Statistical and Regression Analysis of Material Removal Rate for Wire Cut Electro Discharge Machining of Ss 304L Using Design of Experiments

8/10/2019 Statistical and Regression Analysis of Material Removal Rate for Wire Cut Electro Discharge Machining of Ss 304L

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Vishal Parashar et. al. / International Journal of Engineering Science and Technology

Vol. 2(5), 2010, 1021-1028

Statistical and regression analysis of Material

Removal Rate for wire cut Electro Discharge

Machining of SS 304L using design ofexperimentsVishal Parashar a*, A.Rehman b, J.L.Bhagoria c, Y.M.Puri d

a, b ,cDepartment of Mechanical Engineering, Maulana Azad National Institute of Technology, Bhopal, M.P.,

462051, India.dDepartment of Mechanical Engineering, Vishweshvariya National Institute of Technology, Nagpur, Maharastra,

India.

Abstract

In this paper, statistical and regression analysis of Material removal rate (MRR) using design of experiments is

proposed for WEDM operations. Experimentation was planned as per Taguchis L32 (21X 44) mixed orthogonalarray. Each experiment has been performed under different cutting conditions of gap voltage, pulse ON time, pulseOFF time, wire feed and dielectric flushing pressure. Stainless Steel grade 304L was selected as a work material to

conduct the experiments. From experimental results, the MRR was determined for each machining performance

criteria. Analysis of variance (ANOVA) technique was used to find out the variables affecting the MRR.Assumptions of ANOVA were discussed and carefully examined using analysis of residuals. Variation of the MRR

with machining parameters was mathematically modeled by using the regression analysis method. Finally, the

developed model was validated with a new set of experimental data and appeared to be satisfactory.

Keywords: ANOVA, Material Removal Rate (MRR), Taguchi method, WEDM.

1. Introduction

Wire cut electro discharge machining (WEDM), a form of EDM, is a non-traditional machining methodthat is widely used to pattern tool steels for die manufacturing. WEDM uses electro-thermal mechanisms to cut

electrically conductive material. The material is removed by a series of discrete discharges between the wire

electrode and the work material in the presence of a dielectric fluid. Which creates a path for each discharge as the

fluid becomes ionized in the gap. The region in which discharge occurs is heated to extremely high temperatures, so

that the work surface is melted and removed. The flowing dielectric then flushes away the removed particles. The

strength and hardness of the work materials are not significant factors in EDM. Only the melting point of the workmaterial is an important property. Although WEDM machining is complex, the use of this machining process in

industry has increased because of its capability in cutting complicated forms, especially created in hard materials

[1]. Among the various non-conventional machining methods available, EDM is the most widely used andsuccessfully applies one for the difficult to machine materials [2]. WEDM has become the essential part of many

manufacturing process industries, which need variety, precision and accuracy. Therefore, in order to improve the

various performance characteristics in WEDM process, several researchers attempted previously. However, the full

potential utilization of this machining process is not completely solved because of its complex and stochastic nature

and the increased number of variables involved in the operation [3-5]. The setting of machining parameters reliesstrongly on the experience of operators and machining parameter tables provided by machine tool builders. It is

difficult to utilize the optimal functions of a machine owing to there being too many adjustable machining

parameters [6]. The Taguchis dynamic experiments are simple, systematic and efficient method to determine

optimum or near optimum settings of machining parameters [7-9]. The analysis of variance (ANOVA) is widelyused to consider effects of factors on responses. In experimental investigations, ANOVA is often employed prior to

other statistical analysis. Then regression analysis which establishes a relation between independent variables and

dependent variables is widely applied [6]. The most important performance measure in WEDM is material removal

rate. In WEDM operations, material removal rate (MRR) determines the economics of machining and rate of

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production. In setting the machining parameters, the main goal is the maximum MRR with the minimum Kerf

Width. It is the measure of the amount of material that is wasted during machining.

The main purpose of this paper is to investigate effects of machining parameters on the material removalrate of wire EDMed Stainless Steel grade 304L. From the basic principle and characteristic feature of the WEDM

process for the machining of SS 304L , It has been observed that the machining parameters, such as gap voltage,

pulse on-time, pulse off-time, wire feed and dielectric flushing pressure are the important controllable process

parameters of the WEDM process, therefore, these machining parameters are used for the investigation. A properdesign of experiments (DOE) is conducted to perform more accurate, less costly, and more efficient experiments. Inthe present research, an L32 (21X 44) Taguchi standard orthogonal array was selected for the design of experiments

[10]. Analysis of variance (ANOVA) was used as the analytical tool in studying effects of these machiningvariables. Assumptions of ANOVA were discussed and carefully examined using analysis of residuals. A

mathematical model was developed using multiple regression method to predict MRR.

2. Experimental details

2.1 Material

In this study, stainless steel grade 304 L was applied as work material for experimentation. The chemical

composition of the selected work material is shown in table 1.Table 1: Chemical composition of Stainless Steel grade 304L.

S.no. Chemical Percentage

1. Chromium 18.37%

2. Nickel 8.19%

3. Manganese 1.80%

4. Copper 0.58%

5. Silicon 0.54%

6. Phosphorus 0.039%

7. Nitrogen 0.037%

8. Carbon 0.021%

9. Sulphur 0.019%

10. Fe Balance

2.2 Machine, electrode and dielectric

The Experiments were carried out using CNC Ezeecut plus WEDM machine. Brass wire of 0.25 mm

diameter was used as tool electrode in the experimental set up. This is a diffused wire of brass of type Duracut-E.

Blasocut 4000 strong that is used as a dielectric fluid was chosen for this experimentation. This is a water misciblemetal working fluid.

2.3 Planning of experiments

In each experiment, a 10 mm width of work material was made to cut. The work material height was

selected as 15.75 mm, 25 mm and 29.50 mm respectively for the three replications of the experiment. The reason for

selecting the variable thickness is to obtain the results for wide range. During the process, the wire diameter was

kept constant. Therefore the MRR for WEDM operation was calculated using Eq. (1), which is shown below:

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MRR = Vc x B x H (mm3/min) (1)

Where, Vc = machining speed (mm/min),B = (2Wg + d) (mm)

Wg = wire gap (mm)

D = diameter of electrode wire (mm)

H = thickness of the job (mm)

The machining parameters which vigorously affect the MRR are identified based on experience, discussion made

with the expert, survey of literature [1, 3, 4, 8, 9]. Those are shown in table 2.

Table 2: Selected machining parameters and their levels

S.no. Factor Unit Level

1 2 3 4

1 Gap Voltage Volts 75 100 - -

2 Pulse ON time Milliseconds 0.12 0.16 0.15 0.08

3 Pulse OFF time Milliseconds 0.5 0.6 0.7 0.8

4 Wire Feed RPM 700 800 900 1000

5 Flushing Pressure Kgf/cm2 0.02 0.04 0.06 0.08

3. Data analysis

To obtain a reliable database, each experiment was repeated three times and the mean values were

calculated. After all experiments are conducted, decisions must be made concerning which parameters affect theperformance of a process and a mathematical model is developed to predict output amounts close to the actual

amounts.

4. Analysis of variance

Analysis of variance (ANOVA) for material removal rate was performed to study influences of the wire

EDM machining variables. It is used to test the null hypothesis with regard to the data gained through experiments.

Through null hypothesis it is assumed that there is no difference in treatment means (H0: 1= 2= .. = a). Table3 is ANOVA table for MRR. Before any inferences can be made based on ANOVA table, the assumptions used

through ANOVA process have to be checked. The assumptions underlying the ANOVA tell the residuals are

determined by evaluating the following Equation [11].

eij= yij- ij (2)

Where eij is the residual, yij is the corresponding observation of the experimental runs, ijis the fitted value.

A check of the normality assumption may be made by constructing the normal probability plot of the residuals.

Figure 1 depicts normal plot of residuals. This plot is used to test the normal distribution of errors. If the underlyingerror distribution is normal, this plot will resemble a straight line [12]. This distribution shown in figure 1 presents

that the error normality assumption is valid. Figure 2 shows plotting of the residuals in time order of data collection.

This method is helpful in checking independence assumption on the residuals. It is desired that the residual plotshould contain no obvious patterns. Figure 2 presents that independence assumption on the residuals was fulfilled

for this experiment. Figure 3 shows plot of residual versus fitted values. The structure less distribution of dots aboveand below the abscissa (fitted values) shows that the errors are independently distributed and the variance is constant

[12]. Therefore it can be concluded that the assumption of constant variance of residuals was satisfied. Now those

assumptions are proved not to be violated through this experimentation it can be relying on ANOVA results.Confidence level is chosen to be 95% in this study. So the p values which are less than 0.05 indicate that null

hypothesis should be rejected, and thus the effect of the respective factor is significant. The variance ratio denoted

by F in ANOVA tables, is the ratio of the mean square due to a factor and the error means square. In robust design Fratio can be used for qualitative understanding of the relative factor effects. A large value of F means that the effect

of that factor is large compared to the error variance. So the larger value of F, the more important that factor is in

influencing the process response [11]. In present study, from table 3, the most important factor was gap voltage with

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478.16 F ratio and importance of other factors based on the F ratio was respectively pulse on time and pulse off

time. Wire feed with 1.03 F ratio and flushing pressure with 1.55 F ratio has no effect on material removal rate.

Table 4 provides information about proportionality of influential factors with regard to ANOVA results.

Table 3: Analysis of variance for MRR

Source DF Seq SS Adj SS Adj MS F P

Gap vol t age 1 91. 598 91. 598 91. 598 478. 16 0. 000Pul se on t i me 3 33. 803 33. 803 11. 268 58. 82 0. 000Pul se of f t i me 3 51. 622 51. 622 17. 207 89. 83 0. 000Wi r e f eed 3 0. 593 0. 593 0. 198 1. 03 0. 402Fl ushi ng pr essur e 3 0. 890 0. 890 0. 297 1. 55 0. 236Er r or 18 3. 448 3. 448 0. 192

Tot al 31 181. 954

Fig1: Normal plot of residuals

5 10 15 20 25 30

-0.5

0.0

0.5

Observation Order

Residual

Residuals Versus the Order of the Data(Response is material removal rate)

Fig 2: Residuals in time order

-0.5 0.0 0.5

-2

-1

0

1

2

NormalScore

Residual

Normal Probability Plot of the Residuals(Response is material removal rate)

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Regression analysis is then performed on the response variable as a function of coded factors. The general model to

predict the MRR over the experimental region can be expressed as Equation 3.

y = 0+ 1x1+ 2x2+ 3x3 (3)Where y is the response and x1,x2, x3are the coded factors respectively. s are regression coefficients. The

derived regression equation is as follows

MRR = 9.29 + 6.77 Gap voltage + 1.09 Pulse on time 1.57 Pulse off time (4)

From Equation 4, the factors gap voltage and pulse on time have an additive effect on the MRR and pulseoff time has negative impact on MRR. Analysis of the residuals of the model shown in equation 4 was performed totest assumptions of normality (fig 4), independence (fig 5), and constant variance (fig 6) of residuals. The

quantitative test methods mentioned earlier were employed again, and none of the assumptions was violated.

-1 0 1

-2

-1

0

1

2

NormalS

core

Residual

Normal Probability Plot of the Residuals

(response is MRR)

Fig. 4 Normal plot of residuals

5 10 15 20 25 30

-1

0

1

Observation Order

Residual

Residuals Versus the Order of the Data(response is MRR)

Fig 5: Residuals in time order

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1 2 3 4 5 6 7 8 9

-1

0

1

Fitted Value

Residual

Residuals Versus the Fitted Values

(response is MRR)

Fig 6: Residuals vs. fitted values

Table 5: ANOVA for regression analysis

Source DF SS MS F P

Regr essi on 3 164. 531 54. 844 88. 14 0. 000Resi dual Er r or 28 17. 423 0. 622

Tot al 31 181. 954

Analysis of variance was derived to examine the null hypothesis for the regression model that is presented

in table 5. The results indicate that the estimated model by the regression procedure is significant at the level of

confidence (0.05). R-squared (R2) amount was calculated to check the goodness of the fit. R2 is a measure of the

amount of reduction in the variability of response obtained by using the regressor variables in the model. Because R2

always increases as we add terms to the model, some regression model builders prefer to use an adjusted R2

statistic.In general, the R2adjstatistic will not always increase as variables are added to the model. In fact, if unnecessary

terms are added, the value of R2adjwill often decrease. When R2and R2adjdiffer dramatically, there is a good chance

that non significant terms have been included in the model [12]. For this experiment the R2value indicates that the

predictors explain 90.4% of the response variation. Adjusted R2 for the number of predictors in the model was

89.4% both values shows that the data are fitted well.

The prediction model was then validated with another set of data. Table 6 shows verification of the tests

results for material removal rate. The predicted machining parameters performance is compared with the actualmachining performance and a good agreement is observed between these performances. In table 6 process factors

are shown in terms of natural factors and their corresponding coded factors. In order to evaluate the accuracy of the

prediction model, percentage error and average percentage error were used. Percentage of prediction errors is shown

in the last column of table 6. The maximum prediction error was 9.2 % and the average percentage error of thismethod validation was about 4.7 %. As a result, the prediction accuracy of the model appeared satisfactory.

6. Conclusion

This paper illustrates that the application of statistical analysis coupled with Taguchi design of experiments is

simple, effective, and efficient in developing a robust and versatile EDM process. Results from this study were in

agreement with findings in literature in which material removal rate of EDMed workpiece depended on gap voltage,

pulse on time and pulse off time [1, 3, 5, 6, 8, 11]. Although those research efforts performed on different materialsother than SS304L, the outcomes were in accordance. The parameters affecting the MRR were identified using

ANOVA technique. Assumptions of ANOVA were tested using residual analysis. After careful testing, none of the

assumptions was violated. Results showed that gap voltage, pulse on time

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Table 6: Prediction values and errors

Natural factors Coded factors Predicted

values

(mm3/min)

Experimental

values

(mm3/min)

Percentag

e error

(%)

Gap

voltage

(volts)

Pulse on

time

(milliseconds)

Pulse off

time

(milliseconds)

X1 X2 X3

75

75

7575

100

100100

100

100

100

100

100

0.12

0.16

0.160.08

0.16

0.15

0.08

0.120.16

0.15

0.08

0.15

0.5

0.6

0.5

0.70.7

0.6

0.5

0.8

0.70.6

0.5

0.5

-1

-1

-1

-1

-0.5

-0.5-0.5

-0.5

-0.5-0.5

-0.5

-0.5

-1

-0.5

-0.51

-0.5

0.51

-1

-0.5

0.5

1

0.5

-1

-0.5

-10.5

0.5

-0.5

-11

0.5

-0.5

-1

-1

3.00

2.76

3.542.82

6.14

7.23

8.56

3.24

6.147.23

8.56

8.02

2.96

2.84

3.90

2.54

5.96

7.708.40

3.14

5.676.82

8.64

8.65

1.2

2.89.2

9.2

2.9

6.11.8

3.0

7.6

5.60.9

7.2

and pulse off time are the significant factors, while wire feed and flushing pressure are the non significant factors to

the MRR of wire EDMed SS304L. Finally a mathematical model was developed using multiple regression method

to formulate the gap voltage, pulse on time and pulse off time to the MRR. The developed model showed highprediction accuracy within the experimental region. The maximum prediction error of the model was 9.2% and the

average percentage error of prediction was 4.7%.

References

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[2] P.M. George, B.K. Raghunath , L.M.Manocha, Ashish M. Warrier, EDM machining of carboncarbon compositea Taguchi approach,Journal of Materials Processing Technology 145 (2004) 6671.

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[4] Shajan Kuriakose, M.S. Shunmugam, Multi-objective optimization of wire-electro discharge machining process by Non-Dominated SortingGenetic Algorithm, journal mater. Process.technol.170 (2005)133-141.

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[9] Aminollah Mohammadi, Alireza Fadaei Tehrani, Ehsan Emanian, Davoud Karimi, A new approach to surface roughness and roundnessimprovement in wire electrical discharge turning based on statistical analyses, Int J Adv Manuf Technol (2008) 39:6473.

[10] M.S. Phadke, Quality Engineering Using Robust Design, Prentice- Hall, Englewood Cliffs, NJ, 1989.[11] P. Matoorian, S. Sulaiman, M.M.H.M. Ahmad, An experimental study for optimization of electrical discharge turning (EDT) process,

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Statistical and Regression Analysis of Material Removal Rate for Wire Cut Electro Discharge Machining of Ss 304L Using Design of Experiments