CHAPTER 3 EXPERIMENTAL DESIGN

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CHAPTER 3
EXPERIMENTAL DESIGN
3.1
INTRODUCTION
The objective of this study is to investigate the effect of process
parameters such as radial rake angle, nose radius, cutting speed, cutting feed,
and axial depth of cut on machining performance such as surface roughness,
cutting force, tool wear acceleration amplitude of vibration and temperature
rise in end milling operation. It is important to generate data by conducting
experiments by varying various levels of process parameters and recording
the response of machining performance at each set of levels. It is necessary in
the experiment to have a clear layout of what exactly is to be studied, how the
data to be collected and qualitative understanding of how these data are to be
analyzed.
This chapter describes the experimental setup used to conduct the
experiments. Brief description of the tool material, workpiece material,
instruments used to measure the response is also included. Experimental
design methods used to select factors levels, range and also to select the
suitable run order of the experimental trials are briefly described. Central
composite rotatable design matrix which has been employed for conducting
experiments are described and presented in this chapter.
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3.2
EXPERIMENTAL SETUP
The experiments were conducted on a HAAS vertical machining
center (Figure 3.1): model tool room mill TM-1 with high speed steel end mill
cutter under dry condition. The HAAS Vertical Computer Numerical Control
machining center provides a room for a lager work piece with xyz travels 30”
X 12” X 16”(762 mm X 305 mm X 406 mm). The specifications of HAAS
vertical machining center used for conducting experiments are:
(i)
Power of spindle motor
7.5/5.5 kW
(ii) Speed rage of the spindle motor
60–10000 RPM
(iii) Guide ways type
LM
(iv) Max load on table
300 kgf
(v) Feed (X & Y dir)
1–10000 mm/min
(vi) Power supply (Basic machine)
14 kVA
Figure 3.1 HAAS CNC vertical machining centre
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The workpiece material Aluminum alloy 7075-T6 is acknowledged
in Aircraft fittings, gears and shafts, fuse parts, meter shafts and gears, missile
parts, regulating valve parts, worm gears, keys, and various other Commercial
aircraft, aerospace and defense equipment owing to its high strength to weight
ratio. The use of materials with low specific weight is an effective way of
reducing the weight of structures. The favorable characteristic features such as
moderate hardness, better transmission, heat treatable, high tensile strength
and high corrosion resistance leads to the choice of Aluminum alloy 7075-T6.
For conducting experiments to determine surface roughness, cutting force,
vibration amplitude, tool wear and temperature rise test specimens of
following sizes (50 mm x30 mm x 30 mm), and (100 mm x 50 mm x 30
mm)were cut from Aluminum alloy 7075-T6 bar. As per experimental design
32 identical specimens were cut to the above dimension as shown in the
Figure 3.2. The workpiece is placed in the machining center using a machine
vice.
Figure 3.2 Work piece material (AluminiumAlloy, Al 7075-T6)
The tool material was high Speed Tool Steels (HSS). HSS is
inexpensive compared to other tool materials, is easily shaped, and has
excellent fracture toughness, fatigue and shock resistance. The end mill cutter
made is solid HSS used for our experiments. Nine end mill cutters with
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different radial angle, nose radius are utilized for conducting experiments as
shown in the Figure 3.3. The specifications of the geometry of the end mill
used for conducting experiments are:
(i)
Number of flutes
4
(ii) Diameter of cutter
12 mm
(iii) Shank length
70 mm
(iv) Helix angle of flute
45°
(v) Radial Rake angle
4°,8°,12°,16°,18°,20°
(vi) Noseradius
0.4mm,0.6mm,0.8mm,1.0mm,
1.2mm
Figure 3.3 End mill cutter with different radial rake angle and nose radius
3.2.1
Experimental Set-up for Surface Roughness Measurement
Various methods are used to assess surface roughness. They can be
divided into three categories: (1) subjective comparison with standard test
surfaces, (2) stylus electronic instruments, and (3) optical techniques.
Standard Test Surfaces Sets of standard surface finish blocks are available,
produced to specified roughness values. To estimate the roughness of a given
test specimen, the surface is compared with the standard both visually and by
the ‘‘fingernail test.’’ In this test, the user gently scratches the surfaces of the
specimen and the standards, judging which standard is closest to the
specimen. Standard test surfaces are a convenient way for a machine operator
82
to obtain an estimate of surface roughness. They are also useful for design
engineers in judging what value of surface roughness to specify on a part
drawing.
Stylus Instruments: The disadvantage of the fingernail test is its
subjectivity.Several stylus-type instruments are commercially available to
measure surface roughness—similar to the fingernail test, but more scientific.
An example is the Profilometer, shown in Figure 3.4. In these electronic
devices, a cone-shaped diamond stylus with point radius of about 0.005 mm
(0.0002 in) and 90º tip angle is traversed across the test surface at a constant
slow speed. The operation is depicted in Figure 3.4. As the stylus head is
traversed horizontally, it also moves vertically to follow the surface
deviations. The vertical movement is converted into an electronic signal that
represents the topography of the surface. This can be displayed as either a
profile of the actual surface or an average roughness value. Profiling devices
use a separate flat plane as the nominal reference against which deviations are
measured. The output is a plot of the surface contour along the line traversed
by the stylus. This type of system can identify both roughness and waviness in
the test surface.Averaging devices reduce the roughness deviations to a single
value Ra. They use skids riding on the actual surface to establish the nominal
reference plane. The skids act as a mechanical filter to reduce the effect of
waviness in the surface; in effect, these averaging devices electronically
perform the computations.
Figure 3.4 Sketch illustrating the operation of stylus-type instrument
83
Stylus head traverses horizontally across the surface, while the
stylus moves vertically to follow a surface profile. Vertical movement is
converted into either (1) a profile of the surface or (2) the average roughness
value. Optical Techniques most other surface-measuring instruments employ
optical techniques to assess roughness. These techniques are based on light
reflectance from the surface, light scatter or diffused, and laser technology.
They are useful in applications where stylus contact with the surface is
undesirable. Some of the techniques permit very-high-speed operation, thus
making 100% inspection feasible. However, the optical techniques yield
values that do not always correlate well with roughness measurements made
by stylus-type instruments.
The average roughness value was measured using MitutoyoSurftest
SJ201 on the surface of the machined specimen as shown in the figure 3.5.
The Surftest SJ201is a shop floor type surface roughness measuring
instrument, which traces the surface of various machine parts, calculates their
roughness standards, and displays the result. The measuring instruments
consist of the detector unit with stylus for tracing. A pickup or stylus of the
detector unit will trace the minute irregularities of the workpiece surface. The
vertical stylus displacement produced during tracing the work surface is
converted into electrical signals. The electrical signals are subjected to
various calculation processes and the calculation results (measurement result)
are displayed on the instrument liquid crystal display. RS 232 port is available
on the instruments to acquire measured surface roughness value using
Mituotyover 3.0 software in the personal computer. The cut off length used
during the measurement was 0.8 mm and the measurement were taken at three
places on the machined surface and the average of those values is noted.
84
Figure 3.5
3.2.2
A schematic diagram of experimental setup for surface
roughness measurement
Experimental Set-up for Cutting force Measurement
The cutting forces:infeed force, crossfeed force and thrust force are
measured by using syscon instruments; three axis milling tool dynamometer.
The instruments works based on the strain gauge wheat-stone bridge
principle. RS232 port is available in the instruments to acquire data while
machining.
The data is acquired in the data acquisition software and
observations are tabulated to obtain the mathematical model. The workpiece
is mounted on the specially designed machine vice with strain gauges
measure the cutting force in all three directions. The experimental setup used
for conducting the experiments is shown in Figure 3.6.
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Figure 3.6
A schematic diagram of experimental setup for cutting force
measurement
Exclusively designed Dynamometers are used to measure the
cutting forces of the tool point. An array of hydraulic, pneumatic and strain
gauge instruments were used by the researchers earlier. But piezoelectric
Dynamometers using quartz load measuring elements are generally employed
for cutting force measurement. The Dynamometer is fixed between the tool or
workpiece and non-rotating part of the machine tool structure. In order to
determine the cutting forces into directional components, coordinate system is
employed. Force components are connected to the axes of motion of the
86
machine tool in the milling process. Infeed force, crossfeed force and thrust
force are the three resolved components of the force. The infeed force, acts in
the x direction of the machine tool, tangent to the rotating tool. Crossfeed
force acts in the y direction of the machine tool, which is normal to the
rotating tool. The thrust force acts in the z direction of the machine tool which
is parallel to the axis of the tool.
3.2.3
Experimental Set-up for Vibration Amplitude Measurement
The experimental set-up for this research is bifurcated into: (1)
hardware, and (2) software. In order to deduce the mathematical model and
analyze the relationships among vibration amplitude, geometrical parameters
(radial rake angle, nose radius of cutting tool) and machining parameters
(cutting speed, cutting feed rate and axial depth of cut), the experimental setup should collect data for analysis.
3.2.3.1
Hardware set-up
The hardware set-up requires the following equipment:
(1) A HAAS vertical machining center with 10 tools with the
capacity of multiple tool-change capability operates at a high
spindle speed ranging to 10000 r. p. m. This machine is
capable of 3-axis movement (along the x, y, and z planes).
(2) A ER32- GPL 70mm tool holder, ER40 collect diameter
12mm with high-speed steel end mill cutting tool.
(3) The piezoelectric accelerometer (Model Number ABRO
AB102-A, S/No AB1234) is used to measure the response of
the acceleration. The accelerometer is used to collect vibration
data generated by the cutting action of the work tool.
87
(4) An ICP (internal integrated circuit preamplifier) battery power
unit is fixed, not only to supply power for the accelerometer,
but also to amplify the voltage of the signal coming from the
accelerometer. In order to initiate a stronger signal, the battery
power supply is set to the sensor kit.
(5) A Handheld data recorder (COCO-80 Real Time FFT
Analyzer & Data Collector) is used for recording data,
analysis and feedback.
Figure 3.7
A schematic diagram of experimental setup for vibration
amplitude measurement
88
(6) An analog high-pass filter at 0.3 Hz @ (-3 dB) and 0.7 Hz @
(-0.1 dB) is constructed to filter unwanted high-frequency
signals and allow only low- frequency information to pass
through unattended (without a reduction in amplitude).
(7) An accelerometer picks up with magnetic base one is attached
to the spindle head (axial direction) to sense the vibration and
another one is attached to the work piece holder (feed
direction) to sense the vibration. The signal absorbed by the
accelerometer pick up is transferred to the FFT analyzer. The
FFT analyzer is interfaced with a computer for vibration
analysis in Engineering Data Management software (EDM).
3.2.3.2
Software set-up
The software set-up requires the following programs:
(1) In this experiment the NC program has been written to operate
the HAAS vertical machining center to perform the end
milling cutting process. The geometrical parameters (radial
rake angle, nose radius of cutting tool) and machining
parameters (cutting speed, cutting feed rate and axial depth of
cut) were reset in the CNC manually for each run according to
different cutting conditions.
(2) A statistical software QA Six Sigma DOE-PC IV
and
Minitap16 were applied to perform the basic statistical
analysis and analyze the relationship among the vibration,
geometrical parameters (radial rake angle, nose radius of
cutting tool) and machining parameters (cutting speed, cutting
feed rate and axial depth of cut).
89
The vibration amplitude is measured with twin-channel FFT
analyzer (COCO 80), shown in Figure3.7 he acceleration amplitude is
determined in the axial cutting direction in the spindle (channel I) and in the
feed direction of the workpiece holder (channel II). The data are acquired in the
FFT analyzers and are tabulated to obtain the mathematical model. Engineering
Data Management (EDM) software received the digital vibration data form
COCO-80 FFT Analyzer through the accelerometer. The data are acquired in the
FFT analyzers and are tabulated to obtain the mathematical model.
3.2.4
Experimental Set-up for Temperature rise Measurement
The temperature was measured by using K-type thermocouple.
A hole of 1 mm was drilled in the work piece specimen at 2.5 mm below the
machining surface. A K-type thermocouple was inserted into the hole and the
initial temperature was noted using the digital thermometer. During machining
maximum temperature was measured, the difference between the maximum and
initial temperature gave the temperature rise as shown in Figure 3.8.
Figure 3.8
A schematic diagram of experimental setup for temperature
measurement
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3.2.5
Experimental Set-up for Tool Wear Measurement
After milling operation, end mills being utilized are changed with
the new end mill. The milling process is interrupted for each experiment after
completion and then the value of the wear is measured. The tool wear was
measured using Metzer tool makers microscope on the flank surface of the end
mill cutter specimen as shown in the figure 3.9. The tool makers microscope
consists of 150mm X 150mm measuring stage, travel of 25mm and extendable
up to 50mm with slip gauges,
Gonimeter eyepieces 10X with scale, base
illumination (diascopic) 12V/20W (variable intensity) incident illumination
12V/20W (variable intensity), Magnification 30X with a field of view 12mm and
working distance 80 mm. The tool after milling is kept on the measuring stage
and with the help of vernier scale and cross wire the tool wear is measured on the
flank surface. The tool wear is measured off line with a tool maker’s
microscope for each combination of cutting conditions in accordance with the
ISO standards 8688. Figure 3.8. Shows experimental setup for the
measurement of tool wear. An average of three measurements was used as a
response value and is tabulated to obtain the mathematical model.
Figure3.9 A schematic diagram of experimental setup for tool wear
measurement
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3.3
STRATEGY OF EXPERIMENTATION
An experiment is a test or series of tests in which purposeful
changes are made to the input variables of a process or system, so that the
reason for changes can be observed and identified in the output response
variables. Experiments are used to study the performance of processes and
systems. The process or system can be visualized as a combination of
machines, men, methods and other resources that transforms some input into
an output that has one or more observable response. Some of the process
variables are controllable, whereas other variables are uncontrollable.
The objectives of conducting experiments are as follows
1.
Determining which variables are more influential on the
response
2.
Determining the limits of input variables which will give the
desired value of the response.
3.
Determining the limits of input variables where the effects of
uncontrollable variables are minimized.
The general approach to planning and conducting the experiment is
called the strategy of experimentation.
It is essential to design the experiments on a sound basis rather than
on the commonly employed trial and error method in conjunction with a small
number of repeat experiments for confirmation of the results. However, for
quality work and future predictions, trial and error methods are often little
better than the guess work. Apart from the trial and error method of
investigations, the commonly employed techniques by the researchers to
analyze the effect of End milling process parameters on machining responses
are: 1) Best-guess approach, 2) One-factor at-a-time approach, 3) Factorial
design and 4) Response Surface Methodology.
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Out of all these approaches RSM has been widely used by
researchers to investigate the effect of process parameters on responses.
Hence it is explained in detail.
3.3.1
Response Surface Methodology
Response surface methodology is a general approach for obtaining
the maximum value of a dependent (response) variable which depends upon
several independent (explanatory) variables. This technique combines the
Design of Experiments (DoE) and multiple regression. DoE is a general
approach for designing any information-gathering exercises where variation is
present. In machining-process modelling, DoE deals mainly with controlled
experiments, where variations in the independent variables are under the
control of the researcher.
Response Surface Methodology (RSM) is a collection of statistical
and mathematical methods that are useful for the modeling and optimization
of the engineering science problems. In this technique, the main objective is
to optimize the responses that are influenced by various input process
parameters. RSM also quantifies the relationship between the controllable
input parameters and the obtained responses. In modeling and optimization of
manufacturing processes using RSM, the sufficient data are collected through
design experimentation (Myers & Montgomery 1995).
RSMhas several advantages compared to the classical experimental
or optimization methods in which one variable at a time technique is used.
First, RSM offers a large amount of information from a small number of
experiments. Indeed, classical methods are time consuming and a large
number of experiments are needed to explain the behavior of a system.
Second, in RSM it is possible to observe the interaction effect of the
independent parameters on the response. The model equation easily clarifies
93
these effects for binary combination of the independent parameters. In
addition, the empirical model that relates the response to the independent
variables is used to obtain information about the process. With respect to
these, it may be said that RSM is a useful tool for the optimization of
manufacturing processes.
It is a collection of mathematical and statistical techniques that are
useful for the modeling and analysis of problems in which a response of
interest is influenced by several variables and the objective is to optimize this
response. Response surface designs are employed to investigate and predict
the following important conditions of a process
1.
The effect of a particular response by a given set of input
variables over some specified region of interest.
2.
The required values of variables are obtained to desirable or
acceptable level of a response.
3.
The required values of variables to achieve a minimum or
maximum response and the nature of response surface near
this minimal or maximal value (Sudhakaran 2012).
If an experiment is conducted to determine the two levels of ‘x 1’
and ‘x2’ that will maximize the yield ‘y’ of a process, then ‘y’ is a function of
the levels ‘x1’ and ‘x2’. This is shown in Equation (3.1)
Y
f ( X 1 , X 2 ) e (3.1)
Where‘e’ represents the noise or error observed in the response ‘Y’. If the
expected response is denoted by E(Y) = Y
f ( X 1 , X 2 ) = , then the surface is
represented as shown in Equation (3.2)
f ( X1, X 2 )
(3.2)
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In response surface methodology problem, the form of relationship
between the response and the independent variables are unknown. Thus the
first step in response surface methodology is to find a suitable approximation
for the true functional relationship between ‘y’ and a set of independent
variables. The function will be a first order model, if the response is a linear
function of the independent variables. This is given by Equation (3.3)
y b0 b1 X1 b2 X 2 .................... bi X i (3.3)
The response will be a second order model if there is a curvature in
the system. The second order model is given by Equation (3.4)
k
y
b0
k
bii X i 2
bi X i
i 1
i 1
bij X i e
(3.4)
i j
The eventual objective of RSM is a very efficient design for fitting
the second order model. Therefore it was decided to use RSM designs which
are well suited for engineering investigations.
3.4
CHOICE OF EXPERIMENTAL DESIGN
Experimental design is a critically important tool in designing and
analyzing an experiment. It is an approach which gives a clear idea in advance
of exactly what is to be studied, how the data are to be collected and a
qualitative understanding of how these data are to be analyzed. The various
steps involved in the design of experiments are as follows
1.
Identifying the important process control variables.
2.
Finding the upper limits and lower limits of the selected
control variables.
3.
Developing the design matrix
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3.4.1
Identification of the Process Variables
The machining variables selected for our investigation are radial
rake angle, nose radius of cutting tool, cutting speed, cutting feed rate and
axial depth of cut. These variables are identified to be the controllable
potential design factors that influence the machining performance such as
surface roughness, cutting force, acceleration amplitude, tool wear and
temperature rise during milling. It is important to choose the ranges over
which these machining variables will be varied, and the specific levels at
which the runs will be made.
3.4.2
Finding the Limits of the Process Variables
The working ranges of all the selected variables are to be found to
fix their levels and to develop the design matrix. The following methodology
was adopted to identify the ranges of process parameters.
The upper and lower limit of each process variable was estimated
initially through trial runs. For instance, trial runs for varying values of
cutting speed between 50 and 160m/min were conducted in order to identify
the lower limit and upper limit of cutting speed. During the trial runs, the
other variables were fixed at a constant value, i.e.
at 12 º, R at 0.8 mm, fzat
0.04 mm/tooth, and ap at 2.5 mm. Later the specimen was scrutinized on the
basis of surface roughness and the same factors form the basis for fixing the
levels. The lower and upper limits for surface roughness were fixed at 75 and
155m/min based on the trial runs and they were coded as (-2) and (+2).
Equation (3.5) (Montgomery2005, Montgomery & Peck 2005) is applied to
measure the other levels of the process variable. All other variables are
identified by applying the same procedure. After conducting trial runs the
range of these machining variables influencing the machining performance
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are found to be for radial rake angle angle 4 0 – 200, Nose radius 0.4mm to
1.2mm for cutting speed 75m/min – 115m/in, for feed rate 0.02 mm/rev –
0.06 mm/tooth and for axial depth of cut 1.5 mm – 3.5 mm.
X i=
2(2X-(X max +X min ))
(3.5)
(X max -X min )
where Xi is the required coded value of a variable X. X is any value of the
variable from Xmin to Xmax. The selected process parameters with their limits
and notations are given in Table 3.1. All machining variables at the
intermediate (0) level constitute the center points while the combination of
each variable at either its lower value ( 2) or its higher value (+2) with the
other two parameters at the intermediate level constitute the star points
(Montgomery2005).
The decided levels of the selected process parameters for the
experiments with their units and notations are given in Table 3.1 and
Table 3.2.
Table 3.1Factors and selected levels for end milling experiments
(5 factors and 5 levels)
Parameter
Units
Levels
Notation
0
-2
4
-1
8
0
12
1
16
2
20
Radial rake angle
Degree ( )
Nose radius
mm
R
0.4
0.6
0.8
1
1.2
Cutting speed
m/min
Vc
75
95
115
135
155
Cutting feed
mm/tooth
fz
0.02 0.03 0.04 0.05 0.06
ap
1.5
Axial depth of cut mm
2
2.5
3
3.5
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Table3.2 Factors and selected levels for finite element method
(3 factors and 5 levels)
Levels
Parameters
Notation
Units
Cutting speed
Vc
m/min
Cutting Feed
fz
mm/tooth
0.06
Depth of cut
ap
mm
0.5
3.4.3
-1.682 -1
0
1 1.682
100 130 160 190 220
0.07 0.08 0.09
1
1.5
2
0.10
2.5
Developing the Design Matrix
The general form of a quadratic polynomial which gives the
relation between response surface ‘y’ and the process variable ‘x’ under
investigation is given by Equation (3.6)
k
Y=bo +
k
bii xi 2 +
bi xi +
i=1
i=1
bij xi xi + i (3.6)
i<j
where b0 is the free term of a regression equation. The coefficient b1, b2, b3,
b4, and b5 are linear terms. The coefficients b11, b22, b33, b44, and b55 are
quadratic terms and the coefficient b12, b13, b14, b15, b23, b24, b25, b34, b35, and
b45 are interaction terms. The term “ ” represents the error term (Cochran &
Cox 1987).
DaviesBox & Hunter (1978) have developed new designs
specifically for fitting second order response surfaces called central composite
rotatable designs which are constructed by adding further treatment
combinations to those obtained from a 2k factorial. The total number of
observations was reduced significantly by employing these designs. Each
design consists of a two-level factorial matrix (2k) augmented by replicated
98
experiments at the center points and symmetrically located star points. For 2
to 4 factors, the central box was a full factorial design; for 5 or more factors it
becomes a half fractional design. The center point was replicated to provide a
measure of experimental error and hence in using second order rotatable
designs no replication was needed in order to find the mean square error.
Rotatable designs means that the standard error of the estimated response
surface at any point on the fitted surface was the same for all points that are at
the same distance from the center of the region.
There were many experimental designs available for conducting the
experiments. These include i) face centredCentral Composite Design (CCF)
ii) central composite rotatable design with circumscribed/inscribed subsets
(CCC/CCI) iii) Box and Hunter design (Montgomery & Peck 2005). In the
present work the experiments were designed based on a central composite
rotatable design with circumscribed subset having 32 and 20 experimental
runs. This design was chosen as it had the following advantages
1.
It is easy to locate the optimum point within the region of
interest as the location of optimum point is not known before
the experiment is conducted.
2.
The ‘ ’ value in rotatable design is higher than that of face
centered design. For example in the case of k = 3 designs, the
experiment ranges will be extended by 1.68 times the original
ranges defined by the experimenter. So it has extended design
region beyond the defined variable bounds. Thus predicted
responses at or near the axial points, which would have been
extrapolations in a face centered design, will be within the
design region in rotatable design. This is a very important
99
factor because the magnitude of prediction error increases
geometrically with distance outside the design region.
3.
Compared to face-centered CCDs, rotatable CCDs offer
reduced prediction error for, and improved estimation of,
quadratic curvature effects.
4.
In rotatable design, second order polynomial function is used
to estimate the response in terms of the machining process
parameter under investigation. The polynomial function is
used to estimate the response at a point on the fitted surface.
These polynomial surfaces have a great advantage as they are
easy to fit and the computation of response is easier.
5.
The circumscribed subset is chosen as inscribing restricts the
actual design region to the defined variable ranges by locating
the axial points at the lower and upper bounds of the variable
ranges. The inscribed design shrinks the design points such
that the axial points are at ±1 values whereas the
circumscribed design puts the design points equidistant from
the centre. Hence the estimated precision of model
coefficients is high in circumscribed design.
The CCD design for five factors with five levels consists of 32
experiments. The design is subdivided into three parts.
1.
One half replicates of a 25 factorial is represented by the first
16 design points which lie at the vertices of the regular
polyhedral. These points are commonly identified as factorial
design points.
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2.
The next 10 points (17-26) are the extra points which form a
central composite design with
as the radius of the sphere
where the point are equi-spaced from the center. These points
are termed as star points. For one half replicate, the extra point
is taken to devise a central composite design.
3.
The final six points (27-32) are included at the center in order
to provide roughly equal precision of standard error yu with
the sphere of radius
. These points are termed replicated
center points or axial points and have two functions. They
provide (n-1) degrees of freedom for determining the
experimental error, and they help to determine the precision of
standard error at and near the center. More degree of freedom
is offered by the replicated points at the center for calculating
the experimental error and they estimate the precision of
response at and near the center. The experimental errors
include noise factor, environmental factor and manual factor
during the measurements of values. The presence of curvature
in the system is reported by the center runs.
The selected design matrix for conducting experiments for surface
roughness, cutting force, vibration amplitude temperature rise, and tool wear
is shown in Table 3.3.
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Table 3.3 Design matrix for conducting experiments for CNC end milling
Specimen
No
01
02
03
04
05
06
07
08
09
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
Control Factors (Machining Parameters)
Radial
Nose
Axial
Cutting
Cutting
rake angle, radius ,
depth of
speed, Vc
feed, fz
R
cut,ap
-1
-1
-1
-1
1
1
-1
-1
-1
-1
-1
1
-1
-1
-1
1
1
-1
-1
1
-1
-1
1
-1
-1
1
-1
1
-1
1
-1
1
1
-1
1
1
1
1
-1
-1
-1
-1
-1
1
-1
1
-1
-1
1
1
-1
1
-1
1
1
1
1
-1
1
-1
-1
-1
1
1
1
1
-1
1
1
-1
-1
1
1
1
-1
1
1
1
1
1
-2
0
0
0
0
2
0
0
0
0
0
-2
0
0
0
0
2
0
0
0
0
0
-2
0
0
0
0
2
0
0
0
0
0
-2
0
0
0
0
2
0
0
0
0
0
-2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Central composite rotatable second order response surface
methodology was employed for determining the experimental run. The central
composite design consists of a 2k factorial run, 2k axial or star runs and center
102
runs. These experimental designs consist of 32 experiments consisting of five
machining variable with five specific levels. In this design matrix, thirty two
experimental runs provide 15 estimates for studying the effect of five
parameters on the responses. Out of the 15 estimates, 1 estimate is for the
main effect of all the five parameters, 5 estimates for the main effects of the
parameters, 6 quadratic estimates due to the main effects of the parameters
and 6 estimates for the two factor interactions. The 32 experimental runs
allowed the estimation of linear, quadratic and two way interactive effects of
the process variables on the surface roughness, cutting force, vibration
amplitude temperature rise, and tool wear for HSS end milling. Experiments
were conducted at random to avoid schematic errors creeping into the
experimental
procedure.The
selected
design
matrix
for
conducting
experiments for finite element method is shown in Table 3.4.
Table 3.4 Design matrix for conducting experiments for FEA
Test No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Control factors
Vc
fz
ap
-1
-1
-1
1
-1
-1
-1
1
-1
1
1
-1
-1
-1
1
1
-1
1
-1
1
1
1
1
1
-1.682
0
0
1.682
0
0
0
-1.682
0
0
1.682
0
0
0
-1.682
0
0
1.682
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
103
The 20 experimental runs allowed the estimation of linear,
quadratic and two way interactive effects of the process variables on response.
Experiments were conducted at random to avoid schematic errors creeping
into the experimental procedure.
3.5
SUMMARY
The responses studied in this research are divided into seven sets of
experiments, namely: experiments 1 to 5 for HSS end milling surface
roughness, cutting force, vibration anmplitude,temperature rise and tool wear
and experiments 6 and 7 for finite element analysis study. The CCD with
circumscribed subset was chosen as it has many advantages compared to
other designs. For experiments 1 to 5, five factor, five level CCD was
employed where as for experiments 6 and 7 three factors, five level CCD was
employed. The experimental setup consists of a HAAS vertical machining
center: model tool room mill
TM-1 for conducting experiments,
MitutoyoSurftest SJ201 for measuring average surface roughness, Syscon
instruments milling tool dynamometer for measuring cutting forces, COCO
80 FFT analyzer for measuring acceleration amplitude, Metzer tool makers
microscope to measure flank tool wear and K-type thermocouple to measure
the temperature rise during milling. A 2D and 3D thermo-mechanically
coupled finite element model of dry 2D and 3D machining operations has
been developed by using the commercial FEA software Deform-3D™.