Optimization of Electric Discharge Machining Process Parameters Using Genetic Algorithm

Optimization of Electric Discharge Machining Process Parameters Using Genetic Algorithm

Shah Fateh Azam 1, Dr.D.K.Singh 2

1. M.Tech. Student Department of Mechanical Engineering M.M.M.E.C., GORAKHPUR, U.P.

2. Head of Department of Mechanical Engineering M.M.M.E.C, GORAKHPUR, U.P.

   Abstract:Proper selection of manufacturing conditions is one of the most important aspects in the Electrical Discharge Machining process, as these conditions determine important characteristics such as Material Removal Rate and Tool Wear Rate. In this work, mathematical models have been developed for relating the Material Removal Rate and Tool Wear Rate to machining parameters like discharge current, pulse-on time and pulse-off time. The developed models predict the machining conditions from rough machining region to finish conditions within the experimental domain. Response Surface Methodology has been applied for developing the models using the techniques of Design of Experiments and Central composite rotatable design was used to plan the experiments. Response surface Quadratic models were found to be the most suitable in the present work. A Quadratic equation is found from the Design Experiment.This equation is used in a GA Tool as a fitness function and optimizes the process parameter of EDM.

   Keywords: Electric Discharge Machining, Material Removal Rate, Tool Wear Rate, Design Expert Software,Response Surface Methodology,Genetic Algorithm.

   1. INTRODUCTION

      Electrical discharge machining (EDM) is one of the most extensively used nonconventional manufacturing processes used for hard materials which are very difficult to machine with conventional techniques. EDM is sometimes referred to as spark machining, spark eroding, burning, die sinking or wire erosion. This is a manufacturing process whereby a desired shape is obtained using electrical discharges (sparks). English chemist Joseph Priestly laid the foundation for EDM by discovering the erosive effect of electrical discharges or sparks in 1770. However EDM was discovered in 1943 by two Russian scientists B. R. Lazarenkoand N. I. Lazarenko when they explored the destructive properties of electrical discharges for constructivepurpose. They developed a controlled process for machining difficult-to-cut materials. They invented and applied resistance capacitance (RC) relaxation circuit inEDM that was widely used till 1950s and after that several developments andadvancements were made by different researchers in the field of EDM. Electrical Discharge Machining

      (EDM) is a non conventional machining process, where electrically conductive materials is machined by using precisely controlled sparks that occur between an electrode and a workpiece in the presence of a dielectric fluid[1].

      It uses thermoelectric energy sources for machining extremely low machinability materials; complicated intrinsic-extrinsicshaped jobs regardless of hardness have been its distinguishing characteristics.

      EDM founds its wide applicability in manufacturing of plastic moulds, forging dies, press tools, die castings, automotive, aerospace and surgical components. As EDM does not make direct contact (an inter electrode gap is maintained throughout the process) between the electrode and the workpiece its eradicate mechanical stresses, chatter and vibration problems during machining [2].Various types of EDM process are available, but here the concern is about die- Sinking (also known as ram) type EDM machines which require the electrode to bemachined

      in the exact opposite shape as the one in the workpiece [1].

      Figure 1.1: Layout of Electric Discharge Machining

      Figure 1.2: Variation of Ip and V in different phases of a spark

      Fig1.3 (a)Fig1.3 (b)Fig1.3 (c)Fig1.3 (d)(e)Fig1.3

      Figure 1.3:(a) Pre-breakdown phase (b) Breakdown phase (c) Discharge phase (d) End of the discharge and (e) Post-discharge phase

   2. EXPERIMENTATION

      In the present study, material removal rate and absolute tool wear rate has been considered for evaluating the machining performance. All these performance characteristics are correlated with machining parameters such as discharge current, pulse-on time and pulse-off time. Proper selection of machining parameters can result in desirable material removal rate and tool wear rate. Experiments were conducted covering wide range of current settings, pulse-on time and pulse-off time. The machining conditions used during experimentation have been shown in Table 1. Work piece material was cut into rectangular cross section and top and bottom faces of the work piece were ground to make flat and good surface finish prior to experimentation. The copper electrode was having rectangular cross section of 20x10mm. The electrode was polished and buffed prior to every experimental run. Machining depth was kept constant at 0.5mm for every experimental run and correspondingly ma-chining time was measured with an accuracy of 1 second. After every run, the work piece and tool were detached from the machine, cleaned, dried and weighed before and after machining.

   3. DESIGN OF EXPERIMENTS

      The design factors, response variable as well as the methodology employed for the experimentation is described below.

      1. Design factors

         The design factors considered in the present work were discharge current (I), pulse-on time (Ton) and pulse-off time (Toff). The selection of these three factors have been made because they are the most important and widely used by re-searchers in the die sinking EDM field [3].

      2. Response variables

         The selected response variables MRR, TWR and SR are defined as follows:

         • Material Removal Rate

           MRR is calculated by using the volume loss from the workpiece divided by the time of machining. The calculated weight loss is converted to volumetric loss in mm3/min as per Equation 1.

           MRR=Vw/t =Ww/wt(1)

           WhereVw is the volume loss from the workpiece, Ww is the weight loss from the workpiece, t is the duration of the machining process, and w= 7700 kg/m3 the density of the workpiece.

           TWR is expressed as the volumetric loss of tool per unit time, expressed as

           TWR =Vt/ t=Wt /tt(2)

           WhereVt is the volume loss from the electrode, Wt is the weight loss from the electrode, t is the duration of the machining process, and t=8960 kg/m3 the density of the electrode.

         • Tool Wear Rate

         TABLE 1

         MACHINING CONDITIONS USED DURING EXPERIMENTATION[7]

         Electrode	Work-piece	Dielectric fluid	Flushing type
         Copper (electrolytic grade)	EN8 Steel	EDM oil	Submerged in
         Rectangular: 20mm X 10mm	Rectangular: 40 mm X 50 mm	(Grade30)	dielectric

         TABLE 2

         MACHINING PARAMETERS AND THEIR CORRESPONDING VARIATION LEVELS[7]

         Symbols machining parameter units levels

         A Discharge current (I) A 3 6 12 18 21

         B Pulse-on time(Ton)s10 200 500 750 1000

         C Pulse-off time (Toff)s10 200 500 750 1000

      3. Factorial design employed

         So, the case of the second order model turned out to be made up of a total of 20 experiments, the previous 14 from the first order model plus the six star points. Based on the Central Composite Design (CCD), experiments were conducted to develop empirical models for MRR and TWR in terms of the three input variables: discharge current, pulse-on time and pule-off time. Each input variable (factor) was varied over five levels: ±1, 0 and ±. Table 2 shows the relationship between the ma-chining parameters and their corresponding selected variation levels, taking into account the entire range of machine parameter.

   4. RESPONSE SURFACE METHODOLOGY

      Response surface methodology is a collection of mathematical and statistical technique that is useful for modeling and analysis of problems in which a response of interest is influence by several variables and the objective is to optimize the response [3], [4]. In order to study the effect of EDM process parameters on the volumetric Material Removal Rateand Tool Wear Rate a second order polynomial response was fitted into the following equation-

      Y = 0 + 1X + 2 + 3 + 12X + 13X + 23 + 11X2 + 222 + 33 2 (3)

      Where Y is the response and X, , are the quantitative variables. 1, 2 and 3 represent the linear effect of X, , and respectively. 11, 22 and 33 represent the quadratic effect of X, and , whereas 12, 13 and 23 represents the linear by linear interaction between X and , X and ,

      and respectively. These quadratic models work quite well over the entire factor space and the regression coefficients were computed according to Least-square procedures.

   5. EXPERIMENTAL RESULTS

      Table 3 shows the design matrix developed for the proposed model as well as the machining characteristics value obtained in the experiments for MRR and TWR.

   6. MODELING RESPONSE VARIABLES

      Equation (4) and (5) presents the prediction models for MRR and TWR respectively.

      MRR= +2.36771 + 1.06292* I + 0.010620* Ton0.029306*Toff+0.031945*I2- 3.02001E-5*Ton2+1.65488E-5*Toff2

      +7.22470E-4*I*Ton-6.94470E-4*I*Toff2

      +2.72328E-5*Ton*Toff (4)

      TWR = – 0.023232+0.082162*I-1.11420E- 3*Ton-9.08270E-5*Toff-1.54239E-3*I2

      +1.25744E-6*Ton2+4.04197E-8*Toff2-

      5.91828E-5*I*Ton+2.07481E-6*I*Toff

      +7.51014E-8*Ton*Toff(5)

      Where, the values of the variables have been specified according to their original units.

      TABLE 3

      DESIGN OF EXPERIMENT MATRIX AND MACHINING CHARACTERISTICS[7]

      and 6 respectively. Least SD and PRESS of quadratic model confirm that quadratic model is most suitable.

      TABLE 4

      MODEL SUMMARY STATISTICS FOR MRR

      Std No.

      Expt. run

      I (A)

      Ton (s)

      Toff (s)

      MRR

      (mm³/min)

      TWR

      (mm³/min)

      Source SD R2 Adj. R2 Pred.R2 PRESS

      6 1 12.0 50050015.476 0.1167

      13 2 12.0 1000 5008.4353 0.0671

      11312.0 500 1022.437 0.1742

      54	6.0	750	7501.5535	0.0248
      95	3.0	500	5000.3095	0.01
      196	12.0	500	50013.436	0.1256
      207	18.0	200	20032.03	0.5348
      18	6.0	200	7502.9114	0.0401
      179	18.0	200	75018.604	0.5131
      810	12.0	500	50014.258	0.1206
      1511	6.0	200	2005.703 0.0292
      1412	12.0	500	100012.805 0.1450
      313	18.0	750	75028.555	0.200
      414	18.0	750	20027.794	0.1067
      215	21.0	500	50029.802	0.0472

      716 12.0 500 50013.254 0.1186

      Linear 4.14 0.8544 0.8271 0.7295 510.49

      2FI 4.10 0.8839 0.8304 0.670621.08

      *Quadratic2.49 0.9672 0.9377 0.7422 486.45

      **Cubic 0.78 0.9984 0.9939 – –

      *=Suggested, **=Aliased, SD=Std. Dev.

      TABLE 5

      ANOVA FOR QUADRATIC MODEL OF MRR

      Source SS DF MS F-value P-value

      Model 1825.20 9 202.80 32.79 <0.0001*

      I 1502.49 1 1502.49 242.92<0.0001*

      Ton 6.92 1 6.921.12 0.3149

      Toff 55.23 1 55.23 8.93 0.0136*

      I2 13.44 1 13.44 2.17 0.1712

      Ton295.07 1 95.07 15.37 0.0029*

      Toff2	28.55	1	28.55 4.62 0.0572
      I*Ton	11.40 1		11.40 1.84 0.2044

      I*Toff 10.54 1 10.54 1.700.2211

      1617	12.0	10	5002.2583	0.8764 Ton*Toff 34.18 1 34.18 5.53 0.0406*
      1018	6.0	750	2002.6596	0.027 Residual 61.85 10 6.19 — — Lack of fit 58.83 5 11.77 19.47 0.0027*
      1219	12.0	500	500	13.825	0.1266	Error	3.02 5	0.60	— —
      1820	12.0	500	500	13.554	0.1373	Total	1887.05 19

      1. Model Adequacy Test for MRR

         A pre-ANOVA model statistics, the ANOVA results and the post-ANOVA model adequacy for the developed model of MRR are shown in Table 4, 5

         *significant terms

         The model F-value of 32.79 implies the model is significant. There is only a 0.01% chance that a Model F-value this large could due to noise. Value of Prob>F less than 0.0500 indicate model are significant. Values greater than 0.100 indicate the model terms are not significant. TheLack of Fit F-

         valueof 19.47 implies the Lack of Fit is significant. There is only 0.27% chance that lack of fit value this large could occur due to noise.

         TABLE 6

         POST ANOVA MODEL ADEQUACY FOR MRR

         R2 0.9672

         Adj.R2 0.9377

         Pred.R2 0.7422

         Adeq.Precisior 18.870

         The Pred R2 of 0.7422 is in reasonable agreement with the Adj.R2 of 0.9377.Adeq.Precision measures the signal to noise ratio. A ratio greater than 4 is desirable. Your ratio of 18.870 indicates an adequate

         TABLE 8

         ANOVA FOR QUADRATIC MODEL OF TWR

         Source SS DF MS F-value P-value

         Model 0.77 9 0.085 6.09 0.0046*

         I 0.12 1 0.12 8.39 0.0160*

         Ton 0.29 1 0.29 20.43 0.0011*

         Toff 1.765E-4 1 1.765E-4 0.013 0.9129

         I2 0.031 1 0.031 2.24 0.1657

         Ton20.16 1 0.16 11.76 0.0064*

         Toff2 1.703E-4 1 1.703E-4 0.012 0.9144

         I*Ton 0.077	1	0.077
         Residual 0.14	10	0.14

         I*Ton 0.077	1	0.077
         Residual 0.14	10	0.14

         5.46 0.0416*

         — —

         Lack of fit 0.14 5 0.028 340.21 <0.0001*

         signal.	Error	4.107E-4	5	8.21E-5	—	—
         	Total	0.91	19

      2. Model Adequacy Test for TWR

         The statistical analysis of the model of TWR is presented in Table 7, 8 and 9respectively. Since quadratic model is having least Standard Deviation (0.12) and Predicted Error Sum of Squares (1.07) among the other models, hence suggested.. The results of the statistical analysis show that model can satisfctorily be used in predicting the response of TWR.

         TABLE 7

         MODEL SUMMARY STATISTICS FOR TWR

         *significant terms

         The model F-value of 6.09 implies the model is significant. There is only a 0.46% chance that a Model F-value this large could due to noise. Value of Prob>F less than 0.0500 indicate model are significant. Values greater than 0.100 indicate the model terms are not significant. TheLack of Fit F- value of 340.21 implies the Lack of Fit is significant. There is only 0.01% chance that lack of fit value this large could occur due to noise.

         TABLE 9

         POST ANOVA MODEL ADEQUACY FOR TWR

         Source SD R2 Adj.R2 Pred.R2 Press

         Linear 0.16 0.5286 0.4402 0.1468 0.77

         2FI0.16 0.6133 0.4349-0.00890.92

         *Quadratic 0.12 0.8457 0.7069 -0.1771 1.07

         **Cubic 9.063E-3 0.9995 0.9983 — —

         *=Suggested, **=Aliased, SD=Std. Dev.

         R2 0.8457

         Adj.R2 0.7069

         Pred.R2 -0.1771

         Adeq.Precisior 9.982

         A negative Pred.R2 implies that the overall mean is a better predictor of your response than the current model. Adeq.Precisionmeasures the signal to noise ratio. A ratio greater than 4 is desirable. Your ratio of 9.982 indicates an adequate signal.

   7. Genetic Algorithms:History

The idea of evolutionary computing was introduced in 1960 by I.Rechenberg in his work evolutionary strategies. Genetics algorithms are computerized search andoptimization algorithms based on the mechanics of natural genetics and natural selection.Prof. Holland of University of Michigan, Ann Arbor, envisaged the concept of these algorithms in the mid sixties and published his seminal work (Holland, 1975) [5].

Introduction:

Evolutionary algorithms (EAs) are population- based meta heuristic optimization algorithms that use biology-inspired mechanisms and survival of the fittest theory in order to refine a set of solution iteratively. Genetic algorithms (GAs) are subclass of evolutionary algorithms (EAs) where the elements of the search space are binary strings or arrays of other elementary types. Genetic algorithms (GAs) are computer based search techniques patterned after the genetic mechanisms of biological organisms that have adapted and flourished in changing highly competitive environment. Last decade has witnessed many exciting advances in the use of genetic algorithms (GAs) to solve optimization problems in process control systems. Genetic algorithms (GAs) are the solution for optimization of hard problems quickly, reliably and accurately. As the complexity of the real- time controller increases, the genetic algorithms (GAs) applications have grown in more than equal measure.

Basic Concepts

Genetic algorithms are good at taking larger, potentially huge, search spaces and navigating them looking for optimal combinations of things and solutions which we might not find in a life time[5].

Three most important aspects of using GA are:

1. Definition of objective function

2. Definition and implementation of genetic representation

3. Definition and implementation of genetic operators.

Working Principle of Genetic Algorithms

The workability of genetic algorithms (GAs) is based on Darwinians theory of survival of the fittest. Genetic algorithms (GAs) may contain a chromosome, a gene, set of population, fitness, fitness function, breeding, mutation and

selection. Genetic algorithms (GAs) begin with a set of solutions represented by chromosomes, called population. Solutions from one population are taken and used to form a new population, which is motivated by the possibility that the new population will be better than the old one. Further, solutions are selected according to their fitness to form new solutions, that is, offspring. The above process is repeated until some condition is satisfied. Algorithmically, the basic genetic algorithm (GAs) [6] is outlined as below.

Step I [Start] Generate random population of chromosomes, that is, suitable solutions for the problem.

Step II [Fitness] Evaluate the fitness of each chromosome in the population.

Step III [New population] Create a new population by repeating following steps until the new population is complete.

1. [Selection] Select two parent chromosomes from a population according to their fitness. Better the fitness, the bigger chance to be selected to be the parent.

2. [Crossover] With a crossover probability, cross over the parents to form new offspring, that is, children. If no crossover was performed, offspring is the exact copy of parents.

3. [Mutation] With a mutation probability, mutate new offspring at each locus.

4. [Accepting] Place new offspring in the new population.

Step IV [Replace] Use new generated population for a further run of the algorithm.

Step V [Test] If the end condition is satisfied, stop, and return the best solution in current population.

Step VI [Loop] Go to step 2.

Objective Function:

Objective function obtained from design expert software and this function use as a fitness function of GA Tool. This fitness function used to optimization and we get the result.

Objective Function For MRR

function y=azam(x)

y(1)=-((2.36771)+(1.06292*x(1))+(.010620*x(2))- (.029306*x(3))+(.031945*x(1)^2)- (.0000302001*x(2)^2)+(.0000165488*x(3)^2)+(.0007 22470*x(1)*x(2))- (.000694470*x(1)*x(3))+(.0000272328*x(2)*x(3)));

TABLE 10

RESULT OBTAINED FROM GENETICALGORITHMS

Objective Functionfor TWR

function y=azam1(x)

y(1)=(-(.023232)+(.082162*x(1))-(.00111402*x(2))- (.0000908270*x(3))- (.00154239*x(1)^2)+(.00000125744*x(2)^2)+(.000000040 4197*x(3)^2)- (.0000591828*x(1)*x(2))+(.00000207481*x(1)*x(3))+(.00 00000751014*x(2)*x(3)));

TABLE 11

RESULT OBTAINED FROM GENETIC ALGORITHMS

BFST FIT GRAPH FOR MRR

BEST FIT GRAPH FOR TWR

RESULT AND DISCUSSION

Because Original Chromosomes are randomly this may induce getting different solution set, so the procedure was repeated many times. The result shows that although the set are slightly different and we get the maximum MRR and minimum TWR for the corresponding parameters.

Table 10 and table11 shows one group set of solution. Parameter listed in number 5 lead to the optimal solution for MRR but not consider because this MRR out of range of experimental data. So in Table10 S.N.10 optimal solution of MRR values are 31.1004 mm3/min, where current 17.893A, pulse on time 460.229s and pulse off time190.2srespectively. Similarlyin Table 11,S.N. 4 the minimum values of TWR is .01760mm3/min, wherecurrent 3A, pulse on time 142.776s and pulse off time776.496srespectively. Compare them with maximum MRR and minimum TWRin table 3,it is clear that MRR and TWR is improved using optimized parameters.

CONCLUSION

In this paper optimize EDM process parameters areintroduced, which uses design expert and GA algorithm. Design expert model was set up to represent the relationshipbetween MRR and input parameter similarly as relationship between TWR and input parameters.

GA is used to optimize parameter. MRR and TWR improvedby using optimized parameter; it is close to experiment result. With the increase of current, MRRcan be improved, similarly with theincrease pulse on time, TWR can be decrease. MRR and TWR can also be improved when we set proper current, proper pulse on time and proper pulse off time.

REFERENCES:

1. Elman C. Jameson, Electrical Discharge Machining, Society of Manufacturing Engineers (2001), p.1.

2. Antoine Descoeudres, Characterization of electrical discharge machining plasmas, Ph.D. Thesis (2006), School PolytechniqueFederal de Lausanne, These EPFL, no 3542.

1. Myers, D.C. Montgomery and Anderson-Cook, Response Surface Methodology. John Wiley-New York, 2009.

2. Neural Network, fuzzylogic, and Genetic algorithms,synthesis and application written by S.Rajasekaram and G.A.VijayalakshmiPai.

3. Chu-KueiTu and Tseng-Hsien Lin. (2000). Applying Genetic Algorithms On Fuzzy Logic System FoUnderwater Acoustic Signal Recognition, Proceedings of the 2000 International Symposium on UnderwaterTechnology, pp. 405-410.

4. S. S. Baraskar, S. S. Banwait, S. C. Laroiya, Mathematical Modelling of Electrical Discharge Machining process through Response Surface Methodology,(2011).