Modelling And Multi-Response Optimization Of Hard Milling Process Based On RSM And GRA Approach

Modelling And Multi-Response Optimization Of Hard Milling Process Based On RSM And GRA Approach

1Lanka Prakasa Rao, 2T Jaya Anand Kumar, 3Thella Babu Rao

1Student, Department of Mechanical Engineering, GIET College of Engineering Rajahmundry, Andhra Pradesh, India

2Associate Professor and Head, Department of Mechanical Engineering, GIET, Rajahmundry, Andhra Pradesh, India.

3Assistant Professor, Department of Mechanical Engineering, GITAM University, Hyderabad campus, Hyderabad, Andhra Pradesh, India 502 329.

Abstract

The study of metal removal rate and cutting temperature is most significant among the others like features of tools and work materials. Since these are the determinant factors of the production rate and cost-efficiency of the tools. Milling of hardened tool steels became a highly expensive for the manufacturing industries today as these are being widely used in many applications like automobile, structural, etc. A significant improvement in the efficiency of this process may be obtained with the development of mathematical relations between the set of input and output parameters of a machining process. The models reveal the level of significance of the process parameter on response. Therefore, the constituencies of critical process control factors leading to desired responses with acceptable variations ensuring a lower cost of manufacturing can be identified. In this investigation, milling experiments are conducted to machine hardened EN 31 tool steel with carbide cutting inserters. Initially, the design of experiments was conducted to plan the experimentation by considering the machining variables of depth of cut, feed and spindle speed. Metal removal rate and cut-ting temperature were measured for each experimental run. Response surface methodology is used to build up the mathematical surface model for the measured values of responses. The ANOVA technique has been used to verify the adequacy of the models at 95% confidence interval. Since the influence of machining parameters on the metal removal rate and cutting temperature are with conflicting nature, the problem is considered as multi-objective optimization problem. Hence, Gray relational analysis (GRA) was adapted to the response values to obtain the optimal set of input parameters.

Keywords: Hard milling, empirical modelling, RSM, optimization, GRA.

1. Introduction

   Hardened steels are being used in a variety of industrial applications like automotive, aerospace etc. These materials are often classified as difficult- to-machine materials due to high strength and low thermal conductivity. This drives to severe cutting forces and cutting temperatures and hence a shorter the tool life. Tool life is the significant economic factor, particularly for milling and turning of heat resistant alloys [1]. Agawal et al. [2] assessed the relative perfor-mance of coated and uncoated carbide tools (inserts) in the machining of three cast austenic stainless-steels. Uhlmann et al. [3] stated that, the harder diamond tools cannot be used to machine the steels due to reactive nature and the secondary harder tools like cubic boron nitride (CBN) and PCBN are efficient in place of former but are highly expensive. Szymon et al. [4] presented a comparison of tool life of sintered carbide and CBN ball end mills. This investigation revealed that the tool life of sintered carbide is higher than the CBN up to a certain range of cutting speed. Also, the cutting speed was observed as an independent dominating factor on abrasive wear of CBN cutter. Pinaki Chakraborty et al. [5] developed the a mathematical model for tool wear during end-milling of AISI 4340 steel with multi- layer physical vapor deposition (PVD) coated carbide inserts under semi-dry and dry cutting conditions. From this research, it is also observed that cutting speed has the most comprehensive effect on tool wear progression. Aslan et al. [6] performed a comparative study on cutting tool performance in end milling of AISI D3 tool steel with coated carbide, coated cermet, alumina (Al2O3) based mixed ceramic and cubic boron nitride (CBN) cutting tools.

   In the present work, two important performance measures of hard milling responses,

   viz., metal removal rate (MRR) and cutting temperature (T) were considered for investigation. The empirical models of the chosen responses were developed in terms of the prominent process control variables of depth of cut, feed and cutting speed using a well known statistical technique called response surface methodology. Analysis of variance (ANOVA) is then adapted to check the adequacy of the developed models at 95%

   other factors in a given system between the sequences with less data [11]. The processing steps are listed below [13].

   1. Normalize the response matrix from zero to one by using Eq. (2) and (3).

      Lower-the-better (LB) is the criterion:

      i

      confidence interval. The measured response values are the carried to find the optimal machining conditions. A multi- response optimization

      x (k )

      max y (k) y (k)

      i i

      i i

      max y (k) min y (k)

      (2)

      technique, Gray Relational Analysis was implemented to fin the optimal machining conditions.

      Higher-the-better (HB) is the criterion:

      y (k ) min y (k)

      x (k ) i i

      (3)

   2. Response Surface Methodology

      Response surface methodology is a widely used

      i

      where,

      max y (k) min y (k)

      i

      i i

      x (k) is the normalised value of kth

      i

      tool for design and analysis of experiments [7]. It is a collection of statistical and mathematical

      response, min yi (k) is the smallest value of yi (k)

      techniques useful for develop-ing, improving and

      for kth response and max y (k)

      is the largest value

      optimizing process [8]. In its process, a suitable relationship is developed between output of interest y and a set of controllable variables{x1,x2,……xn}. A second-order nonlinear response function usually utilized [13] in the form:

      of y (k) for kth response. x is the normalised array.

      i

      1. Calculation of grey relational coefficient from the normalised matrix.

         n n (k)

         min max

         (4)

         0i

         y b0

         • b x b x 2 b x x

         (1)

         i (k)

         max

         i i ii i ij i j

         i 1

         i 1

         i j

         Where, represents the noise or error observed

         Where, 0i x0 (k) xi (k)

         : is the

         in the response y such that the expected response is

         deviation of absolute value

         x0 (k) and xi (k) . is

         (y-) and bs are the regression coefficients to be estimated.

         In the present work, development of the mathematical models and analysis has done with

         the distinguishing coefficient 0 1 .

         min min min x0 (k) xj

         ji k

         (5)

         the use of a statistical tool called Stat-Ease Design

         max max

         x (k) x (k)

         (6)

         Expert [9].

         max

         ji

         k 0 j

         The adequacy of the predicted models was checked by Analysis of variance (ANOVA). It calculates the F-ratio, which is the ratio between the regression mean square and the mean square error. If the calculated value of F-ratio is higher than the tabulated value of F-ratio for roughness, then the model is adequate at desired significance level to represent the relationship between machining response and the machining parameters.

      2. Determination of overall grey relational grade.

         1 n

   3. Gray Relational Analysis

      i i (k)

      n

      k 1

      (7)

      Grey relational analysis (GRA) proposed by Deng is a method of measuring the degree of approximation among sequences according to the grey relational grade [10]. GRA analyzes uncertain relations between one main factor and all the

      It means, the overall gray relational grade converts the multi-response (multi-gray relational grades) optimization problem into a single response (overall gray relational grade) optimization problem, with the objective function as

      maximization of overall grey relational grade. Hence, the overall grey relational grades rank the experimental runs as; the experimental run having higher grey relational grade refers as that corresponding combination of variables is closer to the optimal values. The optimal parametric combination is then evaluated by maximizing the overall grey relational grade.

   4. Experimental Details

In this work, depth of cut, feed and cutting speed are considered as the control variables and MRR and cutting temperature as the output responses. In order to reduce the number of experimental runs, experiments are planned based on design of experiments (DOE). Central composite design with 27 experiments was selected. Table 1 lists the feasible values of each process variable. Experiments are conducted on a precision CNC milling machine model BFW AGNI

45. Hardened steel EN31 plate of size 150x100x10 mm with 60 HRC is considered as the work piece material and TaeguTec make M9810048402 carbide milling turning inserts and with SCRM90TP45016R18DTGNL milling cutter with 4 cutting inserts was used in machining. For each experimental run, the metal removal rate is calculated by the weight loss method. Each experiment is run for a fixed length of 75 mm length. During each experiment the cutting temperature was measured by a IR Thermometer by maintaining 1.5 meter distance between the thermometer and cutting tool edge. Each experiment was repeated for three times and the average of the measures values were considered as the final response values. Table 2 represents the matrix of experimental values. The Fig.1 shows the experimental setup. The Figs.2 and 3 show the cutting tools & cutter and the IR Thermometer for temperature measurement used in experimentations.

Table 1 Machining Variables and their Levels

1. Variables Units Notation Range No -1 0 1

   1. Depth of cut mm DOC 0.1 0.2 0.3

   2. Feed Rate mm/tooth F 0.1 0.3 0.5

   3. Cutting Speed m/min V 120 180 240

Spindle Work piece

Billet

IR Spot

Fig. 1 Experimental setup

Fig. 2 Cutting inserts and the milling cutter

Fig. 3 IR Thermometer

1. Development of Empirical Model

   In the present study, mathematical relationship between control variables and the responses was developed using the response surface methodology. Design Expert 8 is used to analyze the variance and to compute the regression coefficients for the proposed models. For the present case study, the second order model has been postulated because of its more accuracy. This model is checked for adequacy by using analysis of variance (ANOVA). Tables 3 and 4 are the ANOVA of MRR and cutting temperature respectively. From the Table 3 and 4, the model F-values of 95.72 and 201.02 implies that the models are significant and the p- values less than 0.05 indicate the model terms are significant.

   Table2. Experimentally measured values

   The following equations are obtained for the

   Exp. D

   No. mm

   F

   mm/tooth

   V

   m/min

   MRR

   grm/min

   Temp.

   OC

   output responses:

   MRR 0.00088 0.2325D 0.00085F 0.00037V

   0.00045DF 0.00027DV 0.000075FV

   0.2390D2 0.000041F 2 0.000047V 2

   Temp 474.732 346.324D 6.6175F 0.4623V

   2.4651DF 0.3716DV 0.003676FV

   1466.8354D2 0.0301F 2 0.001892V 2

   Table 3 ANOVA of MRR

   (8)

   (9)

   1. 0.1	0.1	120	0.00545	169.05
   2. 0.1	0.1	180	0.00854	181.29
   3. 0.1	0.1	240	0.01055	245.94
   4. 0.1	0.3	120	0.00848	247.29
   5. 0.1	0.3	180	0.01154	278.44
   6. 0.1	0.3	240	0.01358	344.44
   7. 0.1	0.5	120	0.02645	419.28
   8. 0.1	0.5	180	0.02954	460.62
   9. 0.1	0.5	240	0.03152	539.59
   10. 0.2	0.1	120	0.02345	209.12
   11. 0.2	0.1	180	0.02654	231.36
   12. 0.2	0.1	240	0.02855	286.01
   13. 0.2	0.3	120	0.02645	276.39
   14. 0.2	0.3	180	0.02954	307.54
   15. 0.2	0.3	240	0.03156	373.54
   16. 0.2	0.5	120	0.04445	435.84
   17. 0.2	0.5	180	0.04754	477.17
   18. 0.2	0.5	240	0.04951	556.14
   19. 0.3	0.1	120	0.04845	277.42
   20. 0.3	0.1	180	0.05154	299.66
   21. 0.3	0.1	240	0.05353	354.31
   22. 0.3	0.3	120	0.05145	333.71
   23. 0.3	0.3	180	0.05454	364.86
   24. 0.3	0.3	240	0.05652	430.86
   25. 0.3	0.5	120	0.06945	480.62
   26. 0.3	0.5	180	0.07254	591.95

   Sum of Mean F p-value

   Source Squares df Square Value Prob > F

   Model 9.50E-03 9 1.06E-03 95.718 < 0.0001 significant

   27. 0.3 0.5 240 0.05454 580.92

   N o r m a l % P r o b a b i l

   99

   95

   x1 x2 x3 x1x2 x1x3 x2x3 x1x1 x2x2 x3 x3

   Residual

   Lack of Fit R-Squared

   2.26E-03 1 2.26E-03 204.60 < 0.0001

   5.86E-04 1 5.86E-04 53.070 < 0.0001

   7.56E-06	1	7.56E-06	0.6851	0.4193
   3.46E-05	1	3.46E-05	3.1387	0.0944
   3.60E-05	1		3.2626	0.0886
   3.77E-05	1	3.77E-05	3.4136	0.0821
   3.43E-05	1	3.43E-05	3.1077	0.0959
   1.98E-04	1	1.98E-04	17.931	0.0006
   1.99E-05	1	1.99E-05	1.8051	0.1967
   9.20E+03	6	1.53E+03
   8.98E+03	5	1.80E+03 0.980648	8.1417	0.2597 not significant

   90 Adj R-Squared 0.970403

   80

   70

   30

   50 To check whether the fitted model actual

   20 model actually describe the experimental data, the

   5

   10 multiple regression coefficient (R2) has been

   2

   1 calculated. The R value for the MRR and cutting

   -2.00 -1.00 0.00 1.00 2.00

   Studentized Residuals

   Fig. 4 Normal Probability plot of MRR

   99

   95

   Normal % Probability

   90

   80

   70

   50

   30

   temperature has been found to be 0.9806 and 0.9907 and it shows that the second order model can explain the variation in the temperature up to the extent of 98.06% and 99.07%. Figs. 4 and 5 show the normal probability plots of the residuals for the output response.

   Table 4 ANOVA of cutting temperature

   Sum of Mean F p-value Source Squares df Square Value Prob > F

   Model 3.88E+05 9 4.32E+04 201.01 < 0.0001 significant

   x

   20

   10

   5

   1

   -2.36 -0.81 0.75 2.30 3.85

   Studentized R esiduals

   1

   x2 x3 x1x2 x1x3 x2x3

   9.08E+03 1 9.08E+03 42.291 < 0.0001

   6.34E+04 1 6.34E+04 295.18 < 0.0001

   1.03E+03	1	1.03E+03	4.7836	0.0430
   6.51E+01	1	6.51E+01	0.3030	0.5891
   8.96E+02	1	8.96E+02	4.1750	0.0568
   1.29E+03	1	1.29E+03	6.0130	0.0253

   2.17E+04 1 2.17E+04 101.09 < 0.0001

   Fig. 5 Normal Probability plot of cutting

   temperature

   x1x1 x2x2

   1.07E+04 1 1.07E+04 49.784 < 0.0001

   3.17E+02	1	3.17E+02	1.4759	0.2410
   3.65E+03	17	2.15E+02
   7.98E+03	5	1.80E+03	8.1417	0.45	not significant

   x3 x3

   Residual Lack of Fit

   R-Squared 0.9907

   Adj R-Squared 0.985763

   has been converted in to single-objective optimization problem.

   Table 6 Gray relational grade and Ranks

   i (k)

   Table 5 Normalized values and grey relational

   coefficients

   Exp.

   MRR

   Temp.

   Rank

   No.

   grm/min

   OC i

   Normalized

   Values oi

   2. 0.3439	0.9453	0.6446	4
   3. 0.3511	0.7333	0.5422	14
   4. 0.3437	0.7299	0.5368	16
   5. 0.3548	0.6591	0.5069	18
   6. 0.3626	0.5466	0.4546	24
   7. 0.4213	0.4580	0.4397	25
   8. 0.4383	0.4204	0.4293	26
   9. 0.4500	0.3633	0.4066	27
   10. 0.4060	0.8407	0.6233	5
   11. 0.4218	0.7724	0.5971	8
   12. 0.4327	0.6439	0.5383	15
   13. 0.4213	0.6633	0.5423	12
   14. 0.4383	0.6042	0.5213	17
   15. 0.4502	0.5084	0.4793	22
   16. 0.5445	0.4421	0.4933	20
   17. 0.5732	0.4070	0.4901	21
   18. 0.5932	0.3533	0.4732	23
   19. 0.5823	0.6612	0.6217	6
   20. 0.6153	0.6182	0.6167	7
   21. 0.6386	0.5330	0.5858	10
   22. 0.6143	0.5622	0.5882	9
   23. 0.6512	0.5192	0.5852	11
   24. 0.6772	0.4468	0.5620	12
   25. 0.9166	0.4043	0.6604	3
   26. 1.0012	0.3333	0.6673	1

   1. 0.3333 1.0000 0.6667 2

   Exp. No.	MRR grm/min	Temp. OC	MRR grm/min	Temp. OC
   1.	0.0000	1.0000	1.0000	0.0000
   2.	0.0461	0.9711	0.9539	0.0289
   3.	0.0761	0.8182	0.9239	0.1818
   4.	0.0452	0.8150	0.9548	0.1850
   5.	0.0908	0.7413	0.9092	0.2587
   6.	0.1213	0.5853	0.8787	0.4147
   7.	0.3132	0.4083	0.6868	0.5917
   8.	0.3593	0.3105	0.6407	0.6895
   9.	0.3888	0.1238	0.6112	0.8762
   10.	0.2685	0.9052	0.7315	0.0948
   11.	0.3145	0.8527	0.6855	0.1473
   12.	0.3445	0.7234	0.6555	0.2766
   13.	0.3132	0.7462	0.6868	0.2538
   14.	0.3593	0.6725	0.6407	0.3275
   15.	0.3894	0.5165	0.6106	0.4835
   16.	0.5817	0.3691	0.4183	0.6309
   17.	0.6277	0.2714	0.3723	0.7286
   18.		0.0847	0.3429	0.9153
   19.	0.6413	0.7437	0.3587	0.2563
   20.	0.6874	0.6912	0.3126	0.3088
   21.	0.7171	0.5619	0.2829	0.4381
   22.	0.6861	0.6106	0.3139	0.3894
   23.	0.7321	0.5370	0.2679	0.4630

   24. 0.7617 0.3809 0.2383 0.6191

   25. 0.9545 0.2633 0.0455 0.7367

   26. 1.0006 0.0000 -0.0006 1.0000

   27. 0.7321 0.0261 0.2679 0.9739

   This plot reveals that the residuals are located on a straight line, which means that the errors are distributed normally on the regression model so that the model predicted is well fitted with the observed values.

2. Implementation of GRA

   In the procedure of GRA, the responses are normalized as the first step using the equations 2 and 3 as shown in Table 5. As a part of the estimation of grey relational coefficients, the quality loss estimates of each individual has been calculated and listed in Table 5. Then the individual gray relational grades and the overall gray relational grade have been calculated by using Eq. 4 and Eq. 6 and are shown in Table 6. Here, the value of distinguishing coefficient is assumed as

   0.5. The overall gray relational grade represents the quality index of multiple responses of the process; hence, the multi-objective optimization problem

   27. 0.6512 0.3392 0.4952 19

   Therefore, the overall grey relational grades rank the experimental runs as; the experimental run having higher grey relational grade refers as that corresponding combination of variables is closer to the optimal values as listed in the Table 6. The optimal parametric combination is then evaluated by maximizing the overall grey relational grade. The optmal set of input parameters is DOC=0.3mm, feed 0.5 mm/tooth and speed 180 m/min and the optmal values of the out response obtained are 0.07254 grms/min metal removal rate and 591.95oC cutting temperature.

3. Conclusions

This paper aimed to develop the empirical models and investigate the optimal machinability parameters of milling process during machining EN

31 tool steel. In this consequence, milling experiments were conducted on vertical milling milling centre based on central composite design with 27 experiments. The response surface methodology was adopted to develop the mathematical models for the responses and

ANOVA is used to check the adequacy of the developed models and were found that the developed second order models can explain the variation in the temperature up to the extent of 98.06% and 99.07%. Then these experimentally measured values were carried to the optimization. GRA was successfully implemented to the measured experimental runs. The resulted optimal values of the milling process were listed. Hence, an operator can easily find out the optimal marching conditions without compromising at either metal removal rate or the cost of tooling with this investigation.

References:

1. Tsann-Rong Lin, Experimental study of burr formation and tool chipping in the face milling of stainless steel, Journal of Materials Processing Technology, 108 (2000) 1220.

2. S. Agrawal, A.K. Chakrabarti, A.B. Chattopadhyay, Astudy of the machining of castausteniticstainless-steels with carbidetools, Journal of Materials Processing Technology, Volume 52, Issues 24, JuneJuly 1995, Pages 610620.

3. E. Uhlmann, J.A. Oyanedel Fuentes, M. Keunecke, Machining of high performance workpiece materials with CBN coated cutting tools, Thin Solid Films 518 (2009) 14511454.

4. Szymon Wojciechowski, Paweá Twardowski, Tool life and process dynamics in high speed ball end milling of hardened steel, Procedia CIRP 1 ( 2012 ) 289 294.

5. Pinaki Chakraborty, Shihab Asfour, Sohyung Cho, Arzu Onar, Matthew Lynn, Modeling tool wear progression by using mixed effects modeling technique when end-milling AISI 4340 steel, journal of materials processing technology 205 (2008) 190-202.

6. N. Camuscu, E. Aslan, A comparative study on cutting tool performance in end milling of AISI D3 tool steel, Journal of Materials Processing Technology 170 (2005) 121126.

7. H.K. Kansal, Sehijpal Sing, P.Kumar, Parametric optimization of powder mixed electrical discharge machining by response surface methodology, Journal of Materials Processing Technology, 2005, 169:427-436.

8. U. Natarajan & PR. Periyanan & S. H. Yang, Multiple-response optimization for micro- endmilling process using response surface methodology, International Journal of Advanced Manufacturing and Technology (2011) 56:177 185

9. B. C. Routara & A. Bandyopadhyay & P. Sahoo, Roughness modeling and optimization in CNC end milling using response surface method: effect of workpiece material variation, International Journal of Advanced Manufacturing and Technology (2009) 40:1166 1180.

10. Design Expert Software, version 8, Users Guide, Technical Manual, Stat-Ease Inc.

11. L. B. Abhang & M. Hameedullah, Determination of optimum parameters for multi-performance

    characteristics in turning by using grey relational analysis, International Journal of Advanced Manufacturing and Technology (2012) 63:13

    24.

12. Nihat Tosun & Hasim Pihtili, Gray relational analysis of performance characteristics in MQL milling of 7075 Al alloy, International Journal of Advanced Manufacturing and Technology (2010) 46:509 515.

13. Mustafa Ay, Ula Çayda, Ahmet Hasçalik, Optimization of micro-EDM drilling of inconel 718 superalloy, International Journal of Advanced Manufacturing and Technology (2012), DOI 10.1007/s00170-012-4385-8.