Taguchi based GRA-PCA hybrid optimization for the forming of AL6061 alloy in automotive application

Abstract

Keywords: Deep Drawing; Punch Force; Thickness Distribution; Grey Relational Analysis; Principal Component Analysis

Introduction

Rotating Environmental pollution, mostly formed by the fuel emanations of the vehicles, is the major unsafe condition that affects the human race.Though the issues have been subsided by replacing the automobiles with light weight material (20% weight reduction)[1], 6-8% fuel usage[2], it is still a minute progress in that direction. This sort of thinking made to concentrate on the manufacturing methodology, i.e Sheet forming which captured the automobile sector. However, process efficiency has to be improved by selecting appropriate conditions to reduce the forming defects such as fracture, wrinkle, excessive thinning etc.[3],[4],[5].Taguchi strategy is commonly used to choose issues, and enhance the cycle variables [6]. Indeed, even the deep drawing procedure joined with Taguchi technique were examined by padmanabham [7] , Lin kuo [8] and Bor-Tsuen Lin [9]etc.,. Bor-Tsuen in his experimentation on microridged drawing improved the cup height by 60% with 7% expansion in the shaping force while drawing. However, most of the processes are single objective optimization. Taguchi Method is an exceptionally evolved process plan for streamlining the exploratory conditions, however contrast with single reaction issues it faces restriction in multi reaction issues [10], [11]. Though Design of experiment plays an efficient role among the progression parameters, the intricacy in forming process, chooses multi objective optimization for better response. Various methods such as Engineering judgment, regression analysis, six sigma, Swarm Optimization, ANT Colony, Grey Relational Analysis (GRA), and so on applied for multi reaction issues to accomplish most ideal solution. All these techniques spare the production time as well as produce the solid parts at sensible expenses. Grey Relational Analysis (GRA), extraordinary compared to other multi advancement strategy was presented by Deng in 1989 [12].Taguchi based GRA, applies the averages of normalized multi objectives to estimate the grading factor. Grey relational grade is a factor that converts the multiple recitals to single grade whose performance is improved by replacing the normalized factors with weighting values in each response. Xie Yan-min[13], applied GRA in examining the flanging process parameters to acquire

Experimental Procedure In this examination, Al6061-T6 aluminum sheet (Al 97.3%; Si 0.057%; Fe 0.279%; Mn, 0.0678; Mg1.199%; Cr0.179%; Cu 0.181% and Zn, 0.048%) was chosen for the Deep drawing process. Three set of sheets having thickness as 1, 1.5 and 2 mm made roundabout cut of 108mm distance across are considered for experimentation. A grid of circles having 5 mm diameter were laser set apart on a surface of the sheet to facilitate the strain estimation subsequent to forming. Inconel steel die of diameters 52.3mm, 53.3mm, 54.3mm having consistent punch diameter of 49.8mm placed with blank holder, upheld on three cushion pins. The forming test were performed at three temperatures RT, 150oC and 300oC at three different die speeds (0.4, 0.7, 1mm/s) keeping up the consistent blank holder force. The selected input factors for tests were: blank thickness, die

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Figure 1. Experimental Setup (a) 2D layout of Equipment (b) Hydraulic Deep Drawing.

Analysis Method

Signal-to-noise Ratio Taguchi Method dependent on the orthogonal array, performs the design of experiments, uses signal –to-noise (S/N) ratio to measure the process performance which, are insensible to noise factor [6]. Noise factors are uncontrolled factors which influence the product or process. The more modest the-better quality trademark is: 1 nij = −10 log  ∑ nj =1 yij2  n 

where yij is the ith test at the jth trial, n is the overall count of tests, and s is the standard deviation. The experimented standards and calculated S/N ratio values are given in Table 2.

and blank temperature, die speed and lubricant. Taguchi’s L27 OA is utilized for experimentation. The forming factors and their ranges considered in this investigation are given in Table 1. Experimentation is performed on Hydraulic Deep Drawing machine of 13 tons as appeared in Fig. 1 to create the example segments ( Figure 2),using the arrangements of boundary level as given in Table 2

Grey Relational Analysis Grey Relational Analysis (GRA), is applied for recognizing the most ideal set of input parameters to attain expert characteristics. Generally applied for assessing the presentation of a complex project with inadequate information. In view of weightages to individual responses, the GRA generates optimum condition for multi-objective problems. The procedure followed while using Grey Relation Analysis is:

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Table 2. The results of experiments and S/N ratios values Expt No Blank Die and Blank Die Speed Lubrication Punch Force, Thickness S/N ratio Thickness Temperature (P) Variation, (Th) for P

8. Performing confirmation experiments.

GRA, is aimed to process the complicated data and transfer into whitening system. Data preprocessing isutilized to distinguish the assessed objective for each impact factor. The linear data pre-processing technique for the S/N proportion is determined as the lower the better rule which can be communicated as,

where xi*(k) is the significance obtained for grey relational generation, min xi0(k) is the nominal significance of xi0(k) for the kth response and max xi0(k) is the prime significance for the kth response where k = 1,2,3,4 …,n and i=1,2,3,……m for the various output responses measured in a sequence. The deviation sequence of the mentioned series is known by Δ0i(K) = |x0*(k) – xi*(k)|

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The GRC is registered to set up a connection between the best information and the genuine normalize data. The GRC is determined as

Where λk is an eigen value, ∑nk=1 λk = n and k = 1,2,…n; Vik = [ak1, ak2,……, akn] T correspond to eigen value λk. (iv) The uncorrelated principal component is set as

Where Δ0i(k) = |x0(k) – xi(k)|, ζ is the distinguishing coefficient lying between 0 ≤ ζ ≤ 1, Δmin is the least value of Δ0i and Δmax is the highest value of Δ0i . ζ is distinguishing or identification coefficient : ζ ∈[0,1]. ζ = 0.5 is generally used. In view of the weighting values wk, the GRG is specified as γi =

Normally the grey relational ranking speaks to the connection between’s the arrangements, yet in addition speaks to the degree of control among comparable and reference sequence. Accordingly, the similarity among sequences generate grade as one or higher than the other grade [7]. Principlal Component Analysis Principal Component analysis (PCA),enlightens the formation of variance covariance by the linear combinations of all features characteristic. It is explained as: (i) Developing  the original multiple performance characteristic array   x1(n)   x1(1) x1(2) x1(3)  x 2(1) x1(2) x1(3)   x1(n)           xi =                      xm(1) xm(2) xm(3)   xm(n)

Where m, the quantity of experiments and n, the quantity of quality characteristics. Here, x is the coefficient of each quality characteristic. (ii) The correlation Coefficient Array is evaluated as Rjl =

l = 1,2,3,…..n, Where Cov (xi(j), xi(l)) are the covariance sequences, xi(j) and xi(l) respectively; σxi(j) is the standard deviation of sequence xi(j); σxi(l) is the standard deviation of sequence xi(l). (iii) Th  e eigen standards and eigen vectors are determined from the correspondence coefficient array

Where Ym1 and Ym2 are the initial and succeeding principal components. The technical aspect of Taguchi/GRA/ PCA optimization method for sheet forming is illustrated in Fig.3. Implementation of The Planned Hybrid Taguchi/GRA/ PCA Optimization Procedures for Deep Drawing In the GRA, the trial results for the Taguchi based experimentation, the S/N proportions of Punch power and uniform thickness variety in Table 2 are first standardized by the small- the-better attribute of the succession by utilizing condition equation (2). The values of punch force and uniform thickness distribution are set as the reference sequence x0(0) (k), k = 1, 2 and the comparability sequences xi(0) (k), i = 1, 2, 3, . . . , 27, k = 1, 2. Table 3 lists all the sequences after data preprocessing. According to Deng [8], a bigger estimation of the standardizedoutcomes relates to better execution and the greatest standardized outcomes that are equivalent to one show the best execution. According to Table 3, the deviation sequences Δ01(k) can be considered as follows: Δ01(1) = | x0*(1) – x1*(1) | = |1.0000–0.589001| = 0.410999 Δ01(2) = | x0*(2) – x1*(2) | = |1.0000–0.750112| = 0.2498888 (12) Therefore, Δ01 = (0.410999, 0.2498888). The same calculating technique is performed for i = 1, . . . , 27, and the outcome of all Δ0i for i = 1, . . . , 27 are given in Table3. On analyzing the statistics shown in Table 3, Δmax(k) and Δ min(k) can be given as follows: Δ max = Δ011(1) = Δ09(2) = 1.0000, Δ min = Δ012(1) = Δ04(2) = 0.0000

Calculation of The Grey Relational Coefficient By means of the coefficient ζ = 0.5 in equation (6), the illustration of GRC ζ1(k)is known as: ζ1(1) =

Thus, ζ1(k) = (0.548848, 0.666766), k = 1, 2. A like process is applied for i = 1, . . . , 27. Table 4 lists the coefficient for every trial of the L27 OA.

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Figure 3. Proposed Optimization technique using hybrid Taguchi/GRA/PCA.

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Table 3. Normalized values and deviation sequences for punch force and uniform thickness variation Expt No

Table 4. Eigen values and explained variation for principal components Principal Component Eigen Value Explained Variations (%) First

Computation Using PCA for Involvement of Feature Characteristics In multi objective optimization, rather than adopting traditional trial and error method, the GRA-PCA is introduced to decide the weightage of all worth characteristic, consequently diminishing the uncertainty in decision

making. The weighting values for every quality trademark are controlled by utilizing the PCA. Considering the coefficient data represented in Table 4 for calculating the correlation coefficient matrix and to make out the equivalent eigen values from Equation 10. (Table 4). The eigenvector is appeared in Table 5, and the square of the eigenvector can speak to the association of the comparing quality trademark to the principal component. The contribution are given as 0.4999, 0.4999, respectively. The variance involvement of initial principal component is almost 51% higher among the two quality trademark. Hence, in this examination, the squares of the respective eigenvectors are picked as the weighting estimations of the concerned quality trademark. Coefficients 𝑤1, and 𝑤2 in (7) are set as 0.4999, and 0.4999, respectively.

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Table 5. The Eigen vectors for principal components and contribution Responses

Computation Grey Relational Grades On the basis of equation (7) and the statistics listed in Table 6, the grey relational grades are considered as follows: γ1 = (0.4999* 0.548848) + (0.4999 * 0.666766) = 0.6076 (15) Following similar method, the grade and level of analysis is performed for all i = 27 experiments and consolidated in Table 6.Rather than thinking about the various quality attributes for upgrading the forming parameters, the preferred optimizing single factor is grey relational grade (GRG).

Results And Discussion

More prominent the GRG value, stronger is the relationship to reference sequence, signify the position of the factor [21], [22]. It indicates that, the greater the GRG, the better the presentation [22], [23]. Hence, the most ideal degree of the process parameters is the best GRG value. In response table, the average of grade rate of corresponding intensity of each forming parameter is taken from the OA. For instance, in the primary column in the OA blank thickness (as shown in Table 2), the test no 5,6,7,9,13,15,16,21 and 27 were the investigational runs at which sheet forming parameter A (blank thickness ) was place at level 1. The associated standards of grey relational grade for A1 are those experimental runs’ grey relational grades. Calculations were performed for all forming parameter levels and the response table was constructed as specified in Table 7. A1 = (0.406585 + 0.616204 + 0.668872 + 0.387685 + 0.375825+ 0.567298 + 0.550391 + 0.456874 + 0.549675)/9 = 4.579409/9 = 0.5088232 Similarly, the usual grey relational grade for A2 and A3 are calculated as follows: A2 = (0.607807 + 0.383853 + 0.532304+ 0.81239 + 0.601211 + 0.431314 + 0.710156 + 0.490534 + 0.41659)/9 = 4.986159/9 = 0.554017

Table 6. Grey Relational Co-efficient, GRA and Rank for Punch force and Uniform thickness variation Expt Grey relational coefficient Grey Rank No Relational Punch force Thickness Variation Grade 1

A3 = (0.5735 + 0.686076+ 0.716727 + 0.464112 + 0.555162 + 0.729019 + 0.582961 + 0.455245+ 0.454832)/9 = 5.217634/9 = 0.579737 Figure 4 represents the GRG graph, where the horizontal line in the representation is the rank of the complete

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mean of the GRG. Mainly, the bigger the GRG, the better are the various performance characteristics. Accordingly, we selected the level that gave the significant average response. From the response table for the GRG shown in Table 7, the greatest blend of the forming parameters is the place with A3 (blank thickness of 2 mm), B3 (die and blank temperature of 300oC), C1(die speed of

A3b3c1d2 A3b3c1d2

Confirmation Test After obtaining the most ideal level of the sheet forming parameters, the subsequent step is to verify the improvement of the presentation characteristics using this optimal combination. Table 9 compares the outcomes of the confirmation tests utilizing the ideal sheet forming parameters (A3, B3, C1, D2) obtained by the proposed method and with those of the initial forming parameters (A3, B3, C1, D1) whose value is near to optimal grade with 10.26% grade variation. As shown in Table 9, punch force changes from 46.5978 KN to 34.5KN; which says that almost 25.96% of punch force is saved, while the uniform thickness variation from 0.274061 to 0.135 mm, shows 50.74% thinning

variation improvement in maintain uniform thinning. By applying optimal forming conditions, as mentioned by [9] the improvement in obtaining minimum punch force and minimum thickness variation is attained. The best combination (A2-B3-C1-D2) with grade 0.812, obtained from unrefined data shows almost 9.58% variations from the proposed method whose grade is 0.741, indicating the precision of experimentation. As indicated in Table 9, an experiment is performed to check the optimality for the predicted combination and achieved 2.11% error in punch force, 8% error in uniform thickness variation and 0.53% error in grade value which is in accepting mode.

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Consequently, these confirmation tests reveal that the proposed calculation for understanding the ideal combinations of the sheet forming parameters in this work improves Punch force, Uniform thickness variation.

Conclusions

The utilization of GRA combined with PCA for optimizing the process parameters in sheet forming of Al6061-T6 has summarized the outcome as follows: 1. The general significance of every performance trademark in solving various execution problems have been controlled by comparing weighting values utilizing PCA.

2. Die and blank temperature, with total part of 80.117%,

is the major controllable feature influencing the multiple performance qualities. 3. Most ideal combination of the sheet forming parameters acquired from the proposed strategy based on response table is A3, B3, C1 and D2 set. On comparing the proposed method grade value of 0.741 to the experimental unrefined range grade of 0.729 from A3, B3, C1, D1 combination indicates 25.96% decrease in punch force to attain almost 50.74% of enhancement in uniform thinning. Thus, the confirmation tests indicate the performance of proposed method. 4. The A2-B3-C1-D2 combination, showing the highest grade of 0.812 is approximately 9.5% variation with the proposed grade of 0.741 from optimum combination exhibits the accuracy of the performed experimentation.

5. Currently, in this experimentation, not just the best

blend of factors are suggested for execution of sheet forming yet additionally proposed the optimization strategy for the sheet forming parameters with various performance attributes.

Conflict Of Interest

The author declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Ethics

There are no ethical issues with the publication of this manuscript.

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