An Integrated Evaluation Approach for Modelling and Optimization of Surface Grinding Process Parameters

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ScienceDirect Materials Today: Proceedings 2 (2015) 1622 – 1633

4th International Conference on Materials Processing and Characterization

An integrated evaluation approach for modelling and optimization of surface grinding process parameters M. Janardhan Principal&Professor, Department of Mechanical. Engg, Abdul Kalam Institute of Technological Sciences, Kothagudem, Khammam DT, T.S, India

Abstract This paper presents an application of a Response surface methodology (RSM) for modeling and non-dominated sorting genetic algorithm-II (NSGA-II) for multi-objective optimization of a surface grinding process. The proposed methodology models the material removal rate (MRR) and surface roughness in terms of the three prominent machining parameters using RSM and developed models are used for optimization. As the chosen machining performances are conflict in nature, the problem under consideration is formulated as a multi-objective optimization problem. An efficient evolutionary optimization algorithm, NSGAII is then applied to obtain the Pareto optimal front of solutions. © 2014 The Authors. Elsevier Ltd. All rights reserved. © 2015 Elsevier Ltd. All rights reserved. the 4th International Selection andpeer-review peer-review under responsibility the conference committee Selection and under responsibility of theofconference committee membersmembers of the 4thofInternational conference conference on Materials on Materials and Characterization. Processing Processing and Characterization. Keywords:Surface grinding; MRR; surface roughness;NSGA-II

1. Introduction

Grinding is most commonly used as a finishing process to achieve material removal and desired surface finish with acceptable surface integrity and dimensional tolerance [1]. It can produce very flat surfaces, cylindrical surfaces with very accurate dimensions. As compared with other machining processes, grinding is costly operation that should be utilized under optimal conditions. Although widely used in industry, grinding remains perhaps the least understood of all machining processes. The application often depends upon the experience of the operator rather than the scientific knowledge. Surface grinding is the common operation for grinding flat surfaces and is likely to produce high tolerances, Corresponding author. Tel.: +0-000-000-0000 ; fax: +0-000-000-0000 . E-mail address: [email protected]

2214-7853 © 2015 Elsevier Ltd. All rights reserved. Selection and peer-review under responsibility of the conference committee members of the 4th International conference on Materials Processing and Characterization. doi:10.1016/j.matpr.2015.07.089

M. Janardhan / Materials Today: Proceedings 2 (2015) 1622 – 1633

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low surface roughness and planar surfaces. Several analytical and empirical expressions have been developed by various investigators in the literature to determine input-output relationships in grinding, which are highly nonlinear, however several of such relationships may not be accurate. Output performance characteristics in grinding are MRR, surface roughness, surface damage, tool wear etc., and the operating parameters [2] are (i) Wheel parameters: abrasives, grain size, grade, structure, binder, shape and dimension, etc.(ii) Work piece parameters: fracture mode, mechanical properties, and chemical composition, etc. (iii) Process parameters: wheel speed, depth of cut, table speed, and dressing condition, etc.(iv) Machine parameters: static and dynamic characteristics, spindle system, and table system. In this case, two performance characteristics of surface grinding process, namely MRR and Ra are considered for optimization. MRR and Ra indicate the production rate and quality of the product respectively. The common practice in the industries is that the selection of grinding parameters is made based on either operator’s experience or grinding parameter tables provided by the manufacturers. However, such criterion does guarantee neither high production rate nor good surface quality. Therefore, there is a need to develop a methodology to optimize MRR and Ra. The following section discusses the major contribution of the researchers with regard to the optimization of surface grinding process. Suresh et al. [3] developed model for surface roughness using response surface methodology to learn the main effects and interaction effects of the process parameters in surface grinding. They also optimized the predicted model using genetic algorithm. Atzeni et al. [4] developed mathematical model for surface roughness and kinematic parameters using regression analysis. The developed model shows that the roughness is mainly influenced by the feed per grain and cutting speed. A smoother surface is produced by decreasing the feed per grain, through the spacing between successive peaks along the work piece and depth of engagement decreases. Choi et al. [5] presented the generalized model for power, surface roughness, grinding ratio and surface burring for various steel alloys and aluminium grinding wheels. Liu et al. [6] conducted a series of experiments using Taguchi method. The result shows that surface roughness is decreased with a slower feed rate and also with larger grinding force. Inasaki et al. [7] used a genetic algorithm based optimization procedure to optimize surface roughness and metal removal rate with depth of cut, work speed, grit size and density as control variables. In their work, the empirical models required for optimization were developed through response surface methodology. Palanikumar [8] also applied the RSM to model the surface roughness in terms of the machining parameters and analysis of variance was used to check the adequacy of the developed model. Xu et al. [9] demonstrated the mechanism of MRR and the effects of machining parameters on the MRR. Choudhary et al. [10] used design of experiments for the modeling of surface roughness using RSM in terms of cutting speed, feed and depth of cut. Daniels et al. [11] investigated the influence of surface grinding parameters. It was found that more severe grinding conditions, such as higher normal forces and power consumption, did not significantly reduce the mean rupture strength of the material. The most encouraging aspect inferred from these results was that grinding conditions could be changed in order to optimize the process without significant structural damage to the work material. Tonshoff et al. [12] described the state-of-the art work done in the modelling and simulation of grinding processes. The relative benefits and drawbacks of various modelling and simulation methodologies were discussed. Liao et al. [13] used back-propagation neural networks for modelling and optimizing the creep-feed grinding of alumina with diamond wheels. Gopal et al. [14] described the selection of optimal conditions for maximum material removal rate with surface finish and damage as constraints in SiC grinding. They developed mathematical methods using the experimental data and adequacy of the models was tested with analysis of variance and genetic algorithm was then developed to optimize the grinding parameters. Dhavlikar et al. [15] optimized surface roughness using Taguchi and RSM for the grinding process. Kwak et al. [16] described the application of Taguchi and response surface methodologies for geometric error in surface grinding process, in which the effect of grinding parameters on the geometric error was studied. Optimum grinding conditions for minimizing the geometric error were determined by establishing a second order response model. Krishna et al. [17] described optimization of surface grinding operations using an optimization technique called differential evolution approach method taking the various constraints from the literature. Johnson et al. [18] applied factorial design and RSM to tune the parameters of a GA program. These efforts were focused on using RSM to determine the parameters of various applications. Khoo et al. [19] integrated RSM with genetic algorithms (GA) to optimize surface grinding process. Lee et al. [20] applied particle swarm approach for

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grinding process optimization analysis, based on the objective of maximizing MRR subject to surface finish and damage. A comparison of the results obtained by GA was made in their work. Shaji et al. [21] presented a study on Taguchi method to evaluate the process parameters in surface grinding. The effect of process parameters such as speed, feed, in feed and modes of dressing were analyzed. Agarwal et al. [22] presented an experimental investigation of surface roughness and MRR mechanism in a grinding with different grinding parameters and the effects of the grinding conditions on the responses were discussed. R.Suresh et al. [23] presented Force Prediction Model of Multilayer Coated Carbide Tool in Hard Turning of AISI 4340 Steel to investigate the effect of cutting parameters on machining forces Using RSM . Shreemoy Kumar Nayak [24] presented multi-objective optimization of machining parameters during dry turning of AISI 304 Austenitic Stainless Steel Using simple Grey Relational Analysis. The present work differs from the other works in the following aspects: Literature survey reveals that the performance measures, surface roughness [Ra] and MRR in surface grinding process are expressed either as single composite objective function or taking one of the measures as a constraint. The researchers have considered the optimization of the problem either as a single objective optimization problem or a constrained optimization problem. This approach is adopted in the literature in all the optimization works such as neural networks, Taguchi method, grey relational analysis etc. as mentioned in previous section. Unlike other previous approaches, the present work formulates a surface grinding process explicitly as a multiobjective optimization problem as the determination of the optimal grinding conditions involves a conflict between maximizing the MRR and minimizing the surface roughness in surface grinding process. This is the first-of–its kind approach to formulate a grinding problem as a multi-objective optimization problem. Although various classical methods of obtaining the solutions to multi-objective optimization problems are available, they have certain drawbacks. Some of the classical optimization methods are min-max, weighed sum, distance function methods. These methods change the multi-objective problem into a single objective, with the corresponding weights based on their relative performance. These methods suffer from a drawback that the decision maker must have a thorough knowledge of ranking of objective functions. Also, these methods fail when the objective functions are discontinuous. On the other hand, Non-dominated genetic algorithm-II possesses an advantage that it does not require any gradient information and inherent parallelism in searching the design space, thus making it a robust adaptive optimization technique. 2. Response Surface Methodology Response Surface Methodology (RSM) is a combination of mathematical and statistical technique that is useful for the modeling and analysis of problem in which a response of interest is influenced by several variables and the objective is to optimize the response [25, 26]. In RSM, it is possible to represent independent process parameters in quantitative form as: Y = f (X1, X2, X3...X) ± e

(1)

Where, Y is the response (yield), ‘f’ is the response function, ‘e’ is the experimental error, and X 1, X2, X3 . . . X are independent parameters. By plotting the expected response of Y, a surface, known as the response surface is obtained. The form of ‘f’ is unknown and maybe complicated. Thus, RSM aims at approximating ‘f’ by a suitable lower order polynomial in some region of the independent process variables. If the response can be well modeled by a linear function of the independent variables, the function can be written as: Y = C0+C1X1+C2X2+…. +CnXn ±e (2) However, if a curvature appears in the system, then a higher order polynomial such as the quadratic model may be written as: Y=‫ ݋ܥ‬൅ σ௡௜ୀଵ ‫ ݅ܺ݅ܥ‬൅ σ௡௜ୀଵ ‫݅ܺ݅ܥ‬2 ± e

(3)

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The objective of using RSM is not only to investigate the response over the entire factor space, but also to locate the region of interest where the response reaches its optimum or near optimal value. By studying carefully the response surface model, the combination of factors, which gives the best response, can then be established. 3.Non-dominated sorting genetic algorithm (NSGA-II) The application of evolutionary algorithms(EAs)for solving multi-objective optimization problems has been explored over a long p e r i od in the l i t e r a t u r e . Among these, the NSGA-II, developed by Deb et al. [27], is a well-known and extensively used algorithm that has b e e n applied successfully to s e ve r a l non- linear complex optimization problems. NSGA-II has proved to be more worthy over its predecess or non- dominated sorting genetic algorithm(NSGA),mainly in four aspects[27]: (a) It has reduced the computational complexity; (b) It uses an elitist approach ,i.e. the best individuals are preserved in each generation; (c) It uses a crowded comparison operator to maintain diversity of solutions; (d) There is an absence of niched operators. 3.1 Non-dominated sorting In this a l g o r i t h m the p o p u l a t i o n is initialized in a similar way t o t h e s i n g l e objective EAs. Once the population is initialized and the fitness function is evaluated, then the p o p u l a t i o n is sorted based on non-domination into di ffer en t fronts. The firstfront comprises the completely non-dominant individuals in the current population and the secondfront comprises only those dominated by the individuals in the firstfront and thethirdfront, of only those dominated by the individuals in the first and secondfronts, and soon. Each individual in each fr on t is as signed rank value, ba s e d on the front in which i t is placed. Individuals in the firstfront are given a fitness value of 1, thoseinthesecondavalueof2,and so on. The ranking scheme for a small number of solutions is illustrated in Fig. 1 ,wheref1and f 2 are the two functions to be minimized. 3.2 Crowding distance Inordertomaintaindiversityamongsolutionsgenerated,aparametercalled c r owd i n g distance is calculated for each individual apart from fitness value. The crowding distance is a measure of how close an individual solution is to its neighbours. Large average crowding distance will result in better diversity in the population. Crowding distance gives an estimate of the density of solutions surrounding a solution i by taking the average distance of two solutions on either side of solutioni along each of the objectives. As shown in Fig. 2 , the crowding distance of the i th solution di represents the average side length of the cuboid. The procedure for calculating the crowding distance in a front F involves the following steps

Fig. 1IllustrationofrankingprocedureinNSGA-II

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Fig. 2Illustrationofcrowdingdistance calculation

1. The number of solutions in FisL. For each solution i in the set, at first di =0. 2. For each objective m=1,2...M, the set is sorted in worst order of fm.Hence the sorted in dices vector Im=sort (fm)is calculated. 3. For m=1, 2….M, a large di s t a n c e is assigned to the b o u n d a r y solutions(I and L ), or dI1m=∞and f o r all other solutions j =2to (L−1),the following equation is used to c o m p u t e their corresponding values where index I j indicates the solution index for the jth member in the s or t e d list. For any objective, I1and I Ldenote the lowest and highest objective function values, respectively. 3.3 Selection Parents for crossover are selected from the population using bi nar y tournament selection as explained below. Among two solutions i and j available for selection, the solution i wins the tournament over j if the following conditions are true: (a) If solution i has better rank over j, i.e. ri dj 3.4 Procedural steps The s t e p s involved in NSGA-II based on t h e m a i n framework of the algorithm[27]shown in Fig. 3 can be stated in the following steps. 1. Select controlparameters:populationsize,maximumnumberofgeneration,crossoverprobability,and mutation probability(generation, g=0) 2. Generate randomly a uniformly distributed parent population, Pg of size N based on the feasible ranges and constraints, if any. the 3. Evaluatethefitnessofindividualsbasedonobjectivefunctionandsortthepopulationaccordingto non-domination. 4. Assign e a ch solution a rank equal to i t s n on - domination level as explained in section 3.1. 5. Calculate the crowding distance of each rank and sort the individuals that ha ve the same ranking ascending order by the cr owdi n g distance as detailed in section 3 .2. 6. Apply the b i n a r y tournament selection as discussed in section 3 .3. 7. Use the simulated binary crossover operator and polynomial mutation to create an off spring population Qg of size N. 8. Combine the off spring and parent population R (g)= (Pg ‫ ׫‬Qg)to form e x t e n d e d population ofsize2N. 9. Sort the extended population based on non- domination to create different fronts. 10. Fill new population, Pg+1of size N with the individuals from the sorting fronts starting from the best. 11. Invoke t h e crowding-distance method to ensure diversity if a f r on t can only partially fill the next generation. The crowding-distance method maintains diversity in the p o p u l a t i o n and

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p r e vents convergence in one direction. 12. Update the number of generations, g=g+1 13. Repeatthesteps3to12until as topping criterion is met.

Fig. 3MainframeworkofNSGA-IIalgorithm

4. Experimental Details A set of experiments were conducted for machining of AISI 4340 steel on surface grinding machine to determine effect of process parameters namely table speed (m/min), wheel speed (rpm), depth of cut(μm) on the responses surface roughness and MRR. The machining conditions at which the experiments were conducted are given in Table 1. Three levels and three factors used to design the orthogonal array by using design of experiments (DOE) and relevant ranges of parameters as shown in Table 2. Grinding wheel with aluminium oxide abrasives with vitrified bond, WA 60K5V is used for the present work. The selected L27 orthogonal array is used to conduct the experiments as shown in the Table 3 along with the output responses, MRR and surface roughness (Ra). MRR was calculated as the ratio of volume of material removed from the work piece to the machining time. In order to determine the volume of material removed after machining, the weights of work piece before machining and after machining are measured. Machining time taken for each cut is automatically displayed on the machine. The surface roughness, Ra was measured in perpendicular to the cutting direction using Mitutoyo Surface Roughness tester SJ201 at 0.8 mm cut-off value. An average of six measurements was taken at six different places to record the surface roughness. These results are further used for modelling and to optimize the responses using NSGA-II. Table 1. Machining conditions (a) (b) (c) (d) (e)

Work piece material: AISI 4340 steel( % of chemical composition by volume C-0.35-0.45, Si-0.10-0.35, Mn 0.45-0.70, Ni 1.30-1.80, Cr 0.90-1.40, Mo 0.20-0.35, S- 0.050, Ph- 0.050 and balance Fe) Work piece dimensions:155mm length x 38mm height x38mm width Physical properties: Hardness-201BHN, Density-7.85 gm/cc, Tensile Strength-620 Mpa Grinding wheel: Aluminium oxide abrasives with vitrified bond wheel WA 60K5V Grinding wheel size :250 mm ODX25 mm widthx76.2 mm ID

Table2. Process variables and their levels Levels of factors S.No

Control Factor

Symbol

1

Wheel speed

2

Table speed

3

Depth of cut

Unit

-1

0

+1

A

1250

1650

2050

RPM

B

7.5

10

12.5

m/min

C

5

10

15

μm

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M. Janardhan / Materials Today: Proceedings 2 (2015) 1622 – 1633

Table 3. Experimental observations of the responses

S.No

Wheel speed (RPM)

Table speed (m/min)

Depth of cut (μm)

Mean of the responses Ra(μm)

MRR (gm/min)

1

1250

7.50

5

1.034

5.510

2

1250

7.50

10

1.440

10.28

3

1250

7.50

15

1.624

15.505

4

1250

10.0

5

1.324

7.350

5

1250

10.0

10

1.591

13.28

6

1250

10.0

15

1.721

22.07

7

1250

12.5

5

1.38

9.190

8

1250

12.5

10

1.679

16.89

9

1250

12.5

15

1.940

26.09

10

1650

7.50

5

1.180

6.260

11

1650

7.50

10

1.56

13.13

12

1650

7.50

15

1.684

17.68

13

1650

10.0

5

1.490

11.63

14

1650

10.0

10

1.641

15.61

15

1650

10.0

15

1.716

21.17

16

1650

12.5

5

1.501

12.42

17

1650

12.5

10

1.697

18.17

18

1650

12.5

15

1.826

25.87

19

2050

7.50

5

1.361

7.760

20

2050

7.50

10

1.582

13.21

21

2050

7.50

15

1.703

19.40

22

2050

10.0

5

1.460

10.35

23

2050

10.0

10

1.632

15.16

24

2050

10.0

15

1.805

24.16

25

2050

12.5

5

1.513

12.64

26

2050

12.5

10

1.734

22.44

27

2050

12.5

15

2.072

30.44

5. Modelling of the responses In the present study, empirical models of second order for the responses,Surfaceroughness(Ra) and MRR in terms of selected machining parameters in actual factors were developed using RSM. The developed models are subsequently used for optimization of the grinding process. To determine the regression coefficients of the developed model, the statistical analysis software, design expert 8.0 v is used. For the present problem, the second order models were postulated for responses due to lower predictability of the first order models. The following equations were obtained in terms of uncoded factors Ra = - 0.4485 + 0.0005A + 0.1236B + 0.0975C - 0.0022B2 - 0.0017C2 - 0.00002AB – 0.000013AC + 0.000053BC (4) MRR = - 0.9022 + 0.0023A - 0.3760B - 0.20041C - 0.000001A2 + 0.0118B2 +

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0.0203C2 + 0.00036 AB + 0.00007AC + 0.1006BC (5) The analysis of variance (ANOVA) of response surface quadratic model for surface roughness and metal removal rate were shown in Table 4 and Table 5 respectively. Analysis of variance (ANOVA) is then employed to test the significance of the developed models. The multiple regression coefficients (R2) of the second order model for surface roughness and metal removal rate were found to be 0.9325 and 0.9781 respectively. The R2 values are very high, close to one, indicates that the second order models are adequate to represent the machining process. The "Pred R-Squared" of 0.8027 is in reasonable agreement with the "Adj R-Squared" of 0.8967 in case of surface roughness. Similarly in case of MRR, the "Pred R-Squared" of 0.9498 is in reasonable agreement with the "Adj RSquared" of 0.9666. The model F-value of 26.09 and 84.51 for Ra and MRR implies that the models are significant. There is only a 0.01% chance that a "Model F-Value" this large could occur due to noise. The P value for both the models is lower than 0.05 (at 95% confidence level) indicates that the both the models could be considered to be statistically significant.The normal probability plots of residuals for Ra and MRR are shown in the Fig 4 and Fig 5 respectively. From these plots, it can be concluding that the residuals lies on a straight line which implies that the errors are distributed normally and the developed regression models are well fitted with the observed valves.These show that the models are adequate without any violation of independence or constant assumption. Table 4. ANOVA for response surface quadratic model of Ra Source

Sum of Squares

dof

Mean square

F Value

Model Linear square Interaction Residual Total

1.180255 0.049208 0.012367 0.011887 0.08545

9 3 3 3 3 26

0.131139 0.016403 0.004122 0.003962 0.085447

26.09 3.2 0.8 0.7

P value Prob>F 0.0001 0.047 0.501 0.517

Table 5. ANOVA for response surface quadratic model of MRR Source Model Linear Square Interaction Residual Total

Sum of Squares 1098.5 1076.1 1.6 20.7 24.5 1126.84

dof 9 3 3 3 17 26

Mean square 122.05 358.5 0.55 6.9 1.4

F Value 84.51 249.29 0.393 4.79

P value Prob>F <0.0001 0.0001 0.765 0.014

Fig.4. Normal probability plot of residuals for Ra

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Fig. 5. Normal probability plot of residuals for MRR

6. Results In the present study, objective is to maximize MRR and to minimize the surface roughness which is given by the equations (4) and (5) respectively. The objective functions are optimized subjected to the feasible bounds (lower and upper limits) of the variables using NSGA- II. The proposed algorithm was implemented using VC++ and run on Pentium IV system. The control parameters required for implementation of the algorithm is listed in Table 6.The algorithm was run for ten times to get more number of points in the Pareto-optimal front. The Pareto-optimal front of the conflicting objective functions with good diversity of the solutions is shown in Fig 6. As can be observed from t h e graph, no solution in the front is better than any other as they are non-dominated solutions. The choice of a solution over the other has to be made purely based on production requirements. The optimal process parameters and corresponding responses are listed in Table 7. Table. 6. Control parameters S.No 1 2 3 4 5 6

Parameter Population size 50 Number of generations 100 Cross over probability 0.9 Mutation probability 0.1 Distribution index for cross over operator 20 Distribution index for mutation operator 20

Fig. 6. Pareto-optimal front with two extreme points

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M. Janardhan / Materials Today: Proceedings 2 (2015) 1622 – 1633 Table 7. A few optimal combinations of parameters and responses.

S.No

Wheel Speed (RPM)

Depth of Cut (μm)

Table Speed (m/min)

Surface roughness (μm)

MRR (gm/min)

1

1730.00

15.00

9.17

1.797

20.548

2

1250.00

14.03

7.50

1.603

14.629

3

1303.33

9.84

7.50

1.443

10.074

4

1356.67

6.94

8.17

1.346

8.026

5

1516.67

15.00

7.83

1.696

17.316

6

1570.00

15.00

7.83

1.704

17.480

7

1676.67

15.00

8.17

1.738

18.434

8

1303.33

12.10

7.83

1.563

13.033

9

1623.33

15.00

9.83

1.818

21.491

10

1356.67

15.00

8.83

1.733

18.607

11

1410.00

15.00

8.17

1.700

17.580

12

1676.67

15.00

7.83

1.720

17.792

13

1623.33

15.00

9.50

1.801

20.842

14

1356.67

15.00

9.17

1.752

19.218

15

1676.67

15.00

9.83

1.824

21.682

16

1730.00

15.00

9.17

1.797

20.548

17

1676.67

15.00

8.83

1.774

18

1730.00

15.00

9.50

1.414

19.725 21.207

19

1996.67

15.00

9.83

1.858

22.712

20

1570.00

15.00

10.17

1.828

21.938

21

1623.33

15.00

9.17

1.784

20.196

22

1570.00

14.68

8.83

1.751

18.923

23

1410.00

15.00

9.50

1.777

20.045

24

1623.33

15.00

7.83

1.712

17.639

25

1250.00

10.81

7.50

1.476

10.933

26

1356.67

15.00

7.50

1.651

16.188

27

1410.00

15.00

8.83

1.740

18.807

28

1356.67

6.94

7.83

1.325

9.693

29

1570.00

15.00

9.83

1.812

21.294

30

1676.67

15.00

10.17

1.839

22.340

31

1250.00

9.84

7.83

1.453

10.321

32

1676.67

14.68

8.83

1.766

19.271

33

1570.00

15.00

10.17

1.828

21.938

34

1356.67

6.61

7.83

1.107

7.384

35

1463.33

15.00

10.83

1.850

22.786

36

1250.00

14.03

7.50

1.603

14.629

37

1570.00

15.00

10.83

1.860

23.236

38 39

1250.00 1836.66

15.00 14.35

7.50 10.50

1.626

15.82

40

1783.33

13.70

12.16

1.80 1.842

22.45 24.45

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7. Conclusions The present work proposed a methodology to determine the optimal machining parameters to achieve high production rate and good surface quality of machined components. Experimentation on surface grinding process with AISI 4340 steel as work piece material was conducted with L27 orthogonal array as per design of experiments. Wheel speed, table speed and depth of cut were considered as grinding parameters and MRR and surface roughness as responses. Response surface methodology was then employed for developing the second order polynomial models on the responses and their adequacy is tested with ANOVA. As the responses are conflict in nature; the problem was formulated as multi-objective optimization problem with upper and lower bounds of grinding parameters as constraints. An efficient evolutionary optimization algorithm, Non- dominated sorting genetic algorithm-II is then applied for optimization and obtained the Pareto optimal set of solutions. References Z.W. Zhong, V.C. Venkatesh, Recent Developments in Grinding of Advanced Materials, International Journal of Advanced Manufacturing and Technology, 41(2009) 468-480. S. Malkin, C. Guo, Theory and applications of machining with abrasives, 2nd ed. Published by Industrial Press, Inc. New York, 2008. Suresh PVS, Rao PV, Deshmukh SG, A genetic algorithmic approach for optimization of surface roughness prediction model. Int J Mach Tools and Manufacture 42(2002)675-680. Atzeni and luliano, L, Experimental study on grinding of sintered friction material” journal of materials processing technology, 196(2008)184-189. Choi,T.J., Subramanya,N,Li,H and Shin,YC.,“Generalized practical models of cylindrical plunge grinding process” International journal of machine tools and Manufacture 48(2008)61-72. Liu C.H. Chen, A and Wang, Y.T. “Grinding force control in an automatic surface grinding system” Journal of material processing Technology, 170(2005), 367-373 I. Inasaki, Grinding of hard and brittle materials, Annals of the CRIP 3 (2) (87) 463-471. K. Palanikumar, Modeling and analysis for surface roughness in machining glass fiber reinforced plastic using response surface methodology, Materials and Design 28(10)(2007)2611-2618. H.H.K. Xu, N.P padutre, S. Jahanmir, Effect of microstructure on metal removal mechanisms and damage tolerance in abrasive machining of silicon carbide, Journal of the American ceramic society 78,(9) (1995) 2443-2448. I.A. Choudhary, M.A. El-Baradie, Surface roughness prediction in the turning of high-strength steel by factorial design of experiments, Journal of materials processing technology 67 (1997) 55-61. Denials, Super abrasives for ceramic grinding and finishing SME Technical paper EM, 1989, 89-125. H. Tonshoff, J. Peters, I. Inasaki, T. Paul, Modeling and simulation of grinding processes, Annals of CIRP 41 (2) (1992) 677-688 T.W.Liao ,A neural network approach for grinding process; Modeling and optimization, International journal of machine tools and Manufacture 34(7) (1994) 919-937. A. Venu Gopal P.V.Rao the selection of optimal conditions for maximum material removal rate with surface finish and damage as constraints in SiC grinding, International journal of machine tools and Manufacture 43 (2003) 1327-1326. M.N. Dhavlikar, M.S.Kulkarni, V.Mariappan, Combined Taguchi and dual response method for optimization of a centerless grinding operation, Journal of materials processing technology 132 (1-3) (2003) 90-94. Jae-Seob Kwak , The application of Taguchi and response surface methodologies for geometric error in surface grinding process, International journal of machine tools and Manufacture 45 (2005) 327-334. A. Gopala Krishna, Optimization of Surface Grinding operations using a differential evolution approach, Journal of materials processing technology 182(23) (2007) 202-209. R. Parsons and M.E. Jhonson, “Case study in experimental design applied to genetic algorithms with applications to

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