 Open Access
 Total Downloads : 627
 Authors : Lanka Prakasa Rao, T Jaya Anand Kumar, Thella Babu Rao
 Paper ID : IJERTV1IS9461
 Volume & Issue : Volume 01, Issue 09 (November 2012)
 Published (First Online): 29112012
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Modelling And MultiResponse 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 costefficiency 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 cutting 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 multiobjective 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.

Introduction
Hardened steels are being used in a variety of industrial applications like automotive, aerospace etc. These materials are often classified as difficult tomachine 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 performance of coated and uncoated carbide tools (inserts) in the machining of three cast austenic stainlesssteels. 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 endmilling of AISI 4340 steel with multi layer physical vapor deposition (PVD) coated carbide inserts under semidry 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].

Normalize the response matrix from zero to one by using Eq. (2) and (3).
Lowerthebetter (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.
Higherthebetter (HB) is the criterion:
y (k ) min y (k)
x (k ) i i
(3)

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 developing, 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 secondorder nonlinear response function usually utilized [13] in the form:
of y (k) for kth response. x is the normalised array.
i

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 StatEase 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 Fratio, which is the ratio between the regression mean square and the mean square error. If the calculated value of Fratio is higher than the tabulated value of Fratio for roughness, then the model is adequate at desired significance level to represent the relationship between machining response and the machining parameters.


Determination of overall grey relational grade.
1 n


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 multiresponse (multigray 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.

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

Variables Units Notation Range No 1 0 1

Depth of cut mm DOC 0.1 0.2 0.3

Feed Rate mm/tooth F 0.1 0.3 0.5

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

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 Fvalues 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 pvalue
Source Squares df Square Value Prob > F
Model 9.50E03 9 1.06E03 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 RSquared
2.26E03 1 2.26E03 204.60 < 0.0001
5.86E04 1 5.86E04 53.070 < 0.0001
7.56E06
1
7.56E06
0.6851
0.4193
3.46E05
1
3.46E05
3.1387
0.0944
3.60E05
1
3.2626
0.0886
3.77E05
1
3.77E05
3.4136
0.0821
3.43E05
1
3.43E05
3.1077
0.0959
1.98E04
1
1.98E04
17.931
0.0006
1.99E05
1
1.99E05
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 RSquared 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 pvalue 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
RSquared 0.9907
Adj RSquared 0.985763
has been converted in to singleobjective 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.

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 multiobjective 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.

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.
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