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Material Selection for Rotational Moulding Process Using Grey Relational Analysis Approach
Available online at www.sciencedirect.com
ScienceDirect Materials Today: Proceedings 5 (2018) 19224–19229
www.materialstoday.com/proceedings
ICMPC_2018
Material Selection for Rotational Moulding Process Using Grey Relational Analysis Approach Bhavesh Chaudharya, PL. Ramkumarb*, Kumar Abhishekc b*,c
a M.Tech student, Mechanical Engineering Student, IITRAM , Ahmadabad Assistant Professor, Department of Mechanical Engineering, IITRAM , Ahmadabad
Abstract Rotomoulding is an emerging industry of present era for manufacturing hollow plastic products of various sizes. Different materials like polyethylene, polypropylene, polyvinylchloride, polycarbonate etc. are used in rotational moulding. As vast variety of materials with diverse physical and mechanical characteristics is available, choosing the best suitable material becomes a challenge. Rotomoulder has to take into account a large number of material selection criteria before arriving at the final decision, otherwise there may be premature failure of the product during its operation. In order to assist the rotomoulder, this paper presents a systematic and efficient multi attribute decision-making approach referred as grey relation analysis for material selection in rotational moulding. In order to elaborate the above said procedure eleven alternatives are evaluated against seven criteria. From the analysis suitable material has been identified. © 2018 Elsevier Ltd. All rights reserved. Selection and/or Peer-review under responsibility of Materials Processing and characterization. Keywords: Rotational Moulding; Material selection; Grey relation analysis; Plastic manufacturing process
1. Introduction Rotational moulding also known as rotocasting, is a process for manufacturing hollow plastic products. Although there are various techniques available for processing plastics, rotational moulding has particular advantages in terms of relatively low levels of residual stresses and inexpensive molds. Rotational moulding is best known for the manufacturing of tanks. Also it is used to make complex medical products, toys, and many highly aesthetic point-ofsale products [1, 2]. From the literature survey it is found that rotomoulding process can be further enhanced by either changing the process parameters or by making changes in the material itself. R.J Crawford et al. [3] investigated the rotomoulding process by applying the pressure inside the mould at specific point during heating * Corresponding author. Tel.: +91 9823256780 E-mail address: [email protected]
2214-7853 © 2018 Elsevier Ltd. All rights reserved. Selection and/or Peer-review under responsibility of Materials Processing and characterization.
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Nomenclature GRA- Grey Relational Analysis MADM- Multi Attribute Decision Making LDPE- Low Density Polyethylene HDPE- High Density Polyethylene LLDPE- Linear Low Density Polyethylene EVA- Ethylene Vinyl acetate PP- Polypropylene PVC- Polyvinyl Chloride PTFE- Polytetrafluroethylene PLA- Poly Lactic Acid ABS- Acrylonitrile Butadiene Styrene PC- Polycarbonate WEDM- Wire Electric Discharge Machining Org-MMT- organophilically modified montmorillonite SEBS-g-MA- maleated styrene–ethylene–butylene–styrene
cycle and found that it can reduce the pinhole formation and decreases the cycle time. S.C. Tjong et al. [4] conducted an experiment to increase the impact fracture toughness of rotomoulding material. They selected HDPE/2%Org-MMT and HDPE/4%Org-MMT nanocomposites and added different amount of SEBS-g-MA. A nearly twofold increase in impact fracture toughness of the HDPE/2%Org-MMT and HDPE/4%Org-MMT nanocomposites was achieved by adding 10%SEBS-g-MA. Maria Jovita Oliveira et al. [5] studied the effect of temperature on the reactions taking Place in rotomoulding. They suggested the optimum level of temperature to be produced inside the mould to control the degradation of the polymer. PL.Ramkumar et al. [6] investigated the effect of foam added with LLDPE on the properties of rotomoulding process. They found 6% of foam in LLDPE is the optimum level to obtain sufficient melt flow index and better impact strength. PL.Ramkumar et al. [7] investigated the effect of oven residence time on the mechanical properties of the rotationally moulded products made using LLDPE. They proposed a favourable processing window where the highest tensile, flexural and impact properties were noticed. Different types of resins are used in rotational moulding process. As plenty of resins with a broad range of processing characteristics are available to the rotational molder, it becomes difficult to select the appropriate resin from a long list. The characteristic of resins varies in terms of the quality of the powder (different particle shapes, distributions, etc.), different forms granules, micro-pellets, liquids, etc. Also, the rheological characteristics of the materials may be quite different in terms of their melt viscosities, melt flow index etc. So, this begs the question. Can we define the material with best characteristics in a rotational molding? Unfortunately there is no simple answer to this, although past experiences and recent research can guide to some extent. When selecting materials for rotomoulding process, various important attributes need to be considered. Material selection attributes are defined as a criteria that influences the selection of a material for a given process or application. These attributes includes physical properties, electrical properties, mechanical properties, material cost, availability, etc. The selection of an optimal material from among two or more alternative materials on the basis of two or more attributes is a multiple attribute decision making (MADM) problem. Various approaches had been proposed in the past to solve the issue of material selection.
19226
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In the past, grey relation is one of the available methods for choosing the suitable material from available alternatives. R. VenkataRao [8] in 2008 proposed a method termed compromise ranking method which can consider any number of quantitative and qualitative attributes for material selection. But the proposed method was considered to be lengther. Adavi Balakrishna et al. [9] used a fuzzy approach to support the material selection decisions in Concurrent environment. A quantitative relationship between mechanical properties of aluminum alloys is presented through the fuzzy logic methodology. The authors concluded that this method can be extendable to any design application. The above methodology can be used to integrate material database with designers criteria and also to assist designer to select suitable material for specific application from the available database at any point of time. This provides material data in machine readable electronic format to clients such as analysis engineers and manufacturing engineers in the CPD (Collaborative Product Development) system. However fuzzy logic is complicated and requires more calculation. W.K.Chan and K.L.Tong [10] used Grey Relation Method for material selection. They found that GRA has the merit of global comparison and it trade-offs no hierarchy structure instead. In order to keep the merit, all the criteria are distributed in a single level to the decision algorithm. They also suggested that the weighting conversion from multiple levels to a single level of performance characteristics should be done if the original decision model is in multi-level hierarchy structure. Chang Chan and Xiao-Bing [11] proposed artificial neural networks and genetic algorithm system to optimize the multi-objectives. In order to elaborate the method authors have considered an example of material selection of drink containers. But these systems were found to be complicated to understand. Ko-Ta Chiang and Fu-Ping Chang [12] applied the grey relational analysis to optimize the WEDM process with the multiple performance characteristics such as the cutting removal rate and the maximum surface roughness. They got the response table and response graph for each level of the machining parameters from the grey relational grade and selected the optimal levels of machining parameters. The authors were quite satisfied with the grey relation method. Tuğba Sarı et al. [13] concluded that the grey relation analysis can help decision makers in finding optimum solutions to complex multi criteria decision making problems by evaluating all the alternatives in an easier manner. Though research work applying Grey relation methods in selection of material for various manufacturing methods have been reported in literatures, it appears that the selection of suitable material using grey relation method for rotomoulding process has not been reported yet. Considering the above fact, the Grey relation method has been applied to select the suitable material for rotational moulding. Using the stated method the manufacturer or rotomoulder can select the best material out few alternatives based on the various criteria’s considered. In this work eleven alternatives are evaluated against seven criteria to demonstrated the selection process. 2. Important characteristics (attributes) of Rotomoudable Materials The selection of suitable material plays a very crucial role in rotational moulding. This selection depends on various characteristics of the material like melting point, flexural modulus, Tensile strength, Shore D hardness, Crystallinity, Heat stability, Cost etc. The above mentioned characteristics are important which affects the rotcomoulding. It is possible that manufacturer or designer may not know all the properties affecting the rotomoulding but they may be important to them then they may consider the critical characteristics (attributes). 3. Results and Discussion In this paper the selection of suitable material for rotomolding has been identified with the help of Grey relation Method which is one of the MADM techniques. The grey theory was first developed by Julong Deng in 1982. The information that is either incomplete or undetermined is called grey information up to this theory. The model includes three types of information points; black, white or grey. The main goal is to transfer black points in the system to the grey points. The grey system provides solutions to problems where the information is limited, incomplete and characterized by random uncertainty. In recent twenty years, the grey theory has become a popular technique providing multidisciplinary approaches. Grey relation analysis is a multi-criteria decision making method that helps managers to take the right decision under circumstances with limited and uncertain data [5]. The Grey Relation Method has been explained below taking an example of the selection of material for rotomoulding. In order to elaborate the above said procedure eleven alternatives are evaluated against seven criteria. The steps involved in GRA are as follows:
Bhavesh Chaudhary et al./ Materials Today: Proceedings 5 (2018) 19224–19229
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Step 1: Collection of data from literature review (Yij).Where i= material and j= criteria or characteristic as shown in table 1. Table 1. Attribute Values of the alternative materials Sr no. Material Melting Tensile point strength (C) (MPa) 1 2 3 4 5 6 7 8 9 10 11
Flexural Modulus
Shore D Hardness
Crystallinity (%)
Heat Stability
Cost
LDPE HDPE LLDPE EVA PP PVC PTFE PLA ABS Nylon PC
135 130 140 110 165 181 327 180 105 185 225
10 37 30 13 35 15 21 53 40 75 70
0.3 1 0.35 0.157 1.3 2.05 0.5 4 2.27 2.5 2.41
45 60 48 50 37 77 65 16 15 71 80
60 80 70 55 60 10 90 37 55 40 40
400 400 400 490 390 280 520 430 600 350 500
91 87 83 150 175 67 750 150 100 120 90
Max Min
105 327
10 75
0.157 4
15 80
10 90
280 600
67 750
Step 2: Normalize Yij as Zij (0 - Zij - 1) by the following formula to avoid the effect of using different units and to reduce variability. Normalization is a transformation performed on a single input to distribute the data evenly and scale it into acceptable range for further analysis. Normalisation of data is shown in table 2. Zij = Normalized value for ith material for jth dependent Characteristic (
Zij =
(
,
Zij =
(
,
, ,… ) (
,
, ,… )
,
, ,… ) (
,
, ,… )
,
, ,… )
, ,… ) (
Table 2. Normalisation of the data Sr no. Material MP
1 2 3 4 5 6 7 8 9 10 11
LDPE HDPE LLDPE EVA PP PVC PTFE PLA ABS Nylon PC
0.711 0.729 0.692 0.803 0.6 0.540 0 0.544 0.822 0.525 0.377
(to be used for S/N ratio with larger—the better case) (to be used for S/N ratio with smaller—the better case)
Tensile strength
0 0.415 0.307 0.046 0.384 0.076 0.169 0.661 0.461 1 0.923
Flexural Modulus
0.037 0.219 0.050 0 0.297 0.492 0.089 1 0.549 0.609 0.586
Shore Hardness
0.428 0.642 0.471 0.5 0.314 0.885 0.714 0.014 0 0.8 0.928
D
Crystallinity
0.625 0.875 0.75 0.562 0.625 0 1 0.337 0.562 0.375 0.375
Heat Stability
0.375 0.375 0.375 0.656 0.343 0 0.75 0.468 1 0.218 0.687
Cost
0.964 0.970 0.976 0.878 0.841 1 0 0.878 0.951 0.922 0.966
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Bhavesh Chaudhary et al./ Materials Today: Proceedings 5 (2018) 19224–19229
Step 3: Compute the grey relational coefficient (GC) for the normalized values. (Table 3) GCij =
where GCij= grey relational coefficient for the ith material and jth characteristic.
= absolute difference between Yoj and Yij which is a deviation from target value and can be treated as quality loss. Yoj= optimum performance value or the ideal normalized value of jth characteristic, Yij = the ith normalized value of the jth characteristic min = minimum value of , max = maximum value of , is the distinguishing coefficient which is defined in the range 01 (the value may be adjusted on the practical needs of the system) Table 3. Grey Relation coefficient (GC) Sr no. Material MP
Tensile strength
Flexural Modulus
Shore Hardness
D
Crystallinity
Heat Stability
Cost
1
LDPE
0.633
0.333
0.341
0.466
0.571
0.444
0.934
2 3 4 5 6 7
HDPE LLDPE EVA PP PVC PTFE
0.649 0.619 0.718 0.555 0.521 0.333
0.460 0.419 0.343 0.448 0.351 0.375
0.390 0.344 0.333 0.415 0.496 0.354
0.583 0.486 0.5 0.421 0.813 0.636
0.8 0.666 0.533 0.571 0.333 1
0.444 0.444 0.592 0.432 0.333 0.666
0.944 0.955 0.804 0.759 1 0.333
8 9
PLA ABS
0.523 0.737
0.596 0.481
1 0.526
0.336 0.333
0.430 0.533
0.484 1
0.804 0.911
10 11
Nylon PC
0.513 0.445
1 0.866
0.561 0.547
0.714 0.875
0.444 0.444
0.390 0.615
0.865 0.936
Step 4: Compute the grey relational grade (Gi), Gi = GCij where m is the number of characteristics. (Table 4) Step 5: Select the best material based on maximum average Gi value.(Table 5) Table 4. Grey Relation Grade (Gi) LDPE 0.532 HDPE 0.610 LLDPE 0.562 EVA 0.546 PP 0.514 PVC 0.549 PTFE 0.528 PLA 0.596 ABS 0.646 Nylon 0.641 PC 0.675
Table 5. Average Gi value LDPE 9 HDPE 4 LLDPE 6 EVA 8 PP 11 PVC 7 PTFE 10 PLA 5 ABS 2 Nylon 3 PC 1
Conclusion In this paper, the Grey Relation method was successfully applied to select the suitable material for rotomoulding. The rotomoulder can apply this method considering different characteristics of materials. This method reduces the time consumption in carrying out the experiments on each and every material. In order to elaborate the above procedure eleven alternatives were evaluated against seven criteria. The ranking of the material was based on the criteria (attributes) values chosen by the manufacturer. Using the above procedure it was concluded that
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Polycarbonate is the best material according to Grey Relational technique. The second most important material is ABS. Although polycarbonate has been ranked as the best material, the selection of material depends upon the no of alternatives and criteria considered for the selection process. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]
R. J. Crawford, Rotational Molding of Plastics, John Wiley, New York, 1992. PL Ramkumar et al., ‘Prediction of heating cycle time in Rotational Moulding’, Materials Today: Proceedings, 2, (2015), 3212 – 3219. R J Crawford et al., ‘Mould pressure control in Rotational Moulding’, Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, (2004), 218-1683. S.C. Tjong and S.P. Bao, ‘Fracture toughness of high density polyethylene/SEBS-g-MA/montmorillonite nanocomposites’, Composites Science and Technology, 67, (2007), 314–323. Maria Jovita Oliveira and Gabriela Botelho, ‘Degradation of polyamide 11 in rotational moulding’, Degradation and Stability, 93, (2008), 139-146. PL Ramkumar et al., ‘Investigation of Melt Flow Index and Impact Strength of Foamed LLDPE for Rotational Moulding Process’, Procedia Materials Science, 6, ( 2014 ), 361 – 367. PL Ramkumar et al., ‘Effect of oven residence time on mechanical properties in rotomoulding of LLDPE’, Sadhana, 5, (2016), 571–582. R. VenkataRao, ‘A decision making methodology for material selection using an improved compromise ranking method’, Materials and Design, 29, (2008), 1949–1954. Adavi Balakrishna, ‘Fuzzy Approach to the Selection of Material Data in Concurrent Engineering Environment’, Engineering, (2011), 3, 921-927. Joseph W.K. Chan and Thomas K.L. Thong, ‘Multi-criteria material selections and end-of-life product strategy: Grey relational analysis approach’, Materials and Design, 28, (2007), 1539–1546. Chang-Chun Zhou et al., ‘Multi-objective optimization of material selection for sustainable products: Artificial neural networks and genetic algorithm approach’, Materials and Design, 30, (2009), 1209–1215. Ko-Ta Chiang and Fu-Ping Chang, ‘Optimization of the WEDM process of particle-reinforced material with multiple performance characteristics using grey relational analysis’, Journal of Materials Processing Technology, 180, (2006), 96–101. Tuğba Sarı et al., ‘Supplier Selection with Grey Relational Analysis’, IJERMT, 5, (2016), 2278-9359.
ScienceDirect Materials Today: Proceedings 5 (2018) 19224–19229
www.materialstoday.com/proceedings
ICMPC_2018
Material Selection for Rotational Moulding Process Using Grey Relational Analysis Approach Bhavesh Chaudharya, PL. Ramkumarb*, Kumar Abhishekc b*,c
a M.Tech student, Mechanical Engineering Student, IITRAM , Ahmadabad Assistant Professor, Department of Mechanical Engineering, IITRAM , Ahmadabad
Abstract Rotomoulding is an emerging industry of present era for manufacturing hollow plastic products of various sizes. Different materials like polyethylene, polypropylene, polyvinylchloride, polycarbonate etc. are used in rotational moulding. As vast variety of materials with diverse physical and mechanical characteristics is available, choosing the best suitable material becomes a challenge. Rotomoulder has to take into account a large number of material selection criteria before arriving at the final decision, otherwise there may be premature failure of the product during its operation. In order to assist the rotomoulder, this paper presents a systematic and efficient multi attribute decision-making approach referred as grey relation analysis for material selection in rotational moulding. In order to elaborate the above said procedure eleven alternatives are evaluated against seven criteria. From the analysis suitable material has been identified. © 2018 Elsevier Ltd. All rights reserved. Selection and/or Peer-review under responsibility of Materials Processing and characterization. Keywords: Rotational Moulding; Material selection; Grey relation analysis; Plastic manufacturing process
1. Introduction Rotational moulding also known as rotocasting, is a process for manufacturing hollow plastic products. Although there are various techniques available for processing plastics, rotational moulding has particular advantages in terms of relatively low levels of residual stresses and inexpensive molds. Rotational moulding is best known for the manufacturing of tanks. Also it is used to make complex medical products, toys, and many highly aesthetic point-ofsale products [1, 2]. From the literature survey it is found that rotomoulding process can be further enhanced by either changing the process parameters or by making changes in the material itself. R.J Crawford et al. [3] investigated the rotomoulding process by applying the pressure inside the mould at specific point during heating * Corresponding author. Tel.: +91 9823256780 E-mail address: [email protected]
2214-7853 © 2018 Elsevier Ltd. All rights reserved. Selection and/or Peer-review under responsibility of Materials Processing and characterization.
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19225
Nomenclature GRA- Grey Relational Analysis MADM- Multi Attribute Decision Making LDPE- Low Density Polyethylene HDPE- High Density Polyethylene LLDPE- Linear Low Density Polyethylene EVA- Ethylene Vinyl acetate PP- Polypropylene PVC- Polyvinyl Chloride PTFE- Polytetrafluroethylene PLA- Poly Lactic Acid ABS- Acrylonitrile Butadiene Styrene PC- Polycarbonate WEDM- Wire Electric Discharge Machining Org-MMT- organophilically modified montmorillonite SEBS-g-MA- maleated styrene–ethylene–butylene–styrene
cycle and found that it can reduce the pinhole formation and decreases the cycle time. S.C. Tjong et al. [4] conducted an experiment to increase the impact fracture toughness of rotomoulding material. They selected HDPE/2%Org-MMT and HDPE/4%Org-MMT nanocomposites and added different amount of SEBS-g-MA. A nearly twofold increase in impact fracture toughness of the HDPE/2%Org-MMT and HDPE/4%Org-MMT nanocomposites was achieved by adding 10%SEBS-g-MA. Maria Jovita Oliveira et al. [5] studied the effect of temperature on the reactions taking Place in rotomoulding. They suggested the optimum level of temperature to be produced inside the mould to control the degradation of the polymer. PL.Ramkumar et al. [6] investigated the effect of foam added with LLDPE on the properties of rotomoulding process. They found 6% of foam in LLDPE is the optimum level to obtain sufficient melt flow index and better impact strength. PL.Ramkumar et al. [7] investigated the effect of oven residence time on the mechanical properties of the rotationally moulded products made using LLDPE. They proposed a favourable processing window where the highest tensile, flexural and impact properties were noticed. Different types of resins are used in rotational moulding process. As plenty of resins with a broad range of processing characteristics are available to the rotational molder, it becomes difficult to select the appropriate resin from a long list. The characteristic of resins varies in terms of the quality of the powder (different particle shapes, distributions, etc.), different forms granules, micro-pellets, liquids, etc. Also, the rheological characteristics of the materials may be quite different in terms of their melt viscosities, melt flow index etc. So, this begs the question. Can we define the material with best characteristics in a rotational molding? Unfortunately there is no simple answer to this, although past experiences and recent research can guide to some extent. When selecting materials for rotomoulding process, various important attributes need to be considered. Material selection attributes are defined as a criteria that influences the selection of a material for a given process or application. These attributes includes physical properties, electrical properties, mechanical properties, material cost, availability, etc. The selection of an optimal material from among two or more alternative materials on the basis of two or more attributes is a multiple attribute decision making (MADM) problem. Various approaches had been proposed in the past to solve the issue of material selection.
19226
Bhavesh Chaudhary et al./ Materials Today: Proceedings 5 (2018) 19224–19229
In the past, grey relation is one of the available methods for choosing the suitable material from available alternatives. R. VenkataRao [8] in 2008 proposed a method termed compromise ranking method which can consider any number of quantitative and qualitative attributes for material selection. But the proposed method was considered to be lengther. Adavi Balakrishna et al. [9] used a fuzzy approach to support the material selection decisions in Concurrent environment. A quantitative relationship between mechanical properties of aluminum alloys is presented through the fuzzy logic methodology. The authors concluded that this method can be extendable to any design application. The above methodology can be used to integrate material database with designers criteria and also to assist designer to select suitable material for specific application from the available database at any point of time. This provides material data in machine readable electronic format to clients such as analysis engineers and manufacturing engineers in the CPD (Collaborative Product Development) system. However fuzzy logic is complicated and requires more calculation. W.K.Chan and K.L.Tong [10] used Grey Relation Method for material selection. They found that GRA has the merit of global comparison and it trade-offs no hierarchy structure instead. In order to keep the merit, all the criteria are distributed in a single level to the decision algorithm. They also suggested that the weighting conversion from multiple levels to a single level of performance characteristics should be done if the original decision model is in multi-level hierarchy structure. Chang Chan and Xiao-Bing [11] proposed artificial neural networks and genetic algorithm system to optimize the multi-objectives. In order to elaborate the method authors have considered an example of material selection of drink containers. But these systems were found to be complicated to understand. Ko-Ta Chiang and Fu-Ping Chang [12] applied the grey relational analysis to optimize the WEDM process with the multiple performance characteristics such as the cutting removal rate and the maximum surface roughness. They got the response table and response graph for each level of the machining parameters from the grey relational grade and selected the optimal levels of machining parameters. The authors were quite satisfied with the grey relation method. Tuğba Sarı et al. [13] concluded that the grey relation analysis can help decision makers in finding optimum solutions to complex multi criteria decision making problems by evaluating all the alternatives in an easier manner. Though research work applying Grey relation methods in selection of material for various manufacturing methods have been reported in literatures, it appears that the selection of suitable material using grey relation method for rotomoulding process has not been reported yet. Considering the above fact, the Grey relation method has been applied to select the suitable material for rotational moulding. Using the stated method the manufacturer or rotomoulder can select the best material out few alternatives based on the various criteria’s considered. In this work eleven alternatives are evaluated against seven criteria to demonstrated the selection process. 2. Important characteristics (attributes) of Rotomoudable Materials The selection of suitable material plays a very crucial role in rotational moulding. This selection depends on various characteristics of the material like melting point, flexural modulus, Tensile strength, Shore D hardness, Crystallinity, Heat stability, Cost etc. The above mentioned characteristics are important which affects the rotcomoulding. It is possible that manufacturer or designer may not know all the properties affecting the rotomoulding but they may be important to them then they may consider the critical characteristics (attributes). 3. Results and Discussion In this paper the selection of suitable material for rotomolding has been identified with the help of Grey relation Method which is one of the MADM techniques. The grey theory was first developed by Julong Deng in 1982. The information that is either incomplete or undetermined is called grey information up to this theory. The model includes three types of information points; black, white or grey. The main goal is to transfer black points in the system to the grey points. The grey system provides solutions to problems where the information is limited, incomplete and characterized by random uncertainty. In recent twenty years, the grey theory has become a popular technique providing multidisciplinary approaches. Grey relation analysis is a multi-criteria decision making method that helps managers to take the right decision under circumstances with limited and uncertain data [5]. The Grey Relation Method has been explained below taking an example of the selection of material for rotomoulding. In order to elaborate the above said procedure eleven alternatives are evaluated against seven criteria. The steps involved in GRA are as follows:
Bhavesh Chaudhary et al./ Materials Today: Proceedings 5 (2018) 19224–19229
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Step 1: Collection of data from literature review (Yij).Where i= material and j= criteria or characteristic as shown in table 1. Table 1. Attribute Values of the alternative materials Sr no. Material Melting Tensile point strength (C) (MPa) 1 2 3 4 5 6 7 8 9 10 11
Flexural Modulus
Shore D Hardness
Crystallinity (%)
Heat Stability
Cost
LDPE HDPE LLDPE EVA PP PVC PTFE PLA ABS Nylon PC
135 130 140 110 165 181 327 180 105 185 225
10 37 30 13 35 15 21 53 40 75 70
0.3 1 0.35 0.157 1.3 2.05 0.5 4 2.27 2.5 2.41
45 60 48 50 37 77 65 16 15 71 80
60 80 70 55 60 10 90 37 55 40 40
400 400 400 490 390 280 520 430 600 350 500
91 87 83 150 175 67 750 150 100 120 90
Max Min
105 327
10 75
0.157 4
15 80
10 90
280 600
67 750
Step 2: Normalize Yij as Zij (0 - Zij - 1) by the following formula to avoid the effect of using different units and to reduce variability. Normalization is a transformation performed on a single input to distribute the data evenly and scale it into acceptable range for further analysis. Normalisation of data is shown in table 2. Zij = Normalized value for ith material for jth dependent Characteristic (
Zij =
(
,
Zij =
(
,
, ,… ) (
,
, ,… )
,
, ,… ) (
,
, ,… )
,
, ,… )
, ,… ) (
Table 2. Normalisation of the data Sr no. Material MP
1 2 3 4 5 6 7 8 9 10 11
LDPE HDPE LLDPE EVA PP PVC PTFE PLA ABS Nylon PC
0.711 0.729 0.692 0.803 0.6 0.540 0 0.544 0.822 0.525 0.377
(to be used for S/N ratio with larger—the better case) (to be used for S/N ratio with smaller—the better case)
Tensile strength
0 0.415 0.307 0.046 0.384 0.076 0.169 0.661 0.461 1 0.923
Flexural Modulus
0.037 0.219 0.050 0 0.297 0.492 0.089 1 0.549 0.609 0.586
Shore Hardness
0.428 0.642 0.471 0.5 0.314 0.885 0.714 0.014 0 0.8 0.928
D
Crystallinity
0.625 0.875 0.75 0.562 0.625 0 1 0.337 0.562 0.375 0.375
Heat Stability
0.375 0.375 0.375 0.656 0.343 0 0.75 0.468 1 0.218 0.687
Cost
0.964 0.970 0.976 0.878 0.841 1 0 0.878 0.951 0.922 0.966
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Bhavesh Chaudhary et al./ Materials Today: Proceedings 5 (2018) 19224–19229
Step 3: Compute the grey relational coefficient (GC) for the normalized values. (Table 3) GCij =
where GCij= grey relational coefficient for the ith material and jth characteristic.
= absolute difference between Yoj and Yij which is a deviation from target value and can be treated as quality loss. Yoj= optimum performance value or the ideal normalized value of jth characteristic, Yij = the ith normalized value of the jth characteristic min = minimum value of , max = maximum value of , is the distinguishing coefficient which is defined in the range 01 (the value may be adjusted on the practical needs of the system) Table 3. Grey Relation coefficient (GC) Sr no. Material MP
Tensile strength
Flexural Modulus
Shore Hardness
D
Crystallinity
Heat Stability
Cost
1
LDPE
0.633
0.333
0.341
0.466
0.571
0.444
0.934
2 3 4 5 6 7
HDPE LLDPE EVA PP PVC PTFE
0.649 0.619 0.718 0.555 0.521 0.333
0.460 0.419 0.343 0.448 0.351 0.375
0.390 0.344 0.333 0.415 0.496 0.354
0.583 0.486 0.5 0.421 0.813 0.636
0.8 0.666 0.533 0.571 0.333 1
0.444 0.444 0.592 0.432 0.333 0.666
0.944 0.955 0.804 0.759 1 0.333
8 9
PLA ABS
0.523 0.737
0.596 0.481
1 0.526
0.336 0.333
0.430 0.533
0.484 1
0.804 0.911
10 11
Nylon PC
0.513 0.445
1 0.866
0.561 0.547
0.714 0.875
0.444 0.444
0.390 0.615
0.865 0.936
Step 4: Compute the grey relational grade (Gi), Gi = GCij where m is the number of characteristics. (Table 4) Step 5: Select the best material based on maximum average Gi value.(Table 5) Table 4. Grey Relation Grade (Gi) LDPE 0.532 HDPE 0.610 LLDPE 0.562 EVA 0.546 PP 0.514 PVC 0.549 PTFE 0.528 PLA 0.596 ABS 0.646 Nylon 0.641 PC 0.675
Table 5. Average Gi value LDPE 9 HDPE 4 LLDPE 6 EVA 8 PP 11 PVC 7 PTFE 10 PLA 5 ABS 2 Nylon 3 PC 1
Conclusion In this paper, the Grey Relation method was successfully applied to select the suitable material for rotomoulding. The rotomoulder can apply this method considering different characteristics of materials. This method reduces the time consumption in carrying out the experiments on each and every material. In order to elaborate the above procedure eleven alternatives were evaluated against seven criteria. The ranking of the material was based on the criteria (attributes) values chosen by the manufacturer. Using the above procedure it was concluded that
Bhavesh Chaudhary et al./ Materials Today: Proceedings 5 (2018) 19224–19229
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Polycarbonate is the best material according to Grey Relational technique. The second most important material is ABS. Although polycarbonate has been ranked as the best material, the selection of material depends upon the no of alternatives and criteria considered for the selection process. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]
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