A study of the EDM [80]

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A study of the electrical discharge machining of semi-conductor BaTiO 3

Ming-Guo Her, Feng-Tsai Weng *

Department of Mechanical Engineering, Tatung University, 40 Chung-Sang North Road,3rd Section, Taipei 10451, Taiwan, ROC

Received 5 January 2000

Abstract

This paper investigates the machining performance of BaTiO 3 using the electrical discharge machining (EDM) process. The Taguchiorthogonal array technique is used for experimental design. A surface roughness model of the EDM process of semi-conductor BaTiO 3 canbe obtained by regression of the experimental data. A genetic algorithm is used to calculate the machining parameters of the optimumsurface roughness. To obtain a better surface roughness, positive polarity machining should be chosen in the EDM process of BaTiO 3 ,whilst the current cannot be selected at too great a value or the workpiece may be broken during the process. # 2002 Elsevier Science B.V.All rights reserved.

Keywords: EDM; Semi-conductor; Genetic algorithm

1. Introduction

Generally the material BaTiO 3 is hard and brittle, and it isdif®cult to machine with traditional processes. Electricaldischarge machining (EDM) is able to cut materials that arehard of high strength and complex geometry [1]. In EDM,material is removed by repetitive spark discharge across agap between the tool and workpiece. In order to improve theEDM performance, an electrode rotating mechanism ismounted on the traditional EDM machine [2,3]. Simplegenetic algorithms (GAs) have been applied successfullyto the single objective optimization problem [4,5]. TheTaguchi orthogonal array has been proven very useful inengineering applications, and can save time and cost of experiments [6,7]. GAs are search algorithms based on themechanics of natural selection and natural genetics proposedin 1975 by Holland [8]. GAs are different from more normaloptimization and search procedures in four ways [9]: (1)GAs work with a coding of the parameters set, not with theparameters themselves; (2) GAs search from a population of points, not from a single point; (3) GAs use payoff (objectivefunction) information, not derivatives or other auxiliary

knowledge; (4) GAs use probabilistic transition rules, notdeterministic rules. With the above excellent points, GAs

can be easily employed to achieve a global optimum from alocal optimum.

To avoid the workpiece being broken during an experi-ment, the discharge current as well as the on-pulse is set to beconstant and small, and positive polarity machining (thepositive of the power supply connected to the electrode) isselected. The conductivity of semi-conductor BaTiO 3 isabout 10

À2 s/cm.

2. Experimental design

A Taguchi orthogonal array L 25 (53 ) is used in the experi-mental design. The parameters are selected as follows:

1. Electrode rotary speed . In order to improve the removalrate, an electrode rotary mechanism is mounted on atraditional EDM machine. The electrode rotary speed isselected in the range of 75±200 rpm.

2. The pulse duration . The on-pulse duration is set to aconstant value 10 ms, while the off-pulse duration isselected in the range of 75±1200 ms.

3. The discharge voltage . Stable machining can beobtained when the discharge voltage is selected in therange of 30±50 V.

Journal of Materials Processing Technology 122 (2002) 1±5

* Corresponding author. Fax: 886-5-6310824.E-mail address : [email protected] (F.-T. Weng).

0924-0136/02/$ ± see front matter # 2002 Elsevier Science B.V. All rights reserved.PII: S 0 9 2 4 - 0 1 3 6 ( 0 1 ) 0 1 0 5 4 - 8



Cylindrical copper rods of 8 mm diameter were selectedas the electrodes. Semi-conductor BaTiO 3 with a diameter of 12 mm and a thickness of 1.3 mm was selected as the

workpiece. Experiments were carried out on a traditionalEDM machine. The experimental matrix of the data of process parameters and the machining performance wasobtained, as presented in Table 1. Tables 2 and 3 wereobtained from the analysis and regression of the experimentdata.

A model of the surface roughness of the EDM process of BaTiO 3 can be obtained by a parameter estimate, which isdescribed as follows:

Y � À 20:945458 0:231022 x1 À 0:023528 x2 0:88709 x3

À 0:00016 x21 0:000002807 x2

2 À 0:005894 x23

À 0:005004 x1 x3 0:00052 x2 x3 (2.1)

In the above equation, Y is the surface roughness, x1 theelectrode revolution, x2 the off-pulse duration, and x3 thedischarge voltage.

3. Genetic algorithm

GAs are search algorithms based on the mechanics of natural selection and natural genetics. Simple GAs havebeen applied successfully to single objective optimizationproblems. A GA has the characteristic of maintaining apopulation of solutions and can search in a parallelmanner for many non-dominated solutions. It requiresno gradient information and produces multiple optimarather than a single local optimum. The ¯ow chart of aGA is shown in Fig. 1. The three main operators of the

rule of GAs are reproduction, cross-over, and mutation.GA represents complex models by simple encoding anduses a random process to process an initial population, andthese simple operators are applied to the string populationto produce a new string population. The new population isreferred to as offspring and the original population asparents.

Reproduction is a selection process to determine thesurvival potential of a string according to that string's ®tness.Fitness is a non-negative merit measure of an optimizationobjective function with respect to a string. Strings with ahigher ®tness value have a higher probability of proceedingto the next generation.

Cross-over involves random exchange of correspondingbites between two parent strings to produce two new off-spring strings. Mutation introduces diversity in a modelpopulation by occasional random change in the bit valuesof strings. The value of the bit of a randomly chosen string ata randomly selected position is changed.

The simple GA randomly produces a ®nite initial popula-tion in a de®ned space. Then subjecting the initial populationto simple genetic operators, i.e. ®tness evaluation, reproduc-tion selection, cross-over, and mutation, a new generationpopulation can be generated. This process is repeated until asatis®ed solution evolves.

Table 1Experimental matrix including parameters and performance

Electrode rotatingspeed (rpm)

Off-pulse(ms)

Voltage(V)

Surfaceroughness ( mm)

75 75 30 4.50475 150 35 6.208

75 300 40 6.03875 600 45 4.21575 1200 50 5.616

100 75 35 6.086100 150 40 5.858100 300 45 5.939100 600 50 5.633100 1200 30 3.761125 75 40 6.49125 150 45 5.049125 300 50 4.308125 600 30 4.197125 1200 35 5.105150 75 45 6.718150 150 50 5.871

150 300 30 5.514150 600 35 5.512150 1200 40 5.216200 75 50 6.396200 150 30 6.28200 300 35 6.226200 600 40 6.321200 1200 45 5.67

Table 2Analysis of variance ( F 0:05 8; 16 � � 2:98)

Source DF Sum of squares

Meansquare

F- value

Model 8 6.93762 0.86720 4.585Error 16 3.02625 0.18914

C total 24 9.96387

Table 3Parameter estimates ( t 0:05;24 2:064)

Variable Parameterestimate

S.E. T for H 0 :parameter 0

Intercept À20.945458 7.67274319 À2.730 x1 0.231022 0.13169513 1.754

x2 À0.23528 0.00690826 À3.406 x3 0.887090 0.19918985 4.453 x2

1 À0.00016 0.00070848 À0.226 x2

2 0.000002807 0.00000439 0.640 x2

3 À0.005894 0.00207923 À2.835 x1 x2 0 0.00000000 x2 x3 À0.005004 0.00131225 À3.814 x1 x3 0.000520 0.00013795 3.769

2 M.-G. Her, F.-T. Weng / Journal of Materials Processing Technology 122 (2002) 1±5



3.1. Optimum result

Objective function:

Y � À 20:945458 0:231022 x1 À 0:023528 x2 0:88709 x3

À 0:00016 x21 0:000002807 x2

2 À 0:005894 x23

À 0:005004 x1 x3 0:00052 x2 x3 (3.1)

Population: 1000, crossover rate: 0.8, mutation: 0.005.Constrain condition:

75 < x1 < 200 ; 75 < x2 < 1200 ; 30 < x3 < 50

After iteration the minimum value of Y (surface roughness)converges closely to the points x1 100, x2 1200, x3 33. The average value of Y is 3.3.

Veri®cation . Three experiments were conducted. The

values of the model and of experiments correspond closely.The data of veri®cation are shown in Table 4.

4. Experimental result and discussion

Fig. 1 shows the ¯ow chart of the GA, Fig. 2 shows theschematic electrode rotating mechanism, and Fig. 3 shows

Fig. 1. Flow chart of the GA.

Table 4The data of verification

Model Experiment

Electrode rotate speed (rpm) 83 7595 10079 75

Off-pulse ( ms) 1157 12001060 12001136 1200

Voltage (V) 33 3332 3233 33

Surface roughness ( mm) 3.52 3.683.45 3.713.61 3.8

Fig. 2. The electrode rotating mechanism.

M.-G. Her, F.-T. Weng / Journal of Materials Processing Technology 122 (2002) 1±5 3





References

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[3] P. Koshy, V.K. Jain, G.K. Lal, Experimental investigations into

electrical discharge machining with a rotating disk electrode, Precis.Eng. 1.15 (1) (1993) 6±15.[4] S.S. Rao, V.B. Venkayya, N.S. Khot, Game theory approach for

integrated design of structures and controls, AIAA J. 26 (4) (1988)464±469.

[5] F.Y. Cheng (Ed.), Recent Developments in Structural Optimization,American Society of Civil Engineers, New York, 1986.

[6] D.C. Montgomery, Design and Analysis, Wiley, New York,1984.

[7] K.-H. Fuh, C.-F. Wu, A proposed statistical model for surface qualityprediction in end-milling of Al alloy, Int. J. Mach. Tools Manuf. 35 (8)(1995) 1187±1200.

[8] J. Holland. Adaptation in Natural and Artificial System, University of Michigan Press, Ann Arbor, MI, 1975.

[9] D.E. Goldberg, Genetic Algorithms in Search, Optimum, and MachineLearning, Addison-Wesley, Reading, MA, 1989.

M.-G. Her, F.-T. Weng / Journal of Materials Processing Technology 122 (2002) 1±5 5

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A study of the EDM [80]