Methods of validation and optimization techniques

Transcription

Methods of validation and
optimization techniques
Simulation Techniques in Manufacturing Technology
Lecture 11
Laboratory for Machine Tools and Production Engineering
Chair of Manufacturing Technology
Prof. Dr.-Ing. Dr.-Ing. E.h. Dr. h.c. Dr. h.c. F. Klocke
© WZL/Fraunhofer IPT
Outline
1
Learning Goals
2
Relevant Process Quantities in Cutting Tools
3
Technical Sensors in Metal Cutting
4
Measurement techniques: Strain, Force, Acceleration, Pressure, Power, Temperature
5
Measurement Integration in the Cutting Process
6
Validation of Cutting Process Models
7
Optimization: Definition, History, Procedure and Applications
8
Optimization Algorithms, Software and Examples
9
Integration of Optimization in FE Cutting Simulation
Seite 2
Objectives of the Lecture
This lecture is intended to…
 … Help you to understand the relevant variables from
the perspective of cutting.
 … Explain the design and function of industrial sensors.
 … Convey basics of measurement techniques.
 … Clarify the validation of cutting process models.
 … Teach the optimization technique.
Seite 3
Outline
1
Learning Goals
2
3
4
5
6
7
8
9
Seite 4
■ Force
■ Moment
■ Active Power
■ Temperature
■ Acceleration
■ Mechanical Vibration (AE)
■…
Seite 5
Outline
1
Learning Goals
2
3
4
5
6
7
8
9
Seite 6
Cutting force
Acceleration
Measuring platform
Rotating cutting force
dynamometer
Acceleration sensor
Force measuring pin
vc
Process remarks
Load ring
Pyrometer
Source: Kistler Instrumente AG
Seite 7
Procedure for measuring value in a Sensor
 Measuring signal &
 Sensor selection
processing
& application
 Process related
signals
AE-Signal
[U
]
Ze
it [s]
Measure
Filtering offset corrector
Measuring principle
m
Temperature
[°C
]
Amplification
Force
m
[N
]
Sensor selection
Application
A/D Converter
A
D
Acceleration
m
2
s
I
Active Power
[A
]
Seite 8
Outline
1
Learning Goals
2
3
4
5
6
7
8
9
Seite 9
Strain Gauges - DMS
Function:
■ An external force causes stress and
eventually strain in the component
■ Strain gauges convert mechanical strain into
electric resistance.
Messmäander
SiO2 Isolation
Measuring direction
Stress
Strain
F
   E 
A
L

L
Contact
Träger,
Klebstelle
Class: Passive Sensor
Seite 10
Measuring Principle


R0 + R
R0
R
l
A
R  l A0

 
R0  0 l0 A
R
R0
k
R0 - R
l

l0
R / R0

k
Seite 11
Load Cell
Load [kg]
Deformation of the body [mm/m]
Display in kg
Resistance change at DMS [R/R]
Standardized Transducer
Ex – Load Cell after consideration of
principle of Double beam
Source: HBM
Seite 12
Stress Measurement
■ Component Optimization (R&D)
■ Operations Monitoring
■ Vulnerability analysis to identify
the causes of damage
Load induced Stress:
F

A
Residual Stresses
(for resolution)
  E  
Thermally induced Stress:
 

E
Source: HBM
Seite 13
Advantages and Disadvantages of Strain Gauges
Advantages
Disadvantages
 Universally and easily applicable
 Relative change in resistance is very low
 Small / Low Mass
 Wide Frequency Range (0… > 50kHz)
 Low Reaction on the measuring object
 Excellent Linearity over a wide range of
strain range
 Low and predictable temperature effects
 High stability over a long usage
 Low Cost
(electrical bridge circuit is always used)
 Temperature Limits
 Cannot be reused
 Precautions required against:
– Humidity
– Temperature (Temperature gradient!)
– Ionizing Radiation
– Magnetic Field
Source: HBM
Seite 14
Piezoelectric Sensor
 Greek. piézein = drücken, pressen
Force and Moment
 Piezoelectric Effect:
Deformation along polar axis produces a
dipole moment on opposite surfaces.
 Charge displacement is converted by a
charge amplifier to a voltage signal.
 Class: Active Sensor
Acceleration
Strain
Mechanical Vibration
Seite 15
Piezoelectric Material
Suitable Material:
 Quartz
 Tourmaline
 Ferroelectric Ceramics
Seite 16
Longitudinal effect (1)
unbelasteter Kristall
belasteter Kristall
Fx
---------+
Si
Q ~ F:
+
O
-
-
-
-
Qx  d11  Fx  n
x
y
+
-
+
+
+
++++++++++
Fx
(1)
The charge occurs on
the mechanical surface by
pressure
with
d II
Piezoelectric co-efficient in x-direction
Fx
n
Load in x-direction
Number/Valency in piezo element
Seite 17
Shearing effect (2)
belasteter Kristall
Fx
--------O
Si
y
+
-
+
-
x
-
(2)
The charge occurs on
the mechanical surface by shear
stress
Q ~ F:
+
-
+
Qx  2  d11  Fx  n
+
+
+++++++++
with
Fx
d II
Fx
n
Load in the x-direction
Valency / Number of the piezo element
Seite 18
Transversal effect (3)
belasteter Kristall
belasteter Kristall
Fy
Fy
O
O
+
-
y
+
+
Si
+
- Si
xx
y
--
-
++
-
++
++
++
++
+
- +
-
y
+ +
-
x
-
-
+
+
--
Fy F
y
Q ~ F:
b
- Qx  d11  Fy  a
Mit:
b
a
(3) The charge occurs on the
vertical surface by mechanical
stresses
c
d II
Fy
Load in the y-direction
b
a
Geometric relationship
Seite 19
Piezoelectric Co-efficients
Materials
Quarz
Li2B4O7
GaAs
ZnO
LiNbO3
LiTaO3
PZT
PVDF
Piezo- und Ferroelectric Materials
Piezoelectric Co-efficient d [pC/N]
2,31
19,4
2,69
12,4
69,4
23,1
380 – 590
20 – 35
TCurie [°C]
ca. 570
ca. 150
ca. 150
ca. 150
1145
603
190 – 360
170 – 200
 Jaques und Pierre Curie in 1880 discovered the Piezoelectric effect.
 Upon reaching the Curie temperature Piezoelectric effect ceases.
 Development of a mixed crystal of Pb(Zn1/3 Nb
2/3)O3
und PbTiO3 with Piezoelectric
co-efficient of d = 1500 pC/N
Seite 20
Construction of 3 force component sensors (Fx, Fy, Fz)
 Multi-layered structure by pairs of dics
Shear effect
Longitudinal effect
Isolation
Shear effect
Isolation
Seite 21
4-Component Sensor (Fx, Fy, Fz, Mz)
Fs
r
Torque Measurement:
Arrangement of shear sensitive
elements to form a ring
M =  Fs • r
Seite 22
Force Sensors and Dynamometer
Measuring Range
Fx, Fy: +/- 1 to 60 kN
Fz: +/- 2 to 100 kN
Measuring Range
Fx, Fy: +/- 5 kN
Fz:
+/- 10 kN
Measuring Range Fx, Fy: +/- 5 kN
Fz: - 5 bis +20 kN
Mz: +/- 200 Nm
Measuring Range Fx, Fy: +/- 5 kN
Fz: +/- 20 kN
Mz: +/- 200 Nm
Seite 23
3-Component force measurement platform:
Measuring Fc, Ff, Fp
Kraft [N]
Force
/N
Cutting Force Measuring in Turning
200
Fc
150
FP
Ff
100
50
Fx Vorschubkraft
0
Fy Passivkraft
Fz Schnittkraft
-50
0
5
10
15
20
25
Cutting time Zeit
tc /[s]s
Seite 24
Wirkleistung [V]
1.5
1.25
1
0.75
0
2
4
6
8
10
12
Vorschubkraft Fz [N]
3
2.75
2.5
2.25
2
1.75
1.5
1.25
1
0.75
0.5
0.25
0
0
1.5
1000
Feed force Fz / N
Wirkleistung [V]
3
2.75
2.5
2.25
2
1.75
1.5
1.25
1
0.75
0.5
0.25
0
Vorschubkraft Fz [N]
Drehmoment Mz [Nm]
Drehmoment Mz [Nm]
Rotating Tool Dynamometer
Measuring Mz, Fx, Fy, Fz
Torque Mz / Nm
Cutting Force Measuring in Drilling, Milling, Tapping, Reaming
14
16
18
20
Bohrweg [mm]
2
4
6
8
10
12
14
16
18
20
Drilling depth / mmBohrweg [mm]
900
1.25
800
1
700
600
0.75
500
400
0.5
300
0.25
200
100
0
00
0
2
2
4
4
6
6
8
8
10
10
12
12
14 16 18 20
14 16 18 20
Bohrweg [mm]
Bohrweg [mm]
Drilling depth / mm
Seite 25
Strain Sensor
Main expansion
direction
Elongation
F
Dl

l
F

l0
A E
Equivalent strain
l0
q 
d
d0
Sensitivity
weakening
d0
d
2
Poisson equation
A
q
m

Typical Values:
1/m  3 … 4 for Steel
1/m  5 … 9 for Cast Iron
Seite 26
Acceleration Sensor
 Basic Components
Housing
Seismic mass
Electrode
Piezoelectric
Material
Female connector
Base Plate
 Various 3 axis acceleration sensors
Measuring range:
Frequency range:
Sensitivity:
Mass:
+/- 5 g m/s²
1 – 3.000 Hz
1000 mV/g
16 g
Measuring range:
Frequency range:
Sensitivity:
Mass:
+/- 50 g m/s²
0,5 – 5.000 Hz
100 mV/g
29 g
Measuring range:
Frequency range:
Sensitivity:
Mass:
+/- 500 g m/s²
2,5 – 10.000 Hz
10 mV/g
7,6 g
Seite 27
Application of three axis acceleration sensor
Tool revolver
Tool
Magnet
Acceleration sensor
Seite 28
Structure-borne sound
Structure-borne sound is sound that propagates as a transverse wave in a
solid body
 Basic Components
Piezoelectric
piezoelektrisches
Element
Element
Dämpfungsmasse
Damping mass
Housing
 The measuring ranges of the
sensors are limited for the reason
of resonance.
Membrane
Coupling
Membran
und and
Koppelelement
Accessible range
50 - 400 kHz bzw. 100 - 900 kHz
Element
Seite 29
Causes for Structure-borne sound (AE = Acoustic Emission)
5
1 Plastic Deformation in the Shear Plane
2 Friction on the rake face.
3 Crack initiation and crack propagation.
6
4 Friction between tool and workpiece.
7
5 Impact of the chip on the workpiece or
tool.
1
6 Chip Breaking.
3
4
vc
2
7 Friction through check of the chip on
the rake face.
Seite 30
Fields of Application and Application notes
Fields of Application
■ Monitoring of the finishing process
■ Wear monitoring in turning, drilling and milling.
■ Recognizing unfavorable chip shapes.
Joined Time Frequency Analysis for wear indication
■ Detection of overheating.
400 kHz
900 µm
■ The damping of the joints is highly dependent
on frequency and is approximately 11 db
i.e. application close to site of action.
■ Good coupling conditions require a high
Amplitude [dB]
Application notes
surface quality at the installation site.
■ Coupling via liquid jet possible.
Seite 31
Pressure Sensors
 Basic components
Fields of application.
 Monitor the clamping transported away
Plug
during deep drilling.
 Monitoring of contact pressure of the
ceramic balls for hard burnishing.
 Monitoring systems for high pressure
Sensor housing
coolant supply
Sealing shoulder
Contact spring
Transversal sensitive Quartz rod
Connecting Piece
Sleeve
Membrane
Source: Chip Blaster
Seite 32
Application for flow measurement
 Monitor the clamping during deep drilling.
Absolute Pressure
Sensor
For a flow rate
Orifice
QC
2  p

with
Differential Pressure
Sensor
Q
Flow rate
C
p

Constant
Pressure difference
Density
Seite 33
Advantages and Disadvantages of Piezoelectric Sensor
Advantages
Disadvantages
 Large Measuring Range
 Suitability only for dynamic and quasi-
 High Resolution, ex. <10 mN within a
measuring range of 5 kN
 Good Linearity and very less hysteresis.
 Easy handling through reset.
 High Curie Temperatures crystals used
static measurements.
 Crosstalk between the axis.
 Structural weakness through sensor
integration.
 High Cost with DMS.
available from 573°C to 400°C.
 High overload protection with DMS
 No aging
Seite 34
Temperature Sensor
 Thermo-element
 Two color pyrometer
 Resistance thermometers
 Infrared camera
Seite 35
Thermo-element
 Two dis-similar metals are connected at one
end electrically.
A
 Temperature difference between TM und Tref
generates a small electrical voltage Uth

U th  k A  k B  TM
Uth
+
-
(Seeback-Effect)
TM
Tref
 Uth is also influenced by materials A & B and
B
their reference temperatures.
Manager
Type
positive
negative
Temperature Uth [mV] Seeback-range [°C]
coeff. ar0°C
[µV/°C]
E
Chrome
Constantan
-270 to 1000
-9.835 bis
76.358
58.70
J
Iron
Constantan
-210 to 1200
-8.096 bis
69.536
50.37
K
Chrome
Aluminium
-270 to 1372
-6.548 bis
54.874
39.48
-6.258 bis
20.869
38.74
T
Copper
Constantan
-270 to 400
Material
kxPt [mV/100 K]
Constantan
-3.47…3.04
Nickel
-1.9…-1.3
Platin
0.0
Copper
0.75
Iron
1.9
Nickel-Chrom
2.2
Ferro-silicon
42..50
Seite 36
Two Color Pyrometer
The Planck's radiation law
E T  
  C1

  1
5   exp C2
 
   T 

…Provides for the ratio of radiation intensities of two wavelengths Eλ and λ1,2:




1
1
1 
TR   
 ln 
2 
 T C   1  1 
2 



 1  2 


1
with:
T = True Temperature
TR = Measured Temperature
ε1,2 = Emissivities
C1,2 = Constants
Features
 Measuring the radiation density at two different
wavelengths.
 No reference is required (absolute measuring
method)
 Contactless
 Spatial and temporal high resolution.
 Low influence of surface type on emissivity.
 Sensitive incident against ambient light and
contamination of optics.
Source: WSA RWTH Aachen
Seite 37
Measuring the Surface Temperature of the Workpiece
Workpiece
Chip
HM-Tip
Quarz fibre of two
colour pyrometer
(0,42 mm dia)
vc
 Preparation of the insert is required.
 Perform thermal radiation of the component
 1 mm
Heat radiation
surface(secondary cutting) through Quartz fiber unit.
 Bare metal surfaces have low emmisivity. Therefore,
can be measured only from 200 degree Celsius.
 Not suitable for wet processing.
Seite 38
Temperature Measurement by a Two-Color-Pyrometer
workpiece
fiber
chip
measuring spot
major
cutting
edge
insert
0.5 mm
Technical specifications
quartz fiber
( 0.26 mm)
Temperature range: app. 250 -1200 °C
Maximum time resolution: 2 ms
Measured temperature independent of surface emissivity
Seite 39
Combination of Temperature and Force Measurement
Chip temperature
aluminium
feed
0,25 mm
depth of cut
2 mm
steel / titanium
0,1 mm
1 mm
Cutting speed
Cutting force Fc
500
N
300
200
100
0
Seite 40
Alternative Measurement Position - Workpiece Surface
°C
700
Measuring point
Temperature
distance to cutting edge 1 mm
quartz fibre
600
500
4.5 mm
400
300
200
0
20
40
60
Cutting speed
80
100 m/s
Seite 41
Alternative Measurement Position - Top of the Chip
1000
°C
Quartz fibre
Measuring point
Temperatur
Temperature
Cemented
carbide tip
800
optic
Optik
600
400
Cutting insert
Hartmetallspitze
cemented
carbide tip
0
1000 2000 3000 4000 5000 6000 m/min
Schnittgeschwindigkeit
Cutting speed
Seite 42
Surface Metrology
tactile/stationary
optical/
stationary
Quelle: Wyko
tactile/mobile
Quelle: Hommel
Seite 43
3D Coordinate Measuring
Seite 44
Outline
1
Learning Goals
2
3
4
5
6
7
8
9
Seite 45
Features and Technical Data of the Test Bench
 Excellent accessibility for filming and measuring
 𝑣𝑐
relevant characteristics of the chip formation process
 Synchronised measurement of:
– Cutting force components
– Thermal imaging and pyrometer temperature measurement
– Highspeed video analysis of chip formation



 New level validation of metal cutting simulations

 Highspeed Videocamera
 Workpiece + Fixture
 Tool holder for Friction
Experiment (Slide 4)
 Cutting Tool
 Dynamometer
 x-y-Feed Drive
  Also serves as experimental basis for cutting, friction
and material modelling
Technical Data:
 Machine tool: Forst RASX 8x2200x600 M / CNC
 Cutting velocity: 0.5 ≤ vc ≤ 150 m/min
 Cutting length: 0 - 500 mm
 Width / Depth of cut 0 - 15 mm
 Max. cutting force: 80 kN
Seite 46
Features and Technical Data of the Test Bench
 Shaftholder max. 32x32
 Grooving / Parting Tool holders for orthogonal cutting (Inclination angle = 0°, tool edge angle = 0°)
 Phantom v7.3 Highspeedvideocamera, LED Illumination
vc= 20 m/min
f = 0,3 mm
workpieceholder
workpiece
vc
1 mm
Seite 47
Experimental Determination of Friction Coefficients – Test setup
 Force measurement with
3-Component-Dynamometer
 Temperature measurement on
Tool
surface of the workpiece with
Two-Color-Pyrometer
 Workpiece part:
sheets/flat material
 Tool insert:
Indexable inserts
y
z
Pyrometer fiber
Seite 48
High Speed Filming of Friction Process
 Sliding speed Vrel = 60 m/min
 Uncut chip thickness: t = 0.5 mm
 Cutting width: b = 1.5 mm
 Cutting tool material: Sandvik 1005
 Workpiece material: C45E+N
 Frame rate: 6700 FPS
Seite 49
Advanced Experimental Setup: Orthogonal Cut on Broaching Machine
tool
tool holder
workpiece
High-Speed Filming
workpiece holder
HS camera
measurement platform
 High speed camera:
– Type: Vision Research Phantom v7.3
– Frame rate: 6.688 fps by 800 x 600 pixel
500.000 fps by 32 x 16 pixel
tool
workpiece holder
workpiece
IR camera
High-Speed Thermography
 High speed external broaching machine:
– Type: Forst RASX 8x2200x600 M/CNC
– Max. force: 80 kN
– Power: 40 kW
– Max. cutting speed: 150 m/min
– Tool fixed und workpiece moved
– Optimal filming of the cutting zone
 High speed IR camera:
– Type: FLIR SC7600
– Frame rate: 100 fps by 640 x 512 pixel
800 fps by 160 x 128 pixel
– Measurement range: -20°C - 3000 °C (±1°C)
Seite 50
High Speed Filming of Chip Formation (vC = 150 m/min, dry cut)
h = 0.20 mm
 Workpiece:
AISI 1045 normalized
3.5 x 50 x 200 mm
h = 0.40 mm
 Tool:
Carbide, uncoated
Sharp (rß  5 µm)
Seite 51
High Speed Thermography During Chip Formation (vC = 150 m/min)
h = 0.10 mm
h = 0.50 mm
600
400
°C
350
300
250
200
50
0
 Workpiece:
AISI 1045 normalized
3.5 x 50 x 200 mm
 Tool:
Carbide, uncoated
Sharp (rß  5 µm)
Seite 52
High Speed Thermography During Chip Formation (vC = 150 m/min)
Tool
Chip
t = 82 ms
t = 86 ms
End of the cut
50
0
200
250
350
°C
300
Time after
tool-workpiece contact
t = 43 ms
400
t = 6 ms
600
h = 0.5 mm
h = 0.1 mm
End of
the cut
t = 20 ms
t = 90 ms
t = 100 ms
t = 160 ms
Seite 53
Outline
1
Learning Goals
2
3
4
5
6
7
8
9
Seite 54
FE Validation of a Developed FE Cutting Model
Tool
Cutting parameters
Workpiece material:
Tool material:
Cutting speed:
Feed:
Cooling:
AISI 1045
Sandvik H13A,  = 6°
α = 3°, rß  5 µm
150 m/min
variabel
dry
y
Workpiece
vC
x
Developed friction model:
µ = µ (h,vc)
µ < 0.577  only sliding friction (Coulomb friction)
µ  0.577  sliding + sticking friction (hybrid friction)
Boundary conditions
Cutting tool:
Rigid
Workpiece:
Visco-Plastic
With heat dissipation
Contact:
Heat transfer (Conduction & Convection)
Modified Johnson-Cook material law:
  (546 MPa  487 MPa   0.25 )  (1  0.015  ln( /  0 ))  exp( 1.67  [T T 0 ] / Tm )
Seite 55
Material and Friction Laws Validation:
Chip Formation (Orthogonal Cut, vC = 150 m/min, AISI 1045)
h = 0.5 mm
FE simulation
Experiment
h = 0.2 mm
FE simulation Experiment
h = 0.4 mm
FE simulation
Experiment
h = 0.04 mm
FE simulation
Experiment
h = 0.3 mm
FE simulation
Experiment
h = 0.02 mm
FE simulation
Experiment
Seite 56
Material and Friction Laws Validation:
FE Cutting Simulation (vC = 150 m/min, h = 0.50 mm, DEFORM)
Plastic strain
[-]
Effective stress [MPa]
Strain rate
[1/s]
Temperature
[ C]
Seite 57
Turning: Comparison of Simulation and Real Chip Flow
CNMG120408
Chip breaker NF
HC-P15
kr = 95°
n = -6°
s = -6°
C45E+N
ap = 1,9 mm
f = 0,25 mm
vc = 200 m/min
dry
vf
vc
Seite 58
Milling: Verification of the FE Model
Experiment
.
Simulation
Full agreement
Seite 59
Drilling: Verification of the Chip Formation
Experimental chip formation
Chip formation in the simulation
Workpiece material: C45E+N
Cutting speed: vc = 35 m/min
Cutting tool material: HW K20
Feed:
f = 0.012 mm
Seite 60
FE-Based Calibration Process for the Tool Wear Model
Modeling
Verschleißmarkenbreite über die Schnittzeit
16MnCr5 (einsatzgehärtet), Stegbreite = 1 mm, cBN bestückte Einstechplatte der Sorte N151.2-600-50E-G
Schnittgeschwindigkeit vc = 150, 200, 300 m/min und Vorschub f = 0,06 mm
Wear curve
Machining experiments
120
vc = 200 m/min
vc = 150 m/min
Verschleißmarkenbreite VB [µm]
Tool-wear VB
vc = 250 m/min
100
80
t = 10 min
t = 6 min
t = 4 min
t = 1 min
60
40
20
0
0
5
10
15
20
25
Cutting time t
30
35
40
Schnittzeit t [min]
dW
 σ n  v ch  C1  e
dt
C
( 2 )
T
lg C1
lg {w /( n VS)}
Determination of the
specific material
parameters C1 and C2
dW/dt
Regression analysis
FE-analysis
 Temperature
 Normal-
C2
tension
 Sliding speed
1/T
Seite 61
Verification of the Tool Wear Simulation for the Flank Wear
vc = 150 m/min, f = 0.06 mm, ap = 1 mm, dry
eff = -26°
Tool
[mm]
Flank
wear
VB [mm]
Width VB/
Wearwidth
Flank
Time:
5 min
0 = 7°
Time:
15 min
Time:
25 min
Time:
35 min
93 µm
0,1
Experiment
0,08
0,06
Simulation
0,04
0,02
0
0
5
10
15
20
25
30
35
Cutting
time t [min]
Time [min]
Seite 62
Outline
1
Learning Goals
2
3
4
5
6
7
8
9
Seite 63
What is Optimization?
 „Optimization is the act of obtaining the best result under given circumstances”
 “Optimization is a branch of mathematics concerned with the application of scientific
methods and techniques to decision making problems and with establishing the best or
optimal solutions”
 “Optimization can be defined as the process of finding the conditions that give the
maximum or minimum of an objective function”
 „Making things better“
 „Generating more profit„
 „Determining the best“
 „Improving the performance of systems“
 „Do more with less“
 “Optimization is the mathematical discipline which
is concerned with finding the maxima and minima
of functions, possibly subject to constraints”
Source: Papalambros, Altair Engineering
Seite 64
Historical Development
 Newton, 1642-1727: The development of differential calculus methods of optimization
 Bernoulli, 1697: Brachistochrone Problem
 Leibnitz, 1646-1716: Differential calculus methods of optimization
 Euler, 1707-1783: Calculus of variations, minimizing functions
 Lagrange, 1736-1813: Optimization of constrained problems
 Cauchy, 1789-1857: Steepest descent method for unconstrained optimization
 Von Neumann, 1903-1957: Game theory
 Bellman, 1920-1984: Principle of optimality in dynamic programming problems
 Karmarkar, 1957: Interiot point method for linear programming problems
 Bendsoe, Kikuchi, 1988: Topology optimization
 Tucker, 1905-1995: Optimality conditions
 Dantzig, 1914-2005: Linear programming and Simplex method
Source: Nocedal, Spall, Rao, Gill, Goldberg
Seite 65
Main Benefits of Optimization
 More efficient and thorough research
 Decrease of product development costs and time to market
 Reduction of production time and better utilization of capital
 Acceleration of process and product development
 Increase of competitive advantages and innovation
 More engineers having optimization knowledge
 Making a system reliable and robust
 Providing insight in system problem, underlying physics and model weaknesses
 Improving process performance and product quality
 Opening up new research fields and technologies
 Promotion of interdisciplinary research and applications
 Creation of new jobs, new skills and new growth opportunities
Source: Chong, Zak, Rao, Gill
Seite 66
Disadvantages of Optimization
 Proper problem formulation critical!
 Choosing the right algorithm for a given problem
 Many algorithms contain lots of control parameters
 Optimization tends to exploit weaknesses in models
 Optimization can result in very sensitive designs
 Some problems are simply too hard / large / expensive
 Large problems optimization requires lots of computing power
Source: Chong, Zak, Rao, Gill
Seite 67
What is the Optimization Problem?
Minimize (or maximize)
an objective „performance“ function:
taking into account the constraints:
 (x1,x2,…,xn)
F(x1,x2,…,xn)
Gi(x1,x2,…,xn) = 0, i=1,2,…,p
Hj(x1,x2,…,xn) < 0, j=1,2,…,q
are the n system variables
 Gi(x1,x2,…,xn) are the p equality constraints
 Hj(x1,x2,…,xn) are the q inequality constraints
Source:Papalambros
Seite 68
System Definition
Input
System approach
Output
Environment
 What belongs to system / environment?
 What is the level of details?
 What is the system function?
 What is input / output?
Seite 69
System Example: Catilever Beam
L
Steel (E, ρ)
h
b
U(t), Mb(t), V(t)
h
Mathematical model:
FL3
U

3EI
 System variables:
FL3
 bh 3
3E
 12
F(t)
System
U(t)
U(t)
System
F(t)
F(t)
System
Mb(t)
h, b, L
E, ρ
System
V(t)
F(t), U(t), Mb(t), V(t)
 System parameters: h, b, L
 System constants:
4 F L3

 E b h3



E, ρ
F(t)
Seite 70
The Optimization Procedure
Constants
Cj
Responses
System model
f, g, h
System variables
xi
Optimizer
Derivatives of responses
(System sensitivities)
f g h
,
,
xi xi xi
Seite 71
Applications of Optimization
 Mechanic, manufacturing, architecture, electrical circuits, economic, transportation, etc.
– Improving structure
Automotive
Civil infrastructure
– Protein folding
– System identification
– Logistics
– Financial market forecasting (options pricing)
– Traveling salesman problem
– Route planning
– Operations research
Biomedical
Aerospace
– Controller design
– Spacecraft trajectory planning
Source: Red Cedar Technology
Seite 72
Categories of Structural Optimization
 Topology optimization:
 Size optimization:
 Shape optimization:
 Material optimization:
Body in White
of BMW 5 GT
Source: Altair Engineering, BMW, Wikipedia
Seite 73
Outline
1
Learning Goals
2
3
4
5
6
7
8
9
Seite 74
Optimization Algorithms
 Analytical methods
 Numerical stochastic methods
– Variational method
– Robbins-Monro algorithm
– Simultaneous-Mode-Design method
– Kiefer-Wolfowitz algorithm
 Numerical deterministic methods
– Stochastic gradient descent
– Grid/raster method
– Simultaneous perturbation stochastic approximation
– Gradiant method
– Scenario optimization approach
– Steepest descent method
– Simulated / Quantum annealing
– Simplex method
– Swarm algorithms
– Penalty function methods
– Genetic algorithm
– Levenberg-Marquardt algorithm
– Evolution strategies
– Etc.
– Etc.
Source: Wegener, Robbins, Roberto, Dixit, Malliaris
Seite 75
Commercial Software for Optimization
Company
General
optimization
Web address
Structural
optimization
Altair Engineering
www.altair.com
HyperOpt
OptiStruct
Ansys
www.ansys.com
-
Ansys-CADOE
Engineous Software
www.engineous.com
iSIGHT
-
MSC Software
www.mscsoftware.com
-
MSC.Nastran
Noesis
www.noesissolutions.com
Optimus
-
Opttek
www.optteck.com
OptQuest
-
Oculus Technologies www.oculustech.com
CO
-
Phoenix Integration
www.phoenix-int.com
Model Center
-
UGS PLM
www.ugs.com
-
NX.Nastran
Vanderplaats R&D
www.vrand.com
VisualDOC, BIGDOT GENESIS
Seite 76
Example: Design Optimization
Problem Definition
Initial Models
Database
Multi-Models Generation
Multidisciplinary Computations
Optimization Algorithm
Objective Constraints
Optimized Models
Database
Source: Selmin
Seite 77
Topology Driven Vehicle Concepts: Concept Development Process
 Define all available package space, loading and BC’s
 Topology optimization for gross concept features
 Interpret into first concept design
 Topology optimization for concept
refinement
 Interpret concept for final optimization
and design details
Final concept
Source: Altair Engineering
Seite 78
Topology Driven Vehicle Concepts: Results
 Final concept design
–
–
–
–
–
–
–
Primary Hydroformed Sections
Mid-Rail “C” Section
Welded Body Mount Brackets
23% lower mass
25% fewer parts
50% less weld length
Cost penalty:
$0.25 cost per lb saved
 Performance results
–
–
–
–
–
Twist:
Vertical bend:
Lateral bend:
Bending stiffness:
Torsion stiffness:
25.0 Hz (+34%)
27.8 Hz (+2.5%)
26.4 Hz (-9%)
3278 N/mm (0%)
159 kNm/rad (+31%)
Source: Altair Engineering
Seite 79
Hydroformed Lower Rail
Crush zone
Crush zone
67 design variables
 Maximize energy absorbed in crush zone
 Identify the rail shape and thickness
66 control points
and one gage thickness
 Subject to constraints on:
– Peak force
– Mass
– Manufacturability
Source: Red Cedar Technology
Seite 80
Validation: Lower Rail Benefits
 Compared to 6-month manual design effort:
– Overall crash response resulted in equivalent of five star rating
– Energy absorption increased by 100%
– Peak force reduced by 30%
– Weight reduced by 20%
Source: Red Cedar Technology (Goodman)
Seite 81
Outline
1
Learning Goals
2
3
4
5
6
7
8
9
Seite 82
The Great Challenges of the Cutting Process
Process
Strain
Strain rate / s-1
Thomolog
Extrusion
2–5
10-1 – 10-2
0,16 – 0,7
Forging /
Rolling
0,1 – 0,5
10 – 10+3
0,16 – 0,7
Sheet metal
forming
0,1 – 0,5
10 – 10+2
0,16 – 0,7
Cutting
1–5
10+3 – 10+6
0,16 – 0,9
Cutting process
Extreme conditions in the cutting process
Source: Jaspers
Seite 83
Influencing Factors on the Cutting Process
Bild
eines
Prozesses
Workpiece material
structure
Cutting zone
chip forming
mechanisms
texture
mechanical
properties
hardness
residual stresses
Tool
cutting material
Machine
machine design
coating
cooling lubricant
geometry
cutting parameters
contact
conditions
e.g.: friction, wear
heat transfer
drive system
M
tool holder
clamping device
Seite 84
Cutting Simulation: Input- und Output Parameters
Chip formation
Temperature
Tension
Deformation
Rate of deformation
Chip type
Chip flow
Chip crack
Component / tool
Geometry
Material data
Contact conditions
Boundary conditions
Cutting conditions
Tool
Strain
Tension
Temperature
Cutting forces
Wear
Component
Strain
Temperatures
Deformation
Burr formation
Distortion
Future:
Residual stresses
Surface quality, e.g.: roughness,
changes in shape,
Measurement and position
Seite 85
Integration of the Optimization in the FEM
Change physical
problem
Physical problem
Improve mathematical
model
Mathematical model
Numerical model
Optimization
FEM
Does answer
make sense?
No!
Refine analysis
Process improvement and optimization
Yes!
Seite 86
FE Based Sensitivity Analysis
Varied input
parameters:
Goal output
parameters:
 Heat capacity
 Thermal conductivity
 Cutting force Fc
 Passive force Fp
 Flow stress
 Feed force Ff
 Friction coefficient
 Temperature T
 Tool micro-geometry
Legend
Influence
Heat
capacity
Thermal
conductivity
Flow
stress
Tool
micro-geometry
Friction
Cutting force
low
Feed force
medium
Passive force
high
Temperature
Seite 87
Benchmark-Analysis to Choose the Best Tool Geometry
Fixed input
parameter
material parameter,
friction coefficients
Cutting parameter 2
vc2, ap1, f1
+
Tool
B
C
Determination of the
thermomechanical
loadspectrum, chip
flow, chip form
A
Temp
+
Coating
TiN TiAlN AlO2
Flank wear VB
Q,
T,
Fi,
Cutting parameter
1
2
A
Cutting parameter 1
#
+
vc1, ap1, f1
Benchmark-Analysis
Cutting
simulation
Wear
B
Tool
Stress
C
Chip
flow
Tool A
+
-
++
-
Tool B
-
--
o
+
Tool C
++
++
+
+
Optimised
tooland
tool carriergeometry
Seite 88
Thank you for your attention!
Seite 89
Questions
 Which measuring sensors do you know?
 Describe the Piezoelectric effect.
 What is the Seeback effect?
 What is Optimization?
 Name the main benefits and disadvantages of optimization.
 Please describe the Optimization Problem.
 What are the categories of structural optimization?
 Please give some optimization Algorithms.
 Which influencing factors on the cutting process do you know?
 List the input- und output parameters of cutting simulation.
 Please characterize the Integration of the Optimization in the FEM.
Seite 90

Methods of validation and optimization techniques

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