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A--Application of MOORA method fo r parametric optimiza tion of milling procesS -EIJAER2040.pdf

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INTERNATIONAL JOURNAL OF APPLIED ENGINEERING RESEARCH, DINDIGUL  Volume 1, No 4, 2011  © Copyright 2010 All rights reserved Integrated Publishing Association  RESEARCH ARTICLE  ISSN ­ 0976­4259  Application of MOORA method for parametric optimization of milling  process  Gadakh. V. S.  Department of Mechanical Engineering, Amrutvahini College of Engineering, Sangamner,  Ahmednagar, Maharashtra– 422 608, India  gadakh_vijay@mec.vnit.ac.in  ABSTRACT  In the present work, application of multi­obj
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  INTERNATIONAL JOURNAL OF APPLIED ENGINEERING RESEARCH, DINDIGUL Volume 1, No 4, 2011 © Copyright 2010 All rights reserved Integrated Publishing Association RESEARCH ARTICLE ISSN - 0976-4259   743   Application of MOORA method for parametric optimization of milling process   Gadakh. V. S. Department of Mechanical Engineering, Amrutvahini College of Engineering, Sangamner, Ahmednagar, Maharashtra– 422 608, India gadakh_vijay@mec.vnit.ac.in  ABSTRACT  In the present work, application of multi-objective optimization on the basis of ratio analysis (MOORA) method is applied for solving multiple criteria (objective) optimization problem in milling process. Six decision-making problems which include selection of suitable milling  process parameters in different milling processes are considered in this paper. In all these cases, the results obtained using the MOORA method almost match with those derived by the  previous researchers which prove the applicability, potentiality, and flexibility of this method while solving various complex decision-making problems in present day manufacturing environment.  Keywords:  Decision making, MOORA method, Multi-objective optimization, Milling  1. Introduction  The milling operation is a metal cutting process using a rotating cutter with one or more teeth. The determination of optimal cutting parameters such as depth of cut, cutting speed and feed, which are applicable for assigned cutting tools, is one of the vital modules in process  planning of metal parts, since the economy of machining operations plays an important role in increasing productivity and competitiveness. The objective of any selection procedure is to identify appropriate selection criteria, and obtain the most appropriate combination of criteria in conjunction with the real requirement. Thus, efforts need to be extended to identify those criteria that influence an alternative selection for a given problem, using simple and logical methods, to eliminate unsuitable alternatives, and to select the most appropriate alternative to strengthen existing selection procedures (Brauers, 2004). Although, a lot of multi-objective decision-making (MODM) methods is now available to deal with varying evaluation and selection problems, this paper explore the applicability of a new MODM method, i.e. the multi-objective optimization on the basis of ratio analysis (MOORA) method to optimize different milling parameters. This method is observed to be simple and computationally easy which helps the decision makers to eliminate the unsuitable alternatives, while selecting the most appropriate alternative to strengthen the existing selection procedures (Brauers, et al., 2008).  2. The MOORA method  Multi-objective optimization (or programming), also known as multi-criteria or multi- attribute optimization, is the process of simultaneously optimizing two or more conflicting attributes (objectives) subject to certain constraints. The MOORA method, first introduced by Brauers (2004) is such a multi-objective optimization technique that can be successfully applied to solve various types of complex decision making problems in the manufacturing  INTERNATIONAL JOURNAL OF APPLIED ENGINEERING RESEARCH, DINDIGUL Volume 1, No 4, 2011 © Copyright 2010 All rights reserved Integrated Publishing Association RESEARCH ARTICLE ISSN - 0976-4259   744 environment. The MOORA method (Brauers, et al. 2006, 2008, 2009, Kalibatas, et al. 2008, Lootsma, 1999) starts with a decision matrix showing the performance of different alternatives with respect to various attributes (objectives).  Step 1:  The first step is to determine the objective, and to identify the pertinent evaluation attributes.  Step 2:  The next step is to represent all the information available for the attributes in the form of a decision matrix. The data given in eq. (1) are represented as matrix X mxn . Where x ij is the  performance measure of i th alternative on j th attribute, m is the number of alternatives, and n is the number of attributes. Then 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.   ú ú ú ú û ù ê ê ê ê ë é =   mn m m n n  x  x  x  x  x  x  x  x  x  X   . . . . . . . 2 1 2 22 21 1 12 11 (1)  Step 3:  Brauers et al. (2008) concluded 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 below:   ú û ù ê ë é = å =  mi ij ij ij  x  x  x   1 2 * (j = 1, 2, ...., n) (2) Where x ij is a dimensionless number which belongs to the interval [0, 1] representing the normalized performance of i th alternative on j th attribute.  Step 4:  For multi-objective optimization, these normalized performances are added in case of maximization (for beneficial attributes) and subtracted in case of minimization (for non  beneficial attributes). Then the optimization problem becomes:   å å + = = - =   n  g  j ij  g  j ij i  x  x  y   1 * 1 * (3) Where g is the number of attributes to be maximized, (n−g) is the number of attributes to be minimized, and y i is the normalized assessment value of i th alternative with respect to all the attributes. In some cases, it is often observed that some attributes are more important than the others. In order to give more importance to an attribute, it could be multiplied with its corresponding weight (significance coefficient) (Brauers et al. 2009). When these attribute weights are taken into consideration, Eq. 3 becomes as follows:   å å + = = - =   n  g  j ij  j  g  j ij  j i  x w  x w  y   1 * 1 * (j = 1, 2, ...., n) (4)  INTERNATIONAL JOURNAL OF APPLIED ENGINEERING RESEARCH, DINDIGUL Volume 1, No 4, 2011 © Copyright 2010 All rights reserved Integrated Publishing Association RESEARCH ARTICLE ISSN - 0976-4259   745 Where w  j is the weight of j th attribute, which can be determined applying analytic hierarchy  process (AHP) or entropy method.  Step 5:  The y i value can be positive or negative depending of the totals of its maxima (beneficial attributes) and minima (non-beneficial attributes) in the decision matrix. An ordinal ranking of y i shows the final preference. Thus, the best alternative has the highest y i value, while the worst alternative has the lowest y i value.  3. Decision-making problems  In order to demonstrate the applicability and potentiality of the MOORA method in solving multi-objective decision making problems in real-time manufacturing environment, the following six illustrative examples are considered.  3.1 Example 1: Side milling process  Kao and Lu (2007) have proposed orthogonal array with grey-fuzzy logics applied to optimize the side milling process with multiple performance characteristics. Gadakh and Shinde (2011) have also solved the same problem using graph theory and matrix approach (GTMA). The considered example problem is related with selection of suitable cutting  parameters in side milling process. The cutting parameters selection problem considers nine alternatives and two attributes, and the data are given in Table 1 and 2.  Table 1:  Quantitative data of the factors of example 3.1 (Kao and Lu, 2007 reprinted with  permission from Springer by author) Exp.  No. V (rpm) F (mm/t) D a (mm) D r (mm) Cutting Time (min.) 1 1,500 0.0592 7 0.4 281.53 2 1,500 0.074 11 0.7 225.23 3 1,500 0.0888 15 1 187.69 4 2,000 0.0592 15 0.7 211.15 5 2,000 0.074 7 1 168.92 6 2,000 0.0888 11 0.4 140.77 7 2,500 0.0592 11 1 78.04 8 2,500 0.074 15 0.4 135.14 9 2,500 0.0888 7 0.7 112.61  Table 2:  Quantitative data of the factors of example 3.1 continued (Kao and Lu, 2007 reprinted with permission from Springer by author) Exp. No. Cutting Time (min.) TWR (mm/min) MRR (mm³/s) 1 281.53 1.2574×10 -4 16.58 2 225.23 1.7760×10 -4 56.98 3 187.69 1.7582×10 -4 133.2 4 211.15 2.2022×10 -4 62.16 5 168.92 2.0070×10 -4 51.8 6 140.77 2.7918×10 -4 39.07  INTERNATIONAL JOURNAL OF APPLIED ENGINEERING RESEARCH, DINDIGUL Volume 1, No 4, 2011 © Copyright 2010 All rights reserved Integrated Publishing Association RESEARCH ARTICLE ISSN - 0976-4259   746 7 78.04 5.8431×10 -4 65.12 8 135.14 3.0412×10 -4 44.4 9 112.61 3.1436×10 -4 43.51 MRR is considered as beneficial attribute (i.e. higher values are desirable), and TWR considered as non-beneficial attribute (i.e. lower values are desirable).  Table 3:  Assessment values for example 3.1 Exp. No. TWR (mm/min) MRR (mm³/s) Rank 1 1.2574×10 -4 16.58 8 2 1.7760×10 -4 56.98 6  3 1.7582×10 -4 133.2 1  4 2.2022×10 -4 62.16 7 5 2.0070×10 -4 51.8 9 6 2.7918×10 -4 39.07 5 7 5.8431×10 -4 65.12 2 8 3.0412×10 -4 44.4 4 9 3.1436×10 -4 43.51 3 Table 3 shows the MOORA-method-based solution for cutting parameter selection problem which suggests that optimal cutting parameters are: Cutting Speed (V): 1,500 rpm, Feed rate (F): 0.0888 mm/t, axial depth of cut (D a ):15 mm, Radial depth of cut (D r  ):1mm. The results were matched to those suggested by Kao and Lu using orthogonal array with grey-fuzzy logics and Gadakh and Shinde using GTMA and few other Multi-Attribute Decision Making (MADM) methods.  3.2 Example 2: End milling process  Gopalsamy et al. (2004) has used Taguchi method to find optimum process parameters for end milling while hard machining of hardened steel. In this study three performance measures are considered i.e. surface finish, tool wear and tool life and four machining parameters (cutting speed, feed, depth of cut and width of cut) are considered as shown in Table 4.  Table 4:  Quantitative data of the factors of example 3.2 (Gopalsamy et al., 2004) Exp.  No. Avg. Surface finish Avg. Tool wear Avg. Tool Life 1 0.9233 108.33 280.07 2 0.8366 110 410.11 3 0.9233 96.66 301.77 4 0.9066 105 250.77 5 0.85 96.66 304.17 6 0.8 100 421.28 7 0.6433 100 441 8 0.42 95 914.66 9 0.8333 96.66 782.25
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