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DEVELOPMENT OF MULTI OBJECTIVE OPTIMIZATIONMODEL FOR ELECTRICAL DISCHARGE MACHINING

(EDM)

N. Harikannan Asst. Prof.R.Murali Krishnan, C.Senthil kumar, V.Vigneswaran, T.Vinodh

Department of Mechanical EngineeringPSNA College of Engineering and Technology,

\Dindigul-624622,India.

Email: kannan.me@gmail.com

Abstract

The paper investigates the parameter optimization of an electrical discharge machining process for improving the cutting performance. A suitable selection of machining parametersfor the EDM process relies heavily on the operators technologies and experience because of their numerous and diverse range. In this paper, voltage, peak current, pulse-on time and gapcurrent are considered as machining parameters and the major performance characteristicsselected to evaluate the process are metal removal rate, electrode wear and surfaceroughness. By applying grey relational analysis, the grey grade is evaluated to represent themulti objective model. Multiple regression models have been developed to map therelationship between process parameters and objectives in terms of grade. The predicted grade is found and then the percentage deviation between the experimental grade and

predicted grade is calculated for each model. The average percentage deviations for the dataof the linear regression model and logarithmic transformation model, excluding interactionterms are examined. Based on the testing results of grey relational analysis, the optimal

process parameters are identified. Finally, ANOVA is used to identify the significance of multiple regression model.

Keywords: Electrical Discharge Machining, Grey Relational Analysis, Regression Model, Analysis of variance

1. INTRODUCTION

Electrical discharge machining (EDM) is a thermo electric process, which producesinnumerable sparks between the tool electrode and the work piece [1]. Electricaldischarge machining (EDM) processes are now gaining in popularity, since manycomplex 3D shapes can be machined using a simple shaped tool eletrode. The pair

of electrodes is sunken into a dielectric fluid and open voltage is applied. Aservomechanism maintains a space of about the thickness of a human hair betweenthe electrode and the work, preventing them from contacting each other as shown inFig. 1. B oth parts are placed very close with the gap distance of the order of m, topermit plasma channel creation between the anode and the cathode. When gapwidth between the tool and the electrode achieves the maximum sparking gap width,a micro-conductive ionized path appears and the electric spark occurs achievingtemperatures up to 15,000 or 20,000 C . Conductive material is then molten and/or vaporized from the work piece. Since the EDM process does not involve mechanicalenergy, the removal rate is not affected by either hardness, strength or toughness of the work piece material [2]. The absence of direct contact between the tool and theelectrode caused by the nature of the process avoid common process problems suchas mechanical stresses and vibrations as in conventional machining processes.Many researchers have so far concentrated on the process improvement in EDM, but

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not on the development of multi-objective models to correlate the various machiningparameters on the predominant electrical discharge machining criteria. Keeping thisconsideration in view, the attempt have been made to develop multi-objective modelsto study the influence of machining parameters on machining performance criteriasuch, as Metal removal rate ( MRR ), Electrode wear ( EW ) and surface roughness(SR ).

Figure 1 Electrical Discharge Machine

2. EXPERIMENTAL WORK

The experimental setup is shown in Fig. 1. The setup consists of Machining cell EDM control system Electrolyte circulation

2.1 Machining cell

The electro-mechanical assembly is a sturdy structure, associated with precisionmachined components, servomotorized vertical up/down movement of tool, anelectrolyte dispensing arrangement. All the exposed components and parts haveundergone proper material selection and coating/plating for corrosion protection.

Tool area- 500 mm2 Cross head stroke- 250 mm Job holder- 100 mm opening50 mm depth100 mm width

2.2 EDM control system

The power supply is a perfect integration of high current electrical, power electronicsand precision programmable micro-controller-based technologies. Since the machine

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operates at very low voltage, there are no chances of any electrical shocks duringoperation.

Electrical output rating- 060 Amps Voltage from 0100 V Supply- 415 v +/ 10%, three-phase AC, 50 Hz

2.3 Electrolyte circulation

The electrolyte is pumped from a tank, lined by corrosion resistant coating with thehelp of corrosion resistant pump and is fed to the job. The reservoir providesseparate settling, filtering and siphoning compartments.

2.4 Machining processes

The job to be machined is fixed in the vice. The machining chamber is corrosion

resistant. A window allows the operator to view the machining process. The toolprogress is maneuvered vertically by the servo motor and is governed by a micro-controller based programmable drive. In EDM, generally a cathode tool is made outof non-reacting material, such as copper. The process parameters, like voltage, peakcurrent, pulse-on time and gap current are set. The process is started in thepresence of an electrolyte flow that is circulated with the help of special pump fillingthe gap between anode (job) and cathode (tool). Electrolyte flow is adjusted by flowcontrol valve. During the operation, a sophisticated control panel system takes careof any damage to the machine with overload and short circuit protections. After thedesired time interval, a hooter gives an indication of completion of the process.

Table 1. Level of machining parameters

Levels Low Medium HighVoltage 30 40 45

Peak current 2 10 40Pulse on time 10 500 1000Gap current 1.3 10 14

The specimen is prepared as a rectangular blank of 24 mm length, 12 mm breadthand 19 mm height and is made up of oil hardened non shrinking steel which ismachined by EDM. The dielectric fluid used is distilled water. The observations of themachining process are based on taguchi L9 orthogonal array design and variouslevels as shown in Table 1 and 2 resp., A total of four machining parameters(voltage, peak current, pulse-on time and gap current) were chosen. The machiningresults after EDM process are evaluated based on three machining performances,MRR (mm 3/min), EW (%) and SR (m). The observation of the EDM process isshown in Table 3.

Table 2. L9 Orthogonal array Table 3. Observations of the EDM process

Machining parameters Responses

Trialno.

A B C D Voltage(V)

Peakcurrent

(A)

Pulseon

time(s)

Gapcurrent

(A)

MRR(mm 3 /min )

EW(%)

SR(m)

1. 1 1 1 1 30 2 10 1.3 9.388 7.450 2.120

2. 1 2 2 2 30 10 500 10 22.450 3.390 5.8903. 1 3 3 3 30 40 1000 14 34.010 1.040 3.6504. 2 1 2 3 40 2 500 14 10.565 9.550 2.410

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5. 2 2 3 1 40 10 1000 1.3 23.372 3.910 6.2306. 2 3 1 2 40 40 10 10 34.460 1.110 3.9807. 3 1 3 2 45 2 1000 10 11.393 10.830 2.7308. 3 2 1 3 45 10 10 14 24.660 5.020 6.8409. 3 3 2 1 45 40 500 1.3 35.090 1.610 4.870

3. MULTI RESPONSE MODEL USING GREY RELATIONAL ANALYSIS

The relationship between various factors mentioned in the previous section isunclear. Such systems are called grey, implying poor, incomplete and uncertaininformation. Their analysis by standard statistical procedure may not be acceptableor reliable without large data sets. In this work, grey relational analysis (GRA) hasbeen used to convert the multi-response optimization model into a single responsegrey relational grade. Instead of using experimental values directly in multipleregression model, grades are used to study about multi-response characteristics.

The following steps to be followed while applying grey relational analysis:

(a). Normalizing the experimental results of MRR and surface roughness to avoid theeffect of adopting different units to reduce the variability.

(1)

(2)(b). Performing the grey relational generating and calculating the grey coefficient for the normalized values yield

(3)Where,

1. j=1,2,n; k=1,2,m, n is the number of experimental data items and m is thenumber of responses.

2. is the reference sequence( =1, k=1,2,m); is the specificcomparison sequence.

3. is the absolute value of the difference betweenand

4. is the smallest value of 5. is the largest value of 6. is the distinguishing coefficient which is defined in the range 0 1 (the

value may adjusted based on the practical needs of the system)

(c). Calculating the grey relational grade by averaging the grey relational coefficientyields

(4)Where,

is the grey relational grade for the j th experiment and k is the number of performance characteristics.Equation ( 1) is used to normalize the experimental value when the target of theoriginal value is having the characteristic of higher the better. Here MRR isnormalized using the above equation. When the lower the better is a characteristic

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of the original sequence, then the original sequence is normalized using Eq. ( 2), i.e.,EW and SR are normalized using this equation. Using Eq. ( 3), we calculate the greyrelational coefficient for MRR, EW and SR as shown. Also the grey relational gradeis computed as per Eq. ( 4). and shown in Table 4.Table 4. Grey relational coefficient and the grey relational grade

S.No Normalizedvalues for

MRR

Normalizedvalues for

EWR

Normalizedvalues for SR

GRCvalues

for MRR

GRCvalues

for EWR

GRCvaluesfor SR

Grade

1. 1 0.6547 0 1 0.5915 0.3330 0.64152. 0.5233 0.2400 0.7987 0.5719 0.3968 0.7129 0.54053. 0.0420 0 0.3241 0.3429 0.3330 0.4252 0.36704. 0.9542 0.8692 0.0614 0.9160 0.7926 0.3475 0.68535. 0.4559 0.2931 0.8707 0.4788 0.4142 0.7945 0.56256. 0.0245 0.0071 0.3940 0.3388 0.3349 0.4520 0.37527. 0.9219 1 0.1292 0.8649 1 0.3647 0.74328. 0.4058 0.4065 1 0.4569 0.4572 1 0.63809. 0 0.0582 0.5826 0.3330 0.3467 0.5450 0.4082

4. MODEL DEVELOPMENT

In order to predict the behavior of the grey relational grade, approach which havebeen developed to map the relationship between process parameters and outputresponses using multiple regression models. The process parameters voltage (V),peak current (C), pulse on-time (T) and gap current (G) are considered asindependent variables and the grey grade as a dependant variable.

4.1 Multiple Regression models

Multiple regression methods are used to analyze data from unplanned experiments,such as might arise from observation of uncontrolled phenomena or historical data.Regression methods are also very useful in designed experiments where somethinghas gone wrong. The general purpose of multiple regressions is to learn moreabout the relationship between several independent or predictor variables and adependent or criterion variable. The following two models have been developed toanalyze the process variable in EDM process. (a) Model I: Linear model excluding interaction terms.(b) Model II: Exponential model excluding interaction terms.

4.1.1 Model I

This model is a linear multiple regression model without considering interactionterms. A multiple regression model using independent variables V, C, T and G anddependent variable grade can be represented as

Grade = b 0 +b 1V+b 2C+b 3T+b 4G+e

Where,b0, b1, b2, b3 and b4 are the regression coefficients to be estimated. The regression

model developed using MINITAB software based on the data is as

Grade = 0.475 + 0.00493 V- 0.00765 C + 0.000006 T + 0.00201 G

The predicted values are calculated through the regression. The percentagedeviations are computed for the data sets and the results are listed in the Table 5.

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Table 5. Percentage deviation between experimental grade and predicted grade values of multipleregression model I

S.No Experimental grade Predicted grade Percentage deviation1. 0.6415 0.6101 4.8792. 0.5405 0.5694 5.3523. 0.3670 0.3508 4.3884. 0.6853 0.6880 0.3935. 0.5625 0.6043 7.4386. 0.3752 0.3861 2.9077. 0.7432 0.7076 4.7768. 0.6380 0.6484 1.6349. 0.4082 0.3963 2.914

Average percentage deviation 3.853

4.1.1.1. ANOVA

The purpose of the ANOVA is to investigate the significance of data sets. This isaccomplished by separating the total variability of the percentage deviation amongthe data. The F-test is used to determine the significance of the data sets. Theresults of ANOVA is shown in the Table 6 indicate that there is no significant changeamong the data. Hence this multiple regression model can be used as a predictionmodel.

Table 6. ANOVA for model I

Source Degree of freedom

Sum of squares Mean square F ratio

Regression 4 0.150668 0.037667 27.57

Residual Error 4 0.005464 0.001366Total 8 0.156132

4.1.2 Model II

This model is an exponential model with logarithmic transformed variables and theinteraction terms are not considered. A logarithmic transformation can be applied toconvert the non-linear form of equation into the following additive (linear) form. Thefunctional relationship between grey relational grade and independent variablesunder investigation could be represented as

ln grade = lnK + a lnV + b lnC + c lnT + d lnG

This is one of the most popularly used data transformation methods in model buildingequations. The model assumes that there is a normal distribution of the dependentvariable for every combination of the values of the independent variables. Theregression equation developed using MINITAB software based on this model isshown as below,

Grade = - 1.33 + 0.308 VL - 0.193 CL - 0.0005 TL + 0.0091 GL

The predicted values are calculated by using the developed regression. Thepercentage deviation is computed between the experimental grade and predictedgrade of the data sets and results are listed in the Table 7.

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Table 7. Percentage deviation between experimental grade and predicted grade values of multipleregression model II

S.No Experimental grade Predicted grade Percentage deviation1. -0.4439 -0.4149 6.5332. -0.6152 -0.7089 15.2303. -1.0023 -0.9738 2.8434. -0.3778 -0.3066 18.8455. -0.5753 -0.6392 11.1076. -0.9802 -0.8859 9.6207. -0.2967 -0.2738 7.7188. -0.4494 -0.5790 28.8389. -0.8959 -0.8702 2.868

Average percentage deviation 11.511

4.1.2.1 ANOVA

The ANOVA is performed on the percentage deviations among the data sets. Theresult of ANOVA is shown in Table 8. From this, it is clear that there is no significantdifference among the data sets. Hence model II can also be used as a predictionmodel.

Table 8. ANOVA for model II

Source Degree of freedom

Sum of squares Mean squares F ratio

Regression 4 0.53054 0.13264 11.43Residual Error 4 0.04644 0.01161

Total 8 0.57698

5. COMPARISON OF RESULTS

Table 9 shows the comparison of percentage deviation between regression model Iand model II. While examining the percentage deviation of multiple regression modelI and model II, it is found that regression model I is having less percentage deviation.So the optimal process parameters are selected based on the data of regressionmodel I.

Table 9. Grey relational grade and its order

S.No Grey relational grade Order 1. 0.6415 32. 0.5405 63. 0.3670 94. 0.6853 25. 0.5625 56. 0.3752 87. 0.7432 18. 0.6380 49. 0.4082 7

6. SELECTION OF OPTIMUM MACHINING PARAMETERS

The response Table 10 of taguchi was employed to calculate the average greyrelational grade for each machining parameter level. It was done by sorting the greyrelational grades corresponding to the levels of the machining parameter in eachcolumn of the orthogonal array (as shown in the Table 2) the no.1, no.2 and no.3were the experimental runs at which machining parameter A was set at level 1. Theassociated values of grey relational grade for A 1 are those experimental runs greyrelational grades. Therefore, their average is the average grey relational grade for A 1:

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A 1 = (0.6415 + 0.5405 + 0.3670) / 3 = 0.5163

Similarly, the average grey relational grade for grade for A 2 and A 3 are calculated asfollows:

A 2 = (0.6853 + 0.5625 + 0.3752) / 3 = 0.5410

Table 10. Response table for the grey relational grade

Symbol Processparameter

Level 1 Level 2 Level 3 Max Min

A Voltage 0.5163 0.5410 0.5964 0.0801B Peak current 0.6900 0.5803 0.3834 0.3066C Pulse on time 0.5515 0.5446 0.5575 0.0129D Gap current 0.5374 0.5529 0.5634 0.0260

Average grey relational grade: 0.5512

Using the same method, calculations are performed for each machining parameter level and the response table was constructed as shown in Table 10. Fig 2 shows the

grey relational grade graph, where the dashed line the figure is the value of the totalmean of the grey relational grade. Basically, the larger the grey relational grade, thebetter are the multiple-performance characteristics. Accordingly, the parameter wasselected based on the level that gave the largest average response. From theresponse table shown in Table 10, the best combination of the machining parametersis the set with the A3 (voltage of 45V), B1 (peak current of 2A), C 3 (pulse on time of 1000s), D3 (gap current of 14A).

Figure 2 Grey relational grade graphs

7. CONCLUSION

A practical method of optimizing machining parameters for EDM based on multipleregression models are presented in this paper. Voltage, Peak current, Pulse on timeand Gap current have been considered as machining parameters. Metal removalrate, Electrode wear and surface roughness have been obtained as responses fromthe EDM process. Metal removal rate, Electrode wear and surface roughness arecombined to have a single objective as grey relational grade by the application of grey relational analysis. Linear regression model and logarithmic transformationmodel excluding interaction terms have been developed to map the relationshipbetween machining parameters and output responses. It is clearly noted thatregression model I gives the better prediction based on the percentage deviation andthe same has been used to find the optimal machining parameters of EDM. Finallythe optimal conditions obtained as i.e., A3 (voltage of 45V), B1 (peak current of 2A),C 3 (pulse on time of 1000s), D3 (gap current of 14A) for maximizing MRR,minimizing electrode wear and surface roughness simultaneously among the 9

experimental data. The most influencing factor obtained by the response table is thepeak current for the EDM process. It is also proposed to integrate the ANN models

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0

0.2

0.4

0.6

0.8

A1 A2 A3 B1 B2 B3 C1 C2 C3 D1 D2 D3

Parameter level

G r a d e

Voltage

Peak current

Pulse on time

Gap current

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with meta heuristics for finding the optimal machining parameters as future scope of this work.Acknowledgments Acknowledgments may appear before the list of references. The author(s) isresponsible for obtaining the necessary permissions to quote or reproduce material,including figures, from already published works and to reprint them from other publications. An appropriate credit line should be included. REFERENCES [1] J.A. McGeough, Advanced Methods of Machining, Chapman and Hall, NewYork, 1998.[2] B.H.Yan, C.C.Wang, W.D.Liu and F.Y. Huang,

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