Selection of Material for Optimal Design Using Multi-criteria Decision Making

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Procedia Materials Science 6 ( 2014 ) 590 – 596

Selection and peer review under responsibility of the Gokaraju Rangaraju Institute of Engineering and Technology (GRIET) doi: 10.1016/j.mspro.2014.07.073

ScienceDirect

3rd International Conference on Materials Processing and Characterisation (ICMPC 2014)

Selection of Material for Optimal Design using Multi-Criteria

Decision Making

Rajnish Kumar

a

, Jagadish

b

, Amitava Ray

c

a_{Department of Mechanical Engineering, National Institute of Technology, Silchar and 788010, India} bc_{Department of Mechanical Engineering, National Institute of Technology, Silchar and 788010, India}

Abstract

Selection of suitable material in all the engineering design is often observed to be a multi-criterion decision-making problem with conflicting and different objectives. This paper presents a methodology to evaluate optimum material for engineering design using an integrated approach, in which criteria weights are computed using the entropy method and ranking of the alternatives is computed using the TOPSIS (Technique for order performance by similarity to ideal solution) method. In this research seven number of alternative martial and six criteria for material selection is used for the optimal design. The result from the research shows that nitridedd steel material is best for the engineering design. The procedure is illustrated using a case study.

Selection and peer-review under responsibility of the Gokaraju Rangaraju Institute of Engineering and Technology (GRIET).

Keywords: Entropy Method, TOPSIS, Ranking of material, MCDM

1. Introduction

Material selection has great importance in product development and design. It is also vital for the success and competition of products in market, because productivity and buyer needs must be fulfil. Improper selection of material may result in failure to fulfil customer and manufacturer requirements (Karande & Chakraborty, 2012). Also, improper selection of materials may result in failure or disappoint of an assembly and significantly reduces the efficiency and performance of products, thus adverse affecting productivity, profitability and reputation of organization. Material selection for real engineering is based on several requirements. Selecting the materials that best meet the needs of the design and give maximum performance and minimum cost is the goal of optimum product design (Shanian & Savadogo, 2006). In recent past, many traditional materials are being replaced by new materials and the available set of materials is rapidly growing both in type and number.

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* Corresponding author. Tel.: +0-000-000-0000 ; fax: +0-000-000-0000 .

E-mail address: [email protected]

This large number of materials together with the complex relationships between different selection parameters often makes the material selection for a given component a difficult and tedious task. Consequently, with the ever increasing choice of materials and variety of manufacturing processes available to the designers, the selection of an optimal material is more complex and more challenging than before (Rao & Patel, 2010).

In order to address the issue of material selection and to increase the efficiency in design process, a variety of methods had been proposed in the literature, such as Ashby approach, analytic hierarchy process (AHP), Entropy, technique of order preference by similarity to ideal solution (TOPSIS) , gray relational analysis (GRA), graph theory and matrix approach, ELECTRE (Elimination Et Choix Traduisant la REalite), VIKOR (VIsekriterijumska optimizacija Kompromisno Resenje), and COPRAS (Complex PRoportional Assessment). In addition, some researchers used multiple decision making methods for solving the considered material selection problems. Under many conditions, however, exact data are inadequate to model real-life situations because of the complexity of material selection problem. Therefore, fuzzy set theory was incorporated to deal with the vagueness and ambiguity in decision making process. For example, , Dagdeviren et al. (2008) developed an evaluation model based on AHP and TOPSIS for the selection of optimal weapon in a fuzzy environment and Rathod and Kanzaria projected a systematic evaluation model for the phase change material selection based on AHP and fuzzy TOPSIS methods. Prasenjit et al. (2012) used to solve material selection problem by Preferential Ranking Methods. R. Khorshidi et al. (2013) use MCDM approach for Comparative Analysis between TOPSIS and PSI Methods of Materials Selection to achieve a desirable combination of strength and workability in al/sic composite. Deng Y-M et al. (2007), apply multi criteria decision method to explain the Role of Materials Identification and Selection in Engineering Design. R. kumar et.al (2013) Selection of cutting tool material by TOPSIS method and Selection of material: A multi criteria approach using multi objective optimization on the basis of ratio analysis..

In this paper Entropy method is used to determine the criteria weight and technique of order preference by similarity to ideal solution is used to find the optimal material and worst material from the available alternatives. The aim of this paper is proposed a method to select material for industrial design. In this paper take an example for material selection for exhaust manifold of automobile. Surface hardness, Core hardness, Surface fatigue limit, Ultimate tensile strength, Cost is the criteria for material selection for exhaust manifold and seven material as a alternative as ductile iron, Cast iron, cast alloy steel, surface hardened alloy steel carburized steels, nitride steels.

2. Multi Criteria Decision making methods

2.1 Entropy method

Entropy measures the uncertainty in the information formulated using probability theory. Shannon’s Entropy, which demonstrates that a broad distribution represents more ambiguity than does a sharply peaked one, is applied to determine the objective weight in our study. Formally, the rationale of entropy analysis is denoted as:

Step-1: Decide the Decision matrix X1 X2 .... Xn 1 11 12 1 2 21 22 2 3 1 2 n n m m mn

A X

X

A X

X

A

A X

X

ª

º

«

»

«

»

«

»

«

»

¬

¼

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Xij (i = 1,2,….,m; j = 1, 2, ……, n) is the performance value of ith alternative to the jth criteria. Step-2: Normalize the decision matrix

ܳ௜௝ൌ ௑೔ೕ

ටσ೘ ௑మ

೔సభ

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Step-3: Entropy value Ej of jth criteria obtained as:

Ej= -K σ௠௜ୀଵܳ௜௝݈݊൫ܳ௜௝൯݆ ൌ ͳǡʹǡ ǥ ǥ ǡ ݊ (3) Where k=1/ln m is a constant the guarantees 0 ≤ Ej ≤ 1 and m is the number of alternatives.

Step-4: The degree of divergence (Dj) of the average information contained by each criterion can be obtained from

equation (4)

1

j j

D

E

(4) Step-5: Weight of Entropy of jth criterion can be defined as:

1 j j n j j

D

B

D

¦

(5) 2.2 TOPSIS approach

TOPSIS approach was developed by Hwang and Yoon (1981). This approach is used when the user prefers a simpler weighting approach. In this paper TOPSIS method is used in to obtain a solution, which is closest to the ideal solution and farthest from the negative ideal solution. The method needs information on relative importance of properties that are considered in selection process. The TOPSIS method consists of the following steps:

Step-1: Normalization of the decision matrix is calculated by below equation ݊௜௝ൌ

௑೔ೕ

ටσ೘ ௑మ

೔సభ

j=1, 2...., n; i = 1, 2..., m (6)

Step-2: The normalised decision matrix multiplies with associated weights, Wj taken from Table 2 obtained by

following equation:

Vij = nijBj j = 1, 2. . . n; i = 1, 2..., m (7)

Step-3: The ideal and nadir ideal solutions are determined using Eqs. In below (8) and (9) respectively: {ܸଵାǡ ܸଶାǡ Ǥ Ǥ ǥ ǡ ܸ௡ାሽ ൌ ൜ܯܽݔܸ௜௝ȁ݆ א ܭሻǡ ሺܯܸ݅݊௜௝ห݆ א ܭ′ሻȁ݅ ൌ ͳǡ ʹǡ ǥ Ǥ ǡ ݉ൠ (8) {ܸଵିǡ ܸଶିǡ Ǥ Ǥ ǥ ǡ ܸ௡ିሽ ൌ ൜ܯܸ݅݊௜௝ȁ݆ א ܭሻǡ ሺܯܽݔܸ௜௝ห݆ א ܭ′ሻȁ݅ ൌ ͳǡ ʹǡ ǥ Ǥ ǡ ݉ൠ (9) Where K is the index set of benefit criteria and K’_{is the index of cost criteria.}

Step-4: The distance from the ideal and nadir solutions computed by below equations (10) and (11) respectively: ܵ௜ାൌ ቄσ௡௝ୀଵ൫ܸ௜௝െ ܸ௝ା൯ଶቅ ଴Ǥହ j = 1, 2. . . n; i = 1, 2..., m (10) ܵ௜ିൌ ቄσ ൫ܸ௜௝െ ܸ௝ି൯ ଶ ௡ ௝ୀଵ ቅ ଴Ǥହ j = 1, 2. . . n; i = 1, 2..., m (11) Step-5: Relative closeness computed from the ideal solution is from below equation (12):

ܥ௜ൌ ௌ೔

ష

ௌ೔శାௌ೔ష i = 1, 2..., m; Ͳ ൑ ܥ௜൑ ͳ (12)

Result of equation (12) Contain higher value is best rank and smallest value got worst rank that means ranking is in decreasing order.

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3. Validation of the proposed methodology

For validation of this methodology take an example, material selection for exhaust manifold from alternative criteria and alternative material. For this example take seven alternative material which shown in Table-2 and criteria of material which shown in Table-1. From the material data handbook create a decision matrix which is shown in Table-3.

Table-1: Criteria of material Table-2: List of Alternative material

Material Sel. No. Ductile iron 1 Cast iron 2 Cast alloy steel 3 Hardened alloy steel 4 Surface hardened alloy steel 5 Carburised steels 6 Nitrided steels 7

Table-3: Decision matrix of material

S.No. SH CH SFL BFL UTS C 1 220 220 460 360 880 0.342 2 200 200 330 100 380 0.171 3 270 270 630 435 590 0.119 4 270 270 670 540 1190 1.283 5 585 240 1160 680 1580 3.128 6 700 315 1500 920 2300 2.315 7 750 315 1250 760 1250 4.732

4. Result and Discussion

In this paper, Entropy method is used to determine the criteria weight (Bj) which is shown in table-4. In order to solve the material selection problem, the TOPSIS method was employed first. For calculating criteria weight first Normalize the decision matrix (Table-3) from equation two and result be shown in Table five. Using equation five to determine criteria weighting and result is shown in table four.

Table-4: Criteria weighting by Entropy method

S.No. SH CH SFL BFL UTS C

Bj 0.20134 0.39475 0.22708 0.21041 0.2059 0.23949 Table-5: Normalized decision matrix

S.No. SH CH SFL BFL UTS C 1 0.17237 0.31421 0.18291 0.22737 0.2537 0.05453 2 0.1567 0.28564 0.13122 0.06316 0.10955 0.02726 3 0.21155 0.38562 0.25051 0.27474 0.17009 0.01897 Criteria Unit Surface hardness(SH) Bhn Core hardness(CH) Bhn Surface fatigue limit(SFL) N/mm2 Bending fatigue limit(BFL) N/mm2

Ultimate tensile strength(UTS) N/mm2 Cost(C) USC/lb

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4 0.21155 0.38562 0.26642 0.34106 0.34307 0.20455 5 0.45836 0.34277 0.46126 0.42948 0.4555 0.4987 6 0.54846 0.44989 0.59646 0.58107 0.66307 0.36908 7 0.58764 0.44989 0.49705 0.48001 0.36037 0.75443

Table-6: Weighted and normalized decision matrix, Vij.

S.No. SH CH SFL BFL UTS C 1 0.03471 0.12403 0.04154 0.04784 0.05224 0.01306 2 0.03155 0.11276 0.0298 0.01329 0.02256 0.00653 3 0.04259 0.15222 0.05689 0.05781 0.03502 0.00454 4 0.04259 0.15222 0.0605 0.07176 0.07064 0.04899 5 0.09229 0.13531 0.10474 0.09037 0.09379 0.11943 6 0.11043 0.17759 0.13545 0.12226 0.13653 0.08839 7 0.11831 0.17759 0.11287 0.101 0.0742 0.18067

Table-7: The ideal and nadier ideal solutions:

V+ 0.118314 0.177593 0.135445 0.122263 0.136528 0.180674 V- 0.03155 0.112757 0.029798 0.013289 0.022557 0.004544

Table-8: Distance from ideal and nadier solution and Ci

S- S+ Ci

Rank

0.049216 0.221846 0.181566 6 0.001985 0.044558 0.042657 7 0.067458 0.259728 0.206178 5 0.101628 0.318791 0.24173 4 0.184468 0.429498 0.300454 3 0.23126 0.480895 0.324733 2 0.302039 0.549581 0.354664 1

Technique for order preference by similarity to ideal solution method used to determine best material and worst material from alternative material. In step-1 normalize the matrix that is shown in Table-5. From equation six, normalized matrix is multiply by criteria weighting in step-2 using equation seven shown in Table-6. In step-3 determine ideal and nadir ideal solutions using equation eight and nine shown in Table-7. In Step five determine relative closeness computed from the ideal solution is from equation twelve and higher value have most appropriate material and least value are worst material which is shown in table eight. In Graph-1 shown between ranking of material and alternative material. By this method nitride steel is best material among the other alternative material and carburized steel is second best material and cast iron is worst material among alternatives.

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Fig: 1 ranking of material

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