mathematical modeling of sink-edm process parameters for different tool...

CHAPTER-5

MATHEMATICAL MODELING

OF SINK-EDM PROCESS PARAMETERS

FOR DIFFERENT TOOL TAPER ANGLE

WITH SIZE FACTOR CONSIDERATION

5.1 INTRODUCTION

As already discussed in tiie previous chapter tlie basis of controlling the

sink Electrical Discharge Machining (sink-EDM) process mostly relies on

empirical methods largely due to the stochastic nature of the sparking

phenomenon involving both electrical and non-electrical process

parameters. Thus the performance of sink-EDM process is commonly

evaluated in terms of Material Removal Rate (MRR) and Tool Wear Rate

(TWR); and to compute MRR and TWR mathematical models are

developed.

Modeling and analysis of the effect of taper tool electrodes with size

factor consideration along with the other process parameters like discharge

current, pulse on-time, pulse off-time and taper angle in sink-EDM process

is described in this chapter. Conventional statistical regression analysis-

based mathematical models have been developed to establish the input-

output relationships. The Material Removal Rate (MRR) and Tool Wear

Rate (TWR) mathematical models have been developed using the data

146

obtained through Central Composite Design (CCD). The lack-of-fit and

adequacy of the developed models was verified by applying Analysis of

Variance (ANOVA). Further, the confirmation tests were performed to

ascertain the accuracy of the developed models.

5.2 EXPERIMENTAL DETAILS

5.2.1 Experimental Set-Up

in the present investigation, the experiments were performed in an

'ELEKTRA PRIDE - T sink-EDM machine. Fig. 4.1 shows the photograph

of sink-EDM machine. The specifications of sink-EDM machine are shown

in Table 4.1. The electrolytic copper is used as a tool material because of

its higher MRR and less TWR, it also yield a better surface finish. The

electrolytic copper tools of different taper angle along with size factor

consideration were used to erode a water quenched medium carbon steel

(ENS) workpiece. The impulse flushing of kerosene (dielectric fluid) was

employed throughout the experimental investigations. The other

quantitative and qualitative sink Electrical Discharge Machining (sink-EDM)

process parameters were kept constant for given set of trials.

General scheme of the sink-EDM process for different taper tools is

shown in Fig. 5.1 and Fig. 5.2 shows an experimental set-up of the sink-

EDM process for taper tool electrodes. Fig. 5.3 shows the detailed drawing

with dimensions and angle of the electrolytic copper taper tools along with

size factor consideration as required for different levels. Fig. 5.4 shows a

147

photograph of the different taper tool electrodes and workpiece used for

experiments.

Constant Parameters

n V

1. Current 2. Pulse on-time 3. Pulse off-time 4. Taper angle

Sink-EDM Process

1.MRR

2. TWR


Sink-EDM Process

1.MRR

2. TWR


1.MRR

2. TWR

Input parameters Process Outputs

Fig. 5.1 General scheme of the sink-EDM process for different taper tool

electrodes

To Quill

Tool Shan

Dielectric Flui

Workpiece

To Pump

/

Fig. 5.2 Experimental set-up of the sink-EDM process for different taper

tool electrodes

5.2.2 Materials Used for the Experiments

a) Workpiece Material

Workpiece material used for the experiments was ENS steel with the

density of 7.77g/cm^ and hardness of 45HRc obtained after water

quenching. Table 5.1 depicts the chemical composition of ENS steel.

Table 5.1 Chemical composition of ENS steel by weight percentage

c. Si. IVIn. s. P. Fe.

0.35-0.45 0.05-0.30 0.60-1.00 0.06 Max 0.06 Max balance

b) Tool Electrode Material

The tool electrode material used for the experiments is a pure electrolytic

copper (99.9% Cu). The physical and mechanical properties of electrolytic

copper are melting point of 1,0S2 °C, density of S.97g/cm , electrical

resistivity of 16.7 nOm and thermal conductivity of 393 W/m K. Fig. 5.3

shows the detailed drawing with dimensions and angle of the electrolytic

copper taper tool electrodes along with size factor consideration as

required for different levels. Fig. 5.4 shows a photograph of the different

taper tool electrodes and workpiece used for experiments.

149

Taper tool shank

Taper tools r-30mm

20 mm

30 Deg 45 Deg 60 Deg 75 Deg 90 Deg

Fig. 5.3 Taper tool electrodes with dimensions and angle for different levels

Fig. 5.4 Photograph of the taper tool electrodes and workpiece

5.2.3 Experimental Procedure

The top and bottom faces of ENS steel workpiece were ground to a good

surface finish using a surface grinding machine before experimentation.

The bottom of the tool was also cleaned using a very fine grade emery

sheet before every trial run. The initial weights of the workpiece and tool

were weighed using a 1mg accuracy digital weighing machine. The

workpiece was held on the machine table using a specially designed

fixture. The workpiece and tool were connected to the positive and negative

terminals of power supply, respectively. The dielectric fluid used was

kerosene with impulse flushing. The experiments were conducted in a

random order to remove the effects of any unaccounted factors. At the end

of each experiment, the workpiece and tool were removed, washed, dried,

and weighed on digital weighing machine. A stopwatch was used to record

the machining time.

5.2.4 Machining Performance Evaluation

Material Removal Rate (MRR) and Tool Wear Rate (TWR) are used to

evaluate machining performance, expressed as the Workpiece Removal

Weight (WRW) and Tool Wear Weight (TWW) per density (p) over a period

of machining time (T) in minutes, that is:

MRR (mm'/min) = WRW / pT (5.1)

151

TWR (mm /min) = TWW / pT (5.2)

Relative Tool Wear (RTW), defined as the ratio of Material Removal Rate

(MRR) to Tool Wear Rate (TWR) and expressed as a percentage, that is:

RTW (%) = TWR / MRR x 100 (5.3)

Higher the MRR is the better, whereas smaller the TWR and RTW is the

better machining performance in EDM process. Therefore, MRR is higher-

the-better, whereas TWR is lower-the-better performance characteristics in

EDM process. The experimental results are given in Table 5.3.

5.3 DEVELOPMENT OF RSM BASED MATEMATiCAL

MODELS

The following steps were used for developing RSM based mathematical

models:

1. Identifying the important process parameters.

2. Developing the design matrix and finding upper and lower limits of

process parameters.

3. Conducting the experiments as per the design matrix and recording the

Responses.

4. Evaluating the regression coefficients and developing the mathematical

152

models for MRR and TWR.

5. Checking the adequacy of the mathematical models.

6. Conformity experiments of mathematical models.

5.3.1 Identification of Process Parameters

The independently controllable EDM parameters affecting the MRR and

TWR were identified as current (/), pulse on-time {ton), pulse off-time (W)

and taper angle (9) shown in Table 5.2. The other quantitative and

qualitative EDM parameters were kept constant for given set of trials.

5.3.2 Developing the Design Matrix and Finding Upper and

Lower Limits of Process Parameters

RSM is used in the design matrix formation which Is an empirical modeling

approach using polynomials as local approximations to obtain the true

input/output relationships. The most popular of the many classes of RSM

designs is the CCD, which can be naturally partitioned into two subsets of

points; the first subset estimates linear and two parameter interaction

effects while the second subset estimates curvature effects. CCD is a very

efficient method for providing much information on parameter effects and

overall experimental error in a minimum number of required runs.

[159,160].Thirty-one sets of coded and natural conditions are used to form

the design matrix of full factorial central composite design shown in Table

5.3. The design comprises a 2* full factorial Central Composite Design for

153

four independent parameters each at five levels with sixteen cube points

plus eight star points and seven replicates at centre points [159].AII

parameters at the intermediate (0) level constitute the centre points and the

combinations of each of the process parameters at either it's lowest (-2) or

highest (+2) with the other three parameters of the intermediate levels

constitute the star points. Run number indicates the sequence of trials

under consideration Table 5.3. Xi, X2, Xj and X4 represent the notation

used for controllable parameters as shown in Table 5.2. Intermediate levels

of coded values were calculated from the following relationship:

X, = 2[2X-iX^ +X^^ max mm

)] (5.4)

Where,

Xf. required coded values of a parameter X

X: any value of the parameter from Xmin to X^ax

Xmin and Xmax'- lower and upper levels of the parameter X.

Table 5.2 Experimental parameters with range and levels

Parameters Notation

Unit Range and levels

Parameters Natural Coded

Unit -2 -1 0 1 2

Current / Xi A 4 8 12 16 20

Pulse on-time *on X2 MS 4 27 50 73 96

Pulse off-time toff X3 ps 4 5 6 7 8

Taper angle 9 X4 Deg 30 45 60 75 90

154

5.3.3 Conducting the Experiments as Per the Design Matrix

and Recording the Responses

Thirty-one experimental runs were conducted as per tlie design matrix at

random to avoid any systematic error creeping into the system. The

observed and calculated values of MRR and TWR for different taper angle

tools with size factor consideration are as in design matrix Table 5.3.

5.3.4 Evaluating the Regression Coefficients and

Developing the Mathematical Models for MRR and TWR

The values of the regression coefficients of the linear, quadratic and

interaction terms of the models were determined by the following formula:

b = iX'xr'X'Y (5.5)

Where,

b: matrix of parameter estimates

X: calculation matrix

X^: transpose of X

/ : matrix of measured response

Response surface modeling was used to establish the mathematical

relationship between the response (Vn) and the various machining

parameters [159,164].The general second order polynomial response

155

surface mathematical model, which analysis the parametric, influences on

the various response criteria, could be described as follows:

3 4

(5.6) i=\ i=\ i=\ j=i+l

Where,

Yn. responses under study e.g. MRR and TWR

Xj: coded values for / = /, ton, toff and 9

bo,b,b„bij. second order regression coefficients

The second term under the summation sign of this polynomial equation is

attributable to linear effect, whereas the third term corresponds to the

higher-order effect. The fourth term of the equation includes the interactive

effects of the process parameters.

Design of Experiment (DOE) features of MINITAB statistical

software [162] were utilized to obtain the central composite second order

rotatable design and also to determine the coefficients of mathematical

modeling based on the response surface regression model. MINITAB

software can also produce ANOVA tables to test lack-of-fit of the RSM-

based models, and offers the "graphic option" to obtain a response surface

plot for the selected parametric ranges of the developed response

surfaces. Furthennore, MINITAB software also has features enabling data

and file management, basic statistics and optimization analysis.

156

Based on Eq. 5.6, the effects of the above-mentioned process

parameters on the magnitudes of the MRR and TWR have been evaluated

by computing the values of various constants using MINITAB statistical

software and the relevant experimental data from Table 5.3.

Regression coefficients for Material Removal Rate (MRR) and Tool

Wear Rate (TWR) mathematical models were calculated using the coded

units. Regression analysis (Table 5.4) indicates the individual and higher

order effects of parameters such as current (/), pulse on-time {ton), pulse

off-time (toff), and taper angle (0) with the interaction tenns. Predictors with

significant contributions in mathematical models are identified with their p-

values less than 0.05. Insignificant predictors were eliminated to adjust the

fitted mathematical models. R is another important coefficient called the

determination coefficient in the resulting ANOVA test, defined as the ratio

of the explained variation to the total variation, and is a measure of

goodness of fit [165]. The R value is always between 0 and 1. Values of

R , R (pred) and R (adj) were also calculated (refer to Table 5.5) for the

MRR and TWR mathematical models, as R value approaches unity, the

better the response model fits the actual data [166]. It also indicates the

difference between the predicted and actual values.

157

Table 5.3 Experimental layout plan as per CCD

o z 75 •c 1-

o z c

Coded values Natural values Responses o z 75 •c 1-

o z c Xi X2 X3 X4 / 'on toff 9

MRR mm^/mln

TWR mm^/mln

o z 75 •c 1-

o z c Xi X2 X3 X4 / 'on toff 9

Yi Y2

1 28 -1 -1 -1 -1 8 27 5 45 24.192 0.463

2 18 +1 -1 -1 -1 16 27 5 45 44.114 5.771

3 15 -1 +1 -1 -1 8 73 5 45 25.131 0.091

4 3 +1 +1 -1 -1 16 73 5 45 52.915 0.462

5 29 -1 -1 +1 -1 8 27 7 45 24.189 0.485

6 30 +1 -1 +1 -1 16 27 7 45 44.137 5.696

7 24 -1 +1 +1 -1 8 73 7 45 25.141 0.163

8 13 +1 +1 +1 -1 16 73 7 45 53.321 0.413

9 1 -1 -1 -1 +1 8 27 5 75 26.165 0.402

10 22 +1 -1 -1 +1 16 27 5 75 46.134 5.465

11 4 -1 +1 -1 +1 8 73 5 75 27.127 0.072

12 16 +1 +1 -1 +1 16 73 5 75 54.317 0.182

13 12 -1 -1 +1 +1 8 27 7 75 26.185 0.453

14 27 +1 -1 +1 +1 16 27 7 75 46.122 5.390

15 17 -1 +1 +1 +1 8 73 7 75 27.127 0.147

16 6 +1 +1 +1 +1 16 73 7 75 55.317 0.107

17 14 -2 0 0 0 4 50 6 60 21.189 0.016

18 21 2 0 0 0 20 50 6 60 71.217 5.303

19 10 0 -2 0 0 12 4 6 60 21.452 5.767

20 20 0 2 0 0 12 96 6 60 33.469 0.154

21 9 0 0 -2 0 12 50 4 60 31.798 0.496

22 11 0 0 2 0 12 50 8 60 31.898 0.502

23 19 0 0 0 -2 12 50 6 30 44.261 0.448

24 31 0 0 0 2 12 50 6 90 48.254 0.095

25 5 0 0 0 0 12 50 6 60 47.044 0.256

26 26 0 0 0 0 12 50 6 60 44.430 0.271

27 23 0 0 0 0 12 50 6 60 46.830 0.273

28 2 0 0 0 0 12 50 6 60 45.240 0.288

29 25 0 0 0 0 12 50 6 60 46.588 0.276

30 8 0 0 0 0 12 50 6 60 46.438 0.272

31 7 0 0 0 0 12 50 6 60 47.236 0.273

158

Table 5.4 Estimated regression coefficients for taper tool electrodes (T)

/ f -MRR model Vz-TWR model Predictor Predictor

Coefficient p-value Coefficient p-value

Constant 46.2580 0.000 * 0.27271 0.000 *

Xi 12.1323 0.000 * 1.32433 0.000 *

X2 2.6330 0.000 * -1.40475 0.000 *

X3 0.0685 0.686 -0.00175 0.488

X4 0.9725 0.000 * -0.08467 0.000 *

Xi^Xi -0.0704 0.650 0.59878 0.000 *

X2 ' X2 -4.7561 0.000 * 0.67403 0.000 *

X3 ^ X3 -3.6592 0.000 * 0.05865 0.000 *

X4^X4 -0.0568 0.714 0.00178 0.442

Xi ** X2 1.9730 0.000 * -1.23925 0.000 *

Xi X X3 0.0869 0.675 -0.03087 0.000 *

Xl^X4 -0.0342 0.869 -0.06687 0.000 *

X2 ^ X3 0.0867 0.676 0.00625 0.055

X2 ^ X4 -0.0371 0.858 0.00525 0.101

X3 X X4 0.0358 0.863 0.00037 0.903

indicates the significant term

159

Hence, the mathematical models in coded form for correlating the Material

Removal Rate (MRR) and Tool Wear Rate (TWR) with the considered sink-

EDM process parameters for different tool taper angle with size factor

consideration are given by:

Material Removal Rate (MRR)

Yi = 46.2580 + 12.1323X, + 2.6330Xs + 0.9725X4 - 4.7561X^

- 3.6592 X3^ +1.9730 X1X2 (5.7)

Tool Wear Rate (TWR)

"{2-0.27271 + 1.32433Xi- 1.40475X2- 0.08467X4 + 0.59^78Xi^

+ 0.67403 X^ + 0.05865 Xi~1.23925 X1X2 - 0.03087 X1X3

-0.06687X1X4 (5.8)

These developed mathematical models are used to analyze the effect of

the taper angle with size factor consideration along with the considered

EDM process parameters on the Material Removal Rate (MRR) and Tool

Wear Rate (TWR) values.

5.3.5 Checking the Adequacy of the Mathematical Models

for MRR and TWR

The Analysis of Variance (ANOVA) [159,160] was performed along with

Fisher's statistical test (F-test) to verify the lack-of-fit and adequacy of the

160

developed mathematical models for the desired confidence interval. The

ANOVA table includes sum of squares {SS), degrees of freedom (DF) and

mean square (MS). In ANOVA, the contributions for SS is from the first

order terms (linear), the second order terms (square), the interaction terms,

lack of fit and the residual error. The lack of fit component is the deviation

of the response from the fitted surface, whereas the residual error is

obtained from the replicated points at the center. The MS are obtained by

dividing the SS of each of the sources of variafion by the respective DF.

The p-value is the smallest level of significance at which the data are

significant. The Fisher's variance ratio {F-ratio) is the ratio of the MS of the

lack of fit to the MS of the pure experimental error. As per the ANOVA

technique, the model developed is adequate within the confidence inten/al

if the calculated value of F-ratio of lack of fit to pure error does not exceed

the standard tabulated value of F-ratio and the F- values of model should

be more than the F-critical for a confidence interval.

Table 5.5 presents the ANOVA for Material Removal Rate (MRR)

and Tool Wear Rate (TWR) mathematical models. It is found that the F-

values for MRR and TWR models are greater than the F-critical for a

significance level of a = 0.05 and their calculated p-values for lack-of-fit are

found to be insignificant, as it is desired. Hence, this indicates that the

developed second order regression models that link the various machining

parameters with MRR and TWR for different tool shapes are adequate at

95% confidence level.

161

Table 5.5 ANOVA for MRR and TWR Mathematical Models

5.5.1 Analysis of variance for Vf

Source

Regression

Linear

Square

Interaction

Residual Error

Laclc-of-Fit

Pure Error

Total

DF Seq SS Adj SS Adj MS F P

14 4748.68 4748.68 339.191 510.93 0.000

3721.84 3721.84 930.460 1401.58 4

4

6

16

10

6

30

964.25

62.59

10.62

4.20

6.42

4759.30

964.25 241.064

62.59 10.431

10.62 0.664

4.20 0.420

6.42 1.070

0.000

363.12 0.000

15.71 0.000

0 . 3 9 0 . 9 0 8

R = 99.78% RMpred) = 99.31% R (adj) = 99.58%

5.5.2 Analysis of variance for 2

S o u r c e DF Seq SS Adj SS Adj MS F P

R e g r e s s i o n 14 1 3 5 . 8 1 8 1 3 5 . 8 1 8 5 9 . 7 0 1 3 66449 . .44 0 . 0 0 0

L i n e a r 4 8 9 . 6 2 4 8 9 . 6 2 4 5 2 2 . 4 0 6 1 1 5 3 4 7 1 . ,25 0 . 0 0 0

Square 4 2 1 . 5 3 4 2 1 . 5 3 4 3 5 . 3 8 3 6 36874 ,93 0 . 0 0 0

I n t e r a c t i o n 6 2 4 . 6 6 0 2 4 . 6 5 9 7 4 . 1 1 0 0 2 8 1 5 1 . , 23 0 . 0 0 0

R e s i d u a l E r r o r 16 0 . 0 0 2 0 . 0 0 2 3 0 . 0 0 0 1

L a c k - o f - F i t 10 0 . 0 0 2 0 . 0 0 1 8 0 . 0 0 0 2 2 . ,06 0 . 1 9 5

Pure E r r o r 6 0 . 0 0 1 0 . 0 0 0 5 0 . 0 0 0 1

T o t a l 30 1 3 5 . 8 2 1

R = 100.00% R'(P red) 99.99% RMad l) = 100.00%

162

5.3.6 Conformity Experiments of Mathematical Models

In order to determine the accuracy of developed mathematical models, the

conformity experiments were conducted using the same experimental set

up. The process parameters were assigned the intermediate values other

than that used in the design matrix and the validation test runs were carried

out. The responses were computed and compared with the predicted

values and are given in Table 5.6 and Table 5.7 for Material Removal Rate

(MRR) and Tool Wear Rate (TWR) mathematical models respectively. The

percentage error of the developed RSM based mathematical models is

found to be within ±5%, which clearly indicate the accuracy of the

developed mathematical models. The experimental and the predicted

values of MRR and TWR for validation data set are illustrated in Fig. 5.5

and Fig. 5.6 respectively.

163

Table 5.6 Conformity experiments for MRR mathematical model

Run Natural values Experimental values

Run / ^on toff e MRR - mmVmin

1 6 20 4 30 Am 2 10 40 5 45 35.16 3 14 60 6 60 54.21 4 17 70 7 75 58.23 5 18 80 8 90 50.14

Predicted values % Error

MRR - mm /min Experimental - Predicted x 100 Experimental

3.864 4.12 33.94 3.47 52.99 2.25 59.58 -2.32 50.99 -1.69

40-

60-1

M 50

s s

u

s 2 20

^ 10

-•— Experimental values -O— Predicted values

Run no

Fig. 5.5 Comparison of experimental and predicted values for MRR

164

Table 5.7 Conformity experiments for TWR mathematical model

Run Natural values Experimental values

Run / ton toff e TWR -mm^/min

1 6 20 4 30 0.285 2 10 40 5 45 0.148 3 14 60 6 60 0.344 4 17 70 7 75 0.742 5 18 80 8 90 0.285

Predicted values % Error

TWR -mm^/min Experimental - Predicted x 100 Experimental

0.293 -2.81 0.154 -4.05 0.331 3.78 0.733 1.21 0.275 2.82

0.8 n

.S 0.6-

s

2 0.4-u

o H 0.2-

-^— Experimental values -O- - Predicted values

T ' r T ^

Run no

Fig. 5.6 Comparison of experimental and predicted values for TWR

165

5.4 EXPERIMENTAL RESULTS AND DISCUSSION

The graphical analysis is the most useful approach to predict the response

for different values of the test parameters and to identify the type of

interactions between test variables. Montgomery DC [160].Hence, analysis

of the parametric influences along with the effect of tool shape with size

factor consideration was done based on Response Surface Methodology

(RSM) and presented in a graphical form. The consolidated graphs are

drawn based on the computed response values obtained from Annexure I

and J (refer to pages-203, 204) for analysis of the parametric influences.

5.4.1 Direct Effects of Process Parameters on MRR and

TWR

5.4.1.1 Effect of Discharge Current on MRR and TWR

Experimentally it is found that increasing discharge current increases the

Material Removal Rate (MRR) and Tool Wear Rate (TWR) (Table 5.8 and

5.9)(Fig. 5.7 and 5.8). It can be seen (Fig. 5.7) that the Material Removal

Rate (MRR) increases almost linearly with the increasing discharge current.

Whereas the Tool Wear Rate (TWR) (Fig. 5.8) increases slowly in the

beginning but then starts increasing rapidly with further increase in

discharge current. The increase in discharge current increases the pulse

energy, which leads to an increase in the rate of heat energy, which is

subjected to both of the electrodes, and in the rate of melting and

166

evaporation hence the Material Removal Rate (MRR) as well as the Tool

Wear Rate (TWR) increases with discharge current [40, 41]

Table 5.8 Effect of discharge current (/) on MRR

Discharge current /

Yi - MRR

4 21.991 8 34.125 12 46.258 16 58.391 20 70.525

a S s a

70-

60

50-

S r 30-

X ^ 20

10

Constant parameters Pulse on-time - 50 ^ Pulse off-time -6 its Tool angle - 60 Deg

-r 4

12

Current (A)

16 — I — 20

Fig. 5.7 Effect of discharge current (/) on MRR

167

Table 5.9 Effect of discharge current (/) on TWR

Discharge current /

/2-TWR

4 0.0192 8 0.0521 12 0.2727 16 2.1961 20 5.3162

6 n

5 -

a 1 4 s s

2

9»

o H

3 -

2 -

1-

Constant parameters Pulse on-time - 50 fis Pulse off-time - 6 s Tool angle - 60 Deg

12

Current (A)

Fig. 5.8 Effect of discharge current (/) on TWR

168

5.4.1.2 Effect of Pulse on-Time Duration on l\/IRR and TWR

In EDM process the thermal energy generates a channel of plasma

between the cathode and anode. E.I. Shobert [167].Generally longer pulse

on-time duration results in a higher Material Removal Rate (MRR) up to

half way in the beginning but then starts decreasing with further increase in

pulse on-time duration (Table 5.10) (Fig.5.9). This event has been

attributed to the increase of input energy in the high pulse on-time, which

results in more chopping on the gap between the workpiece and the tool-

electrode, creating a short circuit which decreases the efficiency of

electrical spark-erosion. In other words short pulse on-time duration cause

less vaporization, whereas long pulse on-time duration causes the plasma

channel to expand, resulting in less energy density on workpiece, which is

insufficient to melt and/or vaporize the workpiece material [15], Chen and

Mahdavian [168].Thus MRR has exhibited increasing tendency in the

beginning and was maximum at half way of pulse on-time, but then started

decreasing with further increase in pulse on-time duration for the range of

investigation carried out.

Tool Wear Rate (TWR) rapidly decreases with increasing pulse on-

time duration in the beginning but then starts decreasing slowly and further

stays constant for longer pulse on-time durations (Table 5.11) (Fig.5.10).

The reasons for low tool wear rate at longer pulse duration settings are:

a) Decreasing spatial cun'ent density of the discharge channel with

increasing discharge pulse on-time duration.

169

b) Longer time for heat transfer from the molten crater to the body of the

tool, which results in less material removal from the crater [42, 43]

c) Higher wear resistance of the tool due to the carbon attached to the

surface [44, 45]

Table 5.10 Effect of pulse on-time duration {ton) on MRR

Pulse on-time 'on

Yi - MRR

4 21.968 27 38.869 50 46.258 73 44.135 96 32.499

50-1

a • mm

a S 40' S

> ^ u

2 o i 30 a •c 4>

20 —r-20

Constant parameters Current -12 A Pulse off-time -6fis Tool angle - 60 Deg

I 40

— I — 60 80

Pulse on-time (}is)

—I 100

Fig. 5.9 Effect of pulse on-time duration (U) on MRR

170

Table 5.11 Effect of pulse on-time duration (ton) on TWR

Pulse on-time 'on

Vz-TWR

4 5.778 27 2.351 50 0.273 73 0.006 96 0.159

Constant parameters Current -12 A Pulse off-time - 6 s Tool angle - 60 Deg

Pulse on-time (^s)

Fig. 5.10 Effect of pulse on-time duration {ton) on TWR

171

5.4.1.3 Effect of Pulse off-Time Duration on MRR

Experimentally it is found that the Material Removal Rate (MRR) almost

increases linearly with increasing pulse off-time duration (Table 5.12)

(Fig.5.11). It is because of correct flushing of the debris with sufficient pulse

off-time duration, otherwise debris/waste particles would collect make the

spark contaminated and unstable, thus decreasing the MRR. However,

longer pulse off-time duration increases spark cycle time which produces

less number of sparks thus decreasing MRR. From (Table 5.13) (Fig.5.12)

it is evident that the TWR decreases with increase in pulse off-time duration

up to halfway in the beginning but then starts increasing with further

increase in pulse off-time duration.

5.4.1.4 Effect of Tool Taper Angle on MRR and TWR

Experimentally it is found that the MRR (Table 5.14) (Fig.5.13) increases

linearly with increasing tool taper angle. Whereas, with increasing tool taper

angle the TWR (Table 5.15) (Fig.5.14) decreases linearly. The MRR

increases with increase in tool taper angle because of reduction in surface

area under erosion. It is also observed that an effective dielectric flushing is

possible with increasing tool taper angle, which helps in effective sparking

and more erosion of metal. On the other hand, TWR decreases with

increase in tool taper angle is mainly due to less heating and melting of tool

electrode because of an improved dielectric flushing and also due to

reduction in tool electrode surface area under erosion.

172

Table 5.12 Effect of pulse off-time duration {toff) on MRR

Pulse off-time toff

Yi - MRR

4 31.621 5 42.599 6 46.528 7 42.599 8 31.621

50-1

JB 1 45

S s

40-u

> o a u

a 35 •c

30

Constant parameters Current -12 A Pulse on-time - 50 fis Tool angle - 60 Deg

- r 4

~r 6

-r 7

Pulse off-time (us)

Fig. 5.11 Effect of pulse off-time duration (toff) on MRR

173

Table 5.13 Effect of pulse off-time duration (toff) on TWR

Pulse off-time toff

Yi-TWR

4 0.507 5 0.331 6 0.273 7 0.331 8 0.507

0.60-|

0.55-J

^ 0.50-a

'i r," 0.45 H

S S r 0.40 u fm 0.35-1 a

- 5 0.30 H o H

0.25 H

0.20-

Constant parameters Current -12 A Pulse on-time - 50 fis

5 6 7

Pulse ofT-time (^s)

Fig. 5.12 Effect of pulse off-time duration (W) on TWR

174

Table 5.14 Effect of tool taper angle (0) on MRR

Tool taper angle e

Yi - MRR

30 44.313 45 45.286 60 46.258 75 47.231 90 48.203

48- Constant oarameters Current -12 A

•mm

a Pulse on-time - 50 ps •mm

a Pulse off-time - 6 fis S 47-S, 9i

2 H 46-

B u

1 45-

AA _ 1 ' 1 '

30 45 1

60 1

75 . 90

Tool angle (Deg)

Fig. 5.13 Effect of tool taper angle (9) on MRR

175

Table 5.15 Effect of tool taper angle (0) on TWR

Tool taper angle 9 Vj-TWR

30 0.442 45 0.357 60 0.273 75 0.188 90 0.103

0.45

0.40-

9 ' 0.35-I "^a 0.30-a, « « 0.25 H u u es % 0.20-

o H 0.15-

0.10-—t— 30

Constant parameters Current -12 A Pulse on-time - 50 fis Pulse off-time - 6 ps

45 60 75 —r-90

Tool angle (Deg)

Fig. 5.14 Effect of tool taper angle (0) on TWR

176

5.4.1.5 Consolidated Graph Showing Direct Effect of

Process Parameters on Material Removal Rate (MRR)

The graph of Material Removal Rate (MRR) is drawn based on the

experimental response values obtained from Table 5.3 for the analysis of

parametric influences.

idfects of pi^cess parametiers on Material removal fate (MRR)

70

10 -2 0 2

" Cnrrcnt -2 0 2

Pulse-on Pulse-off Taper angle

Fig. 5.15 Direct effect of process parameters on Material Removal Rate

(MRR)

177


Process Parameters on Tool Wear Rate (TWR)

The graph of Tool Wear Rate (TWR) is drawn based on the experimental

response values obtained from Table 5.3 for the analysis of parametric

influences.

Direct effects of process parameters on Tool wear rate (TWR)

-2 0 2 -2 ' 0 2 I I I I I I

6-

5-

3 ! ^ -

:• , 1 -

0-

J V ^ ^ _ _ _ _ _ _ ^ ^ ^

-2 0 2 -2 0 2 Current Pulsc-on Poise-off Taper angle

Fig. 5.16 Direct effect of process parameters on Tool Wear Rate (TWR)

178

Table 5.16 Experimental layout plan as per CCD with responses and RTW

o z 16 1-

o . z

c 1}

a:

Coded values Responses Relative tool wear o z 16 1-

o . z

c 1}

a: Xi X2 X3 X4

MRR mm /min

TWR mm /min

TWR/MRRxlOO RTW-%

o z 16 1-

o . z

c 1}

a: Xi X2 X3 X4

Yi Yi Ri 1 28 -1 -1 -1 -1 24.192 0.463 1.913 2 18 +1 -1 -1 -1 44.114 5.771 13.08 3 15 -1 +1 -1 -1 25.131 0.091 0.362 4 3 +1 +1 -1 -1 52.915 0.462 0.873 5 29 -1 -1 + 1 -1 24.189 0.485 2.005 6 30 +1 -1 + 1 -1 44.137 5.696 12.90 7 24 -1 +1 + 1 -1 25.141 0.163 0.648 8 13 +1 +1 + 1 -1 53.321 0.413 0.774 9 1 -1 -1 -1 +1 26.165 0.402 1.536 10 22 +1 -1 -1 +1 46.134 5.465 11.84 11 4 -1 +1 -1 +1 27.127 0.072 0.265 12 16 +1 +1 -1 +1 54.317 0.182 0.335 13 12 -1 -1 + 1 +1 26.185 0.453 1.729 14 27 +1 -1 + 1 +1 46.122 5.390 11.68 15 17 -1 +1 +1 +1 27.127 0.147 0.541 16 6 +1 +1 +1 +1 55.317 0.107 0.193 17 14 -2 0 0 0 21.189 0.016 0.075 18 21 2 0 0 0 71.217 5.303 7.446 19 10 0 -2 0 0 21.452 5.767 26.88 20 20 0 2 0 0 33.469 0.154 0.460 21 9 0 0 -2 0 31.798 0.496 1.559 22 11 0 0 2 0 31.898 0.502 1.573 23 19 0 0 0 -2 44.261 0.448 1.012 24 31 0 0 0 2 48.254 0.095 0.196 25 5 0 0 0 0 47.044 0.256 0.544 26 26 0 0 0 0 44.430 0.271 0.609 27 23 0 0 0 0 46.830 0.273 0.582 28 2 0 0 0 0 45.240 0.288 0.636 29 25 0 0 0 0 46.588 0.276 0.592 30" 8 0 0 0 0 46.438 0.272 0.585 31 7 0 0 0 0 47.236 0.273 0.577

179


Process Parameters on Relative Tool Wear (RTW)

The graph of Relative Tool Wear (RTW) Is drawn based on the computed

values obtained from Table 5.16 for the analysis of parametric influences.

Direct effects of process parameters on Relative tool wear (RTW)

-2 0 2 -2 0 2 1 1 7 I I I

30-

25-

20-

^ 15-

s ID

S'

0-

y \

30-

25-

20-

^ 15-

s ID

S'

0-

y \

• • I 1 1 1

-2 0 2 -2 0 2 Current PuUe-«D Pulse-off Taper angle

Fig. 5.17 Direct effect of process parameters on Relative Tool Wear (RTW)

180

5.4.2 Interaction Effects of Parameters on MRR and TWR

Interaction effects of machining process parameters on IVIRR and TWR are

also presented in graphical form for quick analysis (Tables 5.17, 5.18, 5.19

and 5.20) (Figures 5.18, 5.19, 5.20 and 5.21).

5.4.2.1 Interaction Effect of Current and Pulse on-Time on

MRR

From (Table 5.17) (Fig. 5.18), it is evident that MRR increases with an

increase in discharge current at all levels of pulse on-time duration.

However, if the pulse on-time duration is increased above 70ps, MRR

starts decreasing with further increase in pulse on-time duration for all

levels of discharge current. The reasons for this event have been already

explained and depicted in (Tables 5.8 and 5.9) (Figs. 5.7 and 5.8)

5.4.2.2 Interaction Effect of Current and Pulse on-Time on

TWR

From (Table 5.18) (Fig. 5.19), it can be observed that the TWR increases

with an increase in discharge current for all levels of pulse on-time duration.

It is also evident that the TWR decreases with increasing pulse on-time

duration for all levels of current. But it is interesting to note that, at low

levels (below 8A) of current TWR further starts increasing with pulse on-

time duration above 50iJS. The reasons for this event have been already

explained and depicted in (Tables 5.9 and 5.10) (Figs. 5.9 and 5.10)

181

Table 5.17 Interaction effect of discharge current (/) and pulse on-time

duration {ton) on MRR

Pulse on-time (ton)

Discharge current (/) Pulse on-time (ton) 4 8 12 16 20 4 5.5950 13.781 21.968 30.154 38.340 27 18.550 28.709 38.869 49.028 59.187 50 21.993 34.126 ^46.258 58.390 70.523 73 15.924 30.029 44.135 58.240 72.345 96 0.3430 16.421 32.499 48.578 64.656

80-1

Current ->—04A

08 A 12

Constant parameters Pulse off-time - 6 ^s Tool angle - 60 Deg

40 60

Pulse on-time (^s)

100

Fig. 5.18 Interaction effect of discharge current (/) and pulse on-time

duration (ton) on MRR

182

Table 5.18 Interaction effect of discharge current (/) and pulse on-time

duration {ton) on TWR

Pulse on-time

(U Discharge current (/) Pulse on-time

(U 4 8 12 16 20 4 0.568 2.574 5.778 10.18 15.78 27 0.001 0.387 2.351 5.514 9.874 50 0.019 0.002 0.273 2.196 5.316 73 1.767 0.056 0.002 0.226 2.107 96 4.863 1.913 0.159 0.001 0.246

a 1 s s

> ^ 4>

•<-> et b

o H

Constant parameters Pulse off-time -6 fis Tool angle - 60 Deg

Current ^ -04 A w -04 A

-08 A -08 A -12 A - 1 6 A

t% -20 A w -20 A

40 60

Pulse on-time (fis)

Fig. 5.19 Interaction effect of discharge current (/) and pulse on-time

duration {ton) on TWR

183

5.4.2.3 Interaction Effect of Current and Pulse off-Time

Duration on TWR

From (Table 5.19) (Fig. 5.20). it is evident that Tool Wear Rate (TWR)

increases with an increase in discharge current at all levels of pulse off-

time duration. However, Tool Wear Rate (TWR) decreases with increasing

pulse off-time duration for all levels of discharge current up to halfway in

the beginning but then slowly starts increasing with further increase in

pulse off-time duration. The reasons for this event have been already

explained and depicted in (Table 5.13) (Fig. 5.12).

5.4.2.4 Interaction Effect of Current and Tool Taper Angle on

TWR

From (Table 5.20) (Fig. 5.21), it is evident that Tool Wear Rate (TWR)

increases with an increase in discharge current at all levels of tool taper

angle. However, Tool Wear Rate (TWR) decreases with an increase in tool

taper angle at all levels of discharge cun-ent. The reasons for this event

have been already explained and depicted in (Table 5.15) (Fig. 5.14).

184

Table 5.19 Interaction effect of discharge current (/) and pulse off-time

duration {toft) on TWR

Pulse off-time ( toff)

Discharge current (/) Pulse off-time ( toff) 4 8 12 16 20 4 0.001 0.001 0.507 1.893 3.279 5 0.002 0.001 0.331 1.686 3.041 6 0.019 0.002 0.273 1.597 2.921 7 0.081 0.002 0.331 1.625 2.918 8 0.147 0.003 0.507 1.769 3.032

3.5-1

3.0-

-5^2.5^ •mm

S

^ 1.5-1 2 2 1.0

"o o 0.5 H H

0.0-

Constant parameters Pulse on-time - 50 ^ Tool angle - 60 Deg

5 6 7

Pulse off-time (^s)

Fig. 5.20 Interaction effect of discharge cun-ent (/) and pulse off-time

duration (tafd on TWR

185

Table 5.20 Interaction effect of discharge current (/) and tool taper angle

(0) on TWR

Tool taper angle (e)

Discharge current (/) Tool taper angle (e) 4 8 12 16 20 30 0.001 0.001 0.273 2.329 5.584 45 0.002 0.002 0.273 2.263 5.450 60 0.019 0.003 0.273 2.196 5.316 75 0.002 0.004 0.273 2.129 5.183 90 0.001 0.004 0.273 2.062 5.049

5.5-

5.0-

4.5-

.2 4.0-

s m 3.5 -a a 3.0-

I"-U h 2.0-9>

^ 1.5-

1 i.o: H

0.5-0.0-

Constant parameters Pulse on-time - 50 s Pulse off-time - 6 ^s

—r-30

— I — 45

—f—

60 — r — 75 90

Taper angle (Deg)

Fig. 5.21 Interaction effect of discharge current (/) and tool taper angle {&)

on TWR

186

5.5 EFFECT OF PROCESS PARAMETERS ON RESPONSES

5.5.1 Area Graph for Material Removal Rate (MRR)

The Area graph of Material Removal Rate (MRR) is drawn based on the


parametric influences. The area graph of Material Removal Rate (MRR) for

taper tool electrodes with size factor consideration is shown in Figure 5.22.

' t ^ . . - . ^ -

80-f

Area graph of Metal removal rate (MRR)

15 18 Run DOS

Fig. 5.22 Area graph of Material Removal Rate (MRR)

187

5.5.2 Area Graph for Tool Wear Rate (TWR)

The Area graph of Tool Wear Rate (TWR) is drawn based on the


parametric influences. The area graph of Tool Wear Rate (TWR) for taper

tool electrodes with size factor consideration is shown in Figure 5.23.

Area graph of Tool wear rate (TWR)

Fig. 5.23 Area graph of Tool Wear Rate (TWR)

188

5.5.3 Area Graph for Relative Tool Wear (RTW)

The Area graph of Relative Tool Wear (RTW) is drawn based on the

computed values obtained from Table 5.16 for the analysis of parametric

influences. The area graph of Relative Tool Wear (RTW) for taper tool

electrodes with size factor consideration is shown in Figure 5.24.

30

Area graph of Relative tool wear (RTW)

3 6 9 12 15 18 21 24 27 30 ' '• ' •' Runnos

Fig. 5.24 Area graph of Relative Tool Wear (RTW)

189

Summary

The present work deals with the Response Surface Methodology (RSM)

based Investigations on Material Removal Rate (MRR) and Tool Wear Rate

(TWR) to study the effect of tool taper angle with size factor consideration

in sink Electrical Discharge Machining (sink-EDM) process. The

experiments were planned as per Central Composite Design (CCD) and

second order mathematical models were developed to establish the

relationships between the process parameters (discharge current, pulse

on-time, pulse off-time and tool taper angle) and the responses (MRR and

TWR). The Analysis of Variance (ANOVA) was employed along with

Fisher's test (F-test) at 95% confidence interval to verify the lack-of-fit and

adequacy of developed models. Based on the experimental results, the

conclusions are drawn within the ranges of the process parameters

selected.

<N» " * ^ * # ^ * • * *

190

mathematical modeling of sink-edm process parameters for different tool...

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