uniform heat
transfer, a) within a mould cavity plate, and b) pocket
design
Figure 5-19 Conformal surface cooling for ideal uniform heat transfer
Figure 5-20 The geometric designs of cooling passageways for rapid
tool or injection mould in PIM process
Figure 5-21 CPPC, a) hollow hexagonal elements assembly, and b)
CPPC within the mould plate
Figure 5-22 Numerous scaffold elements
- xxiv -
5.16
5.16
5.17
5.17
5.18
5.19
5.19
5.19
5.20
5.20
5.23
5.24
5.25
5.27
5.28
Figure 5-23 Cavity mould plate with scaffold configuration, a)
cross-sectional view, and b) side view
Figure 5-24 Workflow design of feasibility check algorithm for
conformal surface cooling passageway
Figure 5-25 Mould surface of a mobile panel
Figure 5-26 Point light setting for a CPPC on a mould surface of a
mobile phone panel
Figure 5-27 Geometric design of a cooling network for the mould
surface
Figure 5-28 Approximated surface formation for point light source
setting for feasibility check algorithm
Figure 5-29 Topological representation for CPPC passageway
Figure 5-30 Visualization of the mould surface without point light
source setting (as the standard model for comparison) by
3D rendering
Figure 5-31 Coloured visualization output results of CPPC by 3D
rendering of the mould surface
Figure 5-32 Gray scale visualization output results of CPPC by 3D
rendering of the mould surface
Figure 5-33 CPPC integrated inside the mould cavity plate for a
mobile panel, a) CPPC, and b) mould cavity plate
Figure 6-1 3D CAD model of soap container
Figure 6-2 Mould core and cavity plates of a CAD soap container
Figure 6-3 Cavity plate of test model
Figure 6-4 Position and orientation of the test model with bounding
box creation
Figure 6-5 Geometric design of the proposed cooling channel for
the test model
Figure 6-6 Proposed cooling channel axis for the test model
Figure 6-7 Point light source setting for a straight-line drilled
Figure 6-8 3D rendering of the test model without point light source
setting
Figure 6-9 The 3D rendering in coloured visualization output result
of the straight-line drilled cooling channel
- xxv -
5.29
5.30
5.31
5.32
5.32
5.34
5.34
5.35
5.36
5.36
5.36
6.2
6.2
6.2
6.4
6.4
6.4
6.5
6.7
6.7
Figure 6-10 The 3D rendering in gray scale visualization output result
of the straight-line drilled cooling channel
Figure 6-11 Image data point capturing at different positions in Case
1
Figure 6-12 Normal vectors on the surface of the test model
Figure 6-13 Point light source settings within the bounding box
region for VRCCC’s
Figure 6-14 Connected point light sources as cooling channel axes of
the VRCCC’s
Figure 6-15 The coloured visualization output result after 3D
rendering of the VRCCC’s
Figure 6-16 The gray scale visualization output result after 3D
rendering of the VRCCC’s
Figure 6-17 Image data point capturing at different positions for the
test model
Figure 6-18 CCC generation of the VRCCC’s for the mould surface
of the test model
Figure 6-19 Cooling channels and 3D model designs in melt flow
analysis for Case 1, a) SLDCC, b) CCC, and c) VRCCC
Figure 6-20 Isometric view of a solid model of mouse (upper part)
Figure 6-21 Mould core and cavity plates of a CAD mouse model
Figure 6-22 Cavity plate of 3D CAD test model
Figure 6-23 Position and orientation settings in virtual environment
with bounding box creation
Figure 6-24 Proposed CCC design for the test model
Figure 6-25 Cooling channel axis formation for the test model
Figure 6-26 Point light source setting for the test model
Figure 6-27 Isometric view of the test model after 3D rendering
(without point light source setting) (view from left hand
side)
of the proposed CCC (view from left hand side)
Figure 6-29 The 3D rendering in gray scale visualization output
result of the proposed CCC (view from left hand side)
Figure 6-30 3D rendering for the test model without point light
source setting (view from right hand side)
- xxvi -
6.8
6.10
6.11
6.12
6.12
6.14
6.14
6.16
6.17
6.18
6.20
6.21
6.21
6.22
6.22
6.22
6.23
6.25
6.25
6.25
6.26
of the proposed CCC (view from right hand side)
result of the proposed CCC (view from right hand side)
Figure 6-33 Image data point capturing at different positions for the
test model for the proposed CCC (view from right hand
side)
Figure 6-34 Normal vectors on the mould surface of the test model
for maximum visibility
Figure 6-35 Point light source setting for the test model of the CPPC
design
Figure 6-36 Point light source settings connected with triangular
network
Figure 6-37 Triangular network of the CPPC for conformal surface
cooling
of the proposed CPPC
result of the proposed CPPC
Figure 6-40 Image data point capturing at different positions of the
test model for the proposed CPPC
Figure 6-41 CPPC for conformal surface cooling design of the test
model (mould cavity surface)
Figure 6-42 CPPC for conformal surface cooling design without
internal structure support of the test model (mould
cavity surface)
Figure 6-43 Cooling channels and 3D model designs in melt flow
analysis for Case 2, a) SLDCC, b) CCC, c) VRCCC, and
d) CPPC
Figure 7-1 Mobile phone panel with fine feature slot on the surface
Figure 7-2 Error formed by normal offsetting in fine features slot on
the mould surface
Figure 7-3 Problem of normal offsetting with complex geometric
design of a curve [Liu 2007]
- xxvii -
6.26
6.27
6.29
6.30
6.31
6.31
6.32
6.35
6.35
6.36
6.37
6.37
6.39
7.15
7.15
7.15
LIST OF TABLES
Table 1-1 Effect of cooling parameters for PIM [Au 2005, Menges
2001, and Rees 2002]
Table 2-1 Modes of heat transfer for PIM
Table 2-2 Thermal properties of commonly used injection mould
materials [Isayev 1987]
Table 2-3 Commonly used coolants [Cracknell 1993]
Table 3-1 Use of visibility in the feasibility check algorithm
Table 3-2 Comparison between heat transferrability, visibility, and light
illumination
Table 3-3 Entities for the set up of the test model
Table 3-4 Common RGB values and their colours on screen
Table 3-5 Image data of RGB and monochromatic values for colour
display by 3D rendering
Table 4-1 Minimum number of point light source for injection mould
Table 4-2 Types of cooling channel with codes for topological
representation
Table 4-3 Topological representation of a single cooling channel design
Table 4-4 Topological representation of multi cooling channel design
Table 4-5 Parameter settings of light illumination for result
visualization
Table 4-6 Topological representation of the CCC
Table 4-7 Percentage of light illuminated region by CCC for the mould
surface
Table 4-8 Mode of illumination at the point light source setting
Table 4-9 Points picked up on the test model after light illumination for
feasibility verification by RGB and monochromatic values
Table 5-1 Relationship between point light source, diameter, coolant
temperature, and light source intensity along the VRCCC
Table 5-2 Differences between conventional cooling channel, CCC,
VRCCC, and conformal surface cooling passageway
Table 6-1 Parameter setting for the result visualization for Case 1
Table 6-2 Topological representation of point light source setting for
straight-line drilled cooling channel
- xxviii -
1.12
2.3
2.17
2.19
3.9
3.13
3.35
3.57
3.60
4.29
4.36
4.37
4.38
4.42
4.43
4.46
4.46
4.47
5.16
5.22
6.6
6.6
Table 6-3 Percentage of light illuminated region by straight-line
drilled cooling channel for the mould surface
Table 6-4 Mode of illumination at the point light source setting for
the straight-line drilled cooling channel
Table 6-5 Image data of RGB and monochromatic values for the
mould surface
Table 6-6 Topological representation of the proposed VRCCC’s
Table 6-7 Parameter settings for the output result visualization for
VRCCC’s
Table 6-8 Intensity of point light source pi for VRCCC1
Table 6-10 Percentage of light illuminated region by VRCCC’s for
the mould surface
Table 6-11 Mode of illumination by the point light source setting for
the VRCCC’s
Table 6-12 3D rendering colour display image data of RGB and
monochromatic values
Table 6-13 Parameter settings for melt flow analysis in Case 1
Table 6-14 Comparison of melt flow analysis results in Case 1
Table 6-15 Topological representation of the proposed CCC design
Table 6-16 Parameter settings for light illumination of the feasibility
check algorithm of the test model
Table 6-17 Percentage of light illuminated region by CCC for the
mould surface
Table 6-18 Mode of illumination by the point light source setting for
the proposed CCC
monochromatic values
Table 6-20 Parameter settings of light illumination of the feasibility
check algorithm for the proposed CPPC
Table 6-21 Topological representation of the proposed CPPC design
Table 6-22 Percentage of light illuminated region by CPPC for the
mould surface
Table 6-23 Mode of illumination for the proposed CPPC
monochromatic values for CPPC
- xxix -
6.9
6.9
6.10
6.13
6.13
6.13
6.13
6.15
6.15
6.16
6.18
6.19
6.23
6.24
6.28
6.28
6.29
6.32
6.33
6.35
6.36
6.36
6.38
6.40
NOTATIONS
The notations being used in this thesis are defined as follows:
∂
∪, ∪ *
Boundary
Ø
CA
D(X)
F, fi (i = 1 to t)
i , j , k
∧
∧
∧
L
L:
II
M
M+
MMA
MB’ (MB’=MB - M)
N
n̂i
→
(OP+ or OP-)
p, q
p i , l i, a i
OP
Pi (i = 0 => q – 1
P0 (P0 = Pq-1)
P1 (P1 = Pq)
Unionization and regularized unionization
NULL set
Cooling channel axis (i = number of CA from 1 to n)
Function of distance
Euclidian space
Facet of mould
Unit direction vectors corresponding to x-, y-, z-axes
Light illumination
Light source
Plane perpendicular to the parting surface for PIM process
Model geometry
Mould core
Mould cavity
Injection mould assembly
Subtraction of MB and M
Non-illumination
Normal vectors
Mould opening direction
Point corresponding to visibility
Types of light sources (point, linear, and area)
Point/node of CA
PL
PS
qi
Cooling channel inlet
Cooling channel outlet
Parting Line
Parting Surface
Point on CAi (i.e. points qi belong to the curve of cooling
R
x, y
channel axis
Parting direction
Points in x-, y-axes
- xxx -
Chapter 1 Introduction
CHAPTER 1 INTRODUCTION
1.1 Background of Plastic Injection Moulding Process (PIM)
In recent years, plastic injection moulding (PIM) process has become one of the
most significant processes in product manufacturing. The use of plastic or polymer
material is diversified in daily products, from toys, engineering or functional
components, and medical devices to elegant consumer goods. Nowadays, rapid
product development (RPD) is the successful strategy to take competitive advantages
of consumer good production and is highly recommended by different product
manufacturing companies. Short lead-time, high quality, and low production cost are
the major characteristics for RPD. Therefore, many product companies and
researchers have done a lot of research works or improvements for all related
disciplines from product design to manufacturing process on the RPD.
The appearances of computer-aided design and computer-aided engineering
(CAD/CAE) can simplify the steps during the stages of design and analysis. With the
solid freeform fabrication (SFF) and rapid tooling (RT) technologies, the integration
between design, analysis, and production can provide speedy and reliable methods
for RPD. In general, the time required for plastic injection mould design and
fabrication occupies a large sector of product development stage. The supports of
1.1
computerized and automatic design, analysis, and fabrication can reduce the time and
cost during product development. The productivity and quality can be enhanced.
The injection mould cooling design influences the quality and productivity of
the moulding part. The cooling performance can be affected by the geometric design
of an adequate cooling channel. However, the cooling channel design still relies on
the experience of the mould designers and mainly empirical formulae. There are no
single solutions for the mould designer to design a cooling channel layout for an
injection mould. Besides, the contemporary computer-aided injection mould design
(CAIMD) software can only provide general cooling analysis results and the simple
cooling channel design. As the cooling channel design is underestimated by mould
designers during the RPD, the verification process of cooling channel design is still
immature. As few theoretical issues and research works can be found in literatures,
this provides the motivation to develop methods to check the feasibility and
performance of the cooling channel of the proposed plastic injection mould cavity (or
core) surface geometries. A design algorithm for an adequate cooling channel design
for its corresponding mould cavity (or core) surfaces is also proposed. The
exploitation of computational geometry (CG) can solve different geometric problems
in engineering application areas efficiently, for examples, computer graphics,
geographic information systems (GIS), or robots. With the proposed design
1.2
algorithm, the geometric design of the cooling channel can be checked effectively
and accurately in the preliminary stage of RPD. Engineers or designers from
different disciplines or practices can handle and check the feasibility and
performance of the injection mould cooling channel design. This provides a new
impact to the design verification of the cooling performance during the CAIMD
stage.
Injection moulding is one of the versatile processes among conventional
manufacturing techniques used for producing plastic products [Rees 2002,
Buckleitner 1993, and Rubin 1972]. It provides diversified benefits to the
manufacturers, such as excellent dimension stability, without finishing operations,
light in weight, and attractive appearance of the final product.
Nowadays, more than one third of all thermoplastic materials and over half of
all polymer-processing equipment are based on PIM processes [Rees 2002 and
Dominick 2000]. PIM is commonly suitable for mass production of parts with
complex geometries.
1.1.1 Fundamental of PIM process
Injection moulding for thermoplastics [Menges 2001 and Smith 1995] is the
most common manufacturing process by which plastic components are transformed
1.3
to diverse useful products for daily life. In essence, PIM is a process whereby a solid
thermoplastic material is heated until a state of fluidity is reached. The polymeric
melt is then transferred under injection pressure into a closed hollow space of mould
cavity. Then the melt is cooled in the mould until a solid state is reached, conforming
the shape to the mould cavity.
PIM is a cyclical process encompassing the following steps: Heating and
melting the process polymeric material, mixing the liquid polymeric melt, injecting
the melt into the mould cavity, cooling, solidifying the melt in the cavity, and
ejecting the finished part from the mould.
1.1.2 Overview of PIM Cycle
The injection moulding cycle [Shoemaker 2006, Osswald 2002, Rees 2002, and
Michaeli 1995] is the complete elapsed time required to go through all the operations
to fabricate the plastic products continuously. The sequence of complete cycle of a
PIM process is shown in Figure 1-1.
Figure 1-1 Injection moulding cycle [Rees 2002]
1.4
The PIM cycle starts with the mould closing step and then is followed by the
injection of polymeric melt into the hollowed mould cavity. A packing pressure is
sustained after the cavity is completely filled so as to compensate any material
shrinkage or trapping air within the cavity. The polymeric melt is sufficiently cooled
until solidification is completed. In the next step, the mould opens and the solidified
plastic part is ejected. Once the PIM cycle is completed, the screw is retracted and
returned to the original position, preparing for the starting of a new cycle. The total
cycle time, Tcycle, for PIM can be varied by the shifting of the corresponding stages of
the following Equation (1-1):
Tcycle = tinjection + tcooling + tclosing + tejecting
(1-1)
where the main components of injection time and cooling time are presented by
tinjection and tcooling respectively. The mould opening and closing stages are represented
by tclosing and tejecting respectively, which includes proportionately little of the total
cycle time.
1.2 Injection Moulded Cooling Process
Cooling process [Rees 2002] can be defined as the reduction in temperature
from a high energy level to a lower energy level under the equilibrium condition.
Under the principle of conservation of energy, no energy can be added or eliminated.
1.5
It can only be removed or transferred via the conduction, convection, or radiation. In
fundamental PIM process, an appropriate mould cooling is essential to the quality of
the part produced by PIM process. When the polymeric melt is injected into the
mould cavity, thermal energy stored in the polymeric melt is removed away for
preceding the material solidification. Better control of the cooling stage can promise
benefits in improving the cooling time required. The difference of mould cycle
between slow and effective cooling is shown in Figure 1-2, and hence increasing the
productivity of the PIM process.
Figure 1-2 The difference of moulding cycle between a) slow cooling, and b)
effective cooling [Rees 2002]
The regulation and control of the mould temperature is typically accomplished
by the insertion of cooling channels within the mould cavity and core. Conventional
cooling channel is a fluid pathway that circulates coolants such as water or oil out of
the mould with heat withdrawn. The conventional cooling channel is fabricated by
1.6
the experienced mould engineer via straight-line drilled machining technique. The
quality management of the cooling performance is depended on their experiences in
the mould production. Generally, the heat removal process based on the
configuration of the conventional cooling channel experiences rigorous restrictions
by contemporary fabrication techniques.
Solid freeform fabrication technologies (SFF) have demonstrated their potential
to produce physical models with complex geometries. It is capable to reduce time
and cost in the development cycle with product quality improvement. SFF
technologies have found widespread use in speeding up tooling or mould production.
Conformal cooling channel (CCC) can be defined as a coolant passageway in tooling
that follows the geometry of the part to be produced, providing the advantages of
higher cooling rates and lower injection cycle times [Ferreira 2005 and Grimm 2004].
Mould engineers or designers take the advantages from the additive nature of the
SFF technologies so as to produce nonlinear CCC’s. Rapid tooling is fabricated
under the layer by layer addition process. The geometry of CCC design can be
convoluted and complicated. Because the CCC’s are uniformly located around the
mould cavity or insert, the uniform cooling effect gives rise to reduce the risk of
thermal stress induced moulded defects. The thermal energy can be transferred out
from the mould effectively.
1.7
1.3 Improper Design of Cooling System for PIM
Nowadays, the complexity of the part increases, the conventional cooling
system of injection mould cannot provide a uniform heat transfer to the whole
contouring of the mould plates (core and cavity). The fabrication of injection mould
cooling channel is based on conventional machining processes, such as straight-line
drilling. As the conventional straight-line drilling method limits the geometric
complexity of the cooling channel, the mobility of cooling fluid within the injection
mould is confined. The shape non-conformance between the cooling channel and
mould cavity (or core) surface will cause various injection moulded defects, such as
thermal stress, warpage, or sink mark. The quality of the plastic part cannot be
ensured. The cooling time for the plastic part after injection will increase. Meanwhile,
the production rate will be decreased. The idea of CCC design is to solve the
problem due to the shape non-conformance between the injection mould cooling
layout and mould cavity (or core) surface. The reduction of temperature difference
within the plastic injection mould enhances a continuous and uniform heat transfer
during the PIM process. Both quality and productivity of the plastic part can be
ensured.
1.8
1.4 Feasibility Verification of Cooling Channel Designs for Plastic Injection
Moulds
Non-uniform cooling adversely affects the plastic part quality and the efficiency
of heat removal. The larger residual stresses accumulated locally inside the plastic
part is caused by the big differences of mould surface temperature distribution. The
conventional cooling channel design for plastic injection moulds still relies on the
past experience and the heuristic data of the mould engineers up to now. A variety of
shapes of cooling channels can be designed for the same mould as there are no
particular guidelines for the mould designers to follow. The suitability of the
proposed cooling channel design can be verified after the mould fabrication and the
plastic part is moulded and ejected. There is no specific guideline or handbook to
verify the suitability of the cooling channel design at the preliminary mould
fabrication stage. A checking method is necessary as it does not only provide a
systematic approach to verify the suitability of the cooling channel design or
positioning in relation to its mould surface cavity (or core), but also the preliminary
cooling performance to the user at the mould design stage in an easy and a
time-saving manner. A workflow of conventional injection mould and cooling
channel design is shown in Figure 1-3.
1.9
Figure 1-3 Workflow of conventional injection mould and cooling channel design
1.10
1.5 Contemporary Design Techniques for Conventional Plastic Injection Mould
Cooling Channel System
During the injection mould cooling design and development stage, the design of
cooling layout is highly dependent on the mould engineers’ experiences, guidelines
from reference, empirical results, or data after the mould fabrication stage and
quality of plastic part after PIM process.
In the past decades, there have been numerous studies in the literature dealing
with the design of cooling channel for PIM process. Many injection moulding
handbooks [Isayev 1987, Menges 2001, and Rees 2002] provide an excellent review
of the theoretical issues and practical suggestions on how to design a conventional
cooling channel adequately. A number of research works, experiments, and practices
have been done to improve or optimize the design of cooling channels. Their design
concepts are summarized in Table 1-1. Early attempts at exploiting these cooling
parameters control are based on mathematical modeling or numerical calculation.
1.11
Table 1-1 Effect of cooling parameters for PIM [Au 2005, Menges 2001, and Rees
2002]
Cooling
parameter(s)
Descriptions
Effect
Influencing
factor (IF)
Hydraulic
pressure for
coolant
The pressure exerted on an enclosed
fluid is transmitted undiminished
throughout the fluid and acts equally
in all directions.
-ve
Indirect
Coolant flow
rate
Coolant flow rate determines the
amount of heat energy being carried
out within a period of time via the
cooling passageway. The flow can be
classified into turbulent flow and
laminar flow.
+ve
Indirect
Coolant
temperature
Coolant temperature at lower or higher
degree can provide various heat
capacities for the heat transfer.
-ve
Direct
Contact area
The larger the contact area of the
cooling passageway for heat transfer,
the greater the region to achieve
uniform cooling.
+ve
Direct
Thermal
conductivity of
mould material
Thermal conductivity is the quantity
of heat, Q, transmitted through a
thickness L, in a direction normal to a
surface of area A, due to a temperature
gradient.
+ve
Direct
Coolant selection Different coolants will have different
thermal conductivities and specific
heat capacities.
+ve
Direct
Coolant
circulation
within the
injection mould
-ve
Indirect
The longer the coolant circulation
distance, the less effective the heat
dissipation will be resulted.
With the advancement of CAD/CAE systems [Lee 1999 and Zeid 1991], the use
of CAD/CAE based system, e.g. MoldFlow, provides a precise method or tool to
1.12
evaluate the geometric design of cooling channel for a plastic part. The system can
also analyze the performance or efficiency of the proposed cooling system for PIM
and provide the result to the user at the earliest stage of mould development.
However, the solution of cooling channel design generated by CAD/CAE system
may not meet the user requirement as the geometric design of cooling layout is
simple and less adaptable to its mould surface geometry. The result of cooling
performance is less accurate to the real case. Besides, it is time consuming to design
a cooling channel with complex geometry by CAD/CAE systems. The design and
analysis of cooling channel layout will become inefficient and difficult. It is
necessary to set up a scientific-base guideline or theory for the injection moulded
cooling channel design for PIM. Thus, injection mould cooling channel design can
be more efficient and integrated. It can give a solution to the user to determine the
most favorable location of the cooling channel to be designed for various plastic
injection moulds. The injection mould design and development time and cost can be
reduced to a large extent. A workflow of CAIMD and cooling channel design is
shown in Figure 1-4.
1.13
Figure 1-4 Workflow of CAIMD and cooling channel design
1.14
1.6 Contribution of the Research
The purpose of this research study is to ascertain the importance of uniform
cooling of PIM process which is important to the quality and productivity of the
plastic product.
The uniform cooling performance can be achieved by the incorporation of
diverse types of CCC designs. The difficulty of building CCC within an injection
mould can be tackled by the advancement of SFF and RT technologies.
There have been numerous studies in the literature or reference books dealing
with the rules or methods for injection mould cooling channel design. The design of
injection mould cooling channel highly depends on the common sense, skills, and the
experience of the mould engineers from industrial practice. There are no single or
integrated solutions to design cooling channels for PIM process.
However, few research works on the verification of the performance and the
feasibility of the proposed cooling channel design can be found in the literature. To
overcome these shortcomings, a new approach to the feasibility check of injection
mould cooling channel design corresponding to the mould surface geometry is
presented in this dissertation. Designers or engineers from different sectors or with
various skills can also be utilized in a concise and a time-effective manner. Cooling
channel design with various geometric complexities can be examined with accurate,
1.15
concise, and speedy manners before the injection mould fabrication stage.
The main goal of this research is to assess the consequences of the proposed
feasibility check algorithm to design and verify an adequate cooling channel design
for the corresponding mould cavity (or core) surfaces for PIM process. Extra uniform
cooling performance between the cooling channel and its corresponding mould
cavity (or core) surface can be achieved. The cost and time required for product
development can be shortened as all the procedures can be controlled in the
preliminary stage of RPD.
1.7 Objectives of the Research
This research is:
y
To investigate an intuitive and implementable methodology to verify the
feasibility and performance of thermoplastic injection mould cooling channel
design.
y
To propose better cooling channel designs that are achievable with the latest
manufacturing and fabrication technologies
1.16
1.8 Outline of the Thesis
The thesis is organized as follows:
Chapter 1 describes the background information, contribution, and objectives of this
research work.
Chapter 2 provides literature review which is relevant to the research study in this
dissertation including design and fabrication methods of conventional cooling
channel for PIM process. RT moulds integrated with copper-tube bending CCC and
CCC by diverse SFF techniques are reviewed. Cooling channel design, analysis, and
verification for PIM process by CAD/CAM systems are discussed.
Chapter 3 describes the inter-relationship between heat transferability, visibility
technique, and light illumination process. A feasibility check algorithm is proposed to
apply in CCC design verification for rapid tool and injection mould in PIM process.
3D rendering for output result visualization in virtual environment via CAID is also
demonstrated.
Chapter 4 describes and demonstrates a CCC generation process for diverse cooling
channel or CCC designs. The verification of the feasibility and the cooling
1.17
performance for CCC design in relation to its mould cavity (or core) surface
geometry are also discussed.
Chapter 5 describes various CCC designs in rapid tool and injection mould in PIM.
First, the heat transfer distance effect using variable radius conformal cooling
channel (VRCCC) is described. The advantages of conformal surface cooling for
uniform heat transfer are discussed. Conformal porous pocket cooling (CPPC) with
internal support to achieve near uniform heat transfer is described. The feasibility of
VRCCC and CPPC are verified and demonstrated in the output result visualization.
Chapter 6 provides the case studies in this research work. Melt flow analysis is
employed to validate the CCC designs of VRCCC and conformal surface cooling as
CPPC.
Chapter 7 presents the details, implementation, and future work. Problems and
shortcomings encountered in this research work are discussed.
Chapter 8 draws the conclusion from this dissertation.
1.18
Chapter 2 Literature Survey
CHAPTER 2 LITERATURE SURVEY
2.1 Overview
In this chapter, various conventional cooling channel designs, cooling
accessories and alternatives employed in PIM process are reviewed. Some design
guidelines and criteria from literature references or experienced mould designers are
discussed. With the advancement of SFF technologies, rapid injection mould with
CCC integration can be realized. Various CCC’s with complex geometric designs
from various existing research studies are reviewed with their design principles,
models, and prototypes.
Conventional cooling channel design depends on machining processes, such as
milling and straight-line drilling process with or without numerical control (NC).
However, some constraints in geometric design and position setting affect the
machining of cooling channel within the plastic injection mould. Problems such as
injection moulded defect formation and long cooling time are difficult to solve.
Nowadays, the advancements of SFF and RT technologies can overcome several
limitations on the cooling channel design. In recent years, CCC design has
established significantly improved cooling performance especially for complex
geometric design of injection moulded products. Injection moulded defects formation
2.1
can be avoided. Recently, various research approaches have attempted to integrate
RT technologies in CCC design for injection mould fabrication rapidly.
2.2 Heat Transfer in PIM Process
Cooling channel design for PIM process is crucial to the plastic mould
development and production. A desirable cooling channel inside the mould plates
(core or cavity) can ensure the heat energy to be transferred uniformly and
effectively towards the cooling channel. The key consideration of cooling channel
design is focused on the heat transfer or heat exchange from the polymeric melt near
the mould parting surface to its nearest cooling channels within the mould plate. The
route of heat transfer within the plastic injection mould depends on the distance and
temperature difference between the center of the cooling channel and the surface of
the polymeric melt. In order to maintain a uniform mould temperature distribution
during the injection mould cooling process, the cooling channels must be placed
evenly inside the mould plates. Under the coolant circulation system, heat can be
transferred away from the mould plate via the cooling channels continuously and
regularly.
Three basic modes of heat transfer from thermodynamic consideration are
essentially involved in the PIM process and are tabulated in Table 2-1.
2.2
Table 2-1 Modes of heat transfer for PIM
Mode of heat transfer
Conduction ( q cond )
Convection ( q conv )
Radiation ( q rad )
The route of heat flow in plastic injection mould
From polymeric melt to the cooling channel
From cooling channel inlet to outlet via coolant circulation
From the mould to surrounding
In the case of heat transfer within a plastic injection mould, heat flows into the
mould by polymeric melt Qpolymer, and flows away via conduction, convention, and
radiation under a heat exchange system. According to energy balance, the heat
flowing in and out the injection mould can be described by Equation (2-1) as
follows:
Qpolymer = q cond + q conv + q rad
(2-1)
2.2.1 Theoretical issues on heat transfer for cooling in PIM process
In case of PIM process, the heat energy transferred from polymeric melt to the
surface of the cooling channel depends on heat conduction. The injection mould
cooling process is governed by simple conductive heat transfer [Menges 2001 and
Janczyk 1994]. The conductive heat transfer is the flow of energy from the region of
higher temperature to the lower temperature region within the system. The
conductive rate of heat transfer q is described by Fourier [Sprackling 1993] and is
shown in Equation (2-2) as follows:
2.3
q =
kA
(T0 − T1 )
l
(2-2)
where q [ws-1] is the heat energy conducted per unit time, k [W/m·K] is the
coefficient of heat conduction of the medium, l [m] is the length or distance traveled,
T0 [K] and T1 [K] are temperatures of different sides of a solid, and A [m2] is the
cross-section area.
The conductive heat transfer from Equation (2-2) can be described by the
schematic diagram of conductive heat transfer. See Figure 2-1.
Figure 2-1 Schematic diagram of conductive heat transfer
Equation (2-2) indicated that the rate of heat transfer is directly proportional to
the change of temperature and inversely proportional to the distance. When the heat
energy flows within the cooling channel from the inlet portion to the outlet portion,
the energy transferred is governed by convective heat transfer. The velocity of
convective heat transfer is determined by the temperature gradient at which the
coolant (such as water) carries away the heat. A large temperature gradient generates
2.4
a higher rate of heat transfer.
To express the effect of convective heat transfer, Newton’s law of cooling
[Sprackling 1993] is applied and is shown in Equation (2-3) as follows:
q = hA (Tw − T∞ )
(2-3)
where h [Wm-2K-1] is the coefficient of convective heat transfer, A [m2] is the surface
area for the coolant flow, and the temperatures of the wall and fluid are Tw [K] and
T∞ [K] respectively.
Different to conduction and convection where energy transfer via a material
medium is required, thermal radiation transfers energy of electromagnetic radiation
via regions where a vacuum state exists [Sprackling 1993]. The energy transferred is
the result of the temperature gradient as shown in Equation (2-4):
q = Fe Fgσ A(T14 − T24 )
(2-4)
where Fe is the emissivity function, Fg is the geometric view factor, σ is the
Stefan-Boltzmann constant, T1 [K] is the temperature of a body at a higher
temperature, and T2 [K] is the temperature of a body at a lower temperature.
2.2.2 Importance of conductive heat transfer in PIM process
The effectiveness of cooling process from polymeric melt to the surface of
cooling channel is governed by conductive heat transfer. Many literature references
2.5
have proposed that conductive heat transfer is of vital importance to the injection
mould cooling process [Dominick 2000 and Signoret 1998].
Up to now, the considerations of heat transfer in cooling channel design,
parameter settings, design guidelines, material selections, CAE tools, or other
cooling methods in PIM process are based on the theory of heat conduction.
2.3 Cooling Methods in PIM
There are no unique solutions to design a conventional cooling channel of an
injection mould for PIM process. Besides, there are several types of cooling methods
that can be applied to improve the cooling performance of a plastic injection mould.
Numerical data, reference books, and contemporary CAD/CAE systems for plastic
injection mould design are employed to provide the appropriate design rule,
guideline, or virtual simulation to mould designers or engineers before the injection
mould fabrication.
In some cases, cooling channel cannot be applied or integrated into the plastic
injection mould. Some features, such as thermal pin or bubbler system, may limit the
use of the channel. The size of the injection mould also affects the incorporation of
cooling channel.
Besides, some internal structures, such as side core or ejector pin, may limit or
2.6
block the cooling layout to pass through it directly. Heat energy from the polymeric
melt cannot be transferred effectively due to poor cooling performance in this region.
There are many types of cooling channel design in practice that is suitable for
different requirements or features of mould core or cavity with complex geometries
or internal structure [Pye 1989]. The alternative designs of cooling channel for the
mould core plate include straight-line drilled cooling channel is shown in Figure 2-2,
stepped type is shown in Figure 2-3, and angled type is shown in Figure 2-4. The
design alternatives are employed to suit the shape of the mould half surface from the
mould plate. However, the performance to achieve a uniform heat transfer between
the mould surface and cooling channel surface cannot reach a satisfactory level in
many cases. In this section, several research works related to cooling channel designs
and methods for PIM process will be reviewed.
Figure 2-2 Straight-line cooling channel design for the core plate [Pye 1989]
2.7
Figure 2-3 Stepped cooling channel design for the core plate [Pye 1989]
Figure 2-4 Angled cooling channel design for the core plate [Pye 1989]
2.3.1 Straight-line drilled cooling channel
The use of conventional cooling channel [Rees 2002, Osswald 2002, Menges
2001, and Pye 1989] allows coolant, such as water or oil, to circulate within the
injection mould and remove the heat energy by dissipation. It is the most common
method of controlling mould temperature. The cooling channel is generated by
conventional machining processes in various sizes and positions as close as possible
2.8
to mould surface of the cavity or core plates. The design of cooling channel depends
on the complexity of the injection mould and mould cavity (or core) surface
geometry. In general, the cooling channel is formed by the conventional machining
processes such as boring tool, milling, or drilling machines to drill a hole at the side
wall of mould plates. The side wall of the mould is plugged for inlet and outlet
portions. See Figure 2-5. The coolant flows directly into cross bores at the inlet
portion and circulates along the cooling channel. The coolant at high temperature
flows out at the outlet plug with heat removal.
Figure 2-5 Cooling channel design for a two-plate mould
In case of straight-line drilled cooling channel design, the fabrication method
depends on the conventional machining processes, such as straight-line drilling.
Straight-line drilled cooling channel design is a quick method to generate a cooling
channel within the mould plate. However, the major problem is that the distance
from the heat source on the mould surface to heat sink on the cooling channel surface
2.9
along the whole cooling channel surface (from inlet to outlet) is not equal. The
design of conventional cooling channel of an injection mould and the positioning of
the conventional cooling channel is shown in Figures 2-6. Even where the cooling
channel can be easily drilled with some angles in order to morph the shape of the
mould surface, non-uniform heat transfer is evitable. Sometimes, thermal stress
accumulation caused by non-uniform heat transfer will lead to defect formation on
the plastic part being moulded.
Figure 2-6 Conventional cooling channel design of a part with rectangular shape for
the cavity plate [Pye 1989]
As shown in Figure 2-7, heat transfer from polymer melt to the cooling channel
surface flows through various mould materials with different values of coefficient of
heat conduction. Besides, internal structures, such as sprue and ejector pin, may
easily hinder the transfer of heat energy to the cooling channel surface. The location
and size settings of cooling channel are limited by internal structures and geometry
of the mould surface within the mould plate. The feasibility of cooling channel
2.10
setting corresponding to its mould surface cannot be known obviously.
Figure 2-7 Position of a cooling channel from an injection mould assembly at
cross-sectional view [Cracknell 1993]
2.3.2 Devices for alternative cooling system
The complexity of geometric design of product will also increase the difficulties
and time of its injection mould design. Especially in core plate, it limits the design
and installment of straight-line drilled cooling channel. Conventional cooling
channel cannot be fitted to some injection mould designs with freeform shapes or
internal devices such as side core. Difficulties in design and installment of the
cooling channel to match these mould designs nearly always happen. There are some
alternatives that can also perform a cooling process inside some restrictive areas such
as core plate.
2.11
2.3.2.1 Baffle and bubbler systems
A baffle [Shoemaker 2006 and Beaumont 2002] is comprised of a hole drilled
across a cooling channel. See Figure 2-8. A thin metal blade is inserted in the hole
such that it interrupts the cooling channel. The blade diverts all the water up to the
top of the baffle and returns on the opposite side of the blade, returning to the same
main cooling channel. Numerous baffles can be positioned on a single cooling
channel to form a cooling channel positioned in a series pattern.
Figure 2-8 Baffle system [Shoemaker 2006]
A bubbler system [Shoemaker 2006 and Beaumont 2002] requires a feed
channel and a separate return channel. See Figure 2-9. It is used to cool cores and for
spot cooling in cavities or other critical areas. Water is directed to the bottom of the
drilled hole either by a baffle or a tube inserted into the hole, and the water is then
returned to the base of the hole. However, the distance between mould surface to the
cooling channel surface from baffler system are different. Temperatures from heat
source to destination are also varied along the whole cooling channel (from inlet to
2.12
outlet). The coefficient of heat conduction of metal blade is different from mould
material. Uniform heat transfer cannot be assured.
Figure 2-9 Bubbler system [Shoemaker 2006]
2.3.2.2 Thermal pin
Thermal pin [Shoemaker 2006 and Pye 1989] is becoming a common means of
cooling small core pin and delicate mould areas which could not be cooled with
water channels. See Figure 2-10. Both baffle, bubbler, and thermal pin encounter the
same problems in varying distances and values of coefficient of heat conductions
between mould surface and the cooling channel surface. Non-uniform heat transfer
almost always occurs in these cases.
Figure 2-10 Thermal pin system [Shoemaker 2006]
2.13
2.3.2.3 Heat pipe system
A heat pipe [Pye 1989] is a heat transfer device which is capable of transferring
heat energy at relatively high rates. See Figure 2-11. It is a hollow cylindrical vessel,
which is sealed at both ends by a cap. However, the differences in coefficient of heat
conduction and temperatures at different positions of mould surface will affect the
cooling performance, such as rate of heat transfer. Uniform heat transfer is difficult
to achieve.
Figure 2-11 Heat pipe system [Pye 1989]
The setting of cooling device or straight-line drilled cooling channel within the
mould plate (such as mould core plate) with respect to limited region or complex
2.14
mould surface geometry cannot provide a uniform heat transfer between the mould
surface and cooling channel surface. The model or performance of heat energy
transferred by conduction from the polymer melts on mould surface to cooling
channel surface cannot be clearly identified when complex geometric designs in
mould surface or internal structures are found.
2.4 Cooling Channel Design Guidelines for PIM
2.4.1 Mould materials
There are many commercially available mould materials that can be selected for
plastic injection mould, including many types of stainless steel, aluminum, copper,
and a combination between them [Fischer 2003, Bryce 1998, and Isayev 1987]. As
the constitutions of these materials for mould making are varied, they are utilized on
different mould components according to their specific physical and mechanical
features. Besides, there are also some materials that can be used for injection mould
fabrication, such as epoxy alloys or aluminum alloys. However, these mould
materials can only be used in lower volume production run in PIM process because
of their weaknesses in physical properties. They cannot endure the strong clamping
force and injection pressure during the PIM process. The mould will be easily
damaged after a higher volume production. The thermal conductivities of the mould
2.15
material have a direct influence on the heat transfer of the mould. If a mould material
has a high thermal conductivity and a low coefficient of thermal expansion, the rate
of conductive heat transfer (from mould material to the cooling channel), and
dimensional stability of this mould are better. The mould material selection stage
cannot be underestimated in a proper design and development of an injection mould.
Fischer [Fischer 2003] has stated that some functions are required to be fulfilled
during the mould material selection. These functions are:
y
Shape the part
y
Withstand the moulding pressure without distortion
y
Act as a heat exchanger to remove heat from the molten melt as quickly and
uniform as possible
The above functions can imply that harder materials usually have lower heat
conductivity. More complex cooling methods or designs are required to employ.
Cracknell [Cracknell 1993] has noted that the addition of alloying elements to
the mould steels can provide a remarkable effect on the conductive feature of the
mould material for PIM process. Rees and Buckleitner [Rees 2002 and Buckleitner
1993] stated that diverse mould materials have different physical properties and
features, such as heat conductivity or mechanical strength. The selection highly
2.16
depends on the designer or mould engineer’s requirements and the product features.
The thermal properties, such as thermal conductivity, k, specific heat capacity, Cp,
and thermal diffusivity, α, of commonly used mould materials are tabulated in Table
2-2.
Table 2-2 Thermal properties of commonly used injection mould materials [Isayev
1987]
Mould material
k [W·km-1]
Cp [kJ·kg-1·K-1]
α [m2·hr x10-3]
Aluminum
130.0
0.924
187.0
Beryllium copper
151.0
1.890
155.0
H13
29.5
0.462
29.4
P6
46.9
0.462
46.7
P20
36.5
0.462
36.3
S7
24.3
0.462
24.2
414SS
25.0
0.462
25.1
420SS
25.0
0.462
25.1
The thermal conductivity of the mould material such as steel is much higher
than that of the polymeric material. The higher the thermal conductivity, the more
heat can be exchanged. Huan and Jacobs [Huan 2002 and Jacobs 1998] found that as
thermal conductivity of the injection mould material decreased, heat removal from
the mould will decrease and the cooling time will become longer. It can be assumed
that the heat energy across the mould and coolant interface will be much higher than
the heat energy across polymeric melt and mould interface. However, the choices of
mould materials for specific parts such as core plate are limited. An injection mould
2.17
cannot be produced by a single mould material. The differences in coefficient of heat
conduction at different positions of the injection mould will affect the performance of
heat transfer.
2.4.2 Types of coolant flow
There are two different types of flow that water can experience when passing
through a cooling channel of an injection mould, they are turbulent flow and laminar
flow [Shoemaker 2006 and Osswald 2002]. As shown in Figure 2-12, both situations
will take away heat from the surrounding mould metal, but laminar flow is not as
effective as the turbulent flow. In the turbulent flow, the coolant is constantly being
tumbled and mixed.
a)
Figure 2-12 Laminar and turbulent flows [Shoemaker 2006]
b)
The creation of turbulence is a function of flow rate, cooling channel diameter,
water viscosity, water temperature, and coolant velocity as it passes through the
channels. Laminar or turbulent flows are characterized by a ratio called the Reynolds
2.18
number. We can obtain the existing Reynolds number by using Equation (2-6)
[Dominick 2000]:
Re =
DVρ
(2-6)
µ
where Re is the Reynolds number, D [m] is a diameter of a channel, V [ms-1] is the
velocity of the coolant, ρ [kg/m3] is the density of the coolant, and µ [kgm-3] is the
viscosity.
To achieve the required injection mould temperature, a range of coolants are
employed [Cracknell 1993]. Water is the most commonly used in plastic injection
mould [ISAYEV 1987] according to its superior thermal properties. The specific heat
capacity of water is high enough to store comparable heat energy. It needs 4200kJ
energy to raise one degree of temperature ºC. Water is the best media for heat
extraction. It is more preferred over other coolants. However, it is restricted to
temperature between 0 ºC to 100 ºC as extreme temperature will damage the mould.
The commonly used coolants are tabulated in Table 2-3.
Table 2-3 Commonly used coolants [Cracknell 1993]
Types of coolants
Thermal working range [ºC]
Antifreeze (e.g. water/glycol)
-20-0
Inhibited chilled/heated water
0-90
Heated oil
90-200
Electrically heated (usually in conjunction with
water or oil, as above)
150-450
2.19
In case of coolant flow, it is an indirect cooling process in PIM as it is governed
by convective heat transfer. The rate of coolant flow in convective heat transfer is
controlled by the size of pumping pressure, diameter, or size of cooling channel.
2.4.3 Location of cooling channel
Cooling channels should be of standard sizes in order to use standard
machine tools, standard fittings, and quick disconnects [Beaumont 2002]. Based on
the part thickness and volume, it is important to determine the design variables, such
as cooling channel diameter and its position between cooling channel and mould
surface cavity (or core) when designing a cooling channel within an injection mould.
The cooling channel must be set with accurate position and proper dimension in
order to obtain the maximum cooling performance in the PIM cooling process.
Previous research works and handbooks have been investigated with the position
setting of cooling channel in an injection mould by simple ratio [Shoemaker 2006
and Fischer 2003].
The appropriate location for cooling channels [Shoemaker 2006, Fischer
2003, Beaumont 2002, Isayev 1987, and Khullar 1981] is inside the mould cavity or
core with proper distance apart from the mould surface and between neighboring
cooling channels. As shown in Figure 2-13, the distance (D) to the surface of the
2.20
cooling channel should be one to two channel diameters from the cavity. The design
rule is that the depth should be 1 diameter for steel, 1.5 diameters for beryllium
copper, and 2 diameters for aluminum. See Figure 2-13. The distance between the
neighboring cooling channel centers should be three to five times the channel
diameter. A typical cooling channel diameter ranges from 8 to 14 mm.
Figure 2-13 Dimensions for cooling channel diameter (d), depth (D), and pitch (P)
[Shoemaker 2006]
2.4.4 Part thickness
To maintain an economically acceptable cooling time, excessive part wall
thickness should be avoided. The required cooling time increases rapidly with wall
thickness. Part thickness should be as uniform as possible [Potsch 2008, Fischer
2003, Rauwendaal 2000, Michaeli 1995, and Malloy 1994]. The cooling channel
design depends on the geometric design of the mould surface. As a simplification in
this research study, part thickness is not considered. See Figure 2-14.
2.21
Figure 2-14 Difference between a) mould surface, and b) mould surface with part
thickness
2.4.5 Arrangement of cooling channel inside an injection mould
The fundamental cooling channel design [Rees 2002] in an injection mould is
in the form of circular holes drilled at convenient positions. The coolant flow through
these passages will take the heat out of the hot regions close to the plastic melt. For a
plastic rectangular box, the cooling channel changes its direction to approximately
follow the geometric design of the part. For setting one coolant flow path, a number
of inter-connecting holes are drilled and some of them are blocked to form the
desired circuit.
The straight-line drilling process can provide flat plate cooling channel with
serial or parallel connections. Many theoretical issues have been studied on the
benefits and weaknesses of these patterns [Gastrow 2002 and Menges 2001]. In
general, flat plate cooling channel can be appropriately applied to an injection mould
with a large flat area and a thin planar plastic part. See Figure 2-15. The conditions
2.22
for serial or parallel connections depend on the geometric design of the plastic part.
Besides, other type of cooling channel, such as spiral (See Figure 2-16) or hexagonal
cooling pattern can be applied to the cooling of a centrally gated part design. The
spiral cooling channel is externally machined into the core insert sleeve. O-ring or
seal groove are inserted to protect around the region after hole-drilling from leakage
of coolant [Menges 2001 and Pye 1989].
Figure 2-15 Cooling channel generation by straight-line drilling process [Menges
2001]
Figure 2-16 Spiral design of cooling channel [Menges 2001]
Diffusion bonding is an advanced solid-state joining technology for moulds and
dies fabrication incorporating complicated cooling channels [HKPC 2008]. Each
2.23
internal workpiece or component is machined before binding into one assembly. The
difference between traditional straight-line drilling and diffusion bonding methods
for an injection mould is shown in Figure 2-17. All these components can be
combined into a single part by high temperature fusion with copper as the fusion
material. A strong mechanical support can be provided by the metallic bonding of
these components. Complex internal structure is feasible.
Figure 2-17 Difference between traditional straight-line drilling and diffusion
bonding methods for injection mould fabrication [HKPC 2008]
For the arrangement of cooling channel inside the mould plate, a more
satisfactory solution is to design and connect the cooling channel for half of the
mould so that all channels are connected in serial or parallel. See Figure 2-18 [Rees
2002].
2.24
a)
b)
Figure 2-18 Arrangement of cooling channel layout, a) in series and b) in parallel
[Rees 2002]
2.4.6 Geometric design of the cross-section of cooling channel
The geometry design of cooling channel is restricted to the conventional
manufacturing and machining processes [Hopkinson 2000a]. Cracknell [Cracknell
1993] proposed that heat energy drawn from the surrounding of mould cavity (or
core) surface into the cooling channel can become uniform if the cross-section of the
cooling channel is circular in shape. Symmetry of circular form cooling channel can
provide a uniform cooling surface at any position for heat removal.
Besides, Hopkinson [Hopkinson 2000b] experimented the possible geometric
design of cooling channel with SFF technologies. See Figure 2-19. He stated that
2.25
circular cross-section drilled cooling channel was ideal as the entire perimeter was
exposed to the coolant with the same distance from the center of cooling channel. He
assumed that there are no air pockets and gravity effects are insignificant. The
change of geometric design from circular cross-section (Figure 2-20) to square or
triangular in shape will reduce the cooling efficiency. The geometric design of
cooling channel for deep core part is shown in Figure 2-21. The corner or edge of star,
triangular, or rectangular shaped cross-section cooling channel causes stress
concentrations under the hydrostatic pressure of the coolant flow. Thus, crack
propagation will be resulted at the edge.
Figure 2-19 Geometry of the cooling channel design by cross-sectional view
[Hopkinson 2000b]
Figure 2-20 Incorporation of spiral cooling circuit for planar mould plate [Cracknell
1993]
2.26
Figure 2-21 Geometry of the cooling channel design for deep core [Rees 2002]
The performance of increasing the surface area on a cooling channel for heat
transfer is less effective as the variation in distance the heat energy traveled from the
mould surface. Geometric design in cross-section of cooling channel cannot assure a
uniform heat transfer between the mould surface and cooling channel surface. The
distance for the heat energy transferred from heat source to heat sink for cooling
channel with different heat sources and heat sinks are compared in Figure 2-22.
Figure 2-22 Distance traveled by heat energy from heat source to heat sink for
cooling channel, a) different heat sources, and b) different heat sink
2.27
2.5 Computerized Cooling Design and Analysis in PIM
Up to now, cooling channel design feasibility can only be identified after
plastic part ejection or pre-production run. The mould engineers make use of the
results of injection moulded part analysis to modify the cooling channel [Shoemaker
2006, Beaumont 2002, and Isayev 1987]. Further improvement of the cooling
channel design is limited as the configuration has already been fabricated. A high
production cost, long time, and complex steps are required for the repair or
modification of the mould. Surface cracking, rusting, water leakage, or damage of
the mould will easily happen.
The design and manufacture of plastic injection mould or tooling commonly
employs manual processes and empirical methods [Fuh 2004 and Kennedy 1995].
There are numerous literature references, handbooks, data books [Rees 2002,
Osswald 2002, Naranio 2001, and Dominick 2000] for plastic injection mould
cooling design. Even with the design of injection mould aided by CAD/CAE systems,
these empirical methods are still used as guidelines or references.
2.5.1 Cooling design using computational and mathematical modeling
In the past, the mould engineers’ skills and experiences are decisive to the
whole injection mould cooling process. The cooling channel design is different from
2.28
one to the other. The performance, cooling time, quality of the plastic part can only
be known after the PIM process. As a result, injection mould defects and high
production cost cannot be easily avoided.
Plastic part performance and cooling time can be accurately predicted and
controlled with the aid of CAD/CAE systems. During the design of conventional
cooling channel, some major cooling parameters are utilized to achieve an optimal
design for the cooling channel model. These data are given by previous trial and
errors of different moulding experiments. These major parameters can be formulated
into various numerical equations to solve various design problems. Optimal design
parameters or models can then be determined by the numerical model analysis or
computational simulation. Much research work had been focused on the cooling
channel design using computational model [Beaumont 2002, Kennedy 1995,
Manzione 1987, and Isayev 1987]. In 1982, Jacques [Jacques 1982] proposed a
computational model for the cooling channel design for flat parts in an injection
mould cavity plate. The computational model is shown in Figure 2-23. His model can
illustrate the potential effect of unbalanced cooling with a simplified two-part
analysis by finite difference simulation.
2.29
Figure 2-23 Computational model for cooling channel design [Jacques 1982]
In 2005, Qiao [Qiao 2005] developed a systematic computer-aided approach to
achieve an optimal cooling channel design. Various issues on optimization processes
for cooling channel design are investigated. This process can contribute to avoid the
trial and error process normally carried out during the conventional cooling channel
design process according to the designer’s experience [Jacques 1982].
In 2000, Li [Li 2000] proposed a new design synthesis method and an algorithm
of part feature recognition to optimize the cooling system of a complex shape plastic
2.30
part in the initial design stage. The plastic part was divided from complex shape into
simpler shape features. Then the individual shape features with their own cooling
channel portions were combined to form the cooling circulation passageway of the
whole part. See Figure 2-24.
Figure 2-24 CCC design based on feature recognition algorithm [Li 2000]
Cooling channel design or its control parameters for an injection mould can be
identified by the calculation of some numerical formula in the literatures [Rao 2004,
Kennedy 1995, and Bernhardt 1983]. These calculations depend on the experiment or
process data. The cooling time [Menges 2001] of PIM process can be estimated by
Equation (2-6). The accuracy of cooling time estimation depends on data acquisition,
equation calculation, and graphical plot.
∂T
∂ 2T
=α 2
∂t
∂x
(2-6)
where T [K] is the temperature, t [s] is the time, α [m2·hr x10-3] is the thermal
diffusivity, and x [m] is the distance between the center of the cooling channel and
2.31
mould cavity (or core) surface.
Different cooling parameters, such as mould temperature or distance between
center of cooling channel and mould cavity (or core) surface, can be obtained if an
accurate cooling time is given. The cooling time will change if the shape factor of the
part design varies [Menges 2001]. However, some cooling parameters cannot be
controlled by the mould designer, such as supply of water coolant.
In 1994, Liang [Liang 1994] has reviewed and investigated the significance of
the rate of cooling to the production cost of the PIM process. He proposed a
simplified heat-transfer model and an equation for calculating the estimated cooling
time. Better control in the cooling time can contribute to effective control of the PIM
process for automatic operation.
2.5.2 Computer-aided cooling channel design and analysis
CAD and CAE systems [Lee 1999] have found a wide range of engineering
applications, for example, robotics design, toolpath generation, 3D modeling and
visualization, or model analysis [Shoemaker 2006 and Lee 1999]. The concurrent
computer-aided injection mould design (CAIMD) tools, such as MoldOffice or
3DQuickMold [3DQuickMold 2008] for SolidWorks [SolidWorks 2008], or
MoldWizard for Uni-Graphics NX [Siemens 2008], can provide an effective and a
2.32
convenient approach to design 3D injection mould assembly model with complex
internal accessories.
Many CAE systems or tools in the mould engineering discipline are available
for design analysis and optimization, for example, Cosmos/Works [SolidWorks 2008]
(Figure 2-25), MoldFlow MPI [MoldFlow 2008] (Figure 2-26), or Moldex3D
[Moldex3D 2008].
Figure 2-25 Design analysis of CAD model by Cosmos/Works
Figure 2-26 Workflow of injection mould cooling channel design by MoldFlow
analysis
2.33
2.6 Conformal Cooling Channel Design and Fabrication in Rapid Plastic
Injection Mould
SFF technologies have demonstrated the potential to produce tools or moulds
with complex geometry. It is natural to extend this capability to improve thermal
management for plastic injection moulds by integrating with a complex geometric
design of CCC. The appearance of SFF technologies can realize the direct fabrication
of CCC. The integration of CCC in the injection mould or RT can provide improved
uniformity and stability of injection mould temperature during the PIM process.
2.6.1 Overview of RT for the potential of CCC integration
Rapid laminating methods predate rapid prototyping by several years, even as
early as 1890 [Beaman 1997]. For instance, laminated tooling for blanking by
Professor Nakagawa was initially published in the late 1980s [Nakagawa 1985], the
term RapidTool was first introduced by the University of Texas at Austin for its metal
based SLS in 1995 [Hejmadi 1996]. However, the most popular and successful rapid
tooling is the two-liquid form (base material plus catalyst) soft tooling. This includes
the room temperature vulcanized silicone rubber mould making and the subsequent
casting with two-liquid form material, like polyurethane, unsaturated polyester,
epoxy, etc. However, the thermal conductivity and mechanical rigidity of silicone
2.34
rubber is not good enough for it to be used in large volume plastic injection mould.
This also holds true for high temperature vulcanized silicone rubber mould
(commonly called spin casting).
Conformal cooling is seldom applied to silicone rubber mould because of the
benefits of thermal properties of silicone rubber. A bridge tool using two-liquid
aluminium filled epoxy or ceramic based composite (CBC) is also used. It is rigid
when hardened but the thermal conductivity allows only small batch plastic injection
moulding [Ferreira 2003]. Also, these tools require a physical shape beforehand for
making the mould cavity and the procedure needs not have any link to CAD or RP.
To improve the thermal conductivities, fronting with metal the core and cavity
surfaces is practiced. For instance, nickel or copper is used in 3D Systems’ Direct
AIM (direct accurate clear epoxy solid injection moulding), sprayed metal mould
(Tafa), and electroformed mould (CEMCOM) are all backed-filled with epoxy or
CBC. Other method includes Cu-PA mould from DTM (now 3D Systems) which
employs bi-modal brass and polyamide powder material in selective laser sintering
(SLS) the plastic injection mould insert to be epoxy backfilled and bent copper duct
inserted for conformal cooling. One advantage of the above-mentioned bridge
toolings is that actual product material (e.g. ABS) can be injected by PIM process.
Rapid production toolings are also available in the market. This includes
2.35
RapidTool from DTM (now 3D Systems), Keltool from 3D Systems, ProMetal (3D
Printing of stainless steel powder) [Schmidt 2000 and Sachs 1997], and direct metal
laser sintering (DMLS) from EOS [Shellabear 2004]. Some other technologies that
support rapid plastic injection mould are Arcam Electron Beam Melting,
LaserCUSING [Edelmann 2004], Optomec Laser Engineered Net Shaping (LENS)
[Chavez 2000], POM Direct Metal Deposition, Metal Laminated Tooling [Himmer
2005], Fast-Form [Knights 2004], etc. Other rapid toolings derived from rapid
prototyping include sand casting mould (Direct Shell Production Casting, ZCast, and
SLS of Croning sand) and investment casting (stereolithography, drop-on-demand Jet,
multi-jet modeling, and even fused deposition modeling).
However, not all SFF technologies can support CCC fabrication. In particular,
only those with support removable, like selective laser sintering (SLS), direct metal
laser sintering (DMLS), and Prometal, allow direct fabrication of mould insert with
complicated CCC have been employed in the recent research works. Besides, there is
no rigorous theory to support the appropriate design of CCC. The design of CCC
depends on manual bending copper duct or human knowledge. Real uniform heat
transfer is difficult to be achieved.
2.36
2.6.2 CCC by copper duct bending
The research study of CCC design and fabrication in the earlier time is to bend a
copper duct as the fluid passageway within a rapid tool or an injection mould. The
CCC formed by copper duct bending approximately follows the shape of a mould
cavity surface. Jacobs [Jacobs 1999a and Jacobs 1999b] seems to be the first to
advocate successfully the term and the potential benefit of CCC in RT or rapid
injection mould. Instead of straight-line drilled cooling channel, mould inserts were
built as electroformed nickel shells backed with CCC encased in copper. See Figure
2-27. From his studies, productivity is increased and part distortion is reduced. An
FEA comparison shows that the maximum temperature is lower and the cooling rate
is faster in CCC [Jacobs 2000].
Figure 2-27 Location of CCC of DTM RapidTool [Jacobs 1999]
In 1997, Decelles [Decelles 1997] from 3D Systems proposed a method to
fabricate direct AIMTM prototype tooling with CCC by manual copper duct bending.
CCC of direct AIMTM prototype tooling (designed by 3D Systems) is shown in
2.37
Figures 2-28a. The injection mould model of copper duct bending as the CCC is
shown in Figures 2-28b.
a)
b)
prototype tooling with CCC design CCC, a) copper duct
Figure 2-28 AIM
bending, and b) bending of cooling duct evenly around the cavity wall
(surrounding the ejector pin) [Decelles 1999]
TM
In addition, Saurkar [Saurkar 1995] also investigated stereolithography-based
rapid tool AIMTM prototype tooling with CCC design to improve the performance of
heat transfer. The cycle time can be shortened and part quality can be improved with
the integration of CCC in a rapid tool. However, the performance cannot be up to the
expectation for effective heat transfer from polymer melt to the CCC formed by
copper duct bending. In 2003, Ferreira [Ferreira 2003] attempted to integrate CCC
and to use rapid soft tooling technology for PIM process. See Figure 2-29. His work
integrated RT with a composite material of aluminium-filled epoxy. The cooling
design of the soft tooling was inserted with a bending copper duct before the epoxy
filling process.
2.38
Figure 2-29 CCC design for soft RT mould by copper duct bending method [Ferreira
2003]
In 2008, Yang et al. [Yang 2008] proposed the capability of the precision spray
forming (PSF) RT process for die inserts or other components with CCC integration
by pre-formed profiled bar to improve the tool life and increase the productivity by
reducing the part cycle time. Some drawbacks are found when bending manually a
hollow copper duct. The geometry of the copper duct can only partially follow the
shape of the moulding part. The area within the mould plate incorporating a CCC
may be blocked by internal structure or component, such as ejector pin. The bending
of the copper duct is limited by its diameter, mechanical strength, shape, and size of
the moulding part.
2.6.3 CCC by laminated steel tooling (LST)
LST is a process that is employed to produce a laminated tool which is made of
sheets of steel from laser-based cutting technology. The process is based on
sequentially combining steel sheets layer by layer with high-strength braze for the
laminated injection mould fabrication. The layer manufacturing feature of LST
2.39
allows insertion of CCC into any shape or position required. In 2001, Bryden et al.
[Bryden 2001] had proposed a hot platen brazing process to manufacture the mould
for LST. This process is to join steel sheets together sequentially using high strength
brazed joints to produce laminated tools. In 2003, Wimpenny et al. [Wimpenny 2003]
presented and developed the use of LST process to produce CCC within the
laminated tooling for automotive applications. The LST tool is fabricated with the
aid of an advanced fabrication technology called Lastform. It is a process that
combines with laser cutting, laser sintering, and laminated joining. A real life
example for the fabrication of LST tools and automotive part was investigated.
LST with CCC fabrication can provide the advantage of dimensional accuracy.
However, LST moulds are used only for low melting thermoplastics and are not
appropriated for PIM process with thermosetting plastics or high temperature glass
fibre. The time and cost required for the production of CCC are higher than other
SFF technologies.
2.6.4 Existing direct fabrication process of CCC for rapid injection mould or RT
In 2000, Hopkinson et al. [Hopkinson 2000b] proposed the use of EOS Direct
Metal Laser Sintering (DMLS) to build tools incorporating with CCC for PIM
process. Their research work also includes the investigation of different geometric
2.40
designs of CCC, for example, circular-shape, star-shape, triangular-shape, or fractals.
The DMLS process provides an easy approach for the design and fabrication of CCC
in different shapes. In 2001, Dalgarno et al. [Dalgarno 2001] proposed the use of
DTM RapidTool process to incorporate CCC within the mould. These results were
compared with the conventional mould making method. The fabrication method can
be fully automated with less finishing step for small features of the mould when
compared to the conventional one. The method can reduce the cooling time of PIM
process. However, the tool durability and tool wear are the weaknesses for the DTM
RapidTool process. The performance of the part produced can only be known after a
large number of trials and errors with little predictable information.
Similar benefits are also confirmed in using three-dimensional printing (3DP) of
steel powder with CCC for rapid injection mould. During the development stage,
Sachs and his partners [Sachs 1997] investigated the mechanical properties of the
mould material, dimensional control, surface finish, and hardness. An injection
mould prototype was designed and developed. Both the plastic product quality and
cooling time have a significant improvement. In 2000, Sachs et al. [Sachs 2000]
proposed how 3DP can be applied to fabricate plastic injection mould with cooling
passageways which were conformal to the moulding cavity.
In 2001, Xu [Xu 2001] proposed a systematic and modular approach to the
2.41
design of complex CCC incorporated within an injection mould. With the direct
fabrication of the injection mould by 3DP process (Figure 2-30), CCC integrated
within an injection mould had shown simultaneous improvement in productivity and
plastic part quality when compared to the conventional one after the PIM process.
Figure 2-30 Green parts of an injection mould with CCC design made by MIT's 3DP
[Xu 2001]
2.6.5 Injection mould design with CCC integration by CAE simulation
A series of designed experiments was also performed by Schmidt [Schmidt
2000] in an attempt to evaluate and quantify the benefits of CCC for injection mould.
The study considered different generic part geometries, gating schemes, mould
materials, plastic resins, and cooling approaches. He suggested an overview of the
mould design approach, cooling simulation (Figure 2-31), and tool fabrication via the
3DP process, as well as part moulding and inspection results.
Figure 2-31 Comparison between conventional and CCC design for cooling
simulation [Schmidt 2000]
2.42
In 2003, Gibbons et al. [Gibbons 2003] reported the development of a RT
manufacturing route for gravity and high-pressure die-casting, which has also
incorporated CCC. Norwood et al. [Norwood 2004] has also demonstrated the ability
to manufacture laminate inserts quickly for die casting, the accuracy of finite element
analysis and the importance of designing CCC. Dimla et al. [Dimla 2005] proposed
to determine the optimal and efficient design of CCC’s using FEA and thermal heat
transfer analysis (T-FEA) in the configuration of an injection moulding tool.
2.7 Chapter Summary
In summary, various conventional cooling channel designs, cooling methods,
and CCC’s with complex geometric designs by SFF technologies in PIM process
from various existing research studies are discussed. Some design guidelines and
criteria for PIM cooling process are reviewed. Besides, a precise and concise
mathematical definition for CCC cannot be found nor the mathematical basis to
design and evaluate the effectiveness of CCC geometric models for near uniform
heat transfer.
2.43
Chapter 3 Feasible Cooling Channel Design for PIM
CHAPTER 3 FEASIBLE COOLING CHANNEL DESIGN
FOR PIM
3.1 Overview
In this chapter, a feasibility check algorithm for verifying the performance and
reliability of a potential cooling channel design in relation to its mould surface
(cavity or core) is proposed. The cooling process of thermoplastic injection moulding
is reviewed from heat conduction. The most effective heat transfer that can be
achieved is formulated in terms of visibility concepts of computational geometry.
Feasibility checks for straight-line drilled cooling channels and conformal ones are
analyzed with light illumination.
3.2 Problems for the Verification of Near Uniform Heat Transfer of Cooling
Channel Design for PIM
As reviewed in Chapter 2, various cooling methods can be applied to the
injection mould design according to its features and geometries. From manual (such
as formula or guidelines) to computer-aided cooling channel design by CAIMD or
CAE, the above methods cannot provide an intuitive verification whether or not the
design can achieve near uniform heat transfer. Some problems are listed as follow:
3.1
Problem 1: It is difficult to check the cooling performance without the aid of design
and analysis tools (such as CAE package or CAIMD software) or by
experienced mould designer. Besides, there are no simple tools or
guidelines for a designer to check the cooling performance without any
knowledge or skill on injection mould cooling channel design.
Problem 2: CAE software provides limited functionalities and modules for the
cooling channel design. The design results and the cooling channel
generation are simple and cannot provide a near uniform heat transfer
for the mould surface which has complex geometry.
Problem 3: It is difficult to interpret the results and feasibility of the proposed
cooling channel design as the procedures of the CAE software are
complicated and different from case to case.
Problem 4: It is difficult to know the performance of cooling channel design before
the mould fabrication and pre-production of parts or testing. The
appropriateness of contemporary cooling channel design can only be
checked from the performance of the plastic part being moulded.
Problem 5: The manual steps for the CAE analysis are difficult to follow by
inexperienced designers or users.
3.2
Problem 6: The time required is very long to validate the feasibility of the proposed
cooling channel design using the traditional methods for injection
mould design and fabrication.
Problem 7: The calculation formula, guidelines, and data are complex to be used for
new case of cooling channel design for PIM.
As discussed before, the feasibility check algorithm is proposed to verify the
performance or capability of heat transfer of the cooling channel design in relation to
the mould surface. The feasibility of the mould surface to the cooling channel can be
verified by the aid of heat transferability [Incropera 2002, Long 1999, O’Neil 1999,
Cengel 1998, Kevorkian 1990, and Kreith 1980], visibility from computational
geometry and light illumination from 3D graphics design. The transformation
between the heat transferrability, visibility, and light illumination can develop a
verification algorithm to check the feasibility of a proposed cooling channel design.
In this study, heat energy is conducted away from the polymer melt on the mould
surface to the cooling channel surface. The polymer melt in liquid state is solidified
into solid state to form the plastic part during the cooling process. The problem from
conductive heat transfer in physics can be solved by visibility and light illumination
in geometry. The feasibility of the cooling channel design corresponding to the
3.3
mould surface can be justified with visibility and output visualization by light
illumination.
For the proposed algorithm, the accuracy of the cooling channel design in
relation to its mould surface can be maintained with less complex mathematical
calculations. The cooling channel design can be checked efficiently. The proposed
algorithm can be contributed to check various types of CCC with complex geometric
designs. The relationship between heat transferability, visibility, and light
illumination process can be shown in Figure 3-1.
Figure 3-1 Relationship
illumination
between
heat
transferrability,
visibility,
and
light
3.2.1 Heat transfer issues
The integration between heat transferability, visibility, and light illumination can
be formulated into the cooling channel design verification for PIM. The major
portion of the proposed algorithm is to check whether the cooling channel design is
feasible or not.
3.4
3.2.1.1 Heat transferrable
Heat is transferable between a heat source and a heat sink if heat energy flows
from the former to the latter. There is no insulation to block the flow. Heat
transferable between heat source and heat sink is shown in Figure 3-2.
Figure 3-2 Heat transferable between heat source and heat sink, a) no insulation, and
b) insulation
Note that by introducing another heat sink (2) in the path of heat flow, the
original heat sink (1) is effectively insulated. See Figure 3-3.
Figure 3-3 Heat flow with two heat sinks
Definition 3-1 Heat transferrability
Heat transferrability can be defined as the ability for the system to transfer heat
energy from the polymeric melt to the cooling channels directly without impediment.
3.5
It is divided into three categories: heat conductibility, heat convectability, and heat
radiatability.
3.2.1.2 Heat conductable
Heat is conducted from the polymeric melt to the surface of the cooling channel
G
according to the temperature gradient. Heat energy located at point p can be
JG
G
directly conducted to the surface of cooling channel at point q along direction d .
Heat is conductable along line segment pq as illustrated in Figure 3-4. On the other
G
G
G
hand, heat transfer between point r and point s is shielded, say at point t of the
mould cavity surface. The method of heat conduction from the heat source to the heat
sink is shown in Figure 3-5. In the second case, heat is conductable from heat source
G
G
G
G
t to heat sink s but not from r to s .
Figure 3-4 Heat transferrability within an injection mould
3.6
Figure 3-5 Heat conduction from heat source to heat sink with distance traveled l
3.2.1.3 Heat convectable
Heat is transferred away within the cooling channel according to the
temperature gradient and the pumping pressure developed by the coolant circulation
system. Heat is not convectable between the mould cavity surface and the cooling
channel surface, see Figure 3-4.
3.2.1.4 Heat radiatable
Heat is transferred to the surrounding from the mould plates via electromagnetic
wave. Negligible heat is radiatable between the mould cavity surface and the cooling
channel surface if there is no obstacle, see Figure 3-4.
3.2.1.5 Heat transferrability detection
For PIM process, the mode of heat transfer inside the plastic injection mould
depends mainly on heat conduction. Heat convection and heat radiation only
contributes a small proportion. Moreover, as obstacle in the path of heat transfer will
3.7
play an important role, the transferrability of heat can be described and illustrated by
visibility technique in computational geometry. Heat conductability will thus be
formulated as visibility. The workflow to verify the feasibility of a new mould
cooling channel design is shown in Figure 3-6.
Figure 3-6 Workflow of mould cooling design verification
3.2.2 Visibility techniques of computational geometry
Visibility is a fundamental topic that has been applied to computer graphics
[Kim 1995 and Karakas 1992], mathematics [Ghosh 2007 and Shermer 1992], art
gallery theorem [O’Rourke 1987, Lee 1986, Chvatal 1975, and Klee 1969], motion
path planning for robotics [Berg 2002], telecommunications [Toth 2002], and many
other industrial applications [Woo 1994, Chen 1993, Kweon 1998, Sack 2000,
O’Rourke 1998, Aki 1993, and Preparata 1985]. Various visibility problems have
been studied in the literature for diverse applications [Yamashita 2004 and Michael
2003]. It can be formulated into different categories: (i) point, (ii) line, or (iii) surface,
3.8
etc. In 2003, Bittner et al. [Bittner 2003] proposed a new taxonomy of visibility
problems that is based on a classification of visibility algorithms in computer
graphics. Various visibility algorithms, concepts, and criteria are summarized and
described. However, no mathematical rigorous definition for visibility in 2D or 3D is
given other than point-to-point visibility.
In this study, visibilities of point-to-point, line-to-point, and finite area-to-finite
area are employed for the proposed feasibility check algorithm. The summary of
various types of visibilities in PIM cooling are tabulated in Table 3-1.
Table 3-1 Use of visibility in the feasibility check algorithm
Visibility
Point
Point
Line segment
Finite area
Justification on heat Cooling channel Light illumination
transferability and axis generation between point
visibility
light source and
mould surface
Volume
Nil
Line
segment
Cooling channel
axis generation
Nil
Nil
Nil
Finite area
Nil
Nil
Light illumination
between cooling
channel surface
and mould
surface
Nil
Volume
Nil
Nil
Nil
Nil
3.2.2.1 Point visibility
G
G
A point q can be visible from the viewpoint p if and only if the interior of
3.9
the line segment pq connecting both points does not intersect any point outside the
G
G
boundary of the polygon containing p and q . The visibility can be identified by a
line segment into convex set and non-convex set. See Figure 3-7.
a)
b)
c)
G
G
Figure 3-7 Point visibility between a line segment from points p and q , a)
within a convex set, b) intersection point on the boundary of a
non-convex set, and c) within a non-convex set
3.2.2.2 Line visibility
Line visibility can be defined as a 2D surface being visible from a parallel light
ray from a line segment without any intersection. The line visibility can be shown in
Figure 3-8. In general, the line can be 2D or 3D, straight or curved.
Figure 3-8 Line visibility in two-dimensional representation
3.10
3.2.2.3 Surface visibility
Apart from representation from two-dimensional visibility, it can be extended to
three-dimensional for surface or multi-planes visibilities. A 3D surface is observed
by a bundle of light ray from the infinity or a definite distance. The multi-planes
visibility can be performed by light sources from different surfaces with various
directions and are projected on a 3D surface to be observed. As the degree of
visibility increases from point to multi-planes, the chance of guarding or blocking of
visible light will also increase. Complete and partial visibilities can be identified.
Figures 3-9 to 3-11 demonstrated a variety of visibilities between the light sources
(by point, line, and surface) and 3D surface geometries (convex surfaces) by the
setting of light sources. In this study, the CAID system Rhinoceros 3.0 [Rhino 3D
2008] is used to model the CAD parts with the models being rendered for visibility
examination. From the model rendering, the range of surface exposed by the light
source is increased from point to plane visibilities. Plane visibility can provide a
more uniform illumination on a surface with different geometric designs. The black
color (or shaded region) from the rendering shows the area that cannot be exposed by
light. It can be defined as invisibility.
3.11
Figure 3-9
a)
b)
Point visibility on a shallow convex 3D solid model a) perspective view
of CAD model, and b) 3D rendering
a)
b)
Figure 3-10 Line visibility on a shallow convex 3D solid model a) perspective view
a)
b)
Figure 3-11 Plane visibility on a shallow convex 3D solid model a) perspective view
3.2.3 Relationship of heat transferrability, visibility, and light illumination
The 3D rendering can give a mould engineer or designer a concise display and
3.12
explanation for the feasibility of the proposed cooling channel design. The close
relationship between heat transfer, visibility, and light illumination can be
interchangeable so that magnitude, movement, and orientation of the light energy
pathway can be clearly expressed. The interchangeable relationship of heat
transferability, visibility, and light illumination can be identified into three categories.
The comparison between heat transferability, visibility, and light illumination are
tabulated in Table 3-2. The classification is based on the degree of light intensity or
effectiveness from a number of point sources to the 3D mould surface (cavity or core)
to the surface model. The relationship between heat transferrability and light
illumination can be explained by the following definitions.
Table 3-2 Comparison between heat transferrability, visibility, and light illumination
Heat transferrability
Visibility
Light illumination
Subjects
Thermodynamics
Computational
geometry
Computer graphics
Principles
Applied physics
Mathematics and Rendering and
geometry
visualization
Source
Heat
energy
physical surface
Applications
Amount of energy
flow
on Point at geometric Light source on 3D
surface
CAD model
GIS, robotic
motion
3.13
Virtual modeling,
simulation, rendering,
and visualization
Theorem 3-1 The relationship between heat transferability, visibility, and light
illumination can be described by a source (heat source, point set, or
point light source, etc.) and a directional vector pointing towards the
object (heat sink, point set, surface, or objected to be illuminated, etc.)
Corollary 3-1 An occluder will be found in-between the object and the source so
that visibility, heat transferrability, or light illumination cannot
proceed.
Corollary 3-2 Intersection point in-between the object and the source will prohibit
the visibility, heat transferrability, or light illumination.
Definition 3-2 (Direct Heat conductability)
A point on a mould surface heat source and a point on a cooling channel surface
heat sink are directly heat conductable if there is no obstacle or occluder in-between
two points.
Definition 3-3 (Complete Light Illumination)
Two point sets are completely light illuminatable from a light source if there is
no occluder or obstacle between the surface and the light source.
3.14
Definition 3-4 (Incomplete Light Illumination)
Two point sets are incompletely light illuminatable from a light source if there is
an occluder between the surface and the light source with intersection point
initiation.
3.2.4 Transformation between heat transferability, visibility, and light illumination
The visibility of computational geometry can be applied to computer graphics
for visualization of 3D models by 3D rendering. The light illumination from CAID
software, such as 3DS max and Rhino 3D can be applied to different industrial
applications, such as finite element analysis for computational fluid dynamic (CFD)
model. The heat transferrability from the mould surface (core or cavity) to the
surface of the cooling channel can be formulated and checked with the aid of
visibility and light illumination on an object surface from the predefined light
sources. For integration between heat transferability, visibility, and light illumination,
the similarities between each other can be transformed or interchanged between each
other. The relationship between heat transferability, visibility, and light illumination
is shown in Figure 3-12.
3.15
Figure 3-12 Relationship between, a) heat transferrability, b) visibility, and c) light
illumination
Apart from point to point heat transfer, visibility, and light illumination are also
in bi-directional relationships. Point A can be visible and illuminable to Point B.
Point B can be visible and illuminable to Point A. See Figure 3-13.
Figure 3-13 Point to point bi-directional relationship for heat transfer, visibility, and
light illumination
In case of point to point set visibility, Point A can be visible to Point set B. The
case is not equivalent to Point set B to Point A. See Figure 3-14.
3.16
Figure 3-14 Point to point set in visibility
For point set to point set visibility, Point set A can be completely visible to Point
set B. However, it is not equivalent to Point set B completely visible to Point set A.
See Figure 3-15.
Figure 3-15 Point set to point set visibility
To check for the feasibility of the proposed cooling channel design to its mould
surface, the heat source is on mould half surface and the heat sink is on the cooling
channel surface. The heat transferrability is in omni-direction from mould half
surface to the cooling channel surface. See Figure 3-16.
3.17
Figure 3-16 Omni-direction of heat source to heat sink from mould half surface to
For light illumination in the feasibility check algorithm, a set of point light
sources is represented as the cooling channel from coolant inlet to coolant outlet. The
point light source is projected on the mould source. The feasibility of the cooling
channel can be verified by the visibility and light illumination. The justification of
light illumination from heat conduction in the feasibility check algorithm is shown in
Figure 3-17.
Figure 3-17 Justification of light illumination from heat conduction in the feasibility
check algorithm
3.18
For the conductive heat transfer and light illumination, grazing point and
grazing region are allowed in the feasibility check algorithm between heat source and
heat sink or light source and object to be illuminated. Comparison between grazing
point and grazing region by point-to-point visibility is shown in Figure 3-18.
Figure 3-18 Comparison between a) grazing point, and b) grazing region by
point-to-point visibility
3.2.5 Heat conduction and visibility
In heat transfer, heat energy can flow in straight line or turn corner by
conduction from heat source to heat sink with heat transfer media (inside an
insulator). As shown in Figure 3-19, the heat energy flown from the heat source to
the heat sink under rectangular heat transfer media (or conductor) in Figure 3-19a) is
more effective than under U-shaped heat transfer media. As heat energy flows from
heat source and heat sink is in straight-line in Figure 3-19a, the shortest distance of
heat conduction can provide the most direct and effective heat transfer than the
curved line in Figure 3-19b. Curved-line is not effective in heat transfer because it
3.19
does not have the shortest distance for heat conduction. Similarity, heat energy flows
in straight-line by heat conduction is equal to the line of visibility. Visibility between
two points is projected in straight-line.
Figure 3-19 Heat conduction between heat source and heat sink with a) straight-line
heat transfer media, and b) U-shaped heat transfer media
3.2.6 Normal vector for heat conduction and visibility
Without loss of generality, a heat source on a mould surface can transfer heat
energy in omni-direction to the heat sink by conduction. See Figure 3-20. Heat
energy flown from heat source on mould surface point with shortest distance is in
orthogonal uni-direction. The difference between omni-direction and uni-direction is
compared in Figure 3-21.
3.20
Figure 3-20 Heat energy flow in omni-direction from a mould surface point, a)
convex, b) reflective/planar, c) convex, d) concave (v-shaped)
Figure 3-21 Difference between the flow of heat energy, a) in uni-direction, and b) in
omni-direction
As shown in Figure 3-22, heat energy flown from a heat source to the heat sink
G
G
position is in omni-direction with p1 and p 2 . The heat energy flown with shortest
distance to the heat sink is in normal direction which is perpendicular to the mould
G
surface at p1 . It implies that heat energy flown as normal vector n has the shortest
distance for heat transfer. In similarity, normal vector n is also important in the
point to point visibility as it represents the shortest distance.
Figure 3-22 Shortest distance for heat transfer
3.21
3.3
Shortest Distance Conduction Feasibility Check Algorithm for Mould
Surface for PIM
In order to verify the heat transfer performance across the mould surface and its
corresponding cooling channel design for PIM, a shortest distance conduction (SDC)
feasibility check algorithm is proposed. The near uniformity of the mould surface can
be obtained by the light illumination. Light illumination on the mould surface can
become the solution of the feasibility check. The proposed algorithm is integrated
with CAD and CAID software under manual control. It can provide an efficient,
accurate, and uncomplicated preliminary verification. It can ensure the possibility of
the proposed cooling channel design in relation to its mould surface (core and cavity)
geometry.
3.3.1 Outline of feasibility check algorithm
The flowchart of the feasibility check algorithm is shown in Figure 3-23. The
mould surface (core or cavity) is the input. By conductive heat transfer, heat energy
transfers from polymer melt on the mould surface to the cooling channel surface. All
other surfaces are not in direct contact with the cooling channel surface. The
feasibility of the cooling channel design depends on the heat transfer between the
heat source and heat sink. For simplification, all other surfaces are removed in the
3.22
feasibility check. The cooling channel generation is a manual process to generate the
cooling channel system such as straight-line drilled cooling channel, copper duct
bending type CCC, or other designs. Both the mould surface and cooling channel
generation process are the inputs in the feasibility check stage. The cooling channel
design is feasible if heat energy can be transferred from the polymer melt on the
mould surface to the cooling channel surface by heat conduction. On the contrary, the
cooling channel design is infeasible if heat energy cannot be transferred from
polymer melt on the mould surface to the cooling channel surface. In this case, heat
energy is trapped and accumulated within the mould plate and cannot be removed
away from the mould during the cooling process. Then, design improvement of
cooling channel system is recommended. Finally, the output of the feasibility check
is to give the verified results to the mould designers for the feasibility of the
proposed cooling channel with near uniform heat transfer on the mould surface.
For simplification of the feasibility check, some assumptions are given. The
mould temperature at any region on the mould surfaces is the same at the
instantaneous time. Besides, the rate of conductive heat transfer is also kept constant
at any region on the mould surface at the instantaneous time.
3.23
Figure 3-23 Flowchart of feasibility check algorithm
3.3.2 Feasible and infeasible of the cooling channel system
The cooling channel design is feasible if all the heat energy from the polymer
melt on the mould surface can be transferred to the cooling channel surface
effectively at the same time. All the heat energy can be removed away by the
proposed cooling channel at the same time.
While the cooling channel design is infeasible if the heat energy cannot be
transferred from the polymer melt on the mould surface to the cooling channel
surface. Heat energy is stored or accumulated on the mould plate and cannot be
removed by the proposed cooling channel.
3.3.3 Uniform and non-uniform heat transfers
The cooling channel system is under uniform heat transfer if all the heat energy
3.24
from polymer melt at any region on the mould surface can be conducted to the
cooling channel surface at the same time. The polymer melt at liquid state can be
cooled uniformly to form the solid state of plastic part. While the cooling channel
system is under non-uniform heat transfer if all the heat energy from polymer at
mould surface cannot be conducted to the cooling channel surface at the same time
and the polymer melt cannot be cooled effectively to change to solid state of plastic
part. Non-uniform heat transfer is caused by undercut, incorporation of ejection pin,
or other internal components on the mould surface. The difference between uniform
and non-uniform heat transfer is shown in Figures 3-24 and 3-25. In real situation,
ideal uniform heat transfer cannot be achieved. It is because heat conduction in PIM
is always blocked by undercut or internal components and the rate of conductive heat
transfer is varied at any region on the mould surface. Thus, the output of the
feasibility check can only be achieved in near uniform heat transfer.
Figure 3-24 Uniform heat transfer between mould surface and cooling channel
surface
3.25
Figure 3-25 Non-uniform heat transfer between mould surface and cooling channel
surface
3.3.4 Problem of non-uniform heat transfer
In case of non-uniform heat transfer, the problem can be expressed by the
differential equation for heat conductive heat transfer (3-1):
G G
dT
∇ ⋅ q = q gen − ∫ c
dt
(3-1)
G
where q [w/m2] is the conductive heat flux and q gen [w/m3] is the heat energy
generation dT/dt is the time rate change of temperature.
Equation (3-2) indicates that conductive heat flux in PIM is closely related to
the change of temperature. For PIM, the mould surface initial temperature Ti is
assumed all over the surface. After the same time duration, heat energy is conducted
to polymer melt with surface temperatures (T1 to T4) at 4 corners being different.
After cooling and mould opening with a mould opening temperature To, warpage is
formed on the surface plastic part being moulded. The relationship between
3.26
conductive heat flux and the change of temperature can be described in Figure 3-31.
The warpage is due to the non-uniform heat transfer on the part surface with
different temperature. By heat contraction at Equation (3-2) and (3-3):
∆l = α∆Tl
(3-2)
where l [m] is the initial length and α [m2s-1] is the thermal diffusivity.
∆l1 = α∆T1l = α (T1 − To )l
≠ ∆l 2 = α∆T2 l = α (T2 − To )l
(3-3)
≠ ∆l3 = α∆T3 l = α (T3 − To )l
≠ ∆l 4 = α∆T4 l = α (T4 − To )l
Thus, the change in temperature in the heat contraction equation will cause the
change in length at different edges of the part with different shrinkage. Non-uniform
heat transfer and injection moulded defect formation of warpage result.
3.3.5 Simplifications for the proposed algorithm
In order to clearly demonstrate the proposed algorithm, the 3D model from
CAIMD or CAD is simplified as follows:
1. The proposed feasibility check algorithm is focused on two plate mould for PIM
process.
2. All accessories such as side core, ejector pin, thermal pin, slider, insert, and sprue
are not considered.
3. Model surface with undercut and side core are not considered.
4. All the CAD models are represented as faceted models for the proposed
3.27
algorithm.
5. The faceted model is considered to be error-free without loss of surface detail
from the triangular elements.
6. Only the geometric information of the mould plates and cooling channels are
considered in the proposed algorithm.
7. The cooling channel design can be conventional or CCC.
3.4 Mould Surface and Cooling Channel Design
As discussed in Section 3.3.1, the mould surface and the cooling channel are
inputs of the feasibility check algorithm. Some simplifications are necessary.
3.4.1 Facet models of the mould surface as the input
In this study, the geometric design of the parting surface of the injection mould
(for cavity plate and core plate), the mould half surface, and the cooling channel are
inputs for the proposed algorithm. See Figure 3-26.
3.28
Figure 3-26 Cooling channel and mould half surface as the input for the feasibility
check algorithm
First of all, the inputs are modelled with any CAD system. The CAD models for
the injection mould and cooling channel represented as surface, shell, or solid models
are then exported as compatible file formats, like STL, IGES, 3DS, or other 3D
exchange formats that form a faceted model before starting the proposed algorithm.
The use of faceted model provides the mathematical representation of relevant
surfaces for numerical calculations. Polygonal facets, such as triangular facet
elements are described by a set of x, y, and z coordinates for each of the three vertices
and a unit normal vector with cos α , cos β, and cos γ to indicate the outward side of
the facet. See Figure 3-27.
3.29
Figure 3-27 Input of the faceted model
3.4.2 Integration of the inputs for the mould surface and cooling channel
An injection mould assembly MA includes a variety of components. In order to
standardize and simplify to the input for the proposed algorithm only, the mould
surface (core and cavity) and the cooling channel from the facet model are extracted.
All other unnecessary components are removed.
A cooling channel C can be defined as a cooling passageway within an injection
mould connected with a coolant inlet and a coolant outlet. The number of cooling
channel Ci (i = 1 to n) can be increased by installing more inlets and outlets. This
cooling channel can be formed by the subtractive machining process to generate a
passageway for coolant flow.
An example CAD model is given in Figure 3-28. The geometric design of the
injection mould assembly is shown in Figure 3-29. The faceted models of the cavity
3.30
and core plates are shown in Figure 3-30. The unnecessary facets are removed to
obtain a simplified input to the feasibility check algorithm. See Figure 3-31.
Figure 3-28 A 3D CAD model for the proposed algorithm
Figure 3-29 Injection mould assembly model
a)
b)
Figure 3-30 A faceted model of the injection mould, a) cavity plate, and b) core plate
3.31
Figure 3-31 Removal of unnecessary facets for the feasibility check algorithm
3.4.3 Cooling channel generation for the input
After the preparation of mould surface (core and cavity), the cooling channel is
designed and proposed as the input to the feasibility check algorithm. The proposed
cooling channel in relation to its mould surface is generated by 3D solid modeller via
CAD software. The cooling channel design is also exported as faceted model.
The 3D models for straight-line drilled channel and CCC are shown in Figure
3-32.
a)
b)
Figure 3-32 Cooling channel generation, a) geometric design of straight-line drilled
channel, and b) geometric design of CCC
3.32
3.4.4 Orientation and position settings for the mould surface and cooling channel
design
After the preparation of the mould surface and the cooling channel design as the
inputs, the position and orientation have to be set appropriately. The position and
orientation of the test assembly can be achieved by the 3D transformation of
translation, and rotation.
3.4.5 Bounding box setting by negative offsetting process
In order to prevent the damage or leakage of coolant from an injection mould
after the fabrication of cooling channel within the mould plate after the straight line
drilling process, the cooling channel cannot be drilled too close to the mould plate
surface. A bounding box inside the mould plate (core or cavity) is needed to provide
a safety distance d away from the boundary or inner surface of the mould plate. The
cooling channel can only be incorporated inside the boundary box to prevent damage
of mould plate. The distance can be controlled by negative offsetting process
[Maekawa 1999, Yu 1995, and Zeid 1991]. The bounding box can be formed by
offsetting the outermost boundary of the mould plate. See Figure 3-33. The aim is to
set a boundary limit so that all the point light sources will not exceed the position.
Otherwise, the mould plate will collapse. See Figure 3-34.
3.33
Figure 3-33 Bounding box creation by offsetting process
a)
b)
Figure 3-34 a) Negative offsetting process for bounding box generation, and b)
relationship of cooling channel diameter ød and the distance d of
bounding box from the edge of mould cavity plate
After the creation of the bounding box, the setting of cooling channel at the
bounding box will have three cases. See Figure 3-35. They include a) inside the
bounding box, b) at the bounding box, and c) outside the bounding box. As the
location setting of cooling channel depends on the cooling channel axis, both cases a)
and b) are acceptable for simplification. The cooling channel axis cannot be set
outside the bounding box.
3.34
Figure 3-35 Setting of cooling channel axis at different situations, a) inside the
bounding box, b) at the bounding box, and c) outside the bounding box
To show the position and orientation of the inputs, the entities required for the
set up of the test model are tabulated in Table 3-3.
Table 3-3 Entities for the set up of the test model
Components
Entities for the set up of the test model
Parting Line
PL
Parting Surface
2D plane
PS
π
Boundary
∂
Cooling channel axis
CAi (i = number of CA from 1 to n)
Function of distance
d(x)
Mould opening direction
OP
G
G
pi (points pi belong to the boundary of the
Point on ∂m
Normal vector
Point on CAi
object to be fixed)
ni
G
G
qi (i.e. points qi belong to the curve of
cooling axis)
Facet of mould
F = fi (i = 1 to t)
Point in 3D coordinates
(x, y, z)
Cooling channel inlet and outlet
PO (PO = Pq-1) and Pi (Pi = Pq)
3.35
The set up of the test model is shown in Figure 3-36. The mould surface (cavity)
aligned on the 2D plane is parallel to the cooling channel and the mould opening
direction.
a)
b)
Figure 3-36 a) Position and orientation of the inputs for the feasibility check algorithm,
and b) illustration of output display of the input
3.36
In summary, the steps to position and to orientate the input are listed as follow:
1) Divide MA into two halves m+ and m-.
→
2) Set m+ on a 3D virtual platform
with mould opening direction OP
(facing upward).
3) Identify ∂m of m+ from top view in 2D.
4) Extract the coordinates of ∂m.
5) Create a new 2D plane π in
above m+.
6) Project the ∂m on π .
7) Project the cooling channel Ci and the cooling channel axis, CAi on π .
8) Identify the Ci and the CAi.
9) Extract the coordinates of CAi.
3.37
The workflow of the proposed algorithm is shown in Figure 3-37.
Figure 3-37 Flowchart for the input of the test model for the feasibility check
algorithm
3.5 Procedures of Feasibility Check Algorithm
The general procedures of the feasibility check algorithm are summarized as
follow:
Feasibility Check algorithm for cooling channel design verification
3.38
A 3D CAD mould half (core or cavity) model with its cooling channel design is
the input.
1. Import m as the faceted model on a 3D platform.
2. Set orientation and position of m (give m+ as example) in
.
3. Define the mould opening direction, OP (OP+ and OP-) of m+.
G G
G G
4. Record all the coordinates, pi ( pi ∈ P : {pi xi , y i , z i } ), (i =1 to n) on ∂m+.
5. Extract the parting surface PS on ∂m+.
6. Delete all unnecessary facets fi in
except ∂m+.
7. Identify all the internal structures or components, IS (such as ejector pin, sprue,
side core, and slider) on ∂m+.
8. Ignore IS of m+
9. Set bounding box to restrict the location of light source for visibility check.
10. Highlight overlapping region between IS and ∂m.
11. Identify CAi above ∂m+
12. Record all points, qi in (xi, yi, zi) coordinates on CAi of the cooling channel route.
13. Extract CAi
14. Subdivide each CAi into node segment, Pn, (n = 1 to q-1), (depend on degree of
resolution)
15. Define cooling channel inlet, PO, and outlet Pi for CAi
3.39
16. Check the light source projection on the object surface boundary by visibility
technique.
17. Check the light shading region of PS on m+
18. Record non-illuminable region of PS on m+
19. Subdivide light shading region and non-illuminable region
20. Display output (illumination and non-illuminable regions) by light illumination
21. Modify non-illuminatable region to illuminatable region
22. End
3.5.1 Definitions and conditions of feasibility check algorithm
G
The feasibility check algorithm via visibility is governed by a point set pi
which is the number of light sources which present light ray emission, and m is the
G
object to be illuminated. The point set pi can be utilized as the basic element to
represent all kind of light sources in the feasibility check algorithm.
G
Definition 3-5 Feasibility check algorithm can be established if a point set pi on
the object boundary can be visible or illuminatable directly from a
point source without any obstacle.
3.40
G
Lemma 3-1 Visibility is established when pi and m are linked up between each
other for the feasibility check algorithm.
Lemma 3-2 Visibility cannot be established if an obstacle ψ is set up between pi and
m for the feasibility check algorithm.
G
G
G
Corollary 3-3 If the visibility between pi (say p1 ) and p 2 on m is blocked by an
G
obstacle ψ or another point, p3 on m, light cannot be illuminated
and the definition cannot be established.
G
G
G
Corollary 3-4 Visibility cannot be established if pi (say p1 ) and p 2 on m has no
linkage.
3.5.2 Feasibility check algorithm by illumination
The verification of the cooling channel design on the mould surface can be
checked by illumination. The cooling channel design is feasible when completely
illuminable on the mould surface and also when a uniform distance between each
G
other is established. A point set pi (or line set li) can be represented as the
geometric design of the cooling channel. The mould surface m can be represented by
a line, curve, or surface. The feasibility check of the mould surface with cooling
channel design with uniform heat transfer is established when the entire region on m
G
is illuminable from its point set (or line set) with a uniform distance between pi
3.41
and m.
G
Feasibility check algorithm can be established if a point set pi or a line set li
above the object boundary can be complete visible or complete illuminable directly
with a uniform distance d without any obstacle.
G
As shown in Figure 3-38, feasibility check is established as all point set on pi
G
from a straight line and qi on m are completely visible and the distance d between
two points sets are the same. The feasibility check algorithm cannot be established as
uniform between the CCC and the mould surface if the distance d between point set
G
pi and m are different even the straight line of m is completely visible.
Figure 3-38 Feasibility check algorithm by visibility, a) a line set, b) a point set, and
c) two point sets
In general, the mould surface is a non-convex surface. A single straight-line
cooling channel design cannot provide a uniform heat transfer to the non-convex
mould surface. CCC is designed according to the geometry of the mould surface. For
the feasibility check, the cooling channel represented by a non-convex curve, li
3.42
follows the shape of the mould surface to provide uniform heat transfer, see Figure
3-39a. The mould surface is completely visible and the distance between li and m
along both of them is the same. A dark side can be found as there is no visibility
establishment at that region. As shown in Figure 3-39b, the non-convex curve set li
G
can be approximated by a number of point sets pi for simplification. The CCC
represented by the point sets can also be completely visible on the mould surface m.
The distance between the point sets and the mould surface are the same. The uniform
G
CCC can be achieved on the mould surface as these point sets pi are directly
visible to the mould surface m with uniform distances between each other. The
feasibility check of the cooling channel design in relation to the mould surface can be
established. Besides, the position of point sets can substitute into the point light
source for the output display by light illumination.
Figure 3-39 Feasibility check between a CCC design with its corresponding mould
surface, a) for visibility, and b) for visibility and light illumination
G
The number of point set pi applied to represent the cooling channel design for
3.43
the visibility and light illumination depends on the resolution and the characteristics
of the checking result and output display. To check the visibility of a complex
geometric design of CCC and a mould surface with non-convex or freeform one with
accuracy, a number of point sets are required. A comparison of visibility on a curved
surface between a) complete visible by a line l1, b) invisible region by two point sets,
and c) complete visible by three point sets is shown in Figure 3-40.
Figure 3-40 A comparison of illumination on a curved surface, a) a line, b)
non-illuminable region by two point sets, and c) complete illuminable
by three point sets
In this study, the number point light source setting along the cooling channel
axis is approximated by interpolation that can be identified by performance of light
illumination. For more complex mould surface geometry, the number of point light
sources can be changed. The more the number of point light source, the more
accurate the verification of the cooling performance. The level of resolution of the
results can be increased with the number of the point light sources. The differences
3.44
of point light source settings at lower and higher levels of resolutions at top view are
shown in Figures 3-41 and 3-42. The most flexible and appropriate method is
suggested by minimum number of point light source setting on object to be
illuminated.
Figure 3-41 Point light source setting with lower levels of resolution at top view
Figure 3-42 Point light source setting with high levels of resolution at top view
3.45
3.5.3 Minimum number of point light source for feasibility check algorithm
With the proposed cooling channel design for the mould surface, point light
source can be inserted uniformly along the cooling channel axis by interpolation. A
trade-off between the performances of light illumination and levels of resolution are
necessary. As discussed before, the more the number of point light source, the more
accurate the result is. However, the same performance of visibility is obtained when
more point light sources are inserted on the cooling channel axis. The performance of
light illumination on the mould surface by point light source setting is not the
influencing factor. Minimization of the number of point light source is recommended
and will be discussed in Chapter 4 in details. Minimization of the number of point
light source along cooling channel axis by interpolation at top view is shown in
Figure 3-43.
Figure 3-43 Minimization of the number of point light source along the cooling
channel axis by interpolation, a) cooling channel axis, b) point light
source setting, and c) minimization of point light sources
3.46
3.5.4 Transformation between point set from visibility and point light source from
light illumination for the feasibility check algorithm
The feasibility check algorithm is governed and verified by the visibility
G
G
between the point set pi on the cooling channel design and point set qi on the
mould surface m. The output result of the mould surface with near uniform cooling
channel design can be displayed by light illumination. The output solution can be
checked by the user after 3D rendering by CAID software. The simple 3D projection
G
of a point light source pi on a sphere O is shown in Figure 3-44. The point light
source can be intersected at a point on the rectangular plane π. The visibility and the
G
light illumination between pi and O can be established up to π.
Figure 3-44 Visibility and light illumination of a single point light source set on a
3D sphere with a rectangular plane intersection
3.5.4.1 Point light source setting for the feasibility check algorithm
In this study, a CAID software, e.g. 3D Studio Max 6.0 [Autodesk 2008] or
3.47
Rhino3D 3.0, is used for output display of the scene of light source setting and
rendering with an object to be illuminated in the 3D virtual environment. A simple
3D rendering by projection of a point light source and a planar object to be
illuminated is shown in Figure 3-45.
a)
b)
Figure 3-45 A scene of point light source a) point light source setting, and b) 3D
rendering
3.5.4.2 Linear light source setting for the feasibility check algorithm
A set of point light sources can be grouped together to form a curve. The linear
light source provided by CAID software is shown in Figure 3-46 for comparison.
The scene of linear light source by a set of point light sources is shown in Figure
3-47.
a)
b)
Figure 3-46 A scene of linear light source, a) linear light source setting, and b) 3D
rendering
3.48
a)
b)
Figure 3-47 A scene of linear light source represented by point light sources, a)
setting of point light source, and b) 3D rendering
3.5.4.3 Area light source setting for the feasibility check algorithm
An area light source provided by CAID software is shown in Figure 3-48. The
rendering effect zone in Figure 3-48b is not that realistic. Therefore, a set of point
light sources is arranged in rows and columns to give a more realistic area light effect.
See Figure 3-49.
a)
b)
Figure 3-48 A scene of area light source, a) area light source setting, and b) 3D
rendering
3.49
a)
b)
Figure 3-49 A scene of area light source projection represented by point light
sources, a) setting of point light source, and b) 3D rendering
3.5.4.4 Linear and area light sources represented by a number of point light sources
From the above section, linear and area light sources can be represented by a
number of single point light sources. By comparing linear or area light source
representations using the same parameter setting, point light source can provide
higher flexibility for setting uniform light illumination to be projected on to the light
illuminated object. The projected light illuminated object can be freeform or
non-planar surfaces. Besides, point light source representation can design various
curved or surface geometries, such as CCC, for the feasibility check algorithm.
3.6 Intuitiveness of Feasibility Check by Light Illumination
The 3D test model visualization shown in CAID software is the core output
process for the result solution illustration and analysis from the proposed feasibility
check approach discussed in the thesis. The interface of the virtual environment is
performed by CAID (3D Studio Max 6.0). The cooling performances of the proposed
3.50
cooling channel design corresponding to its mould cavity (or core) surface can be
determined visually in the light illumination via the 3D rendering process. The 3D
rendering of test model is an important process [Rix 1994 and Slater 2002] in the
CAID to output the model for back up after lighting and environmental settings for
light illumination. The formulation of direct light illumination and heat
transferability for the 3D model can check the cooling performance of the proposed
cooling channel design in relation to the corresponding mould surface on any CAID
software. The cooling performance or heat transfer can be illustrated via the light
illumination. Light sources can be set up in CAID software. The results after 3D
rendering can illustrate how the cooling performance acting on the test model with
the proposed cooling channel designs.
3D Rendering in CAID software is an output process which is important to
shade the scene’s geometry using the lighting applied, materials selected, and
environment settings for background and atmosphere. User can apply the 3D
rendering scene to create renderings and export for backup. 3D rendering process can
be displayed on the screen via frame window.
3.6.1 3D model rendering after light illumination
A trapezoid example of a 3D manifold surface model S is modelled by CAID
3.51
tool. See Figure 3-50a. It is exported as a faceted model. The surface normal vectors
ni can be set on each piecewise surface segment on S. See Figure 3-50b. Five
normal vectors, from n1 to n5 , can be found on S. In order to compare the
difference by virtual visualization between light illuminated surface and light
non-illuminated surface, an original 3D manifold surface model is applied as the
standard model after the 3D rendering process under CAID software. See Figure
3-51.
a)
b)
Figure 3-50 Surface normal vectors on 3D surface model a) perspective view, and b)
normal vectors on surface boundary
Figure 3-51 3D model rendering without point light source setting
G
G
As shown in Figure 3-52, two point light sources, p1 and p 2 are separated by
a manifold surface S. The top side of S is shaded after the light illumination. This
shaded region on S is called the incomplete light illuminated region. After 3D
3.52
rendering by CAID software, the incomplete light illuminated region on S is dark in
colour. The 3D surface model is broken into two pieces. The combination of point
G
G
light sources p1 and p 2 can only produce an incomplete light illumination on S.
a)
b)
Figure 3-52 A scene of incomplete light illumination a) point light source setting,
and b) 3D rendering
In order to illuminate the incomplete light illuminated region on S, extra point
G
G G
light source p3 is added above it. The combination of point light sources, p1 , p 2 ,
G
and p3 can now illuminate the entire surface of S. The further addition of a point
light source can change to complete light illumination. The output display is shown
in Figure 3-53 after 3D rendering by CAID tool.
a)
b)
Figure 3-53 A scene of complete light illumination a) point light sources setting, and
b) 3D rendering
3.53
3.6.2 Contributions of light illumination for feasibility check algorithm
The solution given after the verification of the feasibility check algorithm can
be illustrated by light illumination. The advantages are given as follow:
y
To provide a unique and simple visualization process for users to check the
performance of the proposed conformal cooling channel design in response to
its mould surface geometry.
y
To give user a time effective approach for instant verification results and
modification at the same time for cooling channel design.
y
To give product designer or experienced mould designer an effective and a
cost-saving approach for PIM cooling design. Even a designer without any
mould engineering knowledge or skill can also handle or check easily.
y
To verify intuitions and indicate the cooling performance under virtual model
visualization.
3.6.3 Cooling channel design verification by Illuminance after 3D rendering
In photometry, illuminance Ev can be defined as the surface illumination of an
object or test model and the total luminous flux incident on a surface per unit area. It
is a measure of the intensity of the incident light which has fallen on a surface. In SI
derived units, these are both measured in lux (lx) or lumens per square metre
3.54
(cd·sr·m-2). The lux (lx) is the International System (SI) unit of illuminance and
luminous emittance. It is used in photometry as a measure of the intensity of light,
with wavelengths weighted according to the luminosity function. (1lx is equal to 1
cd·sr·m-2).
In order to illustrate the result for light illumination, the output result can be
checked by the intensity of the surface illumination of the test model after 3D
rendering. The degree and effect of the point light source settings at different
positions to the surface of the test model can be determined on CAID software. The
cooling performance can be formulated with the output result illustration via the
quantity of the illuminance on the test model. The illuminance on the test model can
be visualized via 3D rendering [Boughen 2005 and Dempski 2005].
With the aid of 3D graphic design tool, the test model after 3D rendering can be
shown in coloured style. The coloured style processed by graphic design tool can
display a range of colour spectrum from blue (0) to red (255) on the surface of the
test model. The colour displays the spectrum-to-intensity mapping. The colour
spectrum of illuminance on the surface of the test model is shown in Figure 3-54.
The coloured output display visualization of surface illuminance for some solid
models after 3D rendering is shown in Figure 3-55.
3.55
Figure 3-54 The range of colour spectrum by coloured visualization processed by
graphic design tool
a)
b)
Figure 3-55 Coloured output display visualization of surface illumination after 3D
rendering, a) same intensity light source, and b) weaker intensity light
source
3.6.4 Colour range determination for 3D rendering
RGB values are composed of three 8-bit values, one 8-bit value for each of the
three primary colours (red, green, and blue). 8-bit values are used because, in binary
language, a value of 11111111 is equal to 255. If you count from 0, an 8-bit range
accounts for 256 discrete values. A value of 0 means there is no amount of that
colour in the mix, while a value of 255 means all of that colour is in the mix. Each
colour pick up with a potential value in the mix ranging from 0 to 255. The number
of possible combinations is calculated by multiplying 256 x 256 x 256, resulting in
16,777,216 possible combinations of colours.
RGB values determine the brightness of red, green, and blue pixels on a
3.56
computer monitor. The computer monitor is composed of a grid of small illuminated
dots known as picture elements called pixels. In each grid position, there is a red
element, a green element, and a blue element. If all the red elements were on and all
the green and blue elements were off, the screen would appear red. Each element has
an illumination value ranging from zero (no current is being applied to the element)
to 255 (maximum current is being applied and the element is burning at full
brightness).
In this study, the colour and brightness of the test model can be shown by the
RGB values (from minimum 0 to maximum 255). These RGB values illustrate the
intensity of light illuminance on the surface of test model after lighting setup and 3D
rendering. If all the R, G, and B elements were on, then white colour would be
appeared on the screen. The values of R, G, and B elements are tabulated in Table 3-4
respectively.
Table 3-4 Common RGB values and their colours on screen
Colour
Red (R)
Green (G)
Blue (B)
Red
255
0
0
Green
0
255
0
Blue
0
0
255
Gray
150
150
150
Orange
255
106
38
Cyan
0
255
255
Black
0
0
0
White
255
255
255
3.57
3.6.5 RGB and monochromatic values of the output solution for the feasibility check
algorithm
RGB and monochromatic values can both illustrate the intensity of light
illuminance on the surface of the test model. The ranges of monochromatic and RGB
values are from 0 to 255 and also be illustrated by percentage (%). These values for
some 3D solid models after 3D rendering are shown in Figure 3-56. A 3D solid
model of pyramid in green colour is highlighted with its image data and other
geometric information. The monochromatic value of pyramid in green colour is 106
(41.5%) and RGB values are 69 (27.3%) for red, 178 for green (69.9%) and 89 for
blue (27.3%).
Figure 3-56 RGB and monochromatic values for a 3D solid model of pyramid
3.6.6 Output solution illustrated via light illumination for feasibility check algorithm
The 3D rendering can illustrate the output solution of visibility and light
illumination for the 3D test model. See Figures 3-57 and 3-58. It can formulate into
3.58
the cooling performance of the heat removal from the mould surface cavity to the
cooling channel by CAID software. The performance of the illuminance on the
surface of the test model can be identified by the colour change. A red colour means
that the surface of the test model under direct light illumination is with the strongest
intensity of light illuminance. Black colour on the surface of the test model means
that there is no light illumination on it. The visualized result (illuminance) of the
surface of the test model is under coloured output display after 3D rendering. The
image data of RGB and monochromatic values can be captured from the output
display after 3D rendering. See Figure 3-59. As shown in Figure 3-60, the image data
from coloured output displayed visualization can be captured and tabulated in Table
3-5. Five points are marked and recorded from Figure 3-60 for checking the
illuminance of the test model. The colour range from Table 3-5 can indicate the
performance of illuminance. Point 1 (in red colour) illustrated complete illumination
and point 5 (in blue colour) experienced non-illumination.
G
G
Figure 3-57 Visibility between two point sets pi and qi on object surface
3.59
Figure 3-58 Light illumination on CAID software for 3D rendering
Figure 3-59 Display of image data of the test model
Figure 3-60 Image data point capturing at different positions
Table 3-5 Image data of RGB and monochromatic values for colour display by 3D
rendering
Points R
G
B
Monochromatic value Colour
1
255 (100%)
6 (2.3%)
0 (0%)
87 (34.1%)
Red
2
255 (100%)
222 (87.1%) 0 (0%)
166 (65.1%)
Orange
3
227 (89)
254 (99.4%) 0 (0%)
160(62.8)
Yellow
4
65 (25.6%)
255 (100%)
6 (2.5%)
109 (42.7%)
Green
5
0 (0%)
0 (0%)
0 (0%)
85 (33.3%)
Blue
3.60
The output solution implies the heat energy that can be carried away by the
cooling channel from the mould cavity surface directly. Besides, black colour on the
surface of the test model means that the surface cannot experience any light
illumination. It implies that heat energy cannot be removed directly by the cooling
channel from the mould cavity surface. The cooling performance is unacceptable in
this situation.
3.7 Chapter Summary
In this chapter, the theoretic basis of a feasibility check of a cooling channel
design corresponding to its mould surface for uniform heat transfer verification is
described. The heat transferability of injection mould cooling channel design has
been discussed. The visibility technique from computational geometry can be
formulated into the direct light illumination for the feasibility check of the proposed
cooling channel design corresponding to its mould cavity (or core) surface of the test
model. The cooling performance of the proposed injection mould assembly can be
verified. The output solution for the feasibility check algorithm has been focused
with the illustration by 3D rendering for result visualization with the aid of CAID
software and graphic design tools.
3.61
Chapter 4 Conformal Cooling Channel Generation
CHAPTER 4 CONFORMAL
COOLING
CHANNEL
GENERATION
4.1 Overview
In this section, various methods of CCC configuration are proposed to provide a
near uniform heat transfer solution. The geometric design of CCC is varied from
simple geometry to complex conformal pocket passageway, etc. As the time required
to modify the mould surface is longer than the design of geometry of cooling channel,
CCC generation can give a higher flexibility. The CCC is verified and the result
displayed by the feasibility check algorithm.
CCC design can be defined as a cooling channel which follows the shape of the
part surface. In this study, CCC design is classified by manual copper duct bending
and by the SFFs’ in rapid tool. CCC design is a cooling passageway which follows
the shape of the mould surface geometry to form a near uniform heat conduction
from the mould surface to the CCC surface.
4.2 Issues on CCC in this study
Without loss of generality, various computational methods applied in CCC
design and generation are varied in different literatures. For simplification, it is
4.1
necessary to limit the research focus into several items and make some assumptions
in the research study. First of all, the cooling channel system design with tubular
feature for mould cooling is a 1D line. It can be represented by a straight-line or a
curve in PIM. The study of conformal cooling is different from the definition
proposed in the literature. The term of conformal cooling can be identified in this
study. Conformal applied for CCC generation in this study is represented by a 3D
solid model. The solid models can be in single shell or multi-shell. The difference
between single shell and multi-shell solids is shown in Figure 4-1.
a)
b)
Figure 4-1 Solid models a) in single shell, and b) in multi-shell
In this study, the injection mould geometry in the CCC generation is limited to a
single shell solid model for simplification. The solid for injection mould can be
divided into two halves (1/2 solid) for two injection mould halves (core and cavity).
Side core is not included on the mould half. See Figures 4-2 and 4-3.
4.2
a)
b)
Figure 4-2 An injection mould a) with side core [Fu 2008] and b) without side core
[Kong 2001]
Figure 4-3 CAD model of Injection mould with side core
Half solid as mould geometry (cavity or core) in conformal concept in this study
is a special case of non-convex polyhedron that is called terrain polyhedron. Terrain
[Ilinkin 2002 and Berg 2000] can be defined as a simple n-vertex polygon or
polyhedron in 3D of its edge as the base to which every point in terrain can be joined
by a perpendicular line segment interior to it. See Figure 4-4. Terrain polyhedron on
the mould half geometry can ensure the injection mould halves can be opened for
part ejection in PIM. The terrain polyhedron can be formulated into an injection
4.3
mould half surface model and is shown in Figure 4-5.
a)
b)
Figure 4-4 a) Terrain polyhedron, and b) feature of Terrain polyhedron [Berg 2000]
Figure 4-5 Terrain polyhedron formulated into injection mould half surface model
Another polyhedron for convex can be defined as a polyhedron for which a line
connecting any two points on the surface always lies in the interior of the polyhedron.
Convex polyhedron is seldom found in plastic part geometry for injection mould
design.
Figure 4-6 A convex polyhedron
4.4
The half solid for mould core or cavity is then approximated by triangular
surfaces. The triangular surface is then under decimation in order to simplify the
triangular surface of the mould half geometry. The simplified mould half geometry
after decimation is still conformal to the original mould surface design one. This
process can be done using CAD/CAM tools for RP like CopyCAD [Delcam 2008]
for point data manipulation and transformation on the triangular surface. The
simplified mould surface model can be applied into the CCC generation. The
workflow of the mould surface manipulation can be shown in Figure 4-7.
Figure 4-7 Workflow for the mould surface manipulation for CCC generation
Strictly, conformal can be based on the theory of conformal mapping [Martin
1982 and Mortenson 2007]. Conformal mapping can be defined as angle preserving
transformation. A conformal transformation preserves the angle measures of a
4.5
geometric figure. Normal offset is normally an approximated conformal concept.
Thus, normal offset is alike to conformal transformation in similarity. The taxonomy
of similarity in conformal transformation is shown in Figure 4-8. An example of
similarity is uniform scaling shown in Figure 4-9.
Figure 4-8 Taxonomy of similarity in conformal transformation
Figure 4-9 Uniform scaling of a 2D curved model
4.6
For uniform scaling, conformal transformation is not equivalent to
equal-distance transformation. As shown in Figure 4-10, two distances, d1 and d2 at
different regions on the boundaries between the original curved model and a curve
G
model after positive scaling with center 0 are measured. Two distances d1 and d2 are
not equal in case of uniform scaling.
Figure 4-10 Unequal distances, d1 and d2 at different regions on the boundaries
between the original curved model and a curve model
The cooling channel generation from a terrain polygon as the mould surface is
under normal offsetting (+ve) process and can be formulated into Equation (4-1):
(4-1)
For normal offsetting of a 2D or 3D curve, problem in geometric error of offset
curve model will affect the conformity from the geometry of the original curve
model. The problem of normal offsetting is shown in Figure 4-11.
4.7
a)
b)
Figure 4-11 The problem of normal offsetting a) for a polygon, and b) curved object
The distance d for normal offsetting cannot be large enough as the geometry of
the offset curve or surface will be changed with less similarity to its original curve or
surface. The most effective method for normal offsetting is in shortest distance in n
that can cover the whole terrain for visibility and light illumination. Some research
studies are proposed for distance determination for a terrain. In 1996, Zhu [Zhu 1996]
proposed a watchtower method to determine shortest distance which can see the
whole terrain. It can contribute to find the shortest vertical distance between two
convex polyhedral. Two factors are considered for a terrain as a mould surface in
setting the n distance. Everett et al. [Everett 1997] and Bose et al. [Bose 2003 and
Bose 1997] proposed similar methods for guarding polyhedral terrains or polyhedral
surfaces by line segments and edges with shortest distance. These edge or line
segment guarding methods can be applied and formulated to wireframe as the
cooling channel extracted from the offset surface in terrain. The appropriate n
4.8
offset distance d for the wireframe for entire visible and illuminatable on the mould
surface can be determined via the similarity of guarding methods.
For cooling channel design and generation by normal offsetting from the
injection mould geometry, it is necessary to identify the view or orientation of the
mould in 3D for normal offsetting. For an injection mould (core and cavity) in 3D,
there are 6 views for a whole mould. After the mould opening, the injection mould is
divided into two halves. There are 5 views for each mould half. The difference of
view in 3D between whole mould and mould half is shown in Figure 4-12.
Figure 4-12 Difference of view in 3D between, a) whole mould, and b) mould half
After the view identification of mould half in 3D, the cooling channel can be
designed and generated in wireframe (1D) by normal offsetting from the boundary or
edge of mould surface.
The geometry of the cooling channel and mould surface geometry depends on
the connectivity of mould surface in vertex vi, edge ei, and faces fi. The wireframe in
4.9
1D represents a cooling channel in a straight-line or a curved segment.
The visibility and light illumination depends on the offset wireframe setting
above the mould surface. As shown in Figure 4-13a, Faces f1 (from front view) and f5
(from top view) can be illuminatable by line segment e3 on the wireframe of cooling
channel. While faces f1 (from front view), f2 (from right view), and f5 (from top view)
can be illuminatable by vertex v1 on the offset wireframe. This connectivity between
vertices and edges for offset wireframe can provide visible and illuminatable
performances between the mould surface and cooling channel. The feasibility of the
cooling channel design can be verified. In real situation, there is no point heat sink to
conduct the heat energy from the mould. The heat sink can be represented by
straight-line or curve segment as the cooling channel or manual bending duct.
For complete illumination, a mould surface can be illuminated by two
independent edges e1 and e2 from offset wireframe. See Figure 4-13b. However, the
circuit is disconnected. Then, a completed cooling circuit from offset wireframe can
be formed by adding an extra edge e3. It can be connected with edges e1 and e2 to
form the geometry of a single cooling channel circuit. See Figure 4-13c. Diverse
geometric design of cooling channel circuit can be generated.
4.10
Figure 4-13 a) Offset wireframe above mould surface, b) complete illuminatable
achieved by two edges from offset wireframe, and c) extra edge
addition to form a single circuit
4.2.1 Straight-line cooling channel and CCC generation
As discussed in the Chapter 3, the feasibility check algorithm can verify the
cooling channel design in relation to the mould surface geometry. It is assumed that
there is no undercut, side core, or internal component such as ejector pin to block the
heat conduction between cooling channel surface and mould surface.
4.11
A smooth mould surface is approximated into polyhedral mesh in CAD. The
mould surface with polygonal (or triangular) mesh in wireframe is decimated into
simplified mesh. The mould surface wireframe is under +ve normal offsetting with
an offset distance d to form an offset surface. The cooling channel can be obtained
from the wireframe of the polygonal mesh on the offset surface. A zig zag cooling
circuit can be obtained for cooling channel generation. It is similar to the digraph in
graph theory for connecting the vertices and order edges or arcs [Chartrand 2005].
The workflow of the cooling channel generation process is shown in Figures 4-14
and 4-15.
Figure 4-14 Workflow of cooling channel generation process in CAD
4.12
a)
b)
c)
d)
e)
f)
Figure 4-15 The whole cooling channel generation in CAD, a) smooth mould
surface, b) polygonal mesh, c) simplified polygonal mesh, d) offset
surface, e) cooling channel in wireframe, and e) cooling circuit in zig
zag pattern
In CCC design and generation, the method is similar to the straight-line cooling
channel. The offset surface can be cut by 3D rectangular planes in x-, y-, or z- axes.
4.13
The intersection of the mould surface and rectangular plane provides the geometry of
the CCC axis in wireframe. By connecting all the CCC axes, the whole CCC
geometry can be generated by sweeping process. The normal offsetting of mould
surface is shown in Figure 4-16 and the generation process is shown in Figure 4-17.
Figure 4-16 Normal offsetting of mould surface for CCC design
a)
b)
c)
d)
Figure 4-17 CCC design and generation, a) offset surface cut by rectangular planes, b)
cooling channel in wireframe formed by intersection, c) wireframe
formation, and d) cooling channel generation
4.14
In this study, the CCC geometry from the mould surface can be designed and
verified by visibility and light illumination. The position of CCC can be identified by
setting a number of points for visibility in feasibility check and light sources for
output result visualization. The workflow of cooling channel generation in the
feasibility check algorithm is shown in Figure 4-18.
Figure 4-18 Workflow of CCC generation in the feasibility check algorithm
4.2.2 Simplification for the CCC generation in the feasibility check algorithm
Before the CCC generation, some assumptions are imposed onto the test model.
They are:
1) Faceted model is used as the test model
2) Without loss of generality, single mould core or mould cavity is used.
3) All ejector pin, undercut, side core, insert, slider, sprue, and thermal pin are
ignored.
4.15
4) The test model is painted in white for clearer verification.
4.3 Relationship of CCC Generation and Light Illumination
As discussed in Chapter 3, visibility and light illumination are closely related in
the feasibility check algorithm. The CCC design and generation is based on a set of
point light sources. These point light sources connected by straight-line segments can
guide the route of CCC. The whole path of the CCC can be shown as the cooling
channel axis. The feasibility of the CCC design can then be verified. The relationship
between CCC generation and light illumination is shown in Figure 4-19.
Figure 4-19 Relationship between CCC generation and light illumination, a) a point,
b) heat sink c) a straight-line segment, d) cooling duct, e) geometric
design of cooling channel, f) straight-line drilled cooling channel
4.16
4.4 Procedures of CCC Generation
The steps of the CCC generation are listed as follows:
1 Set up a test model under CAID platform.
2 Create the 3D CAD injection mould assembly (cavity and core) for PIM process.
3 Export the test model as faceted model (such as STL) and extract the mould
surface.
4 Set the orientation and position of the test model.
5 Remove unnecessary surfaces for the mould cavity (or core).
6 Set up a bounding box for the CCC.
7 Display all the normal vectors on the mould surface.
8 Insert point light sources.
9 Connect all the point light sources to create the cooling channel axis.
11 Verify the CCC and its mould surface by the feasibility check algorithm.
11 Render the output solution of the feasibility check algorithm on the test model.
12 Visualize the output solution via light illumination on the mould surface.
For the output solution of the feasibility of the cooling channel design to its
mould surface, it is given by the light illumination and rendering according to the
point light source setting on the mould surface. In this section, the procedures of
4.17
CCC generation are proposed to provide the illumination result of mould surface
with near uniform CCC for the feasibility check algorithm. The geometric design of
CCC is given by a number of point light source setting at different positions. All the
point light sources are connected by a number of line segments. The whole CCC is
approximated. A topological representation for the cooling channel axis is proposed
to represent the connectivity relationship between point light sources. The position of
each point light source above the mould surface can be given. Besides, the route of
the cooling channel is also recognized from the coolant inlet to the coolant outlet.
In this study, the faceted model of a mould cavity (or core) surface is the input
for the CCC generation in the feasibility check algorithm. See Figure 4-20. The
position and orientation of the test model is set parallel to the working platform on
CAID. The mould surface is turned downward for the feasibility check with design
algorithm (see Figure 4-21). The normal vectors creation on the surface of the test
model is shown in Figure 4-22. Before the point light source setting process, a
bounding box is created with the distance d of the cooling channel diameter (ø=4mm)
from the edge of the mould plate (see Figure 4-23).
The faceted model of the mould cavity (or core) surface provides the surface
normals to guide the position setting of the point light sources above these surfaces.
A cooling channel axis is then formed by connecting all the point light sources
4.18
together. The geometric design of the proposed cooling channel can be generated by
sweeping with its cross-sectional geometry. The workflow of CCC geometry is
a)
b)
Figure 4-20 3D CAD model, a) a solid model, and b) a faceted model
Figure 4-21 Position and orientation settings (user view) of the test product
Figure 4-22 Normal vectors display on the surface of the test model
4.19
Figure 4-23 Bounding box creation with a distance d (ø4mm) from the edge of
mould core plate
Figure 4-24 The workflow of CCC generation
4.4.1 Point light source setting for the CCC generation
The setting of point light source for the CCC generation depends on some
guidelines and working principles from 3D graphics design. All the point light
sources are set for providing the path of cooling channel design on CAID. These
point light sources project on the mould surface for the feasibility check algorithm.
The cooling performance and feasibility of the cooling channel design can be
visualized. In this study, the point light source setting for the CCC generation is
guided by the methods of maximum visibility [Young 1998] and Light Source
Minimization. As the point light source should be set properly to reflect the
performance of heat transferrability on the mould surface, a balance is necessary
between maximum visibility and Light source Minimization during the CCC
generation.
4.20
4.4.1.1 Point light source setting for the cooling channel design
First of all, a normal vector n̂1 on the mould cavity surface is found which
G
guides the point light source setting. The position of the first point light source p1
is set at the location near the coolant inlet which is defined by the mould designer.
G
The coordinate of p1 (x1, y1, z1) can be identified by a datum point at the edge of
the mould plate. The point light source setting depends on the normal vectors n̂i on
the mould cavity surface with a distance d from the edges of mould plate and mould
surface geometry. The distance d cannot be smaller than the diameter of the cooling
channel. The position setting of the first point light source at the coolant inlet is
Figure 4-25 Position setting of the first point light source at the coolant inlet
4.4.1.2 Maximum visibility for light source setting in light illumination
In this study, maximum visibility is a guiding method for point light source
setting in light illumination during cooling channel system design. The normal
4.21
vectors on the mould surface can indicate the change of shape on the mould surface
geometry in CAID. The distribution of normal vectors on the mould surface can give
user the indication to set a light source to obtain a maximum region of light
illumination. This method is transformed into visibility in the feasibility check stage.
G
For light illumination, the location setting of point light source p1 can be
defined by using the maximum visibility method on the mould surface design in
CAID. The maximum visibility method can be started from the geometry of the
surface boundary of the mould. Each boundary or edge can identify its normal vector
n̂i by geometric modeling calculations. The normal vector on a surface point is
perpendicular to its tangent vector tˆi . As shown in Figure 4-26, the tangent vector
will change in direction when moving along the curve or surface.
a)
b)
Figure 4-26 Normal vector, a) on a 2D curve, and b) on a planar circle
For 3D geometry, the triangular facet model of a geometric part is in STL
format. Outward normal vector can be identified from the data structure. A normal
4.22
vector n̂i of a facet fi on the part geometry. It can be linked up with the point light
source for the demonstration of light illumination for the feasibility check algorithm.
The surface can be convex, non-convex, concave, or planar. A point on a 3D curve
can give three vectors: normal vector, tangent vector, and bi-normal vector as shown
in Figure 4-27.
a)
b)
Figure 4-27 Normal vector on 3D a) relationship between normal vector, tangent
vector, and bi-normal vector, and b) normal vector on a 3D triangular
facet
For the theory of maximum visibility, the relationship between the position
G
setting of the point light source pi and the normal vector n̂i on the surface of the
part geometry can be shown by Figure 4-28.
a)
b)
Figure 4-28 Identification of maximum visibility of a single point light source on a
2D polygonal surface a) partial visibility, and b) maximum visibility
4.23
The 3D rendering of the part geometry can be modeled by the CAID software
such as Rhino 3D or 3D Studio Max. In this study, CAID is used to verify the
performance of light illumination for the point light source setting under maximum
visibility method.
In Figure 4-29, a cube’s CAD model and a single point light source are used.
Normal vectors erected on the surface of part are illuminated by a single point light
source to illustrate the maximum visibility on the part surface. 3D rendering of a
hemi-sphere in 3D modeling with single point light source setting to illustrate the
maximum visibility method via CAID software is shown in Figures 4-30.
a)
b)
c)
d)
Figure 4-29 Maximum visibility of a cube, a) front view, b) top view, c) perspective
view, and d) 3D rendering at perspective view
4.24
a)
b)
c)
d)
Figure 4-30 Maximum visibility of a hemi-sphere, a) front view, b) top view, c)
perspective view, and d) 3D rendering at perspective view
4.25
In this study, another guiding method Light Source Minimization is given to
optimize the number of light source to give the geometry during CCC design. The
performance of the output result visualization in Light illumination is controlled by
G
the number of light source setting. The point light source pi setting also depends on
the distribution of normal vectors n̂i on the mould surface. The number of point
light source depends on the completeness of light illumination onto the surface.
Insufficient number of point light source will result in incomplete light illumination.
Further increase in the number of point light source will have no improvement in
illumination result on the surface if complete light illumination has already achieved.
This method is also transformed into visibility in the feasibility check stage.
The variation in number of point light sources for non-convex model is shown
in Figure 4-31. On the background of the non-illumination surface, it is identified as
dark side.
4.26
a)
b)
a)
b)
a)
b)
Figure 4-31 Variation in number of point light sources for non-convex model, a)
single point light source, b) rendering of single point light source, c)
two point light sources, d) rendering of two point light sources, e) three
point light sources, and f) rendering of three point light sources
4.27
The minimum number of equivalent point light source can be found for a
variety of cooling methods and cooling channel designs. For example, single point
light source for a thermal pin and two point light sources for a straight-line drilled
G
cooling channel, etc. The number of point light source pi increases with the
complexity of the geometry of the cooling channel.
For CCC design, the minimum number of point light source should be more
than two in order to follow the shape of a model with manifold surfaces. In order to
represent a linear light source, point light source positioned at two end points of the
straight-line segment is used. They can be represented by fluorescent tube and light
bulbs on a 2D surface. See Figure 4-32. The minimum number of equivalent point
light source for various conventional cooling channel designs for PIM process is
tabulated in Table 4-1.
In case of CCC with complex geometry, the number of point light source
increases to enhance the shape conformance between the CCC to the mould surface.
The cooling channel axis formed by connecting neighboring point light sources will
then follow the shape of the mould surface to affect uniform heat transfer. The
variation in number of point light source on a same model is shown in Figure 4-33.
4.28
Figure 4-32 Light illumination of a 2D surface, a) fluorescent tube, and b) two light
bulbs
Table 4-1 Minimum number of point light source for injection mould cooling
channel design
Cooling method
Geometry
Minimum
number of
point light
G
sources pi
Light
illumination
Thermal pin
Point
1
Light bulb
Straight-line
channel
Line
segment
2
Fluorescent
tube
L-shaped
channel
Line
segment
3
Fluorescent
tube
U-shaped
channel
Line
segment
4
Fluorescent
tube
Hexagonal
channel
Line
segment
6
Fluorescent
tube
Conformal
cooling channel
Line or
curve
segment
≥3
Fluorescent
tube
Pocket/ surface
cooling
Area
≥4
Fluorescent
tube
4.29
Example
Figure 4-33 Variation in number of point light source on a 2D circular mould surface,
a) four point light sources, b) five point light sources, and c) eight point
light sources
4.4.2 Connectivity of a set of point light sources by neighboring point location
For the point light source setting, the cooling axis is connected by listing its
G
points in a sequence, starting from the cooling inlet point p 0 (or the starting point).
4.30
The cooling channel axis can be formed by joining all the points. See Figure 4-34. A
G
G
G G G G
point set pi of four points, pi = { p o , p a , pb , p c } is proposed and located at
arbitrary position in a 2D plane with a part geometry in close proximity. The tangent
G
vector called, p neighbour , provides the direction in order to connect with the
G G
G
G
neighboring points p a , pb , and p c . The starting point p 0 is connected with its
G
G
G
neighboring point p a in clockwise order. Then p a changes to p1 , with an order
G
G G
G
G
G
arrangement ( p a → p1 , pb → p 2 , and p c → p3 ):
G
G
G
G
p o → p1 → p 2 → p3
(4-2)
By continuously joining the points, the whole cooling channel axis can be
created. By sweeping with a cross-sectional profile, the cooling channel can be
generated.
a)
b)
c)
Figure 4-34 Steps of point light source selection under neighboring point location, a)
tangent vector (by user specify) towards the neighboring point at
starting point, b) line segment formation, and c) cooling channel axis
formation
4.31
4.4.3 Topological representation for the connectivity of the point light sources of
CCC
In this section, the connectivity of the point light source setting will be given by
the transformation of a set of point light sources into the proposed cooling channel
design. A point light source is represented as a point which achieves a uni-directional
light illumination on the object to the illuminated. For simple demonstration, the
connectivity between the point light sources can be given as a topological
representation. It can provide the geometric definition and sequence of points which
link up with line segments for cooling channel axis formation. By graphical
illustration with the aid of topology [Basener 2006 and Flegg 1974], the connectivity
of the cooling channel can be identified clearly. The topological representation can
be applied to a rapid tool or mould with multi-cavities (or cores) that diverse types of
cooling channel designs can be recognized and recorded easily.
The cooling channel axis can be approximated by a series of line segment
joining adjacent point light sources as shown in Figure 4-35.
4.32
Figure 4-35 Approximating a cooling channel axis in 3D, a) a sequence of points
before curve approximation, b) cooling channel axis is approximated by
a series of line segments joining adjacent points along the cooling
channel axis, c) a cooling axis is interpolated from the points
G
As shown in Figure 4-36, eleven point light sources pi (xi, yi, zi) is located on
G
G
a 2D plane. A curve can be formed from point p1 to p11 . The topological
representation also provides the coolant flow path direction within the injection
mould at different time sequence.
4.33
a)
b)
Figure 4-36 Approximation of the cooling channel axis via the point light sources
setting a) coordinates on point light sources, and b) 3D geometric
modeling of cooling channel design with point light sources
4.4.3.1 Definitions of topological representation
Under the topological representation for the cooling channel axis of an PIM
model, the sequence and the relationship of the coolant flow through a cooling
channel within an injection mould can be identified. P0 and Pi are defined as inlet
point and outlet point of the cooling channel axis. A point Pn is set in order to locate
4.34
the cooling axis coordinate in 3D spaces and it is the point of the cooling channel
axis between P0 and Pi. The number of point Pn highly depends on the level of
resolutions of the user definition. The more the number of point Pn setting, the more
the computation time required. In-between two points Pn is the line segment in
omni-direction in 3D of the cooling channel axis. The combination of these points
and line segments can form a long chain of cooling channel axis. The topological
representation of the cooling channel axis can approximate the sequence of the
passageway for coolant flow through the cooling channel. The topological
relationship of a cooling channel can be identified easily. The number of cooling
channel increases with the number of chain of cooling channel axis CCi. The benefit
of this representation approach can provide mould designers and engineers a clear
depiction on how the coolant flows and the complexity of the cooling channel is.
More complex geometric design, such as CCC can be identified. Besides, it is highly
suitable for conformal surface cooling passageway, such as conformal porous pocket
cooling (CPPC). The sequence or connectivity of this complex cooling network or
passageway for the coolant flow can be identified clearly. The general geometrical
representation can be shown in the following:
j −1, k −1
1,1
n, m
Po ⎯⎯→
Pn ⎯⎯→
⎯
"⎯⎯
⎯→ Pi
C
C
C
(4-2)
Without loss of generality, there are several types of geometric design of cooling
4.35
channels (including straight-line drilled or CCC) in this study. Each type of cooling
channel can be identified individually by a name or code for the topological
representation. The types of cooling channel with codes for topological
representation are tabulated in Table 4-2.
Table 4-2 Types of cooling channel with codes for topological representation
Types of cooling channels
Codes
Straight-line drilled cooling channel
SLDCC
Conformal cooling channel
Variable
channel
radius
conformal
CCC
cooling
VRCCC
Conformal porous pocket cooling
CPPC
The setting of topological representation of a rapid tool or mould depends on the
following guidelines:
1. Each type of cooling channel only has a single coolant inlet and a single coolant
outlet.
2. The line segment cij connected between two point sources Pi,j and Pi,j+1 is in
omni-direction of the line segment from coolant inlet to coolant outlet.
3. Topological representation can be applied to the mould cavity or core plates
within rapid tool or injection mould.
4. Rapid tool or injection mould with single cavity (or core) or multi-cavities (or
cores) can also be represented.
4.36
5. Each mould plate can integrate with single cooling channel or multi cooling
channels.
6. Each mould plate can include more than one type of geometric design of cooling
channel if the mould design is feasible
4.4.3.2 Topological representation for single cooling channel axis
The topological representation of a straight-line drilled cooling channel of PIM
model for single cooling channel axis is shown in Figure 4-37 and Table 4-3.
Figure 4-37 Topological representation of a single cooling channel axis
Table 4-3 Topological representation of a single cooling channel design
Cooling
Topology of each cooling channel
channel(s)
SLDCC1
1,1
1, 2
1, 3
1, 4
1,5
1, 6
1, 7
P1,0 ⎯⎯→
P1,1 ⎯⎯→
⎯
P1,2 ⎯⎯
→P1,3 ⎯⎯→
⎯
P1,4 ⎯⎯→
⎯
P1,5 ⎯⎯→
⎯
P1,6 ⎯⎯→
⎯
P1,i
C
C
C
C
4.37
C
C
C
4.4.3.3 Topological representation for multi-cooling channel axes
Apart from single cooling channel, the topology of multi cooling channel axis
for various complex geometric design of cooling channels can also be represented by
Figure 4-38 and Table 4-4.
Figure 4-38 Topological representation of multi cooling channels axes
Table 4-4 Topological representation of multi cooling channel design
Cooling
Topology of each cooling channel
channel(s)
SLDCC1
SLDCC2
SLDCC3
SLDCC4
1,1
1, 2
1, 3
1, 4
1,5
1, 6
1, 7
P1,0 ⎯⎯→
P1,1 ⎯⎯→
⎯
P1,2 ⎯⎯
→P1,3 ⎯⎯→
⎯
P1,4 ⎯⎯→
⎯
P1,5 ⎯⎯→
⎯
P1,6 ⎯⎯→
⎯
P1,i
C
C
C
C
C
C
C
2,1
2, 2
2,3
2, 4
2,5
2, 6
2, 7
P2,0 ⎯⎯→
⎯
P2,1 ⎯⎯→
⎯
P2,2 ⎯⎯→
⎯
P2,3 ⎯⎯→
⎯
P2,4 ⎯⎯→
⎯
P2,5 ⎯⎯→
⎯
P2,6 ⎯⎯→
⎯
P2,i
C
C
C
C
C
C
C
3,1
3, 2
3, 3
3, 4
3, 5
3, 6
3, 7
P3,0 ⎯⎯
→P3,1 ⎯⎯→
⎯
P3,2 ⎯⎯→
⎯
P3,3 ⎯⎯→
⎯
P3,4 ⎯⎯→
⎯
P3,5 ⎯⎯→
⎯
P3,6 ⎯⎯→
⎯
P3,i
C
C
C
C
C
C
C
4,1
4, 2
4,3
4, 4
4,5
4, 6
4, 7
P4,0 ⎯⎯
→P4,1 ⎯⎯→
⎯
P4,2 ⎯⎯→
⎯
P4,3 ⎯⎯→
⎯
P4,4 ⎯⎯→
⎯
P4,5 ⎯⎯→
⎯
P4,6 ⎯⎯→
⎯
P4,i
C
C
C
C
4.38
C
C
C
4.4.3.4 Topological representation of cooling channel designs for rapid tool
injection mould with single cavity (or core) or multi cavities (or cores)
As discussed before, the connectivity and geometric information of a CCC
design can be recognized with the aid of topological representation. In this study,
rapid tool or injection mould with single cavity (or core) is employed for various
CCC designs in the implementation. The topological representation of a CCC design
is combined with the setting or points and line segments to form the cooling channel
axis. The topologies of single or multi CCC designs can been identified respectively.
Apart from representation in single cavity (or core), rapid tool with multi
cavities (or cores) are common in PIM design. SFF technologies can give the
feasibility to design various types and to integrate multi number of CCC’s in a rapid
tool with multi-cavities. The number of various types of CCC’s in a rapid tool
increase with difficulty in CCC’s identification. Confusion in counting the specific
location of CCC is easy to happen. The topological representations of CCC’s within
a rapid tool can also be recognized by a roadmap design. The graphical
representation of diverse CCC’s designs for a mould cavity plate with multi-cavities
in a rapid tool is shown in Figure 4-39. The topological representation can be applied
to identify various cooling channel designs for various application such as CCC
integrated in rapid tool for micro injection moulding.
4.39
Figure 4-39 Graphical representation of diverse CCC’s designs for a mould cavity
plate with multi-cavities in a rapid tool
As shown in Figure 4-39, four cavities (for mould cavity plate) and diverse
CCC’s designs (such as SLDCC, CCC, and VRCCC) are integrated inside a rapid
tool. For topological representation, each cavity has more than one type of cooling
channels (CCC and VRCCC). For example, Cavity 1 includes both CCC1 and CCC2
respectively. Besides, a cooling channel can be integrated across two cavities. For
example, a SLDCC1 is integrated across Cavity 1 and Cavity 3. A linkage is formed
between Cavity 1 and Cavity 3 for this cooling channel in topological representation.
The connectivity of diverse cooling channel designs for the multi-cavities within a
rapid tool is shown in Figure 4-40.
4.40
Figure 4-40 The connectivity of diverse cooling channel designs for the
multi-cavities within a rapid tool
4.4.4 Procedure of CCC generation
After setting the position and orientation of the test model, the number of point
light sources will be defined by normal vectors on the surface of the faceted model
with the maximum visibility method and Light Source Minimization. The position
setting of the point light sources above the surface of test model is shown in Figures
4-41. In this study, there are ten point light sources (from p1 to p10) inserted to the test
model of the core plate. The coolant inlet is proposed by mould designer. p1 is set
from the datum point at the edge of the mould core plate. A CCC design is proposed
for the test model for uniform heat transfer from the mould core surface to the
cooling channel. Both p1 and p10 are the point light sources at the coolant inlet and at
the coolant outlet respectively. The parameter setting of the output result
visualization is tabulated in Table 4-5.
4.41
Figure 4-41 Point light source settings for the test model
Table 4-5 Parameter settings of light illumination for result visualization
Parameters
Values
Type of light source (Photometric Light)
Free point
Number of cooling channel axis
1 unit
Number of point light source(s)
10 units
Light source
D65 White Diffuse
Light Intensity
300 cd
Red
Green
Blue
Colour
255
255
255
white
Output result visualization
(i) Colour and (ii) Gray scale
After all the point light sources are set, these point light sources are connected
together by a number of line segments. As shown in Figure 4-42, the connection of
the point light sources with line segments serve as the cooling channel axis. This
cooling channel axis can provide the sequence, location, and geometric information
by the topological representation of the whole CCC. The topological representation
of the CCC of the test model is tabulated in Table 4-6. The 3D geometric design of
4.42
the cooling channel can be generated according to its cross-sectional diameter, (for
example ø4mm) with the sweeping process. The geometric design of cooling channel
axis and the CCC of the test model are shown in Figures 4-43 and 4-44.
Figure 4-42 Cooling channel axis by point light sources connectivity
Table 4-6 Topological representation of the CCC
Cooling
Topology for the CCC
channel(s)
CC1
1,1
1, 2
1, 3
1, 4
1, 5
1, 6
1, 7
P1,0 ⎯⎯→
P1,1 ⎯⎯→
⎯
P1,2 ⎯⎯
→ P1,3 ⎯⎯→
⎯
P1,4 ⎯⎯→
⎯
P1,5 ⎯⎯→
⎯
P1,6 ⎯⎯→
⎯
C
C
C
C
C
C
C
1, 8
1, 9
1,10
P1,7 ⎯⎯
→ P1,8 ⎯⎯→
⎯
P1,9 ⎯⎯→
⎯
P1,i
C
C
C
Figure 4-43 Cooling channel axis generation for the CCC design in relation to the
mould surface
4.43
Figure 4-44 3D modeling of the CCC
4.4.5 Output solution of the test model
The test model is then visualized by 3D rendering under CAID tool to verify the
feasibility of the proposed cooling channel design. The visualized results of the test
model by 3D rendering with point light source setting is shown in Figures 4-45.
From the visualized results from coloured displays, light illumination on the
surface can be represented by red colour (see Figure 4-46).
Figure 4-45 3D rendering of test model after light illumination
4.44
Figure 4-46 3D rendering of the test model under colour display
4.4.6 Feasibility verification of the proposed CCC
The conditions and analysed results performed by the feasibility check
algorithm after light illumination in 3D are listed in Tables 4-7 and 4-8. The output
results with each light source related to its surface are verified under illumination (L)
for Case 1 and non-illumination (N) for Case 2. The shaded region (blue) or
non-colouring region after direct light source projection is identified as the
non-illumination. The colour region (red) after direct light source projection is
identified as the illumination. From the results in Table 4-8, all point light sources are
set under illumination. Complete light illumination can be obtained by the proposed
cooling channel design. As shown in Figure 4-47, three points were picked up for
cooling channel design verification from the visualized result. The image data from
the position of point 1 for checking with RGB and monochromatic values is shown
in Figure 4-48.
4.45
Table 4-7 Percentage of light illuminated region by CCC for the mould surface
Conditions
Values
Number of point light sources
10
Number of triangular elements on surface
2166
Number of shaded element
0
% of light Illuminated region
100
Table 4-8 Mode of illumination at the point light source setting
Illumination
(L, N)
p1
p2
p3
p4
p5
p6
p7
p8
p9
p10
L
L
L
L
L
L
L
L
L
L
Figure 4-47 Points picked up for cooling channel design verification
Figure 4-48 RGB and monochromatic values of image data at point one
4.46
From the results illustrated by the feasibility check algorithm, the combination
of point light sources from p1 to p10 can produce a complete light illumination on the
surface of the test model. The results performed by RGB and monochromatic values
are tabulated in Table 4-9. Three sampled points are picked up for checking the
performance of light illumination. The values from the sampled points indicated that
the surface is uniform in light illumination. The proposed CCC design can be
performed a uniform cooling performance for the mould core plate of the test model.
Uniform heat transfer can be achieved by the proposed CCC design corresponding to
the test model from mould core plate.
Table 4-9 Points picked up on the test model after light illumination for feasibility
verification by RGB and monochromatic values
Point(s) R
G
B
Monochrome
value(s) (0-255)
Colour
Point 1
255 (100%)
203 (79.5%)
0 (0%)
153 (59.8%)
Orange
Point 2
255 (100%)
90 (35.3%)
0 (0%)
115 (45.1%)
Yellow
Point 3
255 (100%)
6 (2.3%)
0 (0%)
87 (34.1%)
Red
4.4.7 File Export for further processing
After the proposed feasibility check with design algorithm, the visualized results
of the test model can be exported via graphic tools for further processing or
examination. The proposed algorithm can provide the diverse geometric design of
cooling channel, such as CCC.
4.47
From the above results, the cooling performance of the proposed cooling
channel design by the feasibility check algorithm can be determined and visualized
by 3D rendering on CAID. The visualized result of the test model can further be
validated by the use of simulation packages such as CFD and CAE package. All the
results can be compared with the output result visualization performed by 3D
rendering.
4.5 Chapter Summary
CCC generation in the feasibility check algorithm is proposed for injection
mould cooling channel design. The cooling channel design is created by the point
light source settings and the cooling channel axis. Point light source setting can be
controlled by maximum visibility and Light Source Minimization. The cooling
channel designed can be conventional straight-line drilled and CCC. The
performance and feasibility of the proposed cooling channel design can be visualized
by 3D rendering and checked by image data of RGB and monochromatic values.
4.48
Chapter 5 Variable Radius Conformal Cooling Channel and Conformal Surface Cooling
CHAPTER 5
VARIABLE RADIUS CONFORMAL
COOLING CHANNEL AND
CONFORMAL SURFACE COOLING
5.1 Problems of CCC
In case of cooling by conductive heat transfer, it can be further expressed and
described in Equation (5-1) to suit for injection moulded cooling process.
(5-1)
Equation (5-1) provides a clear concept for the heat transfer from polymer melt
to cooling channel surface with some factors such as coefficient of heat conduction
or cross section area.
The advancement of SFF technologies has made CCC possible. Contemporary
RT fabricated with CCC ensures that the polymeric part in PIM is cooled more
uniformly than the straight-line drilled cooling channel. The shape conformance
between CCC and mould surface (core or cavity) can reduce the injection mould
defect formations. However, there is a temperature difference in the coolant between
the inlet and the outlet regions. The temperature at the outlet portion is typically
higher than the inlet one. In fact, the rate of heat transfer from the polymeric melt to
5.1
the coolant along the cooling circuit drops due to increasing coolant temperature
from inlet to outlet.
In this chapter, a CCC design called variable radius conformal cooling channel
(VRCCC) is proposed for the CCC design to provide a compensation of coolant
temperature increase along the cooling channel and residual thermal stress
accumulation within the mould. Extra uniform cooling between the VRCCC and its
mould surface and more heat can be transfer at the outlet of the VRCCC. The design
of VRCCC is verified by feasibility check algorithm. The theoretical issues and the
design of VRCCC are described. The implementation of the VRCCC in the
feasibility check algorithm will also be given in this section.
5.2 Variable Radius Conformal Cooling Channel for Uniform Cooling
Achievement in PIM Design
VRCCC is a CCC which follows the shape of the moulding part geometry with
various diameters along the coolant flow path. It takes advantage of the SFF
technologies to produce a curvilinear geometry of CCC and integrate with changing
diameters along the cooling channel axis for a rapid tool. The improvement of
cooling uniformity can further increase the efficiency of heat transfer between the
cooling layout and mould cavity surface. The cumulative effect of the polymeric heat
5.2
transferred and temporarily stored within the CCC will influence the cooling time
and injection moulded defect formation and the modified layout of VRCCC can
reduce the maximum coolant temperature. More heat energy can be carried away at
the cooling passageway at the outlet portion. Conventional CCC highly emphasizes
the shape aspect rather than the heat transfer requirements of the rapid mould. In
particular the thermal residual stress in the moulded part should be minimized in the
fastest possible cooling cycle time. Physically, the heat flux from polymeric melt or
mould material should be transferred uniformly to affect uniform strain variation
over time is shown in the heat diffusion equation. The heat diffusion equation for
PIM cooling process is expressed in Equation (5-2):
K K
∂T
q generate = −k∇ ⋅ ∇ + ρc
∂t
(5-2)
where q [Wm-2K-1] is the heat flux generated during PIM process, k [Wm-1K-1] is the
thermal conductivity, T [K] is the mould temperature, ρ is the density, c [Jg-1K-1]is
the specific heat capacity and t [s] is the cycle time.
The heat conducted via mould material to cooling channel depends on the
geometry (distance and geometry) while the instantaneous change in temperature
relies on the efficiency of the cooling channel design. A uniform temperature change
will results in uniform strain in mould cavity or core dimensions and is shown in
Equation (5-3):
5.3
σ thermal = −αE∆T or ε thermal = −α∆T
(5-3)
whereσ [Nm-2] is the thermal stress, α is the linear coefficient of thermal expansion,
E [Nm-1] is Young’s modulus, T [K] is the temperature, and ε[m] is the thermal
strain.
However, in practice, negligible resultant residual thermal stress is difficult to
achieve except for simple geometry. Thus, the importance of VRCCC design cannot
be ignored as it can solve the problems in compensation of coolant temperature
increase along the cooling channel and residual thermal stress accumulation within
the mould during PIM process. The geometric design of a VRCCC is shown in
Figure 5-1.
Figure 5-1 Geometric description of VRCCC with its cooling channel axis a) top
view, b) isometric view, c) front view, and d) side view
To ensure uniform heat transfer from cavity surface to cooling duct, Fourier’s
law [Kreith 1980] of heat conduction is used to find the relationship between inlet
radius, r [m] and outlet radius R [m].
5.4
From Fourier’s equation, the rate of heat conduction with radius r can be
formulated as:
q1 =
− k (2π∆x)
(To − T1 )
d −r
(5-4)
where ∆x [m] is the length of cooling channel, To [oC] (To > T2 > T1) is the
temperature of mould cavity surface and T1 [oC] is the temperature of the cooling
channel near the inlet portion.
While the rate of heat conduction with radius R can be expressed can be
formulated as:
q 2 =
− k (2π∆x)
(To − T2 )
d−R
(5-5)
where T1 [oC] is the temperature of the cooling channel near the outlet portion. The
rate of heat conduction at coolant inlet and outlet for VRCCC are shown in Figure
5-2.
Figure 5-2 Rate of heat conduction at coolant inlet and outlet for VRCCC
5.5
In order to achieve uniform rate of heat transfer being conducted via the cooling
channel at any position from the mould cavity surface, the rate of heat transfer, q1
near the inlet portion must be the same as the outlet portion, q 2 . Inlet heat conduction
and outlet heat conduction along cooling channel is constant:
q1 = q 2
(5-6)
where q1 is inlet rate of heat conduction and q 2 is the rate of outlet rate of heat
conduction.
The design of VRCCC between mould cavity surface and cooling channels is
a)
b)
Figure 5-3 VRCCC design between mould cavity surface and cooling channels, a)
near the inlet portion, and b) near the outlet portion
5.6
According to Figure 5-3, the mathematical formula between inlet radius and
outlet radius for VRCCC can be derived in Equations (5-7) to (5-9).
r
R
(T0 − T1 ) =
(T0 − T2 )
d −r
d−R
(5-7)
where d [m] is the distance between centre of cooling channel and mould cavity
surface, T0 [K] is the temperature at the mould surface, T1 [K] is the temperature of
the cooling channel near the coolant inlet, and T2 [K]is the temperature of the cooling
channel near the coolant outlet.
then:
rd
rR
(T0 − T1 ) −
(T0 − T1 ) = R(T0 − T2 )
d −r
d −r
(5-8)
rd
⎡ r
⎤
(T0 − T1 ) = R ⎢
(T0 − T1 ) + T0 − T2 ⎥
d −r
⎣d − r
⎦
(5-9)
and therefore:
Consequently, the size of the cooling channel radius R [m] near the coolant
outlet can be derived in Equation (5-10):
R=
rd
(T 0 − T1 )
d −r
(5-10)
⎡ r
⎤
⎢ d − r (T 0 − T1 ) + T 0 − T 2 ⎥
⎣
⎦
VRCCC is attempted to provide a better cooling uniformity for the PIM than the
CCC one. By increasing the surface contact area near the outlet portion and
simultaneously increase amount of volumetric coolant flow, more heat energy from
the polymeric melt can be carried away.
5.7
VRCCC can theoretically compensate the inlet-outlet coolant temperature
difference by utilizing large radius cooling channel near and at the outlet. In practice,
VRCCC can be designed and analyzed with the aid of CAD/CAM systems. With the
use of SFF technologies such as 3DP or SLS systems, the VRCCC can be fabricated
with the rapid tool or injection mould for PIM process.
5.2.1 Design methodology for the VRCCC
VRCCC design has three main steps. The first step is to determine the VRCCC
location (See Figure 5-5). A normal offsetting technique [Maekawa 1999 and
Beaman 1997] will be used which can provide the position and shape of the cooling
passageway within the rapid tool. The parametric form of the offset surface So(u, v)
from a given cavity surface S(u, v) can be referred with Equation (5-11) [Kumar
2001 and Piegl 1999] and illustrated in Figure 5-4:
S o (u , v ) = S (u , v ) + dn(u , v )
(5-11)
where d [m] is the offset distance and n(u, v) is the surface normal. The offset
distance d between the underlying mould cavity surface and the cooling channel can
be determined from the theoretical calculation or practical data.
5.8
Figure 5-4 Surface normal offsetting process
The second step is to determine the variable diameter settings for the proposed
cooling passageway from the inlet to the outlet. The cooling channel axis designed
from Figure 5-5b provides the layout of VRCCC.
The final step is the modeling with nonlinear sweeping and shelling operations
as well as fabrication based on SFF technologies [Lee 1999, Zeid 1991, and Rooney
1987]. With the cooling channel axis of the cooling passageway for the whole circuit,
the whole circuit can be subdivided into several portions with the variable channel
diameters for setting the VRCCC. The integration with the variable diameters for the
passageway and cooling channel axis of the circuit can start the sweeping process to
generate the VRCCC (see Figure 5-5c). Finally, a shelling operation is to generate a
hollow object by removing solid thickness for whole cooling passageway. The design
and generation of VRCCC are shown in Figure 5-5d.
5.9
A VRCCC design and fabrication based on contemporary SFF technologies is
proposed and verified by the proposed feasibility check algorithm. The heat transfer
from the mould cavity surface to the coolant circulation via VRCCC can become
extra uniform in order to compensate the rise of temperature during PIM. VRCCC is
also applicable to the design of rapid tool with complex cavity surface so as to reduce
the cooling time and production time.
a)
b)
c)
d)
Figure 5-5 Design methodology of VRCCC, a) offsetting of mould cavity surface, b)
cooling channel axis design along the VRCCC c) variable diameter along
the cooling channel axis and d) 3D modelling of a rapid tool with
VRCCC design
5.10
5.2.2 Consideration of constraints in geometric design of VRCCC
As discussed in Chapter 2, the geometric design of CCC for an injection mould
or rapid tool can be varied. Similar to the design of VRCCC, it depends on the
limitations or constraints that will affect the uniform cooling condition or coolant
flow rate [Osswald 2002].
1. Pressure drop
The allowable pressure drop of the coolant in the CCC design is limited by the
available pumping pressure of the cooling circulation system. The objective of
cooling line design for pressure drop is to find a proper combination of the coolant
flow rate, the cooling channel diameter, and cooling channel length so that the
resulting total pressure drop is smaller than the given pressure setting. The fluid
mechanics of incompressible flow can be used to predict the coolant pressure drop
that is a function of the cooling channel length, the cooling channel diameter, and the
coolant flow rate.
2. Coolant temperature variation
The objective of the design for the coolant temperature uniformity is to check and
make sure that the coolant temperature drop is maintained within a certain range. In
order to reduce the coolant temperature drop, the designer can use coolant with high
specific heat, increase the coolant flow rate, decrease the pitch distance between two
5.11
adjacent cooling channels or reduce the length of the cooling line.
3. Distance between mould cavity (or core) surface and cooling channel surface
The distance between mould cavity (or core) surface and the cooling channel
surface will affect the rate of heat removal of the injection mould. The shorter the
distance between each other, the faster the rate of the heat removal from the
polymeric melt to the cooling channel via the mould cavity surface and away via the
coolant flow. However, the distance between them cannot be smaller than the
diameter of the cooling channel. Otherwise, collapse or mould damage will happen.
4. Obstacles on mould cavity surface which block the route of coolant flow
The injection mould assembly always includes some accessories such as ejector
pin, side core or thermal pin which aid at providing various functions for moulding
the plastic part. These accessories may hinder the route of the cooling channel layout
under the geometrical or symmetrical designs in order to obtain a uniform cooling of
the coolant flow. The blocking of cooling channel on specific region of the mould
cavity surface will affect the cooling performance for the plastic part. Injection
moulded defects may happen easily at this region.
5.12
5.3 Feasibility Check for VRCCC Design
In this study, VRCCC is applied to replace the CCC generation process in the
feasibility check algorithm. The workflow of VRCCC generation for the feasibility
check algorithm is shown in Figure 5-6.
Figure 5-6 Workflow of VRCCC generation for the feasibility check algorithm
5.3.1 Pre-processing of VRCCC generation in the feasibility check algorithm
To show the output of a mould surface with near uniform VRCCC, a mould
surface with complex geometry is designed by a 3D CAD software. With the aid of
CAIMD software, the mould halves (core and cavity) are modeled and saved as
faceted model for the feasibility check algorithm. A mould surface (core or cavity) is
used as the input. The mould surface is then under orientation, position, and
5.13
bounding box settings in virtual environment via CAID tool before point light source
setting.
5.3.2 Point light source setting for VRCCC
Similar to the CCC generation discussed in Chapter 4, maximum visibility and
Light Source Minimization are also applied to the test model to guide for the point
light source setting in the feasibility check algorithm. The feasibility of VRCCC
design based on the point light source settings is checked by visibility to verify the
light illumination of the mould surface. In this study, the intensity of point light
source changes with the coolant temperature. The higher the coolant temperature, the
more intense the light source. The performance of light illumination is changed with
the number of point light source. The degree of light illumination on the mould
source changes with the variation of point light source intensity. See Figure 5-7.
Increase in coolant temperature along the VRCCC can be compensated by changing
the radius of the CCC and corresponding light source intensity. The SDC feasibility
of the VRCCC can be determined by the light illumination on the mould surface.
5.14
a)
b)
Figure 5-7 Relationship between coolant temperature, cooling channel diameter and
light source intensity, a) relationship diagram and b) schematic drawing
for the relationship
For simplification, the point light source is set by varying its light source
intensity in a linear scale. The comparison between the variables of diameters d,
coolant temperatures T, and light source intensities at different position of point light
sources pi along the VRCCC is tabulated in Table 5-1. The diameter d of a VRCCC is
changed, for example, from 6mm to 16mm. While the coolant temperature is
changed from 35 oC to 38oC and the light source intensity is changed from 100lx to
600lx. The changes in point light source intensity by 3D rendering in virtual
environment is shown in Figures 5-8 and 5-9.
5.15
Table 5-1 Relationship between point light source, diameter, coolant temperature,
and light source intensity along the VRCCC
Point light source Diameter d at pi
pi along VRCCC
[m] along
VRCCC
Coolant temperature T Light source
[oC] along VRCCC
intensity (lx)
along VRCCC
p1
0.006
308
200
p2
0.008
309
400
p3
0.01
310
600
p4
0.12
311
800
Figure 5-8 Increase in light source intensity along the cooling channel at different
diameters (p1 = 200lx, p2 = 400lx, p3 = 600lx, and p4 = 800lx)
Figure 5-9 Light illumination on a 3D plane with increasing light source intensity
5.16
The VRCCC is feasible when the mould surface has no non-illuminated region.
Non-illumination region is area that cannot be illuminated by the point light source
or the region is not visible by the point light source. The point light source setting for
a VRCCC of a mould surface (cavity) of a mobile front panel is shown in Figure
5-10. The geometric design of the VRCCC in relation to the mould surface is shown
in Figure 5-11.
Figure 5-10 Point light source setting for a VRCCC in relation to a mould surface
Figure 5-11 Geometric design of a VRCCC in relation to a mould surface
5.17
5.3.3 Output result visualization for VRCCC
The output results for checking the feasibility of the proposed VRCCC design in
relation to its mould surface can be displayed by coloured and gray scale
visualizations by 3D rendering in a virtual environment from CAID tool. The
verification of the VRCCC design can be shown by the light illumination on the
mould surface. Image data can also be obtained with the aid of graphics design tools.
The visualization of the mould surface without point light source setting (as the
standard model for comparison) by 3D rendering is shown in Figure 5-12. The output
results of VRCCC in coloured visualization by 3D rendering in virtual environment
are shown in Figures 5-13 and 5-14. The gray scale visualizations output results of
VRCCC by 3D rendering in virtual environment are shown in Figures 5-15 and 5-16.
The image data of RGB and monochromatic values for the test model can be
obtained by graphical image design tool for furthering analysis of the output results.
Figure 5-12 3D rendering of the mould surface without point light source setting
5.18
Figure 5-13 Coloured visualization output results of VRCCC in by 3D rendering in
virtual environment of the mould surface (isometric view)
Figure 5-14 Coloured visualization output results of VRCCC by 3D rendering in
virtual environment of the mould surface (top view)
Figure 5-15 Gray scale visualization output results of VRCCC by 3D rendering in
virtual environment of the mould surface (isometric view)
5.19
Figure 5-16 Gray scale visualization output results of VRCCC by 3D rendering in
virtual environment of the mould surface (top view)
5.4 Conformal Surface Cooling Passageway
The advantage of VRCCC design is that the maximum coolant temperature
from coolant inlet to outlet is reduced. However, it cannot provide a real uniform
heat transfer from the mould surface to the VRCCC surface. The distance and rate of
heat conduction from the mould surface to the VRCCC surface is varied. See Figure
5-17.
Figure 5-17 Variation of distance and rate of Heat conduction at different region from
mould surface to the VRCCC surface
5.20
Further improvement of CCC design is necessary to achieve a more uniform
cooling than the VRCCC. It is necessary to increase the cooling area or region
corresponding to its mould surface that direct heat transfer from there cannot be
experienced by CCC. SFF technologies can solve the fabrication problem in
traditional machining processes. The additive process of SFF technologies can
fabricate a variety of parts with complex geometries. For example, part with undercut
or solid model with hollow structure [Chiu 2000] can also be produced. The
differences between conventional cooling channel, CCC, VRCCC, and conformal
surface cooling passageway are tabulated in Table 5-2. The difference between CCC
and conformal surface cooling is compared. For CCC, it is a tubular cooling
passageway which follows the contour of the mould cavity (or core) surface in order
to achieve uniform cooling circulation process within the mould cavity (or core)
plate. The difference between various types of CCC depends on the shape
conformance between the mould cavity (or core) surface and the cooling channel
design. The cooling performance of a CCC design is restricted by the selection of
mould material and the geometry of the mould surface.
5.21
Table 5-2 Differences between conventional cooling channel, CCC, VRCCC, and
conformal surface cooling passageway
Cooling
passageways
Conventional
cooling
channel
CCC
VRCCC
Conformal
surface cooling
passageway
Fabrication
process
Conventional
or NC
machining
processes
Copper duct
bending,
SFF’s or RT
technologies
SFF’s or RT
technologies
SFF’s or RT
technologies
Passageway
Tube
Tube
Tube
Pocket
Geometric
design
Straight-line
Curve
Curve
Area
Geometry of
cross-section
of cooling
channel
Circular (by
straight-line
drilling)
Polygonal or
circular shape
Circular in
different sizes
along the
channel
Pocket or shell
like structure on
mould surface
Cooling
Performance
Cooling on
the mould
surface
Cooling on the
mould surface
with shape
conformance
Cooling with
variable
diameters
along the
channel on the
mould surface
for coolant
temperature
compensation
Surface cooling
on the mould
surface with
shape
conformance
5.4.1 Conformal surface cooling design for ideal uniform heat transfer
Conformal surface cooling for ideal uniform heat transfer can be identified as an
pocket or shell cooling passageway which follows the whole contour of the mould
cavity (or core) surface to achieve extra uniform or maximum cooling process within
the mould cavity (or core) plate. Ideal uniform heat conduction in PIM is the distance
and rate of conductive heat transfer at any region from polymer melt on mould
5.22
surface to cooling channel surface is uniform. No internal mechanical support is
needed for surface pocket cooling design. See Figure 5-18. The constraints from
geometric complexity of part design, mechanical structure, or internal components
(such as ejector pins or sprue) of the mould are not the restriction for conformal
surface cooling.
a)
b)
Figure 5-18 Conformal surface cooling for ideal uniform heat transfer, a) within a
mould cavity plate, and b) pocket design
For conformal surface cooling as pocket design, it can provide a uniform heat
transfer from the mould cavity or core surface to its nearest position of cooling
pocket. Every position of the mould cavity or core surfaces can be experienced by
effective heat transferrability for surface cooling. The heat energy on the mould
cavity or core surfaces can be evenly transferred. See Figure 5-19.
5.23
Figure 5-19 Conformal surface cooling for ideal uniform heat transfer
In contemporary cooling channel design for PIM, conformal surface cooling
passageway as pocket design cannot be feasible in RT technologies. The pocket
cooling passageway without internal structure cannot be achieved as it cannot
withstand the compression force during mould closing in PIM.
Conformal surface cooling with internal structure as porous structure can be the
solution to achieve near uniform heat transfer with acceptable and tolerable
mechanical strength. With porous structure cooling passageway as CPPC, more area
or region on the mould surface can be experienced with near uniform cooling. The
cooling performance of CPPC is better than the conventional CCC one. In general,
various geometric designs of cooling passageways for rapid tool or injection mould
in PIM process is summarized and shown in Figure 5-20.
5.24
Figure 5-20 The geometric designs of cooling passageways for rapid tool or injection
mould in PIM process
5.4.2 Conformal porous pocket cooling (CPPC) passageway for rapid tool
A CCC approach using porous metal structure cooling passageway for the
design of more uniform cooling performance in PIM is proposed. A porous metal is
envisaged as a system that heat is transferred from a high temperature mould material
into lower temperature coolant. CPPC can be fabricated with the aids of SFF and RT
technologies. The hollow hexagonal elements assembly for developing CPPC is
shown in Figure 5-21a. Pressure drop will also affect the coolant flow rate to remove
the heat energy. CPPC has acceptable pressure drops and can withstand the intense
clamping force during the PIM process when using strong mechanical strength
5.25
mould material and high pumping pressure of the coolant. Besides minerals from
corrosion and rusting of steel in the coolant (such as water) can be deposited on the
inside of the cooling channels. This fouling of cooling channel builds up and restricts
water flow and acts as an insulator. This accumulation on the inside wall of the
cooling channels will reduce the performance of thermal conductivity from
polymeric melt during PIM process. Muriatic acid [Tim 2002 & Beaumont 2002] can
be used as a cleaning solution. The minerals can be flushed away by the high
pumping pressure of coolant with muriatic acid solution.
With CPPC, a nearer uniform surface cooling passageway with higher effective
heat transfer coefficient can be developed. High heat transfer rate can be achieved by
the large surface area metallic porous structure. Thus, the residual thermal stress can
be reduced in the plastic parts being moulded. Some parts with complex geometries
can experience an effective surface cooling by the proposed coolant passageway. The
3D CAD model with CPPC which covered the part’s boundary profile within the
mould plate is shown in Figure 5-21b.
5.26
a)
b)
Figure 5-21 CPPC, a) hollow hexagonal elements assembly, and b) CPPC within the
mould plate
5.4.3 Conformal scaffold pocket cooling (CSPC) passageway for rapid tool
Scaffolding structure has been widely used in the medical and architectural
disciplines [Fang et al. 2005 and Lal 2004]. In 2005, the scaffolding structure was
applied into the design of conformal cooling passageway for rapid tool. A
passageway with a scaffolding structural design can provide a desirable structure for
3D interconnectivity accomplished with strong mechanical strength (See Figure 5-22)
for the coolant flow. The dimension can be accurately controlled by SFF
technologies. The design and manufacture of diverse complex geometries with a
porous network can be performed by various rapid prototyping (RP) and RT
processes. The maturity and high resolution rapid tool of various RP and RT
techniques allow scaffold architectural model to be developed in different
applications. For the design and manufacture of rapid tool, the scaffolding
architecture can be performed as a cooling surface passageway and provides a more
5.27
uniform cooling surface over the mould cavity (or core) surface, as every region of
the mould cavity surface (or core) and cooling scaffold structure cooling surface can
experience an even rate of heat transfer between each other. The strong mechanical
strength of the scaffold architecture inside the rapid tool can provide an intact
support in order to withstand the injection pressure and clamping force during the
PIM process.
Figure 5-22 Numerous scaffold elements
The shape conformance between scaffold cooling surface and mould cavity (or
core) surface can assure a small range of temperature difference during the cooling
process. Thus, the cooling process within the rapid tool for PIM can become efficient.
However, the pressure drop during the coolant circulation becomes the main problem
of the scaffold architecture as the cooling passageway system. It is necessary to
trade-off or weigh out the pressure drop with other parameters, such as coolant
pumping pressure, type of coolant, or size of scaffold architecture for the rapid tool.
5.28
The cross-sectional view of the cavity mould plate with scaffold configuration is
a)
b)
Figure 5-23 Cavity mould plate with scaffold configuration, a) cross-sectional view,
and b) side view
5.5 Feasibility Check for Conformal Surface Cooling
In this study, conformal surface cooling passageway is applied to replace the
5.29
CCC generation process in the feasibility check algorithm. Conformal surface
cooling passageway can provide nearer uniform cooling for the mould surface in
complex geometric design than the manually bent CCC or VRCCC. The feasibility
of the conformal surface cooling such as porous structure cooling passageway can be
checked by the proposed algorithm to verify its heat transferrability between the
mould surface and its passageway. The workflow of the feasibility check algorithm
for conformal surface cooling passageway design is shown in Figure 5-24.
Figure 5-24 Workflow design of feasibility check algorithm for conformal surface
cooling passageway
5.5.1 Pre-processing of conformal surface cooling passageway generation in the
For the feasibility check of a mould surface with conformal surface cooling
passageway, a mould surface with complex geometric design is modeled by 3D CAD
5.30
software. With the aid of CAIMD software, the mould halves (core and cavity) is
modeled and saved as faceted model for the feasibility check algorithm. See Figure
5-25. A mould surface (core or cavity) is used as the input. The mould surface is also
under orientation, position, and bounding box settings in virtual environment via
CAID tool.
Figure 5-25 Mould surface of a mobile panel
In case of conformal surface cooling like CSPC and CPPC, maximum visibility
and Light Source Minimization are also applied to the test model to guide the setting
of the point light source. Similar to VRCCC, the feasibility of conformal surface
cooling design based on the point light source settings is checked by light
illumination of the mould surface. In this study, a number of point light sources pi are
set above the mould surface according to the normal vectors on the mould surface
5.31
within the boundary box. The point light sources are linked up to form a cooling
network which approximates the geometric design of CPPC. The feasibility of the
conformal surface cooling can be determined by the light illumination on the mould
surface. The point light source setting and the geometric design of CPPC are shown
in Figures 5-26 and 5-27.
Figure 5-26 Point light setting for a CPPC on a mould surface of a mobile phone
panel
Figure 5-27 Geometric design of a cooling network for the mould surface
5.32
5.5.3 Connectivity of conformal surface cooling passageway
For the connectivity of conformal surface cooling, a cooling surface can be
formed by the approximation of the original curved surface from the test model. The
geometric design of the cooling surface depends on the combination of a lot of
control points, line segments, and polygonal surface elements to identify the point
light source setting for feasibility check algorithm. The topological representation of
the point light source settings are based on these surface control points and line
segments as shown in Figure 5-28. These control points can provide the 3D
coordinates and locations for setting the point light sources on the polygonal surface
elements for the feasibility check algorithm. The representation of the connectivity of
CPPC (or CSPC) passageway is a network formed by a branch of control points, pi
and line segments ci with a single coolant inlet pO and coolant outlet pI. The
topological representation for CPPC is shown in Figure 5-29. In case of a CPC
passageway design without internal structure support, the topological representation
is less important as the passageway is covered by a cooling pocket with coolant inlet
and coolant outlet.
5.33
Figure 5-28 Approximated surface formation for point light source setting for
Figure 5-29 Topological representation for CPPC passageway
5.5.4 Output result visualization for conformal surface cooling
The output results for checking the feasibility of the conformal surface cooling
design in relation to its mould surface can also be illustrated by coloured and gray
scale visualizations by 3D rendering in virtual environment from CAID tool. The
verification of the design of conformal cooling surface for rapid tool can be shown
5.34
by the light illumination on the mould surface. Image data can also be obtained with
the aid of graphics design tools for further processing and investigation. The
visualization of the mould surface without point light source setting (as the standard
model for comparison) by 3D rendering is shown in Figure 5-30. The output results
of conformal surface cooling in coloured and gray scale visualizations by 3D
rendering in virtual environment are shown in Figures 5-31 and 5-32. The CPPC
integrated inside the mould cavity plate for a mobile panel is shown in Figure 5-33.
Besides, melt flow analysis software of MoldFlow MPI is employed to validate the
cooling performance of the design of CPPC for conformal surface cooling.
Figure 5-30 Visualization of the mould surface without point light source setting (as
the standard model for comparison) by 3D rendering
5.35
Figure 5-31 Coloured visualization output results of CPPC by 3D rendering of the
mould surface
Figure 5-32 Gray scale visualization output results of CPPC by 3D rendering of the
mould surface
a)
b)
Figure 5-33 CPPC integrated inside the mould cavity plate for a mobile panel, a)
CPPC, and b) mould cavity plate
5.36
5.6 Chapter Summary
In this chapter, the theoretical issues and design methods of conformal surface
cooling passageway for rapid tool or injection mould in PIM is given. Conformal
surface cooling includes CPPC and CSPC with internal structure support. The other
one called CPC provided a conformal pocket cooling without internal structure
support. The major advantage for conformal surface cooling design is to provide an
extra uniform heat transfer from the mould surface (core or cavity) with complex
geometric design to the surface cooling passageway rather than conventional CCC
and VRCCC. The region or area on mould surface experienced by conformal cooling
can be maximized. The region on mould surface with complex geometry can also be
cooled by conformal surface cooling design.
The design of conformal surface cooling is verified by feasibility check
algorithm. The geometric design and generation of proposed cooling passageway is
under the conformal surface cooling generation in the feasibility check algorithm.
The output result of the mould surface with extra uniform conformal surface cooling
passageway is illustrated in coloured and gray scale visualizations in virtual
environment via CAID tool.
5.37
Chapter 6 Case Studies
CHAPTER 6 CASE STUDIES
6.1 Overview
Two real life examples are proposed in this chapter. One example is to check the
feasibility of VRCCC in relation to its mould cavity surface (Section 6.2).
The second example is used to check the proposed conformal surface cooling
design with respect to its mould cavity surface. CPPC passageway is designed in the
cooling channel generation of the feasibility check algorithm. Both output results are
visualized by 3D rendering in CAID for further analysis.
In these studies, melt flow analysis software of MoldFlow MPI is used to
validate the cooling and heat transfer performances of the proposed design of various
types of CCC. The analyzed results of the proposed SLDCC, VRCCC, CCC, or
CPPC are compared.
6.2 Case Study for VRCCC Design of a Soup Container
A CAD model (designed by SolidWorks 2006) of a soap container, shown in
Figure 6-1 is used in the following case study. A single cavity mould is created for
the injection mould assembly configuration. After the creation of the mould core and
cavity plates by CAIMD tool, such as MoldOffice (see Figure 6-2), the test models
6.1
are saved as faceted models for further processing and analysis. In this case study,
the mould cavity portion is given as the example for the feasibility check algorithm
with the VRCCC generation (see Figure 6-3).
Figure 6-1 3D CAD model of soap container
Figure 6-2 Mould core and cavity plates of a CAD soap container
Figure 6-3 Cavity plate of test model
6.2
6.2.1 Position and orientation settings of the test model in virtual environment
The cavity portion of the test model is imported into the virtual environment via
CAID software for the feasibility check algorithm and the cooling channel generation.
After setting the position and orientation of the test model, a bounding box is created
to restrict the location of the point light source setting. A cooling channel axis can be
obtained from the faceted model and the proposed cooling channel design as
illustrated in Figures 6-4, 6-5, and 6-6.
Then the test model is prepared for the feasibility check algorithm under the
virtual environment via CAID tool (3D Studio Max 6.0 in this research). The
geometric design of the cooling channel is provided by the mould designer. In this
case, a single unidirectional straight-line drilled cooling channel is proposed and its
cooling channel diameter is set as 6mm. The distance between the edge of the mould
plate and the edge of the bounding box is 6mm (the same as the cooling channel
diameter). The distance between the mould cavity surface and the center of the
cooling channel is 15mm.
6.3
Figure 6-4 Position and orientation of the test model with bounding box creation
Figure 6-5 Geometric design of the proposed cooling channel for the test model
Figure 6-6 Proposed cooling channel axis for the test model
6.4
6.2.2 Point light source setting for the feasibility check algorithm
Point light source is added above the test model for output result visualization.
The number of point light source being added depends on designer’s requirement. As
the faceted model of the cooling channel is given, the geometric information of the
cooling channel axis can be obtained. Point light source is added one by one along
the cooling axis from the starting point to the end point.
In the preliminary design of the straight-line drilled cooling channel, six point
light sources are added and arranged along the cooling channel axis inside the
bounding box as shown in Figure 6-7.
Figure 6-7 Point light source setting for a straight-line drilled cooling channel design
All parameter settings for the output result visualization for the feasibility check
algorithm under CAID tool are tabulated in Table 6-1. The topology representation of
coolant flow path of the straight-line drilled cooling channel corresponding to the
mould surface is shown in Table 6-2.
6.5
Table 6-1 Parameter setting for the result visualization for Case 1
Parameters
Values
Free point
1 unit
6 units
Light source
D65 White Diffuse
Light Intensity (lx)
500
RGB Colouring
Red
Green
Blue
White
255
255
255
(i) Coloured
(ii) Gray scale
Display type
Illumination
Table 6-2 Topological representation of point light source setting for straight-line
drilled cooling channel
Cooling
channel(s)
SLDCC1
Topology for straight-line drilled cooling channel
1,1
1, 2
1, 3
1, 4
1, 5
P1,o ⎯⎯
→P1,1 ⎯⎯
→P1,2 ⎯⎯→
P1,3 ⎯⎯
→P1,4 ⎯⎯→
P1,i
C
C
C
C
C
6.2.3 Output result visualization of the test model
The feasibility check algorithm verification result of the straight-line drilled
cooling channel design can be shown by 3D rendering via CAID tool. The 3D
rendering of the test model without point light source setting (the standard) is shown
in Figure 6-8 for comparing the performance of the mould surface after light
illumination by the point light source settings.
6.6
Figure 6-8 3D rendering of the test model without point light source setting
The output solution of the mould surface after point light source setting is in
coloured and in gray scale visualizations in CAID. See Figures 6-9 and 6-10
respectively. The 3D rendering of the test model can be translated into heat
transferrability between the mould surface and the straight-line drilled cooling
channel.
Figure 6-9 The 3D rendering in coloured visualization output result of the
6.7
Figure 6-10 The 3D rendering in gray scale visualization output result of the
From the above visualized result, shadow or dark side can be found from the
edges on both sides on the mould surface of the test model. The result indicated that
these dark regions cannot be illuminated by the point light sources. Incomplete light
illumination is resulted from the proposed point light source setting when
considering heat transfer from the mould cavity surface to the straight-line drilled
cooling channel in Case 1. The change of colour or brightness means the change of
cooling effect being experienced by the proposed cooling channel design setting.
To improve the feasibility of the proposed cooling channel design for the mould
surface, design modification is recommended and is discussed in Section 6.2.4. From
the coloured visualization output result as illustrated in Figure 6-9, various colour
regions can be seen from corner region. The colour range indicated that different
6.8
degrees of light illumination are experienced. The percentage of light illuminated
region by straight-line drilled cooling channel for the mould surface is tabulated in
Table 6-3. The mode of illumination at the point light source setting for the mould
surface is tabulated in Table 6-4. The image data of RGB and monochromatic values
obtained from the output visualization result in Case 1 is shown in Figure 6-11. The
RGB and monochromatic values on the mould surface are tabulated in Table 6-5. As
shown in Figure 6-15, non-uniform heat removal happens in region with colour
change from blue to orange. It can be improved by adding a point light source at that
region so that the coolant can be circulated along this region directly.
Table 6-3 Percentage of light illuminated region by straight-line drilled cooling
channel for the mould surface
Conditions
Values
6
1708
421
Percentage (%) of light illuminated region
75.3
Table 6-4 Mode of illumination at the point light source setting for the straight-line
drilled cooling channel
Light source pi
p1
p2
p3
p4
p5
p6
Illumination
(L, N)
L
L
N
N
N
N
(L – Light illumination, N – Non-illumination)
6.9
Figure 6-11 Image data point capturing at different positions in Case 1
Table 6-5 Image data of RGB and monochromatic values for the mould surface
Points
R
G
B
Monochromatic
value
Colour
1
255 (100%)
6 (2.3%)
0 (0% )
254 (99.2%)
Red
2
255(100%)
192 (75)
0 (0%)
231 (90.2%)
Orange
3
238 (93%)
254(99.4)
0 (0%)
202 (79%)
Yellow
4
62 (24.5%)
255(100%)
0 (0%)
187 (73.1%)
Green
5
0 (0%)
140 (54.7%)
Blue
6
0 (0%)
0 (0%)
Dark blue
232 (90.8%) 213 (83.4%)
0 (0%)
0 (0%)
6.2.4 Cooling channel design modification by maximum visibility and Light Source
Minimization of point light source setting
The cooling performance of the test model can be improved by a variety of
design methods. In this study, VRCCC is recommended. This VRCCC design can
compensate the coolant temperature rises along the cooling channel during heat
transfer from the polymer melt. The cooling channel diameter of the VRCCC
increases along the coolant flow path. The position and geometry of the cooling
6.10
channel axis is designed by the number and the distribution of the point light source
setting within the bounding box region. The point light source setting is based on the
maximum visibility and Light Source Minimization to the normal vectors on the
mould surface of the test model. Normal vectors on the surface of the test model are
shown in Figure 6-12. As the CCC design has variable radius, the change in
diameters along the cooling channel is represented by varying the light source
intensity to the point light sources. The increase in temperature of the mould surface
can be controlled by changing the point light source intensity.
Figure 6-12 Normal vectors on the surface of the test model
After all the point light sources are set, the cooling channel axis in 3D can be
created by connecting neighboring point light sources (see Figures 6-13 and 6-14). In
this study, two VRCCC’s are proposed to achieve uniform heat removal from the
mould cavity surface of the test model. The topological representation of the
6.11
proposed VRCCC’s is tabulated in Table 6-6. The parameter setting for the output
result visualization is tabulated in Table 6-7. The feasibility check of the proposed
VRCCC is represented by changing the light source intensities. The light source
intensities for point light source in the two VRCCC designs are tabulated in Tables
6-8 and 6-9.
Figure 6-13 Point light source settings within the bounding box region for VRCCC’s
Figure 6-14 Connected point light sources as cooling channel axes of the VRCCC’s
6.12
Table 6-6 Topological representation of the proposed VRCCC’s
Cooling
Topology for the proposed VRCCC’s
channel(s)
VRCCC1
1,1
1,2
1,3
1,4
1,5
1,6
1,7
1,8
P1,o ⎯⎯
→P1,1 ⎯⎯
⎯
→P1,2 ⎯⎯
⎯
→P1,3 ⎯⎯
⎯
→P1,4 ⎯⎯
⎯
→P1,5 ⎯⎯
⎯
→P1,6 ⎯⎯
⎯
→P1,7 ⎯⎯
⎯
→P1,i
C
VRCCC2
C
C
C
C
C
C
C
2,1
2, 2
2, 3
2, 4
2, 5
2, 6
2, 7
P2,o ⎯⎯→
P2,1 ⎯⎯→
P2,2 ⎯⎯→
P2,3 ⎯⎯→
P2,4 ⎯⎯→
P2,5 ⎯⎯→
P2,6 ⎯⎯→
⎯
⎯
⎯
⎯
⎯
⎯
⎯
C
C
C
C
C
C
C
2,8
2,9
2,10
2,11
P2,7 ⎯⎯→
⎯
P2,8 ⎯⎯→
⎯
P2,9 ⎯⎯→
⎯
P2,10 ⎯⎯→
⎯
P2,i
C
C
C
C
Table 6-7 Parameter settings for the output result visualization for VRCCC’s
Parameters
Values
Free point
Number of cooling axis
1 unit
6 units
Light source
D65 White Diffuse
From 100 to 1100
RGB Colouring
Red
Green
Blue
White
255
255
255
(i) Coloured and (ii) Gray scale
Display type
Illumination
Light
source pi
p1,1
p1,2
p1,3
p1,4
p1,5
p1,6
p1,7
p1,8
Light
100
200
300
400
500
600
700
800
source
intensity
(lx)
Light
p2,1
p2,2
p2,3
p2,4
p2,5
p2,6
p2,7
p2,8
p2,9
p2,10
p2,11
100
200
300
400
500
600
700
800
900
1000
1100
source pi
Light
source
intensity
(lx)
6.13
After the VRCCC’s are designed for the mould surface, the output result is
visualized by 3D rendering in the virtual environment via CAID tool. The 3D
rendering in coloured and gray scale visualization output results of the proposed
VRCCC’s are shown in Figures 6-15 and 6-16 respectively.
Figure 6-15 The coloured visualization output result after 3D rendering of the
VRCCC’s
Figure 6-16 The gray scale visualization output result after 3D rendering of the
VRCCC’s
6.14
As shown in Figures 6-15, red colour can only be observed for the test model by
3D rendering. Comparing with Figure 6-9, the colour found on the test model is
changed to red. This means that the mould surface of the test model can be
illuminated by the point light source setting or the VRCCC’s. Extra cooling can be
achieved after design modification using VRCCC’s to complement the original point
light source settings, see Figure 6-13. Similar output result can also be obtained by
3D rendering in gray scale visualization, see Figure 6-16. The percentage of light
illuminated region by VRCCC’s for the mould surface is tabulated in Table 6-10. The
mode of illumination by the point light source setting for the VRCCC’s is tabulated
in Table 6-11.
Table 6-10 Percentage of light illuminated region by VRCCC’s for the mould surface
Conditions
Values
19
1708
0
Percentage (%) of light illuminated region
100
Table 6-11 Mode of illumination by the point light source setting for the VRCCC’s
Illumination
(L, N)
Illumination
(L, N)
p1
p2
p3
p4
p5
p6
p7
p9
p10
P11
p12
p13
L
L
L
L
L
L
L
L
L
L
L
L
p11
p12
p13
p14
p12
p13
p14
p15
p16
p17
p18
P19
L
L
L
L
L
L
L
L
L
L
L
L
(L- Light illumination, N – Non-illumination)
6.15
In this study, three points (point 1, point 2, and point 3) are picked up and
recorded from Figure 6-17 for checking the illuminance of the test model. The 3D
rendering colour display image data of RGB and monochromatic values can indicate
the performance of illuminance. See Table 6-12. Both Point 1 to Point 3 (in red
colour) illustrates complete illumination.
Figure 6-17 Image data point capturing at different positions for the test model
Table 6-12 3D rendering colour display image data of RGB and monochromatic
values
Points
R
G
B
Monochromatic value
Colour
1
255 (100%)
6 (2.3%)
0 (0% )
254 (99.2%)
Red
2
255 (100%)
6 (2.3%)
0 (0% )
254 (90.2%)
Red
3
255 (100%)
6 (2.3%)
0 (0% )
254 (90.2%)
Red
Finally, the modified point light source setting for the VRCCC design is
recommended in the CCC generation, see Figure 6-18.
6.16
Figure 6-18 CCC generation of the VRCCC’s for the mould surface of the test model
In this study, the proposed VRCCC design for the mould surface in Case 1 (soap
container) is validated by melt flow analysis software of MoldFlow MPI 3.1. For
comparison, SLDCC and CCC melt flow analysis are also conducted with the same
mould surface. The parameter settings for the melt flow analysis are tabulated in
Table 6-13. The coolant flow rate for VRCCC is larger than CCC and SLDCC to
compensate for the pressure drop. The CCC design and the 3D models for the inputs
in the melt flow analysis in Case 1 are shown in Figure 6-19. The comparison of the
melt flow analysis results among SLDCC, CCC, and VRCCC in Case 1 is tabulated
in Table 6-14. The results of melt flow analysis in Case 1 are listed in Appendix A.
6.17
Parameters
Values
Analysis
Cool + Flow
Mold temp. [oC]
100
o
Melt temp. [ C]
300
o
25
Cooling channel diameter [mm]
5mm
Coolant flow rate (Reynolds no.)
10000
Coolant temp. [ C]
a)
b)
c)
Figure 6-19 Cooling channels and 3D model designs in melt flow analysis for Case
1, a) SLDCC, b) CCC, and c) VRCCC
6.18
Parameters
SLDCC
CCC
VRCCC
38.55
36.73
36.60
25.13-25.66
25.07 – 25.76
25.03 - 25.53
Temp. diff. between Tmax
and Tmin [oC]
0.53
0.69
0.503
Maximum temp., part [oC]
43.01
41.78
41.71
Time to freeze [s]
5.786
5.741
5.739
In-cavity residual stress (at
injection point) [MPa]
142.4
141.3
141.3
Volumetric shrinkage (at
injection location) [%]
2.475
2.342
2.314
Average temp., part [oC]
Circuit metal temp.
(Tmin to Tmax) [oC]
The results obtained by melt flow analysis in Table 6-14 illustrate that the
values of VRCCC design is lowest in average temperature, maximum temperature,
and time to freeze. The temperature difference between maximum and minimum is
also lowest. Besides, both in-cavity residual stress and volumetric shrinkage are
lowest in VRCCC. The results show that the narrower range of coolant temperature
from inlet to outlet can give a more uniform cooling performance and a more
efficient heat transfer. The lowest values of in-cavity residual and volumetric
shrinkage in VRCCC can maintain the plastic parts after ejection with better quality
performance.
6.19
6.3 Case study of Conformal Porous Pocket Cooling Passageway of a 3D
Freeform Mouse Model
In this case study, a mould surface of a freeform mouse model is analyzed by
the feasibility check algorithm. CPPC is designed for the mould surface. The cooling
performance of the CPPC is verified. The output result is visualized by 3D rendering
in CAID software.
6.3.1 Input of 3D freeform mouse upper part model
A 3D freeform mouse upper part model is created by the CAD software of
SolidWorks 2006. See Figure 6-20. After the creation of the mould core and cavity
plates of a CAD mouse model via CAIMD tool, the cavity plate is used as the test
model for feasibility check. See Figures 6-21 and 6-22. Before applying the
algorithm, the test model is saved as faceted model for further processing.
Figure 6-20 Isometric view of a solid model of mouse (upper part)
6.20
Figure 6-21 Mould core and cavity plates of a CAD mouse model
Figure 6-22 Cavity plate of 3D CAD test model
6.3.2 Position and orientation settings of the test model in virtual environment
The mould surface of the test model is imported into the virtual environment of
the CAID software with appropriate position, orientation, and bounding box settings.
See Figure 6-23. In this study, a single unidirectional Ø5mm CCC is proposed and
generated within the mould cavity plate. This CCC can be integrated to an RT mould
and fabricated by various SFF technologies. The geometric design of the proposed
6.21
CCC is shown in Figure 6-24. The cooling channel axis can be obtained from the
geometry of the CCC. See Figure 6-25.
Figure 6-23 Position and orientation settings in virtual environment with bounding
box creation
Figure 6-24 Proposed CCC design for the test model
Figure 6-25 Cooling channel axis formation for the test model
6.22
6.3.3 Point light source setting for the cooling channel generation
For an appropriate CCC design, seventeen point light sources are added to
follow closely the shape of the surface geometry of the test model. See Figure 6-26.
The topological representation of the proposed CCC design and the parameter
settings for the light illumination of the feasibility check algorithm are tabulated in
Tables 6-15 and 6-16.
Figure 6-26 Point light source setting for the test model
Table 6-15 Topological representation of the proposed CCC design
Cooling
Topology for the proposed CCC design
channel(s)
CCC1
1,1
1, 2
1,3
1, 4
1, 5
1, 6
1, 7
→P1,1 ⎯⎯→
⎯
→P1,3 ⎯⎯→
⎯
→P1,5 ⎯⎯→
⎯
⎯
P1,o ⎯⎯
P1,2 ⎯⎯
P1,4 ⎯⎯
P1,6 ⎯⎯→
C
C
C
C
C
C
C
1,8
1,9
1,10
1,11
1,12
1,13
1,14
→P1,8 ⎯⎯→
⎯
⎯
⎯
⎯
⎯
P1,7 ⎯⎯
P1,9 ⎯⎯→
P1,10 ⎯⎯→
P1,11 ⎯⎯→
P1,12 ⎯⎯→
P1,13 ⎯⎯→
⎯
C
C
C
C
1,15
1,16
P1,14 ⎯⎯→
⎯
P1,15 ⎯⎯→
⎯
P1,i
C
C
6.23
C
C
C
Table 6-16 Parameter settings for light illumination of the feasibility check algorithm
of the test model
Parameters
Values
Free point
1 unit
17 units
Light source
D65 White Diffuse
500
RGB Colouring
Red
Green
Blue
White
255
255
255
Result visualization
Display type
Illumination
6.3.4 Visualization of the output result of the test model by 3D rendering in virtual
environment
The output result of the feasibility check algorithm is used to verify the
feasibility of the proposed CCC design and can be shown by 3D rendering on CAID.
A 3D rendering of the test model without point light sources setting is shown in
Figure 6-27 for comparing the performance (the standard) of test model in the
feasibility check algorithm.
The 3D rendering visualization results of the proposed CCC are shown in
Figure 6-28 and 6-29. The output solution can be in coloured and in gray scale.
Through the 3D rendering visualization results with point light source setting for
light illumination, the heat transferrability between the proposed CCC design and
6.24
mould surface can be determined.
Figure 6-27 Isometric view of the test model after 3D rendering (without point light
source setting) (view from left hand side)
Figure 6-28 The 3D rendering in coloured visualization output result of the proposed
CCC (view from left hand side)
proposed CCC (view from left hand side)
6.25
For comparison, 3D rendering of test model without point light source setting in
virtual environment via CAID tool is shown in Figure 6-30. In the opposite side
(view from right hand side), the 3D rendering in coloured and in gray scale
visualization output results are shown in Figures 6-31 and 6-32.
Figure 6-30 3D rendering for the test model without point light source setting (view
from right hand side)
Figure 6-31 The 3D rendering in coloured visualization output result of the proposed
CCC (view from right hand side)
6.26
proposed CCC (view from right hand side)
From the above output results, black colour in gray scale and blue colour in
coloured visualizations are found after 3D rendering in the feasibility check
algorithm. Both Figures 6-31 and 6-32 indicate that the surfaces of the test models
cannot be illuminated with the proposed point light source settings or cooling is
insufficient. The percentage of light illuminated region by CCC for the mould
surface and the mode of illumination by the point light source setting for the
proposed CCC are tabulated in Tables 6-17 and 6-18.
From the output result visualization, five points (Point 1, Point 2, Point 3, Point
4, and Point 5) are marked and recorded from Figure 6-33 for checking the
illuminance of the test model (view from left hand side). The 3D rendering colour
display image data of RGB and monochromatic values can indicate the performance
6.27
of illuminance. See Table 6-19. The colour change from Point 1 to Point 5 indicates
an incomplete light illumination on the left hand side of the mould surface of the test
model.
As a colour change is found on the mould surface (both left hand side and right
hand side), a modification of the proposed CCC design is recommended to improve
the heat transferrability from the mould surface to the center of the proposed CCC.
Table 6-17 Percentage of light illuminated region by CCC for the mould surface
Conditions
Values
17
57576
4960
% of light Illuminated region
91.3
Table 6-18 Mode of illumination by the point light source setting for the proposed
CCC
Illumination
(L, N)
Illumination
(L, N)
p1
p2
p3
p4
p5
p6
p7
p9
p10
p11
p12
L
L
L
L
L
L
N
N
N
N
L
p13
p11
p12
p13
p14
p12
p13
p14
p15
p16
P17
L
L
L
N
N
L
L
L
L
L
L
(L- Light illumination, N – Non-Illumination
6.28
Figure 6-33 Image data point capturing at different positions for the test model for
the proposed CCC (view from right hand side)
values
Points
R
G
B
Monochromatic
value
Colour
1
255 (99.7%) 142 (55.8%)
0 (0% )
253 (99.2%)
Red
2
255(100%)
142 (55.8)
0 (0%)
219 (85.6%)
Orange
3
226 (88.6%)
234(91.7)
0 (0%)
150 (58.8%)
Yellow
4
125 (49%)
253(99%)
0 (0.1%)
99 (38.8%)
Green
5
0 (0%)
0 (0%)
255 (100%)
0 (0%)
Blue
6.3.5 CCC design modification by maximum visibility and Light Source Minimization
on the mould surface
The cooling channel design can be modified by using maximum visibility and
Light Source Minimization through checking the normal vectors orientation and
distribution. The point light source settings can be determined by the distribution of
6.29
normal vectors on the mould surface. The orientation settings of the normal vectors
for the test model are illustrated in Figure 6-34.
Figure 6-34 Normal vectors on the mould surface of the test model for maximum
visibility
After setting the normal vectors on the surface of the test model, point light
source settings are determined by the normal vectors on the mould surface according
to maximum visibility. In this study, the type of modification will be a CPPC. The
point light source setting on the mould surface of the test model is shown in Figure
6-35. All the point light sources connected with straight lines can form a triangular
mesh or network for the indication of the CPPC design for the test model. See
Figures 6-36 and 6-37. The geometric design of the triangular mesh or network
forms a CPPC for the test model. The parameter settings of the light illumination of
the feasibility check algorithm for the proposed CPPC is tabulated in Table 6-20. The
6.30
point light source setting gives the connectivity relationship of the CPPC for the test
model and is tabulated in Table 6-21.
Figure 6-35 Point light source setting for the test model of the CPPC design
Figure 6-36 Point light source settings connected with triangular network
6.31
Figure 6-37 Triangular network of the CPPC for conformal surface cooling
Table 6-20 Parameter settings of light illumination of the feasibility check algorithm
for the proposed CPPC
Parameters
Values
Free point
Cooling channel axis
Network
40 units
Light source
D65 White Diffuse
500
RGB Colouring
Red
Green
Blue
White
255
255
255
Result visualization
Display type
Illumination
6.32
Table 6-21 Topological representation of the proposed CPPC design
Cooling
Topology for the proposed CPPC
channel(s)
CPPC1
6.33
The 3D rendering in coloured and in gray scale visualization output results of
the test model are shown in Figures 6-38 and 6-39. In the proposed CPPC design,
only red colour can be observed in coloured visualization. Only white colour can be
found in gray scale visualization. The image data point capturing at different
positions of the test model for the proposed CPPC is shown in Figure 6-40. In this
study, three points (Point 1, Point 2, and Point 3) are marked and recorded for
checking the feasibility of the proposed CPPC in relation to its mould surface.
From the visualization result, a red colour can be found. The mould surface of
the test model can be illuminated completely with the modified point light source
settings or CPPC design. See Tables 6-22 and 6-23. The 3D rendering colour display
image data of RGB and monochromatic values for CPPC is tabulated in Table 6-24.
The results reflected that the freeform surface can be illuminated completely by the
coverage of a number of point light sources to form a cooling pocket or passageway
network.
6.34
Figure 6-38 The 3D rendering in coloured visualization output result of the
proposed CPPC
proposed CPPC
Table 6-22 Percentage of light illuminated region by CPPC for the mould surface
Conditions
Values
40
57576
0
Percentage (%) of light Illuminated region
6.35
100
Table 6-23 Mode of illumination for the proposed CPPC
Illumination
(L, N)
Illumination
(L, N)
Illumination
(L, N)
Illumination
(L, N)
Illumination
(L, N)
p1
p2
p3
p4
p5
p6
p7
p8
p9
L
L
L
L
L
L
L
L
L
p10
p11
p12
p13
p14
p15
p16
p17
p18
L
L
L
L
L
L
L
L
L
p19
p20
p21
p22
p23
p24
p25
p26
p27
L
L
L
L
L
L
L
L
L
p28
p29
p30
p31
p32
p33
p34
p35
p36
L
L
L
L
L
L
L
L
L
p37
p38
p39
p40
L
L
L
L
(L – Light illumination, N – Non-illumination)
Figure 6-40 Image data point capturing at different positions of the test model for
the proposed CPPC
values for CPPC
Points
R
G
B
1
255 (100%)
6 (2.3%)
0 (0% )
254 (99.2%)
Red
2
255 (100%)
6 (2.3%)
0 (0% )
254 (90.2%)
Red
3
255 (100%)
6 (2.3%)
0 (0% )
254 (90.2%)
Red
6.36
Monochromatic value Colour
In real life fabrication under the advancement of SFF technologies nowadays,
many factors will affect the design and fabrication of the CPPC. The designs of
CPPC with or without internal structure for conformal surface cooling of the test
model are shown in Figures 6-41 and 6-42.
Figure 6-41 CPPC for conformal surface cooling design of the test model (mould
cavity surface)
Figure 6-42 CPPC for conformal surface cooling design without internal structure
support of the test model (mould cavity surface)
6.37
6.3.6 Melt flow analysis for CPPC design verification in Case 2
The proposed CPPC design for the mould surface in Case 2 (mouse) is validated
by melt flow analysis software of MoldFlow MPI 3.1. For comparison, melt flow
analysis of SLDCC, CCC, and VRCCC are also conducted with the same mould
surface. The parameter settings for the melt flow analysis are tabulated in Table 6-25.
The coolant flow rate for CPPC is set larger than SLDCC, CCC, and VRCCC to
compensate for the pressure drop in conformal surface cooling by porous structure.
The CCC designs and the 3D models for the inputs in the melt flow analysis in Case
2 are shown in Figure 6-43. The comparison of the melt flow analysis results among
SLDCC, CCC, VRCCC, and CPPC in Case 2 is tabulated in Table 6-26. The results
of melt flow analysis in Case 2 are listed in Appendix B.
Parameters
Analysis
Values
Cool + Flow
Mold temp. [oC]
o
Melt temp. [ C]
o
85
255
Coolant temp. [ C]
25
Cooling channel diameter [mm]
5mm for SLDCC, CCC, and CPPC
5mm to 8mm for VRCCC
Coolant flow rate (Reynolds no.)
20000 for CPPC
10000 for SLDCC, CCC, and VRCCC
6.38
a)
b)
c)
d)
Figure 6-43 Cooling channels and 3D model designs in melt flow analysis for Case
2, a) SLDCC, b) CCC, c) VRCCC, and d) CPPC
6.39
Parameters
Average temp., part [oC]
SLDCC
39.87
CCC
38.66
VRCCC
38.53
CPPC
37.76
Circuit metal temp. (Tmin 25.11–25.94
to Tmax) [oC]
25.10– 25.92 25.10–25.72 25.00–27.24
Temp. diff. between Tmax 0.83
and Tmin [oC]
0.82
0.62
2.24
Maximum temp., part 45.88
[oC]
44.86
44.77
44.27
Time to freeze [s]
1.982
1.973
1.972
1.966
In-cavity residual stress
(at injection location)
[MPa]
141.4
141.3
141.5
140.8
Volumetric shrinkage (at
injection point) [%]
0.7305
0.7041
0.6951
2.832
The results obtained from melt flow analysis in Table 6-26 indicate that the
average temperature, the maximum temperature of part, the time to freeze, and the
in-cavity residual stress of the part cooled by CPPC is lowest in value. The results
indicate that the cooling performance of CPPC is better than other types of CCC’s.
Effective heat transfer can be achieved. The temperature difference between Tmax
and Tmin is largest (2.24 oC) among all CCC designs. The reason for the temperature
variation is that the design of CCC at mould cavity or at core plates is varied. The
conformal surface cooling performed by CPPC can effectively transfer heat energy
from the mould surface to the cooling passageway surface in a short time. The
narrower range of temperature difference of CPPC can ensure a uniform cooling
performance and an effective heat transfer. The cooling time for the polymer melt
can be reduced. The value of volumetric shrinkage is, however, nearly double to
6.40
other CCC’s because the conformal surface cooling of CPPC provides rapid cooling
performance in a short time.
6.4 Chapter Summary
The feasibility check algorithms and the cooling channel generation have been
demonstrated. In the case studies, the 3D CAD models of the injection mould
assembly are converted and exported as faceted models. With proper position,
orientation, and point light source settings for the test models in virtual environment
by CAID, the feasibility of the proposed CCC design can be determined. The 3D
rendering visualization output results of VRCCC and CPPC are presented. The point
light source setting for CCC design modification is proposed by maximum visibility
and Light Source Minimization on the mould surface. These methods can be applied
to various complex geometric designs. The heat transferrability between the mould
surface to the cooling channel surface can be verified by the feasibility check
algorithm. The VRCCC and CPPC in the case studies are feasible to achieve extra
uniform cooling on the mould surfaces with complex geometries. Melt flow analysis
is used to validate the design of VRCCC and CPPPC. The results of cooling
performances between SLDCC, CCC, VRCCC, and CPPC are compared.
6.41
Chapter 7 Discussion and Future Work
CHAPTER 7 DISCUSSION AND FUTURE WORK
7.1 Overview
The main objective of the research is to develop a method to design cooling
channels (conventional or conformal) for rapid plastic injection mould and the design
is verified by proposing feasibility check algorithm with CCC generation process.
This proposed algorithm contributes to provide an extra uniform cooling
achievement for different geometric design of mould surface (core or cavity) for
rapid tool or injection mould in PIM. The CCC generation can aid to provide various
CCC designs such as VRCCC, CPPC, CSPC, or CPC.
7.2 Feasibility Check Algorithm
Previous literature references in cooling channel design for PIM included
numerical calculations, experiences, knowledge and skills of mould engineers and
designers. The appearance of CAE or CFD software can provide an alternative
method for the design of injection mould assembly. With the aid of CAD software,
the injection mould design can be computerized. The utilization of CAD and CAID
software can facilitate to a great extent the manipulation and verification of the test
model in a virtual environment, thus allowing output solution visualization before
7.1
cutting the steel.
The advantages of using the proposed feasibility checking algorithm is that it is
simpler than that in previous design, analysis, and simulation methods as it uses
formulation of light illumination for checking the proposed cooling channel design in
relation to its mould surface. No complex simulation and verification software is
required.
Computational efficiency is an important concern in the processes of design,
simulation and analysis for CAD test model in much previous research. In this study,
efficiency of computation is not a decisive factor as the visualization and 3D
rendering requires little computation time and can be used as a preliminary cooling
channel design feasibility check. Thus, accuracy of feasibility check and quality of
the result visualization of the test model are two highest priority concerns.
The output result can be illustrated in 3D virtual environment via CAID
software and in 2D graphical image processing tools. Engineer and designer can
change the various views instantly to check the performance or model evaluation of
the rendered result of the test model after the visualization. Good communication and
information exchange can be preceded between engineer and design at the earlier
stage of product development. Design improvements of the test model, injection
mould, and CCC can be performed in an effective way. Product with good quality
7.2
can be achieved.
7.2.1 Light illumination in the feasibility check algorithm
The feasibility of the output result of the CCC and mould surface can be
illustrated by light illumination. The CCC design in the light illumination for the
feasibility check algorithm is connected by a number of point light sources to project
on the mould surface (cavity or core) in virtual environment performed by CAID.
The light intensity of the light source is assumed to be constant. The number of the
point light source is set as minimum to achieve illumination for the entire surface
without shaded region. Effective light illumination can be achieved if a single light
source that can be achieved to the entire surface of the object.
7.2.2 Shortcomings of the feasibility check algorithm
During the development of the proposed algorithm, some limitations are found
that may affect the verification of the feasibility of the mould surface with its
corresponding cooling channel design.
7.2.2.1 Ignorance of internal structure or accessory obstruction
The feasibility checking algorithm depends on the range of visible region of
7.3
maximum surface exposure that covered by the proposed cooling channel. Besides,
the visibility depends on the complexity of the mould cavity surface. An injection
moulded plate equipped with various accessories e.g. ejector pins, inserts, thermal
pins or side cores. They will affect the light illumination process between the light
source and surface to be illuminated.
7.2.2.2 Lost of geometric data after file translation
All test models can be designed from CAD software, (like SolidWorks,
ProEngineer, Unigraphics NX or CATIA, etc.) and a variety of geometric
interchange formats (like STL, SLDPRT, IGES, or 3DS, etc.) can be employed. For
simplification and consistent assurance of the input for the proposed algorithm, all
the test models (for mould surface or CCC design) are represented by faceted model.
However, some geometric data of the test model from CAD to CAID lost easily via
file translation or export.
7.2.2.3 Not a fully automatic generation
The design of injection moulded cooling channel under CAD or CAIMD
software cannot provide a fully automatic generation of injection mould assembly.
During the design process, many design parameters are necessary to be defined by
7.4
the mould designer, such as cooling channel diameter, coolant inlet and outlet
position, geometric design of the cooling channel and internal accessory settings.
These parameter settings are required to be input along the 3D CAD injection mould
assembly generation step by step. It is difficult to give a fully automatic generation of
the 3D CAD injection mould assembly without user identification.
7.2.2.4 Performance of output solution by 3D rendering between single and double
point light sources
The output solution for the feasibility check algorithm after light illumination
depends on a number of parameter and assumption settings of the light source in
virtual environment in CAID. For the heat exchange within the plastic injection
mould, heat energy transfers from the polymeric melt to the cooling channel by heat
conduction. As the conservation of energy, heat energy transfers from a higher
temperature gradient (polymer melt) to a lower temperature gradient (cooling
channel). It can be formulated into light illumination for visibility between a light
source and a surface to be illuminated. The light intensity of the light source is
assumed to be constant. Effective light illumination can be achieved if a single light
source that can be visible to the entire surface of the object. The number of the light
source increases progressively, the surface to be illuminated may be converted by
7.5
more than single light source. In this situation, the intensity of light illumination is
assumed to be the same without accumulation effect.
7.3 CCC Generation for the Feasibility Check Algorithm
The CCC generation in the feasibility check algorithm provides diverse types of
CCC design solutions corresponding to its mould surface (core or cavity). Nearer
uniform heat transfer between the mould surface and CCC design can be achieved.
CCC design and generation can also provide the design solutions of CPPC, CSPC,
VRCCC, and CPC for the rapid tool or injection mould with complex geometric
design of mould surface.
It is understood that the cooling channel design depends not only on the
geometric shape of the part, but also on the thermal properties of the plastic and
mould material used. For injection mould that uses materials with similar thermal
properties, the geometric design of CCC can be varied. It is emphasized that the
present study is focused on the initial design of the cooling channel system. The
initial design specifies the number and types of cooling channel to be used, and
suggests the location of each cooling channel. The suggested locations can be
determined appropriately. However, to further develop the initial design into final
design, the trade-off between manufacturing and maintenance cost, product quality
7.6
and productivity have to be considered.
The feasibility of the mould surface with near uniform heat transfer CCC design
is based on the performance of point light source setting. Point light source settings
also control the geometric design of various CCC such as CCC, VRCCC, or
conformal surface cooling. In order to set the point light source in an effective
manner, some methods are proposed as the guidance for the geometric design of
cooling channel in relation to its mould surface. Point light source can represent the
geometric design of CCC by connecting line segments, while linear and area light
sources can be represented by grouping a set of point light sources.
7.3.1.1 Maximum visibility method
In this study, maximum visibility method for the position determination of point
light source settings for CCC design is introduced to find the best position for setting
up the point light sources and cooling channel axis. The CCC design can be
generated from settings of light source and cooling channel axis proposed. This
provides the geometric information and connectivity for the CCC generation.
The maximum visibility method can determine the location of point light
7.7
sources which can illuminate on the test model with maximum surfaces identified by
the normal vectors. The optimal number of point light sources adding on the surface
of the test model can be recognized. The cooling channel axis can also be determined
with the position setting of point light sources.
The number and position of point light source setting can be guided by
maximum visibility method for visibility check and light illumination. The point
light source setting depends on the amount of normal vectors on its mould surface.
The position setting of point light source interacts with the normal vectors on the
mould surface for maximum visibility checking. CCC design can be generated on the
mould surface. Without loss of generality, further increase in the number of point
light source can approximate the CCC design accurately to a large extent. However,
the output visualization for the feasibility check algorithm is in saturation of light
intensity as the further increase of the number of point light sources will accumulate
the intensity of all the light sources. The output result visualization of the mould
surface in light illumination becomes inaccurate. The feasibility of the mould surface
and the point light source cannot be illustrated by the light illumination. Thus, a
trade-off between the performance of output visualization and the number point light
7.8
source in the feasibility check algorithm is necessary. Thus, Light Source
Minimization is proposed to control the number of point light sources acted on the
mould surface in an effective approach. It can optimize the number of light sources at
minimum level which can also provide a better lighting performance in light
illumination for the feasibility check algorithm.
7.3.2 Manual parameter settings in CCC generation
With the aid of maximum visibility method and Light Source Minimization for
the CCC generation, the number and the position of point light source settings on the
mould surface becomes effective. Other parameter settings for point light source such
as position of coolant inlet and outlet in geometric design of CCC depends on
designer’s requirement. The accuracy of the output result is also controlled by the
level of resolutions of the geometric design of mould surface and CCC.
7.3.3 Cooling channel axis approximation
In this study, the cooling channel axis is created according to the point light
source setting. The connectivity of light or line segment between point light sources
is not smooth enough to generate a real geometric design of CCC. The cooling
channel axis approximation and CCC generation cannot reflect the real situation for
7.9
the test model in the output result visualization of the feasibility check algorithm.
7.4 VRCCC for Rapid Tool or Injection Mould in PIM
VRCCC can provide a better uniform cooling for rapid tool or injection mould
in PIM than CCC one. Through the increase of surface contact region near the
coolant outlet and simultaneous increase in volumetric flow of coolant along the
CCC, more heat energy from the polymeric melt can be carried away. VRCCC can
compensate the inlet-outlet coolant temperature variation by utilizing CCC with large
radius near the outlet portion.
The generation of VRCCC in the feasibility check algorithm is controlled by the
point light source setting. The difference between CCC one in the feasibility check is
the light source intensity changed simultaneously along the VRCCC. Both the light
source intensity, variable radius of CCC, and coolant temperature are closely related
in the point light source setting for the feasibility check algorithm.
An implementation for the case of VRCCC is provided with the aid of the
proposed algorithm. The feasibility of the VRCCC in relation to a mould surface is
verified and the output result is shown by 3D rendering after light illumination. The
output solution of VRCCC verified by the proposed algorithm can illustrate better
uniformity in light illumination on the mould source in the feasibility check. The
7.10
output solution reflects that a nearer uniform cooling can be achieved by the mould
surface with the VRCCC.
7.4.1 Potential enhancement in VRCCC design
In this study, the geometric design of VRCCC can provide a nearer uniform
cooling to compensate the inlet-outlet temperature difference for effective heat
transfer. However, the pressure drop of coolant in VRCCC cannot be avoided due to
the increase of radius at the outlet portion of the channel. For simplification, the
effects of process parameters such as pressure drop are ignored in the feasibility
check algorithm. A simple VRCCC design considers heat source (mould surface) to
heat sink (cooling channel surface). But a more accurate design can consider the
coolant flow characteristics, e.g. flow rate. Thus, a full computational fluid dynamics
(CFD) analysis can be conducted in the future works.
7.5 Conformal Surface Cooling for Rapid Tool or Injection Mould in PIM
As discussed before, the conformal surface cooling can provide a nearer
uniform heat transfer between the mould surface and the CCC design via entire
surface cooling rather than CCC. Thermal stress from different regions on the mould
surface can be avoided by the uniform cooling achievement. Conformal surface
7.11
cooling for rapid tool or injection mould in PIM is a new challenge to further
improve the uniform cooling achievement performed by CCC design. Apart from
SFF technologies, some factors are also found that affect the design and fabrication,
such as strength of the mould material.
The proposed feasibility check algorithm and CCC generation can also be
implemented into the verification of the design of conformal surface cooling
passageways. An output solution in light illumination is provided to verify the design
of a nearer uniform heat transfer conformal surface cooling passageway in relation to
its mould surface. Other CAE analysis is difficult to achieve or ignore at this
moment.
For the implementation of conformal surface cooling passageway, the feasibility
of the proposed porous structure cooling passageway design is checked and the
design of passageway can provide a nearer uniform cooling with its mould surface.
The output solution of conformal surface cooling passageway verified by the
proposed algorithm can illustrate a uniform light illumination on the mould surface
in the feasibility check. The output solution reflects that a uniform cooling can be
achieved by the mould surface with the conformal surface cooling design.
7.12
7.5.1 Difficulty in mould material for CPPC
In real situation, limitations are found for the fabrication of CPPC for ideal case
in conformal surface cooling. Up to now, there is no research work that can
successfully design and fabricate a CPPC within a rapid tool or injection mould.
There is no suitable mould material with appropriated mechanical strength and
coefficient of thermal expansion that avoids the damage and distortion of mould from
a large compression pressure during injection mould opening and closing stage.
7.5.2 Topological representation of conformal surface cooling
Topological representation of CCC can reflect the connectivity between point
light sources along the CCC from the coolant inlet to the coolant outlet. The
geometric design and position of the CCC can be obtained. For the design of CPPC,
the topology representation of the conformal surface cooling can be represented by a
network connected by light sources and line segments. However, a shortcoming is
found for the design of CPPC. As the CPPC is represented by a single pocket with a
coolant inlet and coolant outlet, network-like pattern is inappropriate for the design
of CPPC in the topological representation.
7.13
7.5.3 Ignore of process parameters in conformal surface cooling passageway
In this study, the geometric design of conformal surface cooling passageway can
provide a nearer uniform cooling than CCC or VRCCC in earlier sections. Some
process parameters or factors may affect the rate of heat transfer when conformal
surface cooling passageway is applied, for example pressure drop, thermal
conductivity, or mechanical strength. As discussed before, pressure drop in VRCCC
cannot be avoided by changing the radius along the cooling channel. The degree of
pressure drop in conformal surface cooling passageway is larger than VRCCC.
Besides, the mechanical strength of mould material for conformal surface cooling is
higher than the CCC to prevent the damage of mould during PIM process. For
simplification, the effects of process parameters such as pressure drop are ignored in
the feasibility check algorithm.
7.5.4 Impossible of ideal uniform heat transfer
For ideal uniform heat transfer, the heat energy transfer from the mould surface
to the cooling channel surface must occur with the same rate at any region on the
mould surface. In theory, conformal surface cooling as pocket design can give the
possibility. In real situation, some complex and fine feature slots on the mould
surface are difficult to generate an offset surface for cooling system design. See
7.14
Figure 7-1. Geometric error in normal offsetting is easy to happen with fine features
on mould surface. See Figures 7-2 and 7-3. The cooling channel system design for
ideal uniform heat transfer cannot be achieved with complex geometric of mould
surface.
Figure 7-1 Mobile phone panel with fine feature slot on the surface
Figure 7-2 Error formed by normal offsetting in fine features slot on the mould
surface
Figure 7-3 Problem of normal offsetting with complex geometric design of a curve
[Liu 2007]
7.15
To further improve the research study, some possible future works related to this
research in future is suggested.
7.6 Future work
7.6.1 Internal accessories, types of mould and undercut inclusion in the feasibility
check algorithm
For improvement in the feasibility check algorithm, it is recommended that the
proposed algorithm in this study can be extended from two-plate mould to three-plate
one. Internal accessories such as side core, ejector pin, slider, and sprue can also be
considered for the proposed algorithm and illustrated on the output solution after 3D
rendering. Besides, any undercut or complex geometric design of the mould surface
(cavity or core) can also be accessed.
7.6.2 Integration of file format
In this study, the mould surface and CCC generation are exported as faceted
model for the input in the feasibility check algorithm. Further work can be focused
on the compatibility of any export file format from various CAD software as the
input of the proposed algorithm.
7.16
7.6.3 Implementation of commercial package
The implementation of the proposed algorithm can be integrated into
commercial packages of CAD, CAIMD, or CAE to provide a verification module of
the feasibility of the mould surface and cooling channel.
7.7 CCC generation
7.7.1 Fully automatic process in CCC generation
With the aid of maximum visibility method and Light source minimization, the
point light source setting in the CCC generation can be further developed into a fully
automatic process. The whole CCC generation can be operated by computer
programming. The 3D modeling of various geometric design of CCC can be
generated automatically in the feasibility check algorithm.
7.7.2 Cooling channel axis approximation in curve segments
The future work of the cooling channel axis can be focused on the
approximation into curve segment rather than straight-line one. The cooling channel
axis formed by curved segments can provide a smooth geometric design of the CCC
model. The performance of output result visualization of the test model can be
improved.
7.17
7.7.3 CCC generation for other industrial manufacturing processes
The application of CCC generation in the feasibility check algorithm can be
extended to rapid tool design and fabrication in other manufacturing processes, such
as die casting and blow moulding.
Similar to PIM process, casting is also a high productivity process and integral
to many of today’s major manufacturing processes. In the die casting process, a metal
melt is injected into the space between the core and cavity blocks to produce a “near
net-shape” product. Cooling channel design is also important to shorten its cycle time
and improve the quality of the casting part. Complex geometric design of CCC,
porous structure cooling passageway, scaffolding structure cooling passageway, and
VRCCC are also feasible to be integrated into the mould cavity and core blocks for
the mould of casting.
7.8 Improvement in VRCCC
7.8.1 Process parameters in VRCCC consideration
For further study in VRCCC, the effects of process parameters such as pressure
drop and thermal conductivity can be taken into consideration in the feasibility check
algorithm. Practical and test on the effect of pressure drop along the VRCCC can
also be focused. The effect of pressure change in VRCCC can also be verified by
7.18
CFD and CAE analysis. Apart from VRCCC, another CCC design called variable
distance conformal cooling channel can also be focused to compensate the
temperature difference between coolant inlet and coolant outlet along the CCC.
7.9 Improvement in Conformal Surface Cooling
7.9.1 Mould material selection
Materials being used to fabricate rapid tool or injection mould in PIM can
provide another choice for conformal surface cooling passageway. The development
of new alternatives of mould materials are the focus of several research works.
Recently, the research in phase change material (PCM) and BeCu can be an
alternative in mould material selection. The characteristics of strength and thermal
conductivity of the mould material are of high concern. The heat transferrability for
conduction and convection of PCM can be an alternative as the mould material. With
strong mechanical strength of PCM, porous structure cooling passageway and CCPP
can be feasible for long run PIM process without damaging the mould. The
productivity and quality can be improved with shorter injection moulding cycle time.
Beside, the features of VRCCC and CPPC can also be combined to improve near
uniform heat transfer on the mould surface with the compensation of temperature
difference between coolant inlet and coolant outlet. Better control of coolant with
7.19
conformal surface cooling can be achieved on the mould surface.
7.9.2 Pressure drop verification by CFD and CAE analysis
As discussed before, the pressure drop can be prevented by using a clearing
agent or solvent to remove the germ or dirt which is stuck on the inner wall of the
coolant passageway. Further work can be recommended for the study of the effect on
pressure drop for the conformal surface cooling passageway with the aid of CFD and
CAE analysis.
7.9.3 Connectivity of point light sources for CCPP via topological representation
The connectivity of point light sources and cooling channel axes can be further
developed according to the topological representation similar to the cases of porous
structure and scaffolding structure cooling passageway. A simplification method of
representation for the conformal pocket design within the rapid mould or injection
mould can be recommended.
7.20
Chapter 8 Conclusion
CHAPTER 8 CONCLUSION
In order to improve productivity and to reduce the occurrence of defect in PIM,
cooling channel design is of great importance. As there is no rigorous theory or
definition for cooling channel system design in rapid tool or injection mould, a
theoretical based methodology for the design and verification of cooling channel
system is needed.
In this study, an intuitive and implementable methodology is proposed to verify
the feasibility and performance of thermoplastic injection mould cooling channel
system design. A practically feasible cooling channel design depends on the rate and
performance of conductive heat transfer from polymer melt on the mould surface to
the cooling channel surface. The feasibility justification is based on visibility from
computational geometry and light illumination from 3D computer graphics. Cooling
channel design with complex geometry, such as CCC, can also be applied. The
formulation of the CCC geometry is inferred from the light sources. The connectivity
of the light sources for CCC is identified. The corresponding cooling channel axis
provides the whole coolant flow path from inlet to outlet.
In order to achieve a near uniform heat transfer with its mould surface design,
diverse CCC designs such as CCC, VRCCC, and CPPC are proposed. Designs of
8.1
Chapter 8 Conclusion
VRCCC and CPPC are validated and compared by melt flow analysis. It is found that
further improvement in heat transferrability between cooling channel surface and its
mould surface can be obtained. From melt flow analysis results, the cooling
performance of CPPC is also found better than SLDCC. With the aid of the latest
SFF technologies, better cooling channel designs using VRCCC and CPPC can be
implemented.
8.2
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Appendix A: Case 1
APPENDICES
APPENDIX A: CASE 1
Case 1
(i)
SLDCC
i.
ATP
ii.
CMT
A.1
Appendix A: Case 1
iii.
MTP
iv.
TTF
A.2
Appendix A: Case 1
v.
ICRS
vi.
VS
A.3
Appendix A: Case 1
(ii)
CCC
i.
ATP
ii.
CMT
A.4
Appendix A: Case 1
iii.
MTP
iv.
TTF
A.5
Appendix A: Case 1
v.
ICRS
vi.
VS
A.6
Appendix A: Case 1
(iii)
VRCCC
i.
ATP
ii.
CMT
A.7
Appendix A: Case 1
iii.
MTP
iv.
TTF
A.8
Appendix A: Case 1
v.
ICRS
vi.
VS
A.9
Appendix B: Case 2
APPENDIX B: CASE 2
Case 2
(i)
SLDCC
i.
ATP
ii.
CMT
B.1
Appendix B: Case 2
iii.
MTP
iv.
TTF
B.2
Appendix B: Case 2
v.
ICRS
vi.
VS
B.3
Appendix B: Case 2
(ii)
CCC
i.
ATP
ii.
CMT
B.4
Appendix B: Case 2
iii.
MTP
iv.
TTF
B.5
Appendix B: Case 2
v.
ICRS
vi.
VS
B.6
Appendix B: Case 2
(iii)
VRCCC
i.
ATP
ii.
CMT
B.7
Appendix B: Case 2
iii.
MTP
iv.
TTF
B.8
Appendix B: Case 2
v.
ICRS
vi.
VS
B.9
Appendix B: Case 2
(iv)
CPPC
i.
ATP
ii.
CMT
B.10
Appendix B: Case 2
iii.
MTP
iv.
TTF
B.11
Appendix B: Case 2
v.
ICRS
vi.
VS
B.12

chapter 4 conformal cooling channel generation

Transcription

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