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International Journal of Mechanical And Production Engineering, ISSN: 2320-2092,

Volume- 3, Issue-4, April-2015

MULTI RESPONSE OPTIMIZATION OF MILLING PROCESS PARAMETERS USING MOORA METHOD 1

SUHA K. SHIHAB, 2ARINDAM KUMAR CHANDA

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Department of Mechanical Engineering, Jamia Millia Islamia (A Central University), New Delhi, India Deparment of Mechanical Engineering and Automation Engineering, G.B. Pant college of Engineering, Okhla Industerial Estate, Phase- III Email: [email protected], [email protected]

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Abstract: This paper demonstrates application of a simple multi-objective optimization on the basis of ratio analysis (MOORA) method to solve multiple-criteria (objective) optimization problem in the milling processes. Four decisionmaking problems requiring determination of optimum milling parameters in different milling processes such as face milling, end milling, micro-end milling, and micro-ball end milling are considered in this paper. In all these cases, the results obtained using the MOORA method almost agree with those proposed by the past researchers which authenticate applicability, potentiality, and flexibility of this method for solving various complex decision making problems in presentday manufacturing environment. Keywords: MOORA, Milling, Optimization

I. INTRODUCTION numerous multi-objective decision-making (MODM) methods are available to deal with varying nature of evaluation and selection problems. Multi-objective optimization on the basis of ratio analysis (MOORA) method is one such method which has been extensively used by researchers due to its relatively simple and logical computational procedure. In addition, this method enables the decision makers to eliminate the unsuitable alternatives, while selecting the most appropriate alternative. The applicability, potentiality, and flexibility of this method have been proved by several researchers through its application in solving problems related to different fields. Brauers [7] first introduced this method for evaluating stakeholder's society design.

Manufacturing firms using different types of milling processes to manufacture different components are striving hard to increase product quality, safety, and at the same time they also want to decrease production and product costs. There are many variables related to the milling processes, including cutting parameters, tool materials, tool geometry, coating technology, lubricants, etc. which affect quality and production costs of the product. Selecting appropriate milling parameters significantly affect quality of the manufactured parts, productivity and the cost without damaging the cutting tool. The effective optimizations of these variables impact considerably, cost of the machined components, production time, and quality of final products. In addition, the optimization of controllable factors can make a considerable contribution towards solving the problem. Consequently, nowadays, the optimization methods have become the focus of interest for both academics and companies, with the goal of increasing production quality and operating with greater efficiency in milling processes [1- 6]. In manufacturing environment, the decision makers frequently confront with the problems of achieving multidimensional conflicting objectives. Their task is not only to provide various potential alternative options to solve the problem but also to select the best among them. In many situations, a single definite criterion does not work and therefore, decision makers have to take into account a large number of criteria. The decision makers require simple, systematic, and logical methods or mathematical tools to guide them in considering a number of selection criteria and their interrelations. The objective of any selection procedure is to identify appropriate selection criteria and to obtain the most appropriate combination of criteria in conjunction with the real requirement. Literature reveals that

Subsequently, methods were developed for (i) privatization in a transition economy [8], (ii) evaluating road design [9, 10], (iii) appraising contractor's ranking [11], (iv) evaluating the contractor's alternatives in the facilities sector in Lithuania [12], (iv) estimating the inner climate [13], and (v) evaluating project management in a transition economy [14]. Chakraborty [15, 16] applied the method for solving six different problems such as selection of (a) an industrial robot, (b) a flexible manufacturing system, (c) a computerized numerical control machine, (d) the most suitable nontraditional machining process for a given work material and shape feature combination, (e) a rapid prototyping process, and (f) an automated inspection system. Gadakh [17] applied this method for parametric optimization of milling process. Keeping in view the wide application of MOORA method, an attempt has been made in this paper to demonstrate the application of this method in the optimization of different milling process parameters.

Multi Response Optimization Of Milling Process Parameters Using Moora Method 67

International Journal of Mechanical And Production Engineering, ISSN: 2320-2092,

cases, it is often observed that some attributes are more important than others. In order to give more importance to an attribute, it is multiplied with its corresponding weight (significance coefficient) [12]. When these attribute weights are taken into consideration, Eq. (3) becomes as follows:

II. BRIEF DESCRIPTION OF THE MOORA METHOD The MOORA method is a multi-objective optimization, also known as multi-criteria or multiattribute optimization technique. It can be used to solve various types of complex decision making problems in the manufacturing environment [5; 1521] where the requirement is to simultaneously optimize two or more often conflicting objectives which are subjected to certain constraints. First step of the MOORA method is the formulation of a decision matrix, as represented by Eqn. (1), to exhibit performance of different alternatives with respect to various attributes (objectives) [9,10, 13,14, 22-24]  X11 X12 .... .... ....  X 21 X 22 .... .... .... X   .... .... .... .... ....  .... .... .... .... ....  X m1 X m2 .... .... .... 

.... .... .... .... ....

g

yi 

xij m

X1n  X 2n  ....  ……………..(1) ....  X mn 

 j 1

j  g 1

In the following sections, the applicability and potentiality of the MOORA method has been demonstrated through four illustrative examples in which four different multi-objective decision making problems related to the different milling process have been considered: 3.1 FACE MILLING Optimization of milling input parameters has always been an important research problem for many researchers. Kivak [5] applied Taguchi method and regression analysis to evaluate the machinability of Hadfield steel using PVD TiAlN and CVD TiCN/Al2O3-coated carbide inserts under dry face milling conditions. In this study, the cutting tool, A; cutting speed, B (m/min); and feed rate, C (mm/rev) were selected as input parameters and the output parameter was the surface roughness, Ra (µm), as shown in Table 1. The-lower-the-better criterion was considered for Ra. Table 1 also shows the normalized performance scores (yi ) of the alternatives with respect to the considered attributes, as obtained using Eqn. (2) and the normalized assessment values ( ) of all the alternatives with respect to the considered attributes as obtained from Eqn. (3). Further, Table 1 also exhibits the results of the MOORA methodbased analysis which gives a comparative ranking of the alternative when arranged according to the descending order of their assessment values. Thus, optimizing the parameter setting selection problem consists of a single performance measure. It can be seen from Table 1 that the MOORA method-based solution for process parameter selection problem suggests that optimal process parameters are cutting tool (A) is CVD, cutting speed (B) m/min 150, feed rate (C) 0.09 mm/rev. This result was exactly matched to the result suggested by Kivak [5].

 j  1,2,......, n …………………..…. (2)

where xij denotes ith alternative of jth objective. Usually these numbers belong to the interval [0, 1] representing the normalized performance of ith alternative on jth attribute. For multi-objective optimization, these normalized performances are added in case of maximization (for beneficial attributes) and subtracted in case of minimization (for nonbeneficial attributes) [23-25]. Then the optimization problem becomes: n

xija 

 wi xija  j  1,2,......,n ………(4)

III. ILLUSTRATIVE EXAMPLES FOR MULTIOBJECTIVE DECISION MAKING PROBLEMS

i 1

yi 

n

wi xija 

where wj is the weight of jth attribute, which can be determined by applying analytic hierarchy process or entropy method. The yi value can be either positive or negative depending on the totals of its maxima (beneficial attributes) and minima (nonbeneficial attributes) in the decision matrix. An ordinal ranking of yi shows the final preference. Thus, the best alternative has the highest yi value, while the worst alternative has the lowest yi value

 xij2

g

 j 1

where Xij is the performance measure of ith alternative on jth attribute, m is the number of alternatives, and n is the number of attributes. In the subsequent step, a ratio system is developed in which each performance of an alternative on an attribute is compared to a denominator which is a representative for all the alternatives concerning that attribute. Various ratio systems, such as total ratio, Schärlig ratio, Weitendorf ratio, Jüttler ratio, Stopp ratio, Körth ratio etc. are considered in the MOORA method as suggested by Brauers et al. [7-12]. However, it is recommended that for this denominator, the best choice is the square root of the sum of squares of each alternative per attribute. This ratio can be expressed as follows: xija 

Volume- 3, Issue-4, April-2015

 xija …………………………... (3) j  g 1

where g is the number of attributes to be maximized, (n-g) is the number of attributes to be minimized, and yi is the normalized assessment value of ith alternative with respect to all the attributes. In some

Multi Response Optimization Of Milling Process Parameters Using Moora Method 68

International Journal of Mechanical And Production Engineering, ISSN: 2320-2092,

Exp.no. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

Table 1: Objective data of attributes of example 3.1 [5] A B C Ra (µm) yi for Ra PVD 90 0.09 0.51 0.209 0.209 PVD 90 0.12 0.57 0.234 0.234 PVD 90 0.15 0.76 0.312 0.312 PVD 120 0.09 0.50 0.205 0.205 PVD 120 0.12 0.55 0.226 0.226 PVD 120 0.15 0.66 0.271 0.271 PVD 150 0.09 0.47 0.193 0.193 PVD 150 0.12 0.55 0.226 0.226 PVD 150 0.15 0.67 0.275 0.275 CVD 90 0.09 0.50 0.205 0.205 CVD 90 0.12 0.58 0.238 0.238 CVD 90 0.15 0.71 0.291 0.291 CVD 120 0.09 0.46 0.189 0.189 CVD 120 0.12 0.52 0.213 0.213 CVD 120 0.15 0.66 0.271 0.271 CVD 150 0.09 0.45 0.185 0.185 CVD 150 0.12 0.50 0.205 0.205 CVD 150 0.15 0.59 0.242 0.242

A 25 25 25 50 50 50 75 75 75

rank 7 11 18 4 9 14 3 10 16 5 12 17 2 8 15 1 6 13

( ) of all the alternatives with respect to the considered attributes were calculated using Eqn. (3) and the values of are also shown in Table 2. It can be seen from Table 2 that the results of the MOORA method-based analysis which gives a comparative ranking of the alternative when arranged according to the descending order of their assessment values; the experiment no.7 has the highest rank, and the corresponding process parameters are cutting speed (75 m/min), feed rate (0.06 mm/rev), and depth of cut (0.6 mm). The optimal parameter setting suggested by Maiyar et al. [19] was almost matched using the MOORA method with the only difference in the value of the depth of cut (0.4 mm).

3.2 END MILLING Maiyar et al. [19] performed the parameter optimization of end milling operation for Inconel 718 super alloy with multi-response criteria based on the Taguchi orthogonal array with the grey relational analysis. They considered cutting speed (A), feed rate (B) and depth of cut (C) as the input parameters. The multiple performance characteristics considered were surface roughness (Ra) and material removal rate (MRR) as shown in Table 2. The-lower-the-better and the-higher-the-better criteria were considered for Ra and MRR respectively. Table 2 also shows the normalized performance scores (yi) of the alternatives with respect to the considered attributes, as obtained using Eqn. (2). The normalized assessment values

Exp. No. 1 2 3 4 5 6 7 8 9

Volume- 3, Issue-4, April-2015

Table 2: Objective data of attributes of example 3.2 [19] B C Ra MRR yi for Ra yi for MRR 0.06 0.2 0.21 4.308 0.284 0.244 0.09 0.4 0.25 4.480 0.338 0.253 0.12 0.6 0.29 4.503 0.392 0.255 0.06 0.4 0.2 5.643 0.271 0.319 0.09 0.6 0.27 5.731 0.365 0.324 0.12 0.2 0.27 5.904 0.365 0.334 0.06 0.6 0.21 6.906 0.284 0.390 0.09 0.2 0.23 7.080 0.311 0.400 0.12 0.4 0.27 7.530 0.365 0.426

-0.041 -0.085 -0.138 0.048 -0.041 -0.032 0.106 0.089 0.060

rank 6 8 9 4 7 5 1 2 3

better criterion was considered for both response variables. Table 3 shows the results of MOORA method based analysis which gives a comparative ranking of the alternative when arranged according to the descending order of their assessment values. It can be seen from Table 3 that experiment no.9 has the highest rank, and the corresponding process parameters are spindle speed (60 krpm), feed per tooth (0.5 µm/tooth ), and axial depth of cut (60 µm).

3.3 MICRO-END MILLING Thepsonthi and Ozel [18] used Taguchi L9 design in micro-end milling of Ti-6Al-4V titanium alloy to find the optimal process parameters which minimize the surface roughness and burr formation. In their study, they considered three process parameters i.e. spindle speed, Ω (krpm); feed per tooth, fz (µm/tooth); and axial depth of cut, ADOC (µm). As shown in Table 3, the response variables were surface roughness, Ra (µm); and top burr width, w (mm). The-lower-the

Multi Response Optimization Of Milling Process Parameters Using Moora Method 69

International Journal of Mechanical And Production Engineering, ISSN: 2320-2092,

Volume- 3, Issue-4, April-2015

The results were exactly matched to those suggested by Thepsonthi and Ozel [18]. Table 3: Objective data of attributes of example 3.3 [18]

their study, responses were optimized simultaneously using grey relational analysis. Thelower-the better criterion was considered for all response variables. Table 3 also reveals the MOORA method based solution for process parameter selection problem which suggests that optimal process parameters are spindle speed of 10000 rpm, feed per tooth 0.5 µm/tooth, and depth of cut 50 µm. This results was matched to the one suggested by Kuram & Ozcelik [20].

3.4 MICRO-BALL END MILLING Kuram & Ozcelik [20] used Taguchi L9 design in micro-milling of aluminum material with ball nose end mill. The input parameters which they considered were spindle speed (A), feed per tooth (B), and depth of cut (C) and the output responses were tool wear (VB), forces (Fx and Fy), and surface roughness (Ra) as shown in Table 3. In

Exp. no

A

B

1 2 3 4 5 6 7 8 9

10000 10000 10000 11000 11000 11000 12000 12000 12000

0.5 1 1.5 0.5 1 1.5 0.5 1 1.5

Table 4. Objective data of attributes of example 3.3 [20]. C VB Fx Fy Ra yi yi yi for for for VB Fx Fy 50 5.41 1.33 0.71 0.33 0.068 0.192 0.178 75 13.51 1.63 0.86 0.47 0.169 0.235 0.216 100 16.22 2.02 1.02 0.71 0.203 0.291 0.256 75 27.02 1.62 1.08 0.32 0.339 0.233 0.271 100 32.43 2.03 1.49 0.59 0.406 0.292 0.374 50 14.86 2.65 1.52 0.58 0.186 0.382 0.382 100 45.95 2.1 1.36 0.27 0.576 0.302 0.341 50 27.03 2.99 1.66 0.35 0.339 0.431 0.417 75 32.43 3.55 1.81 0.58 0.406 0.511 0.454

yi for Ra 0.225 0.320 0.484 0.218 0.402 0.395 0.184 0.239 0.395

rank

0.662 0.940 1.234 1.061 1.475 1.345 1.404 1.425 1.767

1 2 4 3 8 5 6 7 9

a simple ratio analysis, the computational time is significantly less and it does not require any sophisticated and complex computer software for its implementation. Finally, due to its inherent characteristics this method is observed to be much simpler than many MODM methods and at the same time it provides optimal solution to the multi objective problems quickly.

IV. RESULTS AND DISCUSSION In three examples, i.e. example 3.1, example 3.3, and example 3.4, it is found that the top ranked alternatives exactly matched with those derived by the past researchers. In addition, in example 3.2, the ranked alternative is found to almost match with those derived by the past researchers. While applying the MOORA method, it is observed that this method is simple, logical and requires only a few simple computational steps in getting the optimum solution. Thus, this method can be used by decision makers who do not possess great amount of mathematical and computational skills. Since this method involves only

CONCLUSION This paper has presented application of MOORA method for the selection of optimal process parameters in different types of milling processes.

Multi Response Optimization Of Milling Process Parameters Using Moora Method 70

International Journal of Mechanical And Production Engineering, ISSN: 2320-2092,

The potential application of this method has been explained through four illustrative examples pertaining to the four different types of milling processes. It has been observed that in all the cases, the top-ranked alternatives have almost matched with those derived by past researchers. The MOORA method, indeed, considers all the attributes along with their relative importance which enables this method to provide not only a better but also an accurate evaluation of the alternatives. As compared to many other MODM methods, this method is found to be simple, logical and robust. This method can simultaneously consider any number of quantitative and qualitative selection of attributes and is able to provide optimum solution quickly as computational time required to obtain the solution is reasonably low. However, in case of problems involving a large number of qualitative attributes, this method is not found to be as efficient as other MODM methods. The method has ability to consider any number of quantitative and qualitative selection criteria simultaneously and therefore, it can be employed for any type of selection problem involving any number of selection criteria. This method can be applied to solve several multi objective optimization problems pertaining to a wide range of manufacturing environment.

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