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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

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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

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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.

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Figure 3.5 A schematic diagram of experimental setup for surface roughness measurement

3.2.2 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

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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 set-

up 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.

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(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

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(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).

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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

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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 ‘x1’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)

1 2( , )Y f X X e (3.1)

Where‘e’ represents the noise or error observed in the response ‘Y’. If the

expected response is denoted by E(Y) = 1 2( , )Y f X X = , then the surface is

represented as shown in Equation (3.2)

1 2( , )f X X (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)

0 1 1 2 2 .................... i iy b b X b X b X (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)

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1 1

k k

i i ii i ij ii i i j

y b b X b X b X e (3.4)

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 40 – 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.

max mini

max min

2(2X-(X +X ))X =(X -X )

(3.5)

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 NotationLevels

-2 -1 0 1 2Radial rake angle Degree ( 0 ) 4 8 12 16 20

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

Axial depth of cut mm ap 1.5 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)

Parameters Notation Units Levels

-1.682 -1 0 1 1.682Cutting speed Vc m/min 100 130 160 190 220

Cutting Feed fz mm/tooth 0.06 0.07 0.08 0.09 0.10

Depth of cut ap mm 0.5 1 1.5 2 2.5

3.4.3 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 k2

o i i ii i ij i i ii=1 i=1 i<j

Y=b + b x + b x + b x x + (3.6)

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

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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

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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

Control Factors (Machining Parameters) Radial

rake angle, Nose

radius , R

Cutting speed, Vc

Cutting feed, fz

Axial depth of

cut,ap01 -1 -1 -1 -1 102 1 -1 -1 -1 -103 -1 1 -1 -1 -104 1 1 -1 -1 105 -1 -1 1 -1 -106 1 -1 1 -1 107 -1 1 1 -1 108 1 1 1 -1 -109 -1 -1 -1 1 -110 1 -1 -1 1 111 -1 1 -1 1 112 1 1 -1 1 -113 -1 -1 1 1 114 1 -1 1 1 -115 -1 1 1 1 -116 1 1 1 1 117 -2 0 0 0 018 2 0 0 0 019 0 -2 0 0 020 0 2 0 0 021 0 0 -2 0 022 0 0 2 0 023 0 0 0 -2 024 0 0 0 2 025 0 0 0 0 -226 0 0 0 0 227 0 0 0 0 028 0 0 0 0 029 0 0 0 0 030 0 0 0 0 031 0 0 0 0 032 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

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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. Control factors Vc fz ap

1 -1 -1 -12 1 -1 -13 -1 1 -14 1 1 -15 -1 -1 16 1 -1 17 -1 1 18 1 1 19 -1.682 0 010 1.682 0 011 0 -1.682 012 0 1.682 013 0 0 -1.68214 0 0 1.68215 0 0 016 0 0 017 0 0 018 0 0 019 0 0 020 0 0 0

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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™.