pdf arghya

8/12/2019 PDF Arghya

1/75

TaguchiBased Optimization and Numerical Modelling

of Surface Roughness in CNC Turning Operation

Thesis submitted to

Dr Sudhir Chandra Sur Degree Engg College

F o r aw a r d o f t h e d e g r e e

Of

Master of Technology

Arghya Gupta

Roll Number: 25521912001

Registration Number: 122550410001 OF 2012-2013

Under the guidance of

Dr. Aditi Majumdar

DEPARTMENT OF MECHANICAL ENGINEERING

Dr Sudhir Chandra Sur Degree Engg CollegeMAY 2014


2/75

ii

Acknowledgement

I would like to express my deepest gratitude to my guide Dr. Aditi Majumdar for her

valuable advice, support, numerous interesting ideas, wisdom, encouragement and patience

throughout the period of thesis work, right from the inception of the problem to the

successful completion of this study. It is due to her experience and timely suggestions that

the work has taken its present shape. I feel proud and honoured to be a student of such

personality.

I wish to express my sincere appreciation to The Head, Department of Mechanical

Engg., Dr. Sudhir Chandra Sur Degree Engg. College for extending the infrastructural

facilities of the department.

I would like to take this opportunity to thank Prof. Rahul Bhattacharyya of the

Department of Mechanical Engineering for his valuable advices and suggestions. I also

sincerely acknowledge all other faculty members of the department for their technical

suggestions as well as friendly interactions. I am very much thankful to my Institute and

Department for providing me all necessary assistance in the form of research and guidance.

Lastly but certainly not the least, I extend my sincere gratitude to my parents, for

their patience. I couldnt accomplish my goal without their moral support and

encouragement. Above all I would like to thank the almighty for their continued blessings

that have helped me complete this work successfully.

Dr. Sudhir Chandra Sur Degree Engg. College

540, Dumdum Road.

Kol-700028 (ARGHYA GUPTA)


3/75

iii

CERTIFICATE

This is to certify that the project report entitled Taguchi Based Optimization and

Numerical Modelling of Surface Roughness in CNC Turning Operation submitted by

Arghya Gupta to Dr. Sudhir Chandra Sur Degree Engineering College (under JIS Group of

colleges), is a record of bona fide research work under our supervision and is worthy of

consideration for the award of the degree of Master of Technology of the Institute.

Dated:

Prof. Sujoy Saha Dr. Aditi Majumdar(Thesis Guide)

Head of Mech. Engg. Dept Asst. Prof. of Mech. Engg. Dept

DSCSDEC, Dumdum, Kolkata DSCSDEC, Dumdum, Kolkata

Dr. Salil Halder,

Prof and Head of the department

Department of Aerospace & Applied Mechanics,

Indian Institute of Engineering,Science & Technology, Shibpur


4/75

ABSTRACT

iv

In any machining process, it is most important to determine the optimal setting of machining

parameters in order to reduce the machining cost and also to achieve the desired product

quality. In this Thesis work, the effect of some input cutting parameters like cutting speed,

feed and depth of cut on materials removal rate (MRR) and average surface roughness have

been studied with Aluminium(LM6) as work material and single point cutting tool with

indexable Tungsten Carbide insert on CNC lathe. A solution of Balmerol Protocool SL

20% and Distilled Water 80% is used as a coolant. Optimisation of cutting parameters is done

by using Taguchi method and experiment set up is designed according to Taguchis

orthogonal array. In the first part of this work MRR is calculated theoretically for 16

observations and in the second part, experiments have been carried out with the values as

tabulated through Taguchis method for 16 observations to measure average surface

roughness by Talysurf. The results were analysed using Signal to Noise Ratio ( NS/

Ratio) and Main Effects Plot for NS/ Ratios to obtain optimal values for input cutting

parameters. This paper aims at determining empirical relationships both of linear type and

exponential type between average surface roughness ( ) and the different input cutting

parameters.

Keywords: Surface Roughness, Materials Removal Rate, Cutting Speed, Feed, Depth of Cut,

CNC Lathe, Taguchi Orthogonal Array, NS/ Ratio, Empirical Relationships.


5/75

v

CONTENTS

Title Page No.

Title Page i

Acknowledgement iiCertificate iii

Abstract iv

Content v

List of Tables vii

List of Figures

List of Symbols

viii

ix

1. INTRODUCTION

1.1 General introduction 1

1.2 Overview of Taguchi method 11.3 Properties and use of the workpiece material used (LM6) 2

1.4

1.5

1.6

Introduction to CNC lathe

1.4.1 CNC Lathe features

1.4.2 How CNC Lathe Works

1.4.3 CNC Part Programming Basics

1.4.4 CNC Part Programming Key Letters

1.4.5 Important G codes used

1.4.6 Important M codes used

Surface roughness tester (Talysurf)

1.5.1 Description of the parts of Talysurf

Objective

4

4

5

5

5

6

7

7

8

10

2. LITERATURE REVIEW

2.1 Literature review 11

2.2 Critical observations from Literature review 13

3.MATHEMATICAL FORMULATIONS

3.1 Optimisation method used 14

3.2

3.3

3.4

3.5

3.6

3.7

3.8

3.9

Taguchi experiment design versus traditional design of

experiments

Input cutting parameters used to design Taguchi orthogonal array

Flow chat of Taguchi method

Determining Parameter Design Orthogonal Array

Properties of an orthogonal array

Minimum number of experiments to be conducted

Application of Taguchi method to calculate S/N ratios for MRR

(Materials removal rate)Description of the instrument used to measure surface roughness

15

15

16

17

19

19

2021


6/75

vi

3.10

3.9.1 Features and benefits of Talysurf

Development of empirical relationship between surface roughness

(Ra) and cutting speed (v), depth of cut (d) and feed (f)

22

23

4. RESULTS AND DISCUSSIONS

4.1

4.2

4.3

4.4

4.5

4.6

4.7

4.8

4.9

4.10

4.11

4.12

4.13

4.14

Validation

4.1.1 Critical observation from validation of equations

Experimental design and set up

Selection of the levels of the input cutting parameters

Development of the orthogonal array

Materials removal rate (MRR) calculation and determination of

S/N ratiosSurface roughness measurement and determination of S/N ratios

Analysis of Signal to Noise ratio (S/N ratio) for MRR

Response surface plot for MRR

Analysis of S/N ratio for Surface Roughness

Response surface plots for surface roughness

Analysis of variance (ANOVA) for surface roughness

Determination of empirical relationships between and v, d and

f

4.12.1 Determination of Linear empirical model

4.12.2 Determination of Exponential empirical model

Verification

Calculation of percentage error

4.14.1 Critical observation from percentage error

calculation

24

26

29

34

35

3638

39

41

42

43

45

48

48

49

51

56

57

5. CONCLUSION

5.1 Introduction 61

5.2 Significant contributions 61

5.3 Future scope of work 62

REFERENCES 63


7/75

vii

List of Tables

Table

No. Description

Page

No.

3.1 Layout of orthogonal array 18

4.1Surface roughness values by different published empirical

equations26

4.1.1Percentage error between surface roughness experimental

values and surface roughness from Eq. 4.527

4.2 Selection of the levels of the input parameters 35

4.3 Taguchi orthogonal array ( ) 36

4.4Theoretical calculation for MRR and determination of S/N

ratios37

4.5Experimental results for surface roughness and

determination of S/N ratios38

4.6 Analysis of variance (ANOVA) for surface roughness 47

4.7

Comparative study between surface roughness experimental

values and surface roughness values from developed linear

models

52

4.8


values and surface roughness values from developedexponential models

53

4.9

Percentage error between Surface roughness experimental

values and Surface roughness values from developed linear

model 3 (Eq. 4.14)

56

4.10

Percentage error between Surface roughness experimental

values and Surface roughness values from developed

exponential model 1 (Eq. 4.16)

57


8/75

viii

List of Figures

Figure

No.Description

Page

No.

1.1 Important parts of CNC lathe 4

1.2 Parts of surface roughness tester-Talysurf 7

3.1 Taguchi Method flow chart 16

3.2 Diagram showing job zero 20

3.3 A portable surface roughness tester (Talysurf) 22

3.4 Job placed in a V-block (Front view) 22

3.5Typical set up for measurement of surface roughness with

Talysurf 23

4.1Surface roughness experimental values versus Surface roughness

values from Eq. 4.528

4.2 Experimental set up to measure surface roughness 29

4.2.1 Figure of chips from CNC during experiment (For obs. 1 to 4) 30




4.3 Main effects plot for S/N ratios for MRR. 40

4.4 Response Surface Plot (MRR vs. d vs. f) 41

4.5 Main effects plot for S/N ratios for surface roughness (Ra) 42

4.6 Response surface plot 1 (Ra vs. f vs. v) 44

4.7 Response surface plot 2 (Ra vs. d vs. v) 44

4.8 Response surface plot 3 (Ra vs. d vs. f) 45

4.9Comparative study between experimental values and developed

linear model values. 54

4.10


values and surface roughness values by developed exponential

models.55

4.11 Comparative study between Surface roughness experimentalvalues and Surface roughness values from developed linear model

3 (Eq. 4.14).

58

4.12

Comparative study between Surface roughness experimental

values and Surface roughness values from developed exponential

model 1 (Eq. 4.16).

59

4.13Surface roughness experimental values versus Surface roughness

values from developed linear model 3 (Eq. 4.14).60


9/75

ix

List of Symbols

Most of the symbols are defined as they occur in the thesis. Some of the most common

symbols, which are used repeatedly, listed below:

Average Surface Roughness (m)

f Feed Rate (mm/Rev)

v Cutting Speed (m/min)

d Depth of Cut (mm)

R Nose Radius (mm)

Flank Wear (mm)

N Spindle Speed (RPM )

D Diameter of Workpiece (mm or m)

NS/ Signal to Noise Ratio (dB)

MRR Materials Removal Rate (g/s or mm/s)

Total sum of squared deviations

The mean ratio for experiment

Sum of squared deviations of parameters

The sum of the S/N Ratio involving parameter p and level j

Sum of squared deviation of error

Sum of squared deviation of Spindle Speed

Sum of squared deviation of Depth of Cut

Sum of squared deviation of Feed Rate


10/75

CHAPTER 1

INTRODUCTION

1.1 General introduction:

One of the challenges faced by the engineers in manufacturing sector is to achieve desired

surface quality on machined surface. Within the prescribed limitations on machine tools, cost

in machining and machining time allowed desired quality of finished product is seldom

achieved. Efforts have been given to achieve better surface finish on machined surface. There

are certain factors like work piece material, cutting tool material, cutting tool design,

machining parameters such as cutting speed, feed, depth of cut, nose radius of cutting tool,

flank wear etc, govern the surface roughness of any machined component. Significant

influence of surface roughness is realised on solid bodies particularly at their contact region

due to contact stresses, wear and friction and lubrication conditions. Surface roughness is

found to be a key design feature in many applications such as fasteners, aesthetics parts,

precision fits and parts which are subjected to fatigue loads.

1.2 Overview of Taguchi method:

Quality of finished products is the highest priority in any manufacturing industry. This

process will include selection of a design of experiments that make sense for the company

and its processes. There are various ways of seeking optimization of a process. A Taguchi

Parameter Design Experiment (PDE) [24] is a method that is well studied to address one or

more response parameters with goal of reducing variance in a system. A PDE makes use of

orthogonal arrays that allow for efficient experimentation, and signal to noise ratio (S/N ratio)

that utilize both mean and variance in selecting optimal input cutting parameters.

Basically, classical parameter design, developed by R.A.Fisher [25], is complex and not easy

to use. Especially, a large number of experiments have to be carried out when the number of

the process parameters increases. To solve this task, the Taguchi method uses a special design

of orthogonal arrays to study the entire parameter space with a small number of experiments

only. A loss function is then defined to calculate the deviation between the experimental


11/75

Chapter 1

2

value and the desired value. Taguchi recommends the use of the loss function to measure the

performance characteristic deviating from the desired value. The value of the loss function is

further transformed into a signal-to-noise (S/N) ratio. The S/N ratio for each level of process

parameters is computed based on the S/N analysis. Regardless of the category of the

performance characteristic, the larger S/N ratio corresponds to the better performance

characteristic. Therefore, the optimal level of the process parameters is the level with the

highest S/N ratio. Furthermore, a statistical analysis of variance (ANOVA) is performed to

see which process parameters are statistically significant. In this present work with the help

of S/N ratio and ANOVA analyses, the optimal combination of the process parameters can be

predicted. Smaller the better approach is applied as smaller value of surface roughness is

desirable.

G.Taguchi [19], whose background was communication and electronic engineering,

introduced this same concept into the design of experiments. Two of the applications in

which the concept of S/N ratio is useful, are the improvement of quality through variability

reduction and the improvement of measurement. The S/N ratio transforms several repetitions

into one value which reflects the amount of variation present and the mean response. There

are several S/N ratios available depending on the type of characteristic continuous or discrete;

i) nominal-is-best, ii) smaller-the-better, or iii) larger-the-better. Taguchi recommends usingthe common logarithm of this S/N ratio multiplied by 10, which expresses the ratio in

decibels (dB); which has been used in communications for many years. Thus, for the cases of

continuous and larger the better characteristic, a fixed value is always desired. In the larger-

the-better type of measurement, the larger magnitude of evaluation will be preferred over

smaller ones. Theoretically, there is no upper limit on the results, but in practice, some upper

limit is required for numerical correctness. To achieve consistency, the average performance

can be considered as the target value.

1.3 Properties and use of the workpiece material used (LM6):

In this present study Aluminium (LM6) is used as workpiece material. LM6 exhibits

excellent resistance to corrosion under both ordinary atmospheric and marine conditions. For

the severest conditions this property can be further enhanced by anodic treatment. LM6 can

be anodised by any of the common processes, the resulting protective film ranging in colour

from grey to dark brown. Ductility can be improved slightly by heating at 250-300C, but

apart from stress relieving, the heat treatment of LM6 is of little industrial interest. Suitable


12/75

Introduction

3

for Marine 'on deck' castings, water-cooled manifolds and jackets, motor car and road

transport fittings; thin section and intricate castings such as housing, meter cases and

switchboxes; for very large castings, e.g cast doors and panels where ease of casting is

essential; for chemical and dye industry castings, e.g pump parts; for paint industry and food

and domestic castings. The general use where marine atmospheres or service conditions

make corrosion resistance a matter of major importance. Especially suitable for castings that

are to be welded. The ductility of LM6 alloy enable castings easily to be rectified or even

modified in shape, e.g simple components may be cast straight and later bent to the required

contour. Properties of LM6 is as follows,

LM6 (Aluminium Casting Alloy)

(AlSil2)

This alloy conforms to British Standards 1490 LM6

PERCENTAGE CHEMICAL COMPOSITION

Name Percentage composition

Copper . 0.1 Max.

Magnesium 0.1 Max.

Silicon 10.0-13.0 Max.

Iron 0.6 Max.

Manganese 0.5 Max.

Nickel 0.1 Max.

Zinc 0.1 Max.

Lead 0.1 Max.

Tin 0.05 Max.

Titanium 0.2 Max.

Aluminium Remainder


13/75

Chapter 1

4

1.4 Introduction to CNC lathe:

Figure 1.1: Important parts of CNC lathe.

Fig.1.1 shows important parts of a CNC Lathe. 3 jaw self centering chuck is used to hold theworkpiece. A single point cutting tool with indexable Tungsten Carbide insert is used to cut

the workpiece. Dead centre is used to support the workpiece. But when the length of the job

is short no support is required.

1.4.1 CNC Lathe features:

1. Automated version of a manual lathe.

2. Programmed to change tools automatically.

3. Used for turning and boring wood, metal and plastic.

4. Larger machines have a machine control unit (MCU) which manages operations.

5. Movement is controlled by a motor.

6. Feedback is provided by sensors.

7. Tool magazines are used to change tools automatically.


14/75

Introduction

5

1.4.2 How CNC Lathe Works:

Controlled by G and M codes.

These are number values and co-ordinates.

Each number or code is assigned to a particular operation.

Typed in manually to CAD/CAM by machine operators.

G&M codes are automatically generated by the computer software.

1.4.3 CNC Part Programming Basics:

CNC instructions are called part program commands.

When running, a part program is interpreted one command line at a time until all lines

are completed.

Commands, which are also referred to as blocks, are made up of words which each

begin with a letter address and end with a numerical value.

1.4.4 CNC Part Programming Key Letters:

O -Program number (Used for program identification)

N -Sequence number (Used for line identification)

G -Preparatory function

X -X axis designation

Y -Y axis designation

Z -Z axis designation

R -Radius designation

FFeed rate designation

S -Spindle speed designation

H -Tool length offset designation

D -Tool radius offset designation


15/75

Chapter 1

6

T -Tool Designation

M -Miscellaneous function

1.4.5 Important G codes used:

G00 Rapid Transverse

G01 Linear Interpolation

G02 Circular Interpolation, CW

G03 Circular Interpolation, CCW

G17 XY Plane,

G18 XZ Plane,

G19 YZ Plane

G21/G71 Metric Units

G40 Cutter compensation cancel

G41 Cutter compensation left

G42 Cutter compensation right

G43 Tool length compensation (plus)

G44 Tool length compensation (minus)

G49 Tool length compensation cancel

G80 Cancel canned cycles

G90 Absolute positioning

G91 Incremental positioning


16/75

Introduction

7

1.4.6 Important M codes used:

M00 Program stop

M01 Optional program stop

M02 Program end

M03 Spindle on clockwise

M04 Spindle on counter clockwise

M05 Spindle stop

M06 Tool change

M08 Coolant on

M09 Coolant off

M30 Program stop, reset to start

1.5 Surface roughness tester (Talysurf):

Figure 1.2: Parts of surface roughness tester-Talysurf

1

23

4

5 6

7

8

9

Movement of the

stylus

10 11

13

Display unit

Drive unit

12


17/75

Chapter 1

8

Talysurf- surface roughness tester is used to measure the surface finish in m. There are two

units of Talysurf, one is drive unit and another one is display unit as shown in Fig. 1.2.

These two units are connected with a wire. The units can be driven with both AC power

supply and battery. Instrument calibration is required before measuring any surface. Stylus is

kept at the same level of the surface to be measured. Both vertical and transverse movement

of the stylus is possible to measure the surface finish. Some specifications of Talysurf is

given below;

1.5.1 Description of the parts of Talysurf:

1) Large color monitor: Displays measurement results and setting conditions.

2) POWER/DATA : Power on key. Outputs data, prints data and saves data to the memory

card.

3) START/STOP : Starts and stops the measurement.

4) PAGE : Displays the measurement results for other parameters and evaluation profiles.

5,6) Blue, Red : Performs the function displays on each screen.

7) Cursor keys : Performs functions on the screen.

8) Esc/Guide : Escape key, guide key. Also power off on long press.

9) Enter/Menu : Enter key, Menu key.

10) Detector : Detects the signal generated by the stylus.

11) Extension rod : Connects detector to the drive.

12) Diamond stylus : Measures the roughness of the surface.

13) Drive : Connected to the display unit through a wire.

Detector

Detection methodDifferential inductance method.

Measurement range360 m (-200 m to +160 m)


18/75


19/75

Chapter 1

10

1.6 Objective:

The objective of this present work is to develop efficient linear and exponential empirical

equations of average Surface Roughness ( ) based on some input cutting parameters like

Cutting Speed ( v in m/min), Depth of Cut ( d in mm) and Feed ( f in mm/rev). The

developed equations are intended to validate with the experimental results to find out the

accurate model. Also Taguchi method is used to find out the optimal cutting parameters.

Analysis of Variance (ANOVA) is also done to determine the Fisher Ratio and

Percentage Contribution of the input cutting parameters (Cutting Speed, Depth of cut and

Feed).


20/75

CHAPTER 2

LITERATURE REVIEW

2.1 Literature review:

Gupta[1] et al. have presented the application of Taguchi method with logical fuzzy

reasoning for multiple output optimisation. The machining parameters were optimised with

considerations of the multiple performance measures. They have also fuzzified ANOVA toevaluate contribution of each factor through a single comprehensive output measure (COM).

Ahilan et al.[2] have developed neural network models for prediction of machining

parameters in CNC turning. Results from experiments, based on Taguchis Design of

Experiments (DOE) were used to develop neuro based hybrid models. ANOVA have been

used to decide influence of process parameters hence minimum power consumption and

maximum productivity can be achieved.

Risbood et al.[3] have used neural network to predict surface finish by taking the acceleration

of radial vibration of tool holder as a feed back. Neural network prediction models had

separately been developed for turning of a slender work piece. They have predicted

dimensional deviation by taking radial component of cutting force and acceleration of radial

vibration.

Benardros et al.[4] have presented various methodology and approaches based on machining

theory , experimental investigation, designed experiments and artificial intelligence with theirdrawbacks to avoid any re-processing of the machined work piece.

Karayel[5] had developed a feed forward multi layered neural network, using the scaled

conjugate gradient algorithm (SCGA) for the prediction and control of surface roughness in a

CNC lathe. The results of the neural network approach were compared with actual values.

Abburi et al.[6] have converted knowledge based neural networks into IF- THEN rules with

the help of fuzzy set theory. Boolean operations were used to reduce the TF-THEN rules, for


21/75

Literature review

12

prediction of surface roughness for given process variables as well as for the prediction of

process variables for a given surface roughness.

Nalbant et al.[7] have executed experimental studies on artificial neural networks (ANN). In

the input layer of the ANNs, the cutting tools, feed rate and cutting speed values were used

while at the output layer the surface roughness values were used. They have compared the

ANN predictions and the experimental values by statistical error analysing methods.

Kwon et al.[8] have used a fuzzy adaptive modelling technique, which adapts the

membership functions in accordance with the magnitude of the process variations, to predict

surface roughness.

Krishankant et al.[9] have designed Taguchi orthogonal array with three levels of turning

parameters with the help of MINITAB 15. They have measured initial and final weight of

workpiece (EN24) and also the machining tome to calculate MRR in two sets of experiment

(i.e. first run and second run). S/N ratio was calculated for the larger the better and hence

optimal levels of the machining parameters (speed, feed, depth of cut) were obtained.

Simpson et al. [10] have performed an experiment to determine a method to assemble an

electrometric connector to a nylon tube while delivering the requisite pull off performance

suitable for an automotive engineering application. The pull off force was maximised while

assembly effect was minimised and hence cost is reduced with the help of Taguchis method.

Both the and arrays were develop for noise factors and controllable factors

respectively. They have used Taguchis graphical approach to plot the marginal means of

each level of each factor and pick the winner to determine the best setting for each control

factor.

Quazi et al.[11] have employed orthogonal arrays of Taguchi, S/N ratio, the analysis of

variance (ANOVA) to analyse the effect of the turning parameters.

Lazarevic et al.[12] have analysed different cutting parameters on average surface roughness

on the basis of the standard Taguchi orthogonal array with the help of MINITAB. The

optimal cutting parameter settings were determined based on analysis of means (ANOM) and

analysis of variance (ANOVA).


22/75

Chapter 2

13

Vipindas et al.[13] have performed their experiments on Al 6061 material based on Taguchi

orthogonal array. They have observed that feed is the significant factor at 95% confidence

level.

Durai et al.[14] have taken three levels of process parameters to optimised the minimum

energy consumption with the help of Taguchis orthogonal array. They have shown that,

as material removal rate increases power demand increases and energy consumption

decreases.

Nanbant et al. [15] optimised three cutting parameters namely insert radius, feed rate and

depth of cut with consideration of surface roughness. They have employed the Orthogonal

array, the S/N ratio and ANOVA to study the performance characteristics in turning

operations of AISI 1030 steel bars using TiN coated tools.

Asilturk et al. [16] have used AISI 304 austenitc stainless steel workpiece and carbide coated

tool under dry condition to study the influence of cutting speed, feed and depth of cut on

surface roughness (Ra and Rz). The adequacy of the developed model is proved by ANOVA

and response surface 3D pots.

2.2 Critical observations from Literature review:

The empirical equations which were mostly used in most of the cases that is not very

close to the experimental results.

There are various optimization methods like single variable optimization algorithms,

multi variable optimization algorithms, constrained optimization algorithms,specialized optimization algorithms, non-traditional optimization algorithms used for

parametric study. But Taguchi method gives satisfactorily result than others.

Very few literatures are available in case of parametric study.


23/75

CHAPTER 3

MATHEMATICAL FORMULATION

3.1 Optimisation method used:

The traditional way of conducting the Taguchi method of design of experiments is to set the

level combinations of various influencing factors and conduct the real time experiment and

study the results.

The Taguchi method can be used for obtaining near optimal solution to the analytical

engineering problems. Instead of using the standard mathematical optimization procedure

with all the design variables, one can conduct the experiments based on the Taguchi method

and eliminate the insignificant design variable which does not contribute much to the

objective function. After eliminating the insignificant variables, the standard mathematical

optimization procedure could be used. The initial / starting value of the standard optimization

problem is the near optimum level values obtained based on the Taguchi method of design of

experiments. This results in significant saving of computational time.

Dr. Genichi Taguchi [24] found out empirically that NS/ ratios give the optimal

combination of the input parameters, where the variance is minimum, while keeping the

mean close to the target value. For this purpose, the experimental values should be

transformed into the NS/ ratios. Optimal levels based upon the specific NS/ ratio formula,

are of three types:

3.1.1. Smaller the better: For creating the lowest possible response value.

/ = -10 log ( ) ------------------------- (3.1)

3.1.2. Nominal the best: For targeting a nominal specified value.

/ = 10 log (

) ------------------------- (3.2)

3.1.3. Larger the better: For creating the highest possible response value.

/ = -10 log ( ) -------------------------- (3.3)


24/75

Mathematical Formulation

15

Where, is the average of observed data, is the variance of y, n is the number of

measurements (here value of n is 1 as only one response value will be converted into S/N

ratio) and is the observed data for parameter.

3.2 Taguchi experiment design versus traditional design of experiments:

1. Only the main effects and two factor interactions are considered. Higher order interactions

are assumed to be nonexistent.

2. Experiments are asked to identify which interactions might be significant before

conducting the experiment, through their knowledge of subject matter.

3. Taguchis orthogonal arrays are not randomly generated; they are based on judgement

sampling.

4. Traditional DOEs treat noise as nuisance (blocking), but Taguchi makes it the focal point

of his analysis.

3.3 Input cutting parameters used to design Taguchi orthogonal array:

In this present thesis work the following three input cutting parameters are used to design

Taguchi orthogonal array;

1. Cutting speed: In this present study Aluminium is used as work material and tool is single

point cutting tool with indexable Tungsten Carbide insert. Standard cutting speed with the

combination of cutting tool and work material as stated above is 75 to 105 m/min [26]. The

Cutting Speed in m/min can be converted into Spindle Speed in RPM by the formula

NDv .. where v in m/min, D is work piece diameter in m and N is in RPM.

2. Feed (mm/revolution): This is the advancement of the cutting tool along the spindle axis

in mm, per revolution of the chuck or the spindle of the CNC Lathe.

3. Depth of cut (mm): It is the depth of the material cut by the cutting tool in each pass.


25/75

Chapter 3

16

3.4 Flow chat of Taguchi method:

Selection of input parameters

Levels of input parameters

Taguchi method is an efficient design and experimental technique, which uses a special

orthogonal array to examine the quality characteristics through a minimum number of

experiments. The experimental results based on orthogonal array have been transformed into

NS/ Ratios to evaluate the performance characteristics. The optimal parameters are then

S/N ratio calculation

Analysis of variance

Response surface plot

Orthogonal array

Perform ex eriment

START

Problem formulation

Experimental set up

Analysis of results

Verified

END

Ob ective function

Selection of input parameters

Levels of input parameters

NO

YES

Figure 3.1: Taguchi Method flow chart


26/75


17

determined by performing the parameter design. Analysis of variance (ANOVA ) has been

done to determine the Fisher ratio and Percentage Contribution of each factor. Response

plot shows exactly how the output varies with the changes in the input parameters. The flow

chart of the Taguchi method is illustrated in Fig.3.1. Taguchi method can also be described

by the following three phases;

I) Planning phase

1. Taking the problem.

2. Determination of the objective of the experiment.

3. Selection of the quality characteristics.

4. Selection of the input parameters that may influence quality characteristics the most.

5. Choosing levels for the input parameters.

6. Developing the Taguchi orthogonal array.

II) Execution phase

1. Conducting the experiments as described by orthogonal array.

2. Conversion of the output results into Signal to Noise (S/N) ratios.

III) Analysis phase

1. Analysing the experimental results using analysis of variance (ANOVA).

2. Verification of the results by response surface plot.

3.5 Determining Parameter Design Orthogonal Array:

The effect of many different parameters on the performance characteristic in a condensed set

of experiments can be examined by using the orthogonal array experimental design proposed

by Dr.G.Taguchi [19]. Once the parameters affecting a process that can be controlled have

been determined, the levels at which these parameters should be varied must be determined.

Determining what levels of a variable to test requires an in-depth understanding of the

process, including the minimum, maximum, and current value of the parameters. If the

difference between the minimum and maximum value of a parameter is large, the values

being tested can be further apart or more values can be tested. If the range of a parameter is

small, then fewer values can be tested or the values tested can be closer together. For

example, if the temperature of a reactor jacket can be varied between 20C and 80C and it is


27/75

Chapter 3

18

known that the current operating jacket temperature is 50C, three levels might be chosen at

20, 50, and 80 C. Also, the cost of conducting experiments must be considered when

determining the number of levels of a parameter to include in the experimental design. In the

previous example of jacket temperature, it would be cost prohibitive to do 60 levels at 1

degree intervals. Typically, the number of levels for all parameters in the experimental design

is chosen to be the same to aid in the selection of the proper orthogonal array.

Once the number of input parameters and the number of levels are known, the proper

orthogonal array can be selected. In this present study the numbers of input parameters are 3

(Cutting speed, depth of cut and feed rate) and the numbers of levels are 4. Table 3.1 shows a

standard orthogonal array. There are totally 16 experiments to be conducted and each

experiment is based on the combination of level values as shown in the table. For example,

the third experiment is conducted by keeping the independent design variable 1 at level 1,

variable 2 at level 3 and variable 3 at level 3.

Table 3.1: Layout of orthogonal array

Experiment no. Independent Variables

Variable 1 Variable 2 Variable 3

1 1 1 1

2 1 2 2

3 1 3 3

4 1 4 4

5 2 1 2

6 2 2 1

7 2 3 4

8 2 4 3

9 3 1 3

10 3 2 4

11 3 3 1

12 3 4 2

13 4 1 4

14 4 2 3

15 4 3 2

16 4 4 1


28/75


19

3.6 Properties of an orthogonal array:

The orthogonal array has the following special properties that reduce the number of

experiments to be conducted.

1. The vertical column under each independent variables of the above table has a special

combination of level settings. All the level settings appear an equal number of times. For

array under variable 3, level 1, level 2, level 3 and level 4 appears 4 times. This is

called the balancing property of orthogonal arrays.

2. All the level values of independent variables are used for conducting the experiments.

3. The sequence of level values for conducting the experiments shall not be changed. This

means one can not conduct experiment 1 with variable 1, level 2 setup and experiment 4

with variable 1 , level 1 setup. The reason for this is that the arrays of each factor columns

are mutually orthogonal to any other column of level values. The inner product of vectors

corresponding to weights is zero.

3.7 Minimum number of experiments to be conducted :

The design of experiments using the orthogonal array is, in most cases, efficient when

compared to many other statistical designs. The minimum number of experiments that are

required to conduct the Taguchi method can be calculated based on the degrees of freedom

approach.

= 1 + ( 1) ------------------------ (3.4)

For example, in case of 8 independent variables study having 1 independent variable with 2

levels and remaining 7 independent variables with 3 levels ( orthogonal array), the

minimum number of experiments required based on the above equation is 16. Because of the

balancing property of the orthogonal arrays, the total number of experiments shall be multiple

of 2 and 3. Hence the number of experiments for the above case is 18.


29/75

Chapter 3

20

3.8 Application of Taguchi method to calculate S/N ratios for MRR

(Materials removal rate):

Orthogonal array has been developed by using Taguchi method. Based on this orthogonal

array, MRR values have been calculated. MRRcan be defined as, volume or weight of the

material removed per unit time during machining operation. As higher value for MRR is

desirable so Larger the better formula (Eq. 3.3) can be used to determine the optimal level.

Experimentally, MRR can be calculated as follows,

MRR =( )

g/s ---------------------- (3.5)

The job has been taken out from the chuck to measure the weight after machining (i.e., final

weight). It is required to set the job zero after the job is reloaded in the Lathe chuck. Some

changes in CNC part programming is required every time the job is unloaded from the chuck.

So if possible, weight of the chip for each run can be measured without unloading the job

from the chuck. Hence MRR becomes,

MRR = g/s --------------------- (3.6)

Figure 3.2: Diagram showingjob zero

Theoretically Materials removal rate can be calculated by the formula given below,

fdvMRR .. -------------------------------- (3.7)

Where, v= cutting speed in mm/min; d= depth of cut in mm; f=feed rate in mm/rev.

Eq. 3.7 gives the volume of materials removed per unit time. This volume of materials

removed per unit time can be converted into mass of materials removed per unit time. The


30/75


21

work material used in this present thesis work is Aluminium (LM6). Density of Al is 2.8

g/cm (.

g/mm). Density can be defined as mass per unit volume.

Density () =

( )

( ) --------------------------------- (3.8)

The volume (V) in the Eq. 4.10 is the materials removal rate (MRR) in mm/min. Let us take

an example where,

Cutting speed ( v ) = 75 m/min (75000 mm/min),

Depth of cut ( d ) = 0.8 mm and

Feed rate ( f ) = 0.15 mm/rev.

Therefore, MRR = 75000 x 0.8 x 0.15 = 9000 mm/min.

Now, from Eq. 3.8,

Mass (m ) of materials removed = Density () x MRR ----------------------------- (3.9)

Then, m =.

x g/ sec. = 0.42 g/sec.

3.9 Description of the instrument used to measure surface roughness:

Surface roughness (Ra ) is a determination of surface finish. A lower surface roughness value

indicates better surface finish. So for optimization of surface roughness smaller the better

formula (Eq. 3.1) is used.

A Talysurf is a type contact profilometer where a diamond stylus is moved vertically in

contact with a sample and then moved laterally across the sample for a specified distance and

specified contact force. It can measure small surface variations in vertical stylus displacement

as a function of position. With the help of Talysurf small vertical features ranging in height

from 10 nanometres to 1 millimetre can be measured. The height position of the diamond

stylus generates an analog signal which is converted into a digital signal stored, analyzed and

displayed. The radius of diamond stylus ranges from 20 nanometres to 50 m, and the


31/75

Chapter 3

22

horizontal resolution is controlled by the scan speed and data signal sampling rate. The stylus

tracking force can range from less than 1 to 50 milligrams.

For surface roughness measurement the job is taken out from lathe chuck and placed in a V-

block. The diamond stylus of the Talysurf is kept in the same plane as the surface to be

measured. Then the stylus is allowed to move horizontally. The LCD shows the value of

surface roughness ( ).

3.9.1 Features and benefi ts of Talysur f:

1. 1mm vertical range and 16 nm resolution: It allows both form (contour) measurement and

surface finish measurement.

2.50 mm horizontal traverse: Ideal for majority of shop floor applications.

3. 0.4 um / 50 mm straightness error: The high accuracy traverse datum makes possible

skidless measurement of waviness, form and contour even on large components.

4. 0.5 um horizontal data spacing: Small components can be measured more effectively.

Figure 3.3: A portable surface roughness tester (Talysurf)


32/75


23

Figure 3.4: Job placed in a V-block (Front view)

Stylus Movement of the stylus

Figure 3.5: Typical set up for measurement of surface roughness with

Talysurf.

3.10 Development of empirical relationship between surface roughness ( )

and cutting speed (v), depth of cut (d) and feed (f):-

. The following two models are used to develop the relationship between surface roughness

( ) and cutting speed ( v ), depth of cut (d ) and feed tare ( f ),

A linear empirical model of following type (by Ahilan et al. [2])

= + fcdbva ... ------------------------ (3.10)

V-Block

Drive unit

Display unit

Support

Cylindrical job


33/75

Chapter 3

24

An exponential model of following type as developed by Fang et al.[17]

=X ----------------------- (3.11)

Where A, X, a, b, c are constants.


34/75

CHAPTER 4

RESULT AND DISCUSSION

4.1 Validation:

As discussed earlier, surface roughness is a measure of the technological quality of a product.

Surface finish determination is a necessary step in modern manufacturing industry. Efforts

have been given to determine relationship between surface roughness and input cutting

parameters since 1990s. Empirical relationships were established by various authors. Here in

this work, validation of the empirical relationships is done to determine their accuracy in

reference to our experiment for Aluminium (LM6) with Carbide tip High speed steel (HSS)

cutting tool.

4.1.1 A theoretical arithmetical expression was proposed by Whitehouse (1994) [21] as

follows,

= 0.032 ----------------------------- (4.1)

(f is the feed in mm/rev and R is the nose radius in mm)

4.1.2 The empirical equation developed by Bhattiprolu (1993) [22] has the form,

= -108 + (30.2X f) + (0.568 X ) , ------------------------------- (4.2)

Where f is the feed rate (in/rev) x 1000 and is the flank wear (0 to 0.0065 in) x 10000.

4.1.3 Another empirical equation as proposed by Sarikaya et al.(2013) [23] is as follows,

= ------------------------------ (4.3)

(f is the feed in mm/rev and R is the nose radius in mm)

4.1.4 The following empirical equation for surface roughness in turning was proposed by

Hongxiang et al., 2002[18] with diamond cutting tool and Aluminium alloy workpiece,


35/75

Result and discussion

25

= 13.636 . . . . ------------------------------- (4.4)

Where, = cutting speed; f= Feed; = Depth of cut.

4.1.5An empirical form was developed by Asilurk et al.(2012) [16] for AISI 304 austenitic

stainless steel machined by coated carbide insert under dry conditions as follows,

= - 0.2907 - 0.89v + 12.0593f - 1.4263a -0.00006 + 13.111 + 0.582222 +

0.348889vf + 0.0040333va - 2.06667fa. ------------------------------- (4.5)

Where, v = cutting speed (m/min); f= Feed (mm/rev); a= Depth of cut (mm).

4.1.6 A quadratic model as proposed by Ahilan et al. (2013) [2],

Surface roughness = 9.80674 (0.07608X1) (52.8926X2) (9.17185X3) +

(0.33241X4)+(0.96X1)+(198.00X2+9.18519X3)(0.10417X4)+(0.05404X1X2)

+(0.01849X1X3)(0.00002X1X4)+(5.45185X2X3)(0.13333X2X4)+(0.0037X3

X4) -----------------------------(4.6)

Where, X1 is cutting speed (m/min), X2 is feed rate (mm), X3 is depth of cut (mm) and X4 is

nose radius (mm).


36/75

Chapter 4

26

Table 4.1 Surface roughness values by different published empirical equations

Sl.

No.

Spindle

Speed

(m/min)

Depth

of cut

(mm)

Feed

(mm/rev)

Surface

Roughness

values as

measured

under this

experiment

(m)

Ra values calculated from various published

Empirical Equations

Eq. 4.1

(m)

Eq.

4.2

(m)

Eq.

4.3

(m)

Eq.

4.4

(m)

Eq.

4.5

(m)

Eq.

4.6

(m)

1 75 0.5 0.1 0.294 0.8 1.048 0.781 2.230 0.6593 1.205

2 75 0.8 0.15 0.578 1.8 1.033 1.757 2.697 0.6868 1.740

3 75 0.9 0.2 0.797 3.2 1.018 3.125 3.111 0.8982 1.256

4 75 1.1 0.25 0.744 5.0 1.003 4.882 3.461 0.7296 1.110

5 76 0.5 0.15 0.695 1.8 1.033 1.757 2.738 0.6779 1.025

6 76 0.8 0.1 0.286 0.8 1.048 0.781 2.185 0.6958 1.483

7 76 0.9 0.25 0.649 5.0 1.003 4.882 3.478 0.9860 1.825

8 76 1.1 0.2 0.689 3.2 1.018 3.125 3.079 0.7956 1.786

9 77 0.5 0.2 0.759 3.2 1.018 3.125 3.162 0.7598 1.265

10 77 0.8 0.25 0.71 5.0 1.003 4.882 3.481 0.6235 1.943

11 77 0.9 0.1 0.413 0.8 1.048 0.781 2.167 0.6985 1.387

12 77 1.1 0.15 0.53 1.8 1.033 1.757 2.647 0.7594 1.121

13 80 0.5 0.25 0.701 5.0 1.003 4.882 3.522 0.6656 1.352

14 80 0.8 0.2 0.758 3.2 1.018 3.125 3.086 0.6601 1.546

15 80 0.9 0.15 0.86 1.8 1.033 1.757 2.651 0.715 1.644

16 80 1.1 0.1 0.304 0.8 1.048 0.781 2.137 0.6594 1.565

4.1.1 Critical observation from validation of equations:

Equation 4.1contains feed and nose radius; 4.2 contains feed and flank wear and 4.3 contains

feed and nose radius. In this present study, input parameters are spindle speed, feed and depth of

cut. Equation 4.4 and 4.5 contains feed, spindle speed and depth of cut. So they are closely

related to this work but the combination of cutting tool and work materials used, as mentioned


37/75


27

earlier, were different. From Table 4.1 it is clear that surface roughness values from Eq. 4.5 are

closely related to our experimental work.

Table 4.1.1 shows the percentage error between surface roughness experimental values and

surface roughness from Eq. 4.5. According to Risbood et al.[3] 20% error is reasonable. From

Table 4.1.1 it can be observed that 10 out of 16 percentage error values are within the range as

depicted above.

Table 4.1.1: Percentage error between surface roughness experimental

values and surface roughness from Eq. 4.5

Sl. No. Surface Roughness

experimental values

(m)

Ra from Eq.

4.5(m)

Percentage error

Within 20%

1 0.294 0.6593 X

2 0.578 0.6868

3 0.797 0.8982

4 0.744 0.7296

5 0.695 0.6779

6 0.286 0.6958 X

7 0.649 0.9860 X

8 0.689 0.7956

9 0.759 0.7598

10 0.71 0.6235

11 0.413 0.6985 X

12 0.53 0.7594 X

13 0.701 0.6656

14 0.758 0.6601

15 0.86 0.7015

16 0.304 0.6594 X


38/75

Chapter 4

28

Figure 4.1 Surface roughness experimental values versus Surface

roughness values from Eq. 4.5

Fig. 4.1 shows the Surface roughness experimental values versus Surface roughness values fromEq. 4.5. A line inclined at 45 and passing through the origin is also drawn in the figure. For

perfect prediction, all the points should lie on this line. Here it is seen that most of the points are

close to this line. Hence, Eq. 4.5 for surface roughness provides reliable prediction.

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

RafromE

q.4.5

(m)

Surface roughness experimental values(m)

B


39/75


29

4.2 Experimental design and set up:

CNC LATHE

COMPUTER

SURFACE ROUGHNESS

MEASUREMENTSURFACE

ROUGHNESS

MODEL

CUTTING

PARAMETERS

CNC PART

PROGRAMMING

OPTIMUM CUTING PARAMETERS

Figure 4.2: Experimental set up to measure surface roughness


40/75

Chapter 4

30

Figure 4.2.1: Figure of chips from CNC during experiment (For obs. 1 to 4)


41/75


31



42/75

Chapter 4

32



43/75


33



44/75

Chapter 4

34

Aluminium (LM6) work piece is used as a test sample in this present study. LM6 has been

machined with single point cutting tool with indexable Tungsten Carbide insert on CNC

lathe. During experiment it is required to use the cutting fluid (coolant) to wash out the chips

and to cool the tool tip. A solution ofBalmerol Protocool SL 20% and Distilled Water 80%

is used as a coolant. Appropriate values of input cutting parameters (cutting speed, depth of

cut and feed rate) are chosen and Taguchi orthogonal array has been generated. Then with the

combination of cutting parameters as generated through Taguchi orthogonal array, CNC part

programming is written. As the array generated through MINITAB 16 was (Table 4.3),

number of observations or the number of combinations for which the turning operations have

been carried out is 16. The job was unloaded from the lathe chuck and placed in a V-block

(as shown in Fig. 3.5) to measure the surface roughness value by Talysurf. Once the

surface roughness values have been measured, the values have been used in developing

empirical models. The experimental set up is shown in Fig.4.2 and the photos of the chip

from CNC as generated during experiment have been shown in Fig. 4.2.1, Fig.4.2.2, Fig.

4.2.3 and Fig.4.2.4 for all 16 observations.

4.3 Selection of the levels of the input cutting parameters:

The experimental work was performed in CNC Lathe, with work material as Aluminium

(LM6) and carbide tip HSS as cutting tool. Cutting speed with Aluminium as work material

and HSS as cutting tool is 75 to 105 m/min [26]. The initial diameter (D) of the cylindrical Al

work piece is 38mm. Hence spindle speeds in RPM can be calculated by the formula

NDv .. ( v in m/min and N in RPM). Here 4 levels of spindle speed, depth of cut and

feed values have been chosen, as tabulated in Table 4.2.


45/75


35

Table 4.2: Selection of the levels of the input parameters:

Parameters Levels

1 2 3 4

Spindle speed (RPM) 628 645 668 711

Depth of cut (mm) 0.5 0.8 0.9 1.1

Feed (mm/rev) 0.10 0.15 0.20 0.25

4.4 Development of the orthogonal array:

First step of the Taguchi method is to design an appropriate orthogonal array for the selectedcutting parameters. In this work the most appropriate array is determined as (from 4= 64

possible combination), in order to obtain the optimal cutting parameters and their effects. For

this approach MINITAB 16 software is used. Once the input 4 levels of input cutting

parameters are given as input, orthogonal array has been generated as shown in Table

4.3. Then the experiments have been carried out with the combinations of the input

parameters as tabulated through Taguchi orthogonal array.


46/75

Chapter 4

36

Table 4.3: Taguchi orthogonal array ( ):

Sl. No.

Spindle speed

values (RPM)

Depth of cut

values (mm)

Feed values

(mm/rev)

1 628 0.5 0.1

2 628 0.8 0.15

3 628 0.9 0.2

4 628 1.1 0.25

5 645 0.5 0.15

6 645 0.8 0.1

7 645 0.9 0.25

8 645 1.1 0.2

9 668 0.5 0.2

10 668 0.8 0.25

11 668 0.9 0.1

12 668 1.1 0.15

13 711 0.5 0.25

14 711 0.8 0.2

15 711 0.9 0.15

16 711 1.1 0.1

4.5 Materials removal rate (MRR) calculation and determination of S/N

ratios:

Materials removal rate (MRR ) values have been calculated theoretically by the equation

fdvMRR .. mm/min. Where, v is the cutting speed in mm/min; d is the depth of cut

in mm and f is feed rate in mm/rev. The MRR values can be converted into NS/ ratios

by using MINITAB 16 software; hence optimal values for the input parameters are

determined. NS/ ratios have been plotted graphically as Main effects plot for NS/ ratios


47/75


37

to determine the optimal values of the input cutting parameters. As higher value of MRR is

desirable so NS/ ratio is calculated as per Larger the better (Eq. 3.3). In Table 4.4

theoretical calculations for MRR and determination of NS/ ratios have been tabulated.

Table 4.4: Theoretical calculation for MRR and determination of S/N

ratios.

Sl. No.

Spindle speed

values (RPM)

Depth of cut

values (mm)

Feed values

(mm/rev)

MRR

(mm/min)

S/N ratio

(dB)

1 628 0.5 0.1 3750 71.4806

2 628 0.8 0.15 9000 79.08485

3 628 0.9 0.2 13500 82.6066

4 628 1.1 0.25 20625 86.2878

5 645 0.5 0.15 5700 75.1174

6 645 0.8 0.1 6080 75.6780

7 645 0.9 0.25 17100 84.6599

8 645 1.1 0.2 16720 84.4647

9 668 0.5 0.2 7700 77.7298

10 668 0.8 0.25 15400 83.7504

11 668 0.9 0.1 6930 76.8146

12 668 1.1 0.15 12705 82.0794

13 711 0.5 0.25 10000 80

14 711 0.8 0.2 12800 82.1441

15 711 0.9 0.15 10800 80.6684

16 711 1.1 0.1 8800 78.8896


48/75

Chapter 4

38

4.6 Surface roughness measurement and determination of S/N ratios:

In the next step, with the combination of input parameters (Table 4.3), as generated throughTaguchi orthogonal array, experiments have been carried out and surface roughness value is

measured with Talysurf. Instrument calibration is required before conducting the

experiment. Turning operation was performed for 16 observations with the combination of

input cutting parameters. Surface roughness values are measured for each run. Work piece

must be taken out from chuck and placed in a V-block to measure surface roughness.

Measurements have been carried out in three different places and mean values are taken.

Then with the help of MINITAB 16 software, NS/ Ratios were calculated and Main

Effects Plot for NS/ Ratios have been plotted to obtain the optimal input cutting parameter

values. As a lower value of surface roughness is desirable so NS/ ratio is calculated as per

smaller the better (Eq. 3.1). Table 4.5 shows the experimental results for surface roughness

and determination of NS/ ratios.

Table 4.5: Experimental results for surface roughness and determination of

S/N ratios.

Sl. No.

Cutting

Speed

(m/min)

Depth of cut

(mm)

Feed

(mm/rev)

Surface

Roughness

(m)

S/N Ratio

(dB)

1 75 0.5 0.1 0.29410.633

2 75 0.8 0.15 0.5784.761

3 75 0.9 0.2 0.797 1.9708

4 75 1.1 0.25 0.7442.568

5 76 0.5 0.15 0.6953.1603

6 76 0.8 0.1 0.28610.8726

7 76 0.9 0.25 0.6493.7551


49/75


39

4.7 Analysis of Signal to Noise ratio (S/N ratio) for MRR:

As discussed earlier, Materials removal rate ( MRR ) can be obtained both theoretically and

experimentally. In order to obtain MRR experimentally, weight of the workpiece before and

after machining have been measured, and also the machining time is noted with stopwatch.

The formula to obtain MRR is as follows,

MRR =( )

sg/ ---------------------- (4.7)

In CNC lathe as it is required to set the job zero after each time it is taken out from the

chuck, so some changes in CNC part programming is required every time. So if possible,

weight of the chip for each run can be measured without unloading the job from the chuck.

Hence MRR becomes,

MRR = sg/ ---------------------- (4.8)

In this thesis work MRR have been calculated theoretically by the equation fdvMRR ..

mm/min. The NS/ ratios have been calculated by using MINITAB 16 for 16 observations

as given in Table 3.2. To obtain the optimal values Main Effects Plot for NS/ Ratios is

given in Fig. 4.3.

8 76 1.1 0.2 0.6893.2356

9 77 0.5 0.2 0.7592.3951

10 77 0.8 0.25 0.712.974

11 77 0.9 0.1 0.4137.680

12 77 1.1 0.15 0.535.514

13 80 0.5 0.25 0.7013.085

14 80 0.8 0.2 0.7582.4066

15 80 0.9 0.15 0.861.3103

16 80 1.1 0.1 0.30410.342


50/75

Chapter 4

40

711668645628

84

82

80

78

76

1.10.90.80.5

0.250.200.150.10

84

82

80

78

76

Cutting speed values (RPM)

MeanofSNratios

Depth of cut values (mm)

Feed values (mm/rev)

Main Effects Plot for SN ratios

Data Means

Signal-to-noise: Larger is better

Figure 4.3: Main effects plot for S/N ratios for MRR.

In the Main effects plot for NS/ ratios, X-axes denote cutting speed (RPM ), depth of cut

(mm) and feed ( revmm/ ) values respectively. Regardless of the category of the performance

characteristics, a greater NS/ value corresponds to a better performance. Therefore, the

optimal level of the machining parameters is the levels with the greatest value.

Spindle speed:-

As shown in the Fig.4.3, effect of cutting speed on MRR is increasing with the increasing in

cutting speed and the optimal level is 711 RPM.

Depth of cut:-

Effect of depth of cut on MRR is increasing with the increasing in cutting speed and the

optimal level is 1.1 mm.

Feed rate:-

Effect of feed rate on MRR is increasing with the increasing in cutting speed and the optimallevel is 0.25 mm/rev.


51/75


41

4.8 Response surface plot for MRR:

In Fig. 4.4 three dimensional plots for the measured responses are created based on Table 4.4through ORIGIN 6.0 software. MRR values are kept as the vertical axis and depth of cut (

d ) and feed rate ( f ) values are kept as horizontal axes. Fig. 4.4 reveals that at feed rate

0.26 mm/rev and at depth of cut 1.1 mm, materials removal rate (MRR ) is maximum. As

higher materials removal rate is desirable so this is the optimum value ofMRR . These results

from 3D surface plots matches with Main Effects Plot for NS/ Ratios forMRR .

0.50.6

0.70.8

0.91.0

1.1

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

22000

0.08

0.12

0.16

0.200.24

Figure 4.4: Response surface plot (MRR vs. d vs. f)

MRR

(mm/min)

feed(

mm/re

v)d(mm)

Figure 4.4: Response Surface Plot ( MRR vs. d vs. f)


52/75

Chapter 4

42

4.9 Analysis of S/N ratio for Surface Roughness:

Surface roughness can be measured with an instrument called Talysurf. For the

measurement of the surface roughness, the workpiece is taken out from the chuck and placed

in a V-block. Readings are taken in three different places and average values are taken.

Instrument calibration is required and after calibration it is seen that instrument is showing a

value which is 0.003 m less than the desired value, so 0.003 m is added every time with

the measured value. All the surface roughness values written in Table 4.5 are calibrated

values. As smaller values of Surface roughness is desirable, so signal to noise ratio ( NS/

ratio) is calculated as per smaller the better , using Eq. 3.1. To obtain optimal values Main

effect plot for NS/ ratios is shown in Fig. 4.5. As discussed earlier, optimum values are the

maximum values.

80777675

10

8

6

4

2

1.10.90.80.5

0.250.200.150.10

10

8

6

4

2

Spindle speed (m/min)

MeanofSNrat

ios

Depth of cut (mm)

Feed (mm/rev)

Main Effects Plot for SN ratios

Data Means

Signal-to-noise: Smaller is better

Figure 4.5: Main effects plot for S/N ratios for surface roughness (Ra)

Spindle speed:- As shown in the Fig. 4.5,the effect of cutting speed on surface roughness has

increased at first with the increasing in cutting speed upto 76m/min then it is decreasing with

the increasing in cutting speed. The optimal level is 76 m/ min.


53/75


43

Depth of cut:- Effect of depth of cut on surface roughness has increased with the increasing

in cutting speed at first upto 0.8mm then it has again decreased to a minimum value for depth

of cut 0.9mm and then again increased to reach the optimal level at 1.1 mm.

Feed rate:- Effect of feed rate on surface roughness is maximum at first (i.e. at 0.1 mm/rev)

then it is decreasing with the increasing in cutting speed upto 0.20 mm/rev feed and then the

value has increased again for 0.25 mm/ rev. The optimal level is 0.1 mm/rev.

4.10 Response surface plots for surface roughness:

In order to understand the interaction effect of input cutting parameters on surface roughness,

three dimensional plots for the measured responses are created based on table 4.5 through

ORIGIN6.0 software. Fig. 4.6, 4.7, 4.8 gives the 3D surface graphs for the surface

roughness. value is kept as the vertical axes in all the cases. From the figures value can

be determined by the length of the projectors or projection lines from the points to the

horizontal surface as shown. Fig. 4.6 and 4.7 reveals that at cutting speed ( v ) 1.26 m/s (76

m/min) the length of the projectors are minimum; hence, surface roughness ( ) values are

minimum. It can be concluded from Fig. 4.6 and Fig. 4.8 that at feed rate ( f ) 0.1 mm/ rev,

the length of the projector from the point to the horizontal axis is minimum; so, surface

roughness value is minimum. As minimum surface roughness ( ) value signifies better

surface finish, so cutting speed 1.26 m/s and feed rate 0.1 mm/rev are the optimal values.

These results from 3D surface plots matches with Main effects plot for S/N ratios for surface

roughness.

From figure 4.6, for a particular cutting speed (say 75 m/min), value increases as feed rate

increases but for a particular feed (say 0.26 mm/rev), value does not increase much with

the increase in cutting speed values. So it can be concluded that feed rate has higher

contribution than cutting speed in determining surface finish.

From Fig. 4.8, for a particular depth of cut value (say 1.1 mm), value increases as feed

rate increases but for a particular feed (say 0.1 mm/rev), value does not increase much

with the increase in depth of cut values. So it can be concluded that feed rate has higher

contribution than depth of cut in determining surface finish. Hence it is clear from the


54/75

Chapter 4

44

response surface plots that feed rate has higher contribution than both cutting speed and depth

of cut in determination of surface finish of machined parts.

Figure 4.6: Response surface plot 1 (Ra vs. f vs. v)

Figure 4.7: Response surface plot 2 (Ra vs. d vs. v)


55/75


45

4.11 Analysis of variance (ANOVA) for surface roughness:

The term Analysis of variance was introduced by Prof. R.A. Fisher in 1920s to deal with

problems in the analysis of agronomical data [20]. Variation is inherent in nature. The total

variation in any set of numerical data is due to a number of causes which may be classified

as; i) Assignable causes and ii) Chance causes.

The variation due to assignable causes can be detected and measured whereas the variation

due to chance causes is beyond the control of human hand and can not be traced separately.

Analysis of variance (ANOVA) can also be defined as a collection of statistical models, and

their associated procedures in which the observed variance in a particular variable is

partitioned into components attributable to different sources of variation. ANOVA is used in

the analysis of comparative experiments, those in which only the difference in outcomes is of

interest. In short, the purpose of ANOVA is to investigate which of the input parameters

significantly affect the performance characteristics. The following formulas are required in

analysis of variance,

Figure 4.8: Response surface plot 3 (Ra vs. d vs. f)


56/75

Chapter 4

46

4.11.1 Total sum of squared deviations,

= - [ ] --------------------------- (4.9)

Where m is the no. of observations, is the mean NS/ ratio for experiment.

4.11.2 Sum of squared deviations of parameters,

= ( )

- [ ] ------------------------ (4.10)

Where, t is the repetition of each level of parameters and " " is the sum of the S/N Ratio

involving this parameter p and level j.

4.11.3 Sum of squared deviation of error,

| | = ( + + ) ---------------------- (4.11)

Here in this present work, = 526.894

So, = 526.894 .

= 159.596775.

Sum of squared deviation due to spindle speed,

| |= ( . )

+ ( . )

+ ( . )

+ ( . )

- .

= 340.885225

Sum of squared deviation due to depth of cut,

| | = ( . )

+ ( . )

+ ( . )

+ ( . )

- .

= 355.657.

Sum of squared deviation due to feed,

| | = ( . )

+ ( . )

+ ( . )

+ ( . )

- .

= 366.757225.


57/75


47

Sum of squared deviation of error,

| | = 159.596775340.885225355.657366.757225 = 903.70265

Mean sum of squares can be obtained by .

Fisher ratio can be obtained by .

Table 4.6: Analysis of variance (ANOVA) for surface roughness:

Sources of

variation

Degrees of

freedom

Sum of

Squares

Mean sum of

squares

Fisher ratio Percentage

contribution

Spindle speed 3 340.8852 113.6284 5.65814 31.05428

Depth of cut 3 355.657 118.55233 5.90332 32.6888

Feed rate 3 366.7572 122.252408 6.08757 33.91717

Error 45 903.7026 20.08228 2.33975

Total 54 1967.0021 100

The contribution of the input parameters (i.e., Spindle Speed, Depth of Cut and Feed rate) on

the output (i.e., surface roughness) can be determined by Fisher ratio (or variance ratio). The

higher value of Fisher ratio signifies greater contribution. Here from the Table 4.6 it can be

concluded that, spindle speed has the lowest contribution and feed has the highest

contribution. As both the Fisher ratio and percentage contribution are maximum for feed,

so it can be concluded that feed value has the highest contribution on surface finish of

machined parts.


58/75

Chapter 4

48

4.12 Determination of empirical relationships between and v, d and f:

As discussed in the article Mathematical formulation, Eq. 3.4 and Eq. 3.5 are used to

determine the relationship between surface roughness ( ) and Cutting speed ( v ), depth of

cut (d) and feed ( f ).

4.12.1 Determination of Linear empirical model:

Table 4.3 shows that cutting speed 75m/min remains constant for observations 1 to 4, 76

m/min for obs. 5 to 8, 77 m/min is for obs. 9 to 12 and 80 m/min remains constant for obs. 13

to 16. Hence, effort will be given to derive empirical relationship for a particular cutting

speed. It is clear from the Table 4.3 that 4 set of equations can be made for all 4 level of

cutting speeds, hence 16 equations can be generated, and ultimately 4 empirical relationships

can be derived. So let us take Eq. 3.10 ( = + fcdbva ... ) to develop 16 equations

for all 16 observations;

First set of equations (For obs. 1-4)

0.294 =A+75 +0.5 +0.1

0.578 =A+75 +0.8 +0.15

0.797 =A+75 +0.9 +0.9

0.744 =A+75 +1.1 +0.95

Second set of equations (For obs. 5-8)

0.695 =B+76 +0.5 +0.15

0.286 =B+76 +0.8 +0.1

0.649 =B+76 +0.9 +0.95

0.689 =B+76 +1.1 +0.9

Third set of equations (For obs. 9-12)

0.759 =C+77 +0.5 +0.9


59/75


49

0.710 =C+77 +0.8 +0.95

0.413 =C+77 +0.9 +0.1

0.530 =C+77 +1.1 +0.15

Fourth set of equations (For obs. 13-16)

0.701 =D+80 +0.5 +0.95

0.758 =D+80 +0.8 +0.90

0.860 =D+80 +0.9 +0.15

0.304 =D+80 +1.1 +0.10

Where A, B, C, D and to are constants.

It is required to determine the values of the constants A, B, C, D and to .

The following 4 linear empirical relationships can be obtained after solving the equations

written above,

= 3.73f+0.3249d+0.3045v-0.2415- ---------------------- (4.12)

= 2.996f+0.8639d-0.362599v+0.67759 ---------------------- (4.13)

= 1.684f+0.444d-0.1216v+0.64419 ----------------------- (4.14)

= 2.4899f-0.22499d-0.6355v-1.4899 ----------------------- (4.15)

4.12.2 Determination of exponential empirical model:

An exponential empirical model for surface roughness as a function of cutting speed ( v ),

feed ( f ) and depth of cut ( d) was given in equation 3.5 as,R =X v d f

Now let us write all the 16 equations with reference to the table 4.3 as per the form stated

above,


60/75

Chapter 4

50

First set of equations (for obs. 1-4)

0.294 = A75 0.5 0.1

0.578 = A75 0.8 0.15

0.797 = A75 0.9 0.2

0.744 = A75 1.1 0.25

Second set of equations (for obs. 5-8)

0.695 = B76 0.5 0.15

0.286 = B76 0.8 0.1

0.649 = B76 0.9 0.25

0.689 = B76 1.1 0.2

Third set of equations (for obs. 9-12)

0.759 = C77 0.5 0.2

0.710 = C77 0.8 0.25

0.413 = C77 0.9 0.1

0.530 = C77 1.1 0.15

Fourth set of equations (for obs. 13-16)

0.701 = D80 0.5 0.25

0.758 = D80 0.8 0.2

0.860 = D80 0.9 0.15

0.304 = D80 1.1 0.1

It is required to determine the values of A, B, C, D and a to l.


61/75


51

The equations can be transformed into linear form by taking natural logarithm on both sides.

And after solving them 4 empirical equations can be obtained as follows,

= 0.39806 . . . ------------------ (4.16)

= 0.48951 . . . ------------------ (4.17)

= 0.11033 . . . ------------------- (4.18)

= 1.215672 . . . ------------------- (4.19)

Eq. 4.16 is obtained for cutting speed 75 m/min.,4.17 is for 76m/ min, 4.18 for 77m/min and

4.19 is for cutting speed 80 m/min.

4.13 Verification:

Now it is required to verify the linear and exponential relationships as derived, in reference to

the experimental results. A comparative study has been carried out between surface

roughness experimental values and surface roughness values by linear and exponential

models, as tabulated below. In Fig. 4.7 and 4.8 comparative graphs between surface

roughness experimental values and surface roughness values by linear and exponential

models have been carried out to determine which empirical model is closer to the

experimental values. Table 4.7 is the Comparative study between surface roughness

experimental values and surface roughness values by linear models and Table 4.8 is the

Comparative study between surface roughness experimental values and surface roughness

values by exponential models.


62/75

Chapter 4

52

Table 4.7 Comparative study between surface roughness experimental

values and surface roughness values from developed linear models:

Obs.

No.

Surface

roughness

(Experimental

values) m

Surface roughness values from developed Linear empirical

models

(Linear

model 1) Eq.

4.12 (m)

(Linear

model 2) Eq.

4.13 (m)

(Linear

model 3) Eq.

4.14 (m)

(Linear

model 4) Eq.

4.15

(m)

1 0.294 0.086 0.998 0.742 0.334

2 0.578 0.197 0.889 0.693 0.142

3 0.797 0.416 0.952 0.733 0.004

4 0.744 0.667 0.929 0.728 0.174

5 0.695 0.096 0.151 0.694 0.203

6 0.286 0.007 0.742 0.61 0.260

7 0.649 0.599 1.105 0.818 0.135

8 0.689 0.478 0.783 0.645 0.056

9 0.759 0.277 1.308 0.914 0.065

10 0.710 0.561 1.199 0.865 0.126

11 0.413 0.034 0.663 0.568 0.224

12 0.530 0.285 0.640 0.564 0.055

13 0.701 0.448 1.476 1.004 0.090

14 0.758 0.359 1.067 0.787 0.033

15 0.860 0.205 0.831 0.658 0.068

16 0.304 0.083 0.509 0.485 0.148


63/75


53

Table 4.8 Comparative study between surface roughness experimental

values and surface roughness values from developed exponential models:

Obs.

No.

Surface

roughness

(Experimental

values) m

Surface roughness values from developed Exponential

empirical models

(Exponential

model 1) Eq.

4.16 (m)

(Exponential

model 2) Eq.

4.17 (m)

(Exponential

model 3) Eq.

4.18 (m)

(Exponential

model 4) Eq.

4.19 (m)

1 0.294 0.116 0.223 0.057 1.318

2 0.578 0.229 0.211 0.059 1.067

3 0.797 0.316 0.252 0.066 0.929

4 0.744 0.440 0.258 0.068 0.83

5 0.695 0.163 0.340 0.071 1.09

6 0.286 0.166 0.139 0.047 1.282

7 0.649 0.381 0.317 0.074 0.836

8 0.689 0.368 0.206 0.061 0.917

9 0.759 0.206 0.457 0.083 0.952

10 0.710 0.350 0.358 0.078 0.839

11 0.413 0.181 0.124 0.045 1.27

12 0.530 0.292 0.154 0.052 1.043

13 0.701 0.250 0.579 0.094 0.852

14 0.758 0.295 0.287 0.069 0.921

15 0.860 0.255 0.190 0.056 1.045

16 0.304 0.212 0.102 0.042 1.246

In Fig 4.9 Surface roughness experimental values and surface roughness values by linear

empirical relationships have been plotted as Y-axis and observation number as X-axis. A

polynomial trend line, for surface roughness experimental values, of order 6 has been plotted.

It can be observed from Fig 4.9 that Surface roughness values through Eq. 4.14 i.e., linear

model no.3 is closer to the experimental values.


64/75

Chapter 4

54

In Fig 4.10 Surface roughness experimental values and surface roughness values by

exponential empirical relationships have been plotted as Y-axis and observation number as

X-axis. A polynomial trend line, for surface roughness experimental values, of order 6 has

been plotted. It can be observed from Fig 4.10 that Surface roughness values through Eq.

4.16 i.e., exponential model no.1 is closer to the experimental values.

Figure 4.9: Comparative study between experimental values and developed

linear model values.


65/75


55

Figure 4.10: Comparative study between surface roughness experimental values and

surface roughness values by developed exponential models.


66/75

Chapter 4

56

4.14 Calculation of percentage error:

Table 4.9: Percentage error between Surface roughness experimental

values and Surface roughness values from developed linear model 3 (Eq.

4.14):

Obs.

No.

Surface

roughness

(Experimental

values) m

Surface roughness

(Linear model 3) Eq.

4.14 (m)

Percentage error

Within 20%

1 0.294 0.742 X

2 0.578 0.693

3 0.797 0.733

4 0.744 0.728

5 0.695 0.694

6 0.286 0.610 X

7 0.649 0.818

8 0.689 0.645

9 0.759 0.914

10 0.710 0.835

11 0.413 0.568 X

12 0.530 0.564

13 0.701 1.004 X

14 0.758 0.787

15 0.860 0.698

16 0.304 0.485 X


67/75


57

Table 4.10: Percentage error between Surface roughness experimental

values and Surface roughness values from developed exponential model 1

(Eq. 4.16):

Obs.

No.

Surface

roughness

(Experimental

values) m

Surface roughness

(Exponential model 1) Eq.

4.16 (m)

Percentage error

(%)

1 0.294 0.116 60.544

2 0.578 0.229 60.380

3 0.797 0.316 60.351

4 0.744 0.440 40.860

5 0.695 0.163 76.546

6 0.286 0.166 41.958

7 0.649 0.381 41.294

8 0.689 0.368 46.589

9 0.759 0.206 72.859

10 0.710 0.350 50.704

11 0.413 0.181 56.174

12 0.530 0.292 44.905

13 0.701 0.250 64.336

14 0.758 0.295 61.081

15 0.860 0.255 70.348

16 0.304 0.212 30.263

4.14.1 Critical observation from percentage error calculation:

Table 4.9 shows the percentage error between Surface roughness experimental values and

Surface roughness values from developed linear model 3 (Eq. 4.14) and table 4.10 shows the

Percentage error between Surface roughness experimental values and Surface roughness

values from developed exponential model 1 (Eq. 4.16). According to Risbood et al. [3] 20%

error is reasonable. From table 4.10 it has been observed that all the percentage errors are


68/75

Chapter 4

58

greater that 30%. So, it can be concluded that Eq. 4.16 is not reliable while calculating

surface roughness theoretically.

From Table 4.9 it has been observed that 11 out of 16 cases, percentage error values are

within the range of 20%. The percentage error values are beyond the range as written above

for remaining cases. It can be concluded that Eq. 4.14 can be used to calculate surface

roughness theoretically.

Fig.4.11: Comparative study between Surface roughness experimental values

and Surface roughness values from developed linear model 3 (Eq. 4.14).


69/75


59

Fig.4.11 shows the comparative study between Surface roughness experimental values and

Surface roughness values from linear model 3 (Eq. 4.14) and Fig.4.12 shows the comparative

study between Surface roughness experimental values and Surface roughness values from

exponential model 1 (Eq. 4.16). It has been observed that in Fig. 4.11 Surface roughness

experimental values are closer to Surface roughness values from linear model 3 (Eq. 4.14).

Fig.4.12: Comparative study between Surface roughness experimental values

and Surface roughness values from developed exponential model 1 (Eq. 4.16).


70/75

Chapter 4

60

Fig. 4.13 shows the Surface roughness experimental values versus Surface roughness values

from linear model 3 (Eq. 4.14). A line inclined at 45 and passing through the origin is also

drawn in the figure. For perfect prediction, all the points should lie on this line. Here it is seen

that most of the points are close to this line. Hence, this linear model for surface roughness

provides reliable prediction.

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

Su

rfaceroughness

values

(Linearm

odel3)Eq.

4.1

4

(m)

Surface roughness

experimental value

(m)

B

Fig. 4.13: Surface roughness experimental values versus Surface

roughness values from developed linear model 3 (Eq. 4.14).


71/75

CHAPTER 5

CONCLUSION

5.1 Introduction:

In this experimental based thesis work Taguchi method has been used to develop

Orthogonal Array with 4 levels of certain input cutting parameters like Cutting Speed (v

in m/min), Depth of Cut (d in mm) and Feed (f in mm/rev) . With the combination of

input cutting parameters, Materials Removal Rate ( MRR ) is calculated theoretically and

Surface Roughness ( ) have been measured with Talysurf surface roughness tester. The

output values ( MRR and ) are converted into NS/ Ratios by using MINIITAB 16

software. Main Effects Plot for NS/ Ratios have been plotted for both Surface Roughness

and Materials Removal Rate to obtain the optimal input cutting parameter values. These

optimal input cutting parameter values have been verified through 3-Dimensional Response

Surface Plot. In this thesis work efforts have also been given to develop Linear and

Exponential models to find out the accurate model.

5.2 Significant contributions:

The significant contributions of the present investigation are as follows,

4 Linear empirical models and 4 Exponential empirical models have been developed

based on Cutting Speed (v in m/min), Depth of Cut (d in mm) and Feed (f in

mm/rev).

Surface Roughness experimental values and Surface Roughness values from different

Linear and Exponential empirical models have been compared and throu

pdf arghya

Documents