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International Journal of Mechanical Engineering and Technology (IJMET) Volume 10, Issue 03, March 2019, pp. 487-495. Article ID: IJMET_10_03_051 Available online at http://www.iaeme.com/ijmet/issues.asp?JType=IJMET&VType=10&IType=3 ISSN Print: 0976-6340 and ISSN Online: 0976-6359 © IAEME Publication Scopus Indexed APPLICATION OF GREY RELATIONAL ANALYSIS FOR MULTI VARIABLE OPTIMIZATION OF PROCESS PARAMETERS IN DRILLING OF POLYMER BASED GLASS FIBER REINFORCED COMPOSITE Dr. Murthy BRN and Dr. Rajendra Beedu* 1 Department of Mechanical and Manufacturing, Manipal Institute of Technology, Manipal. Karnataka, India. *Corresponding Author ABSTRACT The present work deals with a simple approach which predicts the optimum setting of process parameters of drilling operation on Polymer Based Glass Fiber (PBGF) composite. The process parameters selected are drill angle (DA), Drill diameter (DD), Material Thickness (MT), Speed (N) and Feed (f). The output parameters are Thrust, Torque, Surface Roughness and Delamination. Three levels of each input parameters are considered. Taguchi’s L27 array is used to set the process parameters. Gray relational analysis (GRA) is used to find the optimum value of process parameters. Conduction of ANOVA on GRA shown the significance of each factor on the process output. A conformation test conducted revealed that the setting of parameters ensures optimum output. Keywords: Drilling, PBGF composite, orthogonal array, Gray relational analysis. Cite this Article: Dr. Murthy BRN and Dr. Rajendra Beedu, Application of Grey Relational Analysis for Multi Variable Optimization of Process Parameters in Drilling of Polymer Based Glass Fiber Reinforced Composite, International Journal of Mechanical Engineering and Technology, 10(3), 2019, pp. 487-495 http://www.iaeme.com/IJMET/issues.asp?JType=IJMET&VType=10&IType=3 1. INTRODUCTION The use of Polymer based glass fiber (PBGF) is extending beyond the initial applications in aerospace and military fields, driven by the advances in manufacturing technologies which has made the production process more cost effective. PBGF composite materials offer excellent mechanical properties, while being much more lightweight than the metallic alloys. As PBGF composite parts are usually integrated in a mechanical assembly, drilling is the most common encountered machining process in the production of such parts. Drilling is http://www.iaeme.com/IJMET/index.asp 487 [email protected] Dr. Murthy BRN and Dr. Rajendra Beedu carried out during the final stages of the manufacturing process in order to create holes for fabrication. Excessive tool wear and delamination are the two major problems highlighted in the drilling process of the PBGF composites. The excessive tool wear makes the drilling process of the fiber reinforced composites very expensive, only a limited number of holes can be drilled with one particular drill. Delamination is the one of the main reasons which is leading rejection of composite parts in the larger quantity. Most of the researchers are focusing on characterization of PBGF composite. But the main problem occurs in drilling holes for the purpose of assembly. The components made by PBGF may fail due to delamination and rough surface, excess thrust force and torque associated with speed. Hence optimization of process parameters is essential to reduce the damage occurs during drilling process in order to reduce the rejection of composite components. Literature review reveals that many researchers are made attempts to optimize the process parameters to achieve the good quality holes by minimizing the thrust force, torque, surface roughness and delamination factor. Palanikumar [1] used Taguchi and response surface methodology to optimese the process parameters to achieve the minimum surface roughness. Enemuoh et al. [2] proposed an approach of combining Taguchi’s technique and multi-objective optimization criterion to select cutting parameter for damage-free drilling in carbon fiber-reinforced epoxy composite materials. Ghani et al. [3] developed a new approach using Taguchi’s method to optimize the cutting parameters in end milling of AISI H1312. K. Karthik et al. [4] optimized the process parameters to minimize the delamination on the drilling of GFRP composites using HSS drill bits. Lewlyn L. R. Rodrigues et al. [5] optimized the process parameters in the drilling of CFRP composites to reduce the surface roughness using Taguchi and RSM methods. S Aril et al. [6] did the optimization in drilling of GFRP composites using HSS drills to achieve the lower delamination. They used an optimization algorithm using simulated annealing with a performance index for this purpose. In this way numerous numbers of researchers used various methods to optimize the process parameters to obtain the desired outputs [7-9]. In the literature review we noticed that they did optimization for one output parameter at a time. But in this present work we tried to develop the optimization for four output parameters at a time. Production of acceptable components with minimum failure is the main purpose of setting proper process parameters. 2. FABRICATION OF COMPOSITE The glass fiber reinforced resin composite required for testing was manufactured through hand layup method. The glass fibers are reinforced in general purpose resin matrix. Chopped glass mat is used for reinforcement which is presented in Figure 1a and the prepared composite sheet in Figure 1b. Figure 1a Chopped glass mat Figure 1b Prepared composite specimen 2.1. Selection of Levels of Drilling Parameters http://www.iaeme.com/IJMET/index.asp 488 [email protected] Application of Grey Relational Analysis for Multi Variable Optimization of Process Parameters in Drilling of Polymer Based Glass Fiber Reinforced Composite The input drilling parameters are selected as per the available literature survey information, solid carbide drill bits are used because of their low wear characteristics. All five parameters and their levels chosen for the present work are shown in Table1. Table 1 Levels of process parameters Parameters Level 1 Level 2 Level 3 Drill angle Drill Diameter Material Speed (N) RPM Feed (f) m/min (DA) degrees (DD) mm Thickness (MT (D) (E) mm) (C) (A) (B) 90 6 8 900 75 103 8 10 1200 110 118 10 12 1500 150 2.2. Selection of process parameters for each trial and measurement of output parameters The process parameters are selected according to Taguchi’s L27 orthogonal array. This array ensures minimum number of experiments to be conducted with nearly accurate solution. The drilling experiments were conducted on a CNC machine which is capable of drilling accurate and precise holes. WC tool is used. The experimentation set up to drill the holes and to measure the thrust and torque produced during the machining is process is shown in Figure 2. The output parameters are measured and listed as shown in table 2. The thrust force and torque are measured using Kistler dynamometer, surface roughness using Taylor Hobson Surtronic 3+ roughness measurement instrument and delamination factor was estimated by taking the images of the drilled with the help of high resolution scanner and measuring the dimensions of scanned images by using CATIA software. Arrangement made to measure surface roughness and delamination is presented in figures 3 and 4. The measured data is illustrated in Table 2. Figure 2 Experimental set-up to drill the holes and to measure thrust and torque. Figure 3 Measurement of surface roughness http://www.iaeme.com/IJMET/index.asp 489 [email protected] Dr. Murthy BRN and Dr. Rajendra Beedu Figure 4 Measurement of delamination factor Table 2 L27 orthogonal array with factors and responses Trial No A B C D E 1 2 3 1 1 1 1 1 1 1 1 1 1 1 1 1 2 3 29.67 36.20 38.20 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 2 2 2 3 3 3 1 1 1 2 2 2 3 3 3 1 1 1 2 2 2 3 3 3 2 2 2 3 3 3 2 2 2 3 3 3 1 1 1 3 3 3 1 1 1 2 2 2 2 2 2 3 3 3 3 3 3 1 1 1 2 2 2 2 2 2 3 3 3 1 1 1 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 31.65 33.99 34.16 36.04 37.86 38.04 34.98 36.38 36.77 44.27 45.83 46.98 40.71 40.29 40.46 42.98 43.36 45.36 40.46 41.32 42.56 58.36 59.38 59.98 Surface Roughness µm Delamination 16.32 2.99 1.06 18.04 3.11 1.07 20.46 3.29 1.08 30.04 30.23 24.66 27.64 28.45 34.23 14.66 14.02 14.34 26.98 27.09 30.65 26.92 29.98 24.97 17.46 18.02 19.18 17.70 17.39 17.67 41.01 41.46 41.96 3.20 3.23 3.24 3.35 3.37 3.40 3.20 3.30 3.33 3.40 3.42 3.48 3.20 3.30 3.31 3.57 3.58 3.59 3.25 3.30 3.11 3.37 3.38 3.39 1.09 1.10 1.11 1.11 1.12 1.13 1.09 1.10 1.16 1.11 1.12 1.13 1.07 1.10 1.10 1.11 1.12 1.13 1.09 1.11 1.14 1.10 1.11 1.11 Torque Thrust (N) (N-mm) Number of replication of each factor is 1 (k=1). The responses are measured in different units and has different ranges. For multi-response optimization, the results are brought in the range 0 to 1 by the process called normalization. Normalisation scales down the responses in an acceptable range for further operation. 2.3. Normalisation The response parameter is of two types i.e, beneficiary (maximum the better) and nonbenificiery (minimum the better). For beneficiary attribute j, the normalized parameter of the trial i and replication k is given by http://www.iaeme.com/IJMET/index.asp and for non beneficiary attribute 490 [email protected] Application of Grey Relational Analysis for Multi Variable Optimization of Process Parameters in Drilling of Polymer Based Glass Fiber Reinforced Composite where k is the replication. In this paper all response parameters are non beneficiary type. The actual response X ijk is modified to X’ijk which ranges from 0 to 1. The maximum value of normalized response, irrespective of response parameter is taken as reference value R. R= 1. 2.4. Calculation of difference value The difference value is calculated by, | |. The difference values arrange the output response in the ascending order for non-beneficiary attribute. These value is used to calculate Gray relational Coefficient 2.5. Calculation of Grey Relational Coefficient GRCijk The Grey Relational Coefficient is calculated by the formula, where ξ is the distinguishing coefficient ranging from 0 to 1. Generally, ξ is taken as 0.5. 2.6. Calculation of Grey Relational Grade The average of GRC in each row is known as Grey Relational Grade ∑ ∑ relational grade is given by the formula, response parameters and n is the number of replications (n=1). The calculated GRG is shown in Table 3 Table 3 Trial No 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 A 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 3 3 . The Grey where m is the number of Orthogonal Array with Gray Relational Grades. B 1 1 1 2 2 2 3 3 3 1 1 1 2 2 2 3 3 3 1 1 C 1 1 1 2 2 2 3 3 3 2 2 2 3 3 3 1 1 1 3 3 http://www.iaeme.com/IJMET/index.asp D 1 1 1 2 2 2 3 3 3 3 3 3 1 1 1 2 2 2 2 2 491 E 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 GRG 0.67 0.58 0.50 0.53 0.51 0.47 0.46 0.45 0.47 0.48 0.44 0.38 0.48 0.47 0.47 0.58 0.51 0.48 0.42 0.41 [email protected] Dr. Murthy BRN and Dr. Rajendra Beedu Trial No 21 22 23 24 25 26 27 A 3 3 3 3 3 3 3 B 1 2 2 2 3 3 3 C 3 1 1 1 2 2 2 D 2 3 3 3 1 1 1 E 3 1 2 3 1 2 3 GRG 0.40 0.50 0.46 0.48 0.71 0.72 0.73 2.7. Calculation of Average GRG for each level The average GRG is calculated for each level. The Level for which the GRG is maximum for each factor j is the optimal setting of that parameter. The average GRG is listed in table 4. The plot of average GRG Vs Levels of each parameter is shown in figure 5. The level with maximum GRG for any factor is the optimum level for that factor. Table 4 The average GRG with corresponding factors Factors Level 1 Level 2 Level 3 Range Rank A 0.515 0.476 0.536 0.060 4 B 0.476 0.485 0.566 0.090 3 C 0.528 0.550 0.449 0.092 2 D 0.591 0.478 0.458 0.132 1 E 0.536 0.503 0.488 0.048 5 0.56 0.6 Factor A Average GRG Average GFG The range for each parameter is the difference between the maximum average GRG and the minimum GRG. The factor with wide range is the most significant one. The ranks are based on average GRG. 0.54 0.52 0.5 0.48 0.46 Factor B 0.55 0.5 0.45 0.4 1 0.44 2 Levels 3 Levels Factor C 0.6 2 3 Average GRG Average GRG 1 0.5 0.4 0.3 0.2 0.8 Factor D 0.6 0.4 0.2 0.1 0 1 2 Levels 0 3 http://www.iaeme.com/IJMET/index.asp 1 492 2 Levels 3 [email protected] Application of Grey Relational Analysis for Multi Variable Optimization of Process Parameters in Drilling of Polymer Based Glass Fiber Reinforced Composite Average GRG 0.54 Factor E 0.52 0.5 0.48 0.46 1 2 3 Levels Figure 5. Main effect plot for Average GRG Vs levels of each factor 2.8. Selection of optimum levels of process parameters The optimum setting is one for which the average GRG for a given factor is maximum The optimum setting is A3-B3- C2-D1-E1 i.e Drill angle 1180- Drill diameter 10 mm – Material Thickness 10mm - Speed 900RPM and Feed 75 m/min. 3. APPLICATION OF ANOVA FOR FINDING THE SIGNIFICANCE OF EACH FACTOR In order to reconfirm optimum setting, ANOVA is performed and the Sum of squares for each level is listed in Table 5. Table 5 The total GRG with corresponding factors Factors Level 1 Level 2 Level 3 Sum of squares SS factors Sum of squares Error SS error A 4.640 4.289 4.829 B 4.287 4.370 5.101 C 4.760 4.956 4.042 D 5.324 4.307 4.127 E 4.829 4.535 4.394 0.017 0.045 0.052 0.092 0.011 0.018 Based on the above calculations, the un-pooled ANOVA on GRG is calculated. The values are shown in Table 6. Table 6 Estimated ANOVA on GRG Factors Sum of squares A B C D E Error Total 0.017 0.045 0.052 0.092 0.011 0.018 0.234 Degrees of Mean sum F table freedom of squares F calculated (5% (DOF) (MSS) risk) 2 0.008 7.56 3.63 2 0.022 20.16 3.63 2 0.026 23.28 3.63 2 0.046 41.79 3.63 2 0.005 4.96 3.63 16 0.001 26 http://www.iaeme.com/IJMET/index.asp 493 Remark Percentage contribution Rank Significant Significant Significant Significant Significant 7.73 20.63 23.82 42.75 5.07 4 3 2 1 5 editor[email protected] Dr. Murthy BRN and Dr. Rajendra Beedu The factor for which F calculated > F table is the significant factor. In addition, percentage contribution for each factor is calculated by dividing each value of F calculated by Total of F calculated. The values of percentage contribution show that the ranks for each factor given in table 4 are confirmed. 4. CALCULATION OF PREDICTED GRG The predicted GRG is calculated using the following formula Let T = Overall average of Gray Relational Grades = Total GRG/27 = 0.509612 The predicted GRG is given by The predicted GRG is given by =0.744 4. CALCULATION OF CONFIDENCE INTERVAL C.I The confidence interval indicates the expected range of GRG for the optimal settings. The calculation for confidence interval is shown below. Half width of confidence interval d = √ where is the effective sample size. The effective sample size = = 2.45 The is 16. (confidence level), DOF of error d =√ =0.045 The confidence interval of predicted mean for 95% confidence level (C.I) is given by, C.I. = Predicted average GRG ; 0.699<C.I.< 0.789 The confirmation test was conducted for the optimal setting as follows Drill angle 1180, Drill Diameter 10 mm, Material thickness 10 mm, Speed 900 RPM and Feed 75 mm/min. The GRG calculated for this setting was 0.712 which is well within the range of Confidence interval. So optimal setting is confirmed. 5. RESULT AND DISCUSSION The optimal setting shows that larger drill angle and drill diameter, medium material thickness, lower speed and feed results in optimum response. This is because, higher drill angle results in ease of penetration due to stronger drill bit, larger drill diameter ensures easy flow of chips resulting in less thrust and good surface finish, Medium material thickness gives firm clamping with moderate resistance , lower speed and speed results in less delamination and hence the combination of these factors results in optimum response. From the ranks of process parameters, it is clear that feed (rank 1) is the most significant factor influencing the responses. Higher feed rate increase delamination and vibrations and spoils the surface finish. 6. CONCLUSIONS 1. The grey relational analysis is found to be most effective and simple approach for optimal setting of process parameters especially in case of multiple response that too http://www.iaeme.com/IJMET/index.asp 494 [email protected] Application of Grey Relational Analysis for Multi Variable Optimization of Process Parameters in Drilling of Polymer Based Glass Fiber Reinforced Composite 2. 3. 4. 5. with contradicting objectives. In this paper all responses were non beneficiary responses (minimum the better). The Taguchi method ensures minimum number of trials to be conducted with minimum error in the prediction. The Gray Relational analysis is useful in finding the optimal setting and also the significance of each parameter on the response as given by ranks. ANOVA applied on GRG reconfirms the fact that the results of GRG are reliable. The Confirmation test indicates the reliability of the predictions of GRG. In this paper the GRG with optimum setting is within the confidence interval depicting proper optimal setting. REFERENCES [1] [2] [3] [4] [5] [6] [7] [8] [9] Palanikumar Evaluation of delamination in drilling of GFRP composites” Materials and Manufacturing Processes, vol. 23, pp. 858-864, April 2008. Enemuoh E.U., El-Gizawy A.S. and Okafor A.C., An approach for development of damage-free drilling of carbon fiber reinforced thermosets, International Journal of Mechanical Tools and Manufacturing, vol. 41 no.12, pp.1795–1814 May2001. Ghani J.A., Choudhury I.A. and Hassan H.H., Application of Taguchi method in the optimization of end milling parameters, Journal of Material Processing Technology, vol.45, pp.84–92 Jan 2004. K. karthik , A. Manimaran, J. Veerendra Rayudu and Diva Sharma., Optimization Of The Process Parameter In Drilling Of GFRP Using HSS Drill, International Journal of Mechanical and Production Engineering Research and Development, vol. 7, pp 403-408, Aug 2017. Lewlyn L. R. 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