Prediction of Surface Hardness in a Burnishing Process Using Taguchi Method Fuzzy Logic Model and Re
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Sigma Journal of Engineering and Natural Sciences 2018, Vol. 36, Issue 4, pp. 1283-1295; doi.org/10.62051/ytu.sigma-journal-of-engineering-and-natural-sciences-prediction-of-surface-hardness-in-a-burnishing-process-using-taguchi-method-fuzz
Abstract
Keywords: Ball burnishing; surface hardness; Taguchi method; fuzzy logic; regression model.
1. Introduction
Recently, substantial interest has been given to the post-machining metal finishing operations like the burnishing, shut pinning, water jet pinning and laser pinning processes in the manufacturing industry. Burnishing is a cold-working process in which the burnishing force is conducted to a workpiece surface by hard smooth ball and roller [1, 2]. Burnishing is regarded as a fast, simple and low-cost process with advantages like enhancing mechanical properties of the manufactured pieces [3], reducing surface roughness [4, 5], proposal of good finishing accuracy, improving hardness on the workpiece surface [6], enhances wear resistance [7], fatigue [8], corrosion resistance [9], and maximum residual stress in compression [10]. Most of the ball burnishing process parameters such as burnishing speed, ball material, ball size, lubrication, burnishing force, workpiece material, feed rate, number of passes affect mechanical properties [110]. In the literature, some statistical methods such as response surface methodology (RSM) [6], desirability function analysis [11], fuzzy logic [4], artificial neural network [5], grey relational *
Corresponding Author: e-mail: gokhanbasar@osmaniye.edu.tr, tel: (328) 827 10 00 / 3432
analysis [2], and Taguchi method [12] have been performed for optimization and prediction of quality characteristics. Basak and Goktas [4] optimized the burnishing parameters using fuzzy logic. Kurkute and Chavan [13] modeled and optimized the surface roughness and microhardness roller burnished aluminum alloy using RSM. Kumar et al. [14] used Taguchi technique and fuzzy logic model in roller burnishing process for estimation of surface roughness and hardness of AA 2014 and AA 6063 aluminum alloy. These models were compared to each other to obtain minimum surface roughness and maximum hardness. El-Taweel and El-Axir [12] analyzed and optimized the ball burnishing process on surface roughness and micro-hardness of brass using Taguchi technique. Sarhan and El-Tayeb [15] performed the estimation of surface roughness in burnishing of brass C3605. The approach used the fuzzy rule-based approach. The results, which acquired from the fuzzy model, are immensely coherent with the experiments. Esme et al. [16] focused on the surface roughness and microhardness of AA 7075 aluminum alloy using greybased fuzzy algorithm. Kahraman [6] developed an empirical model for the prediction surface hardness of AA 7075 aluminum alloy using RSM with central composite design. Sagbas and Kahraman [17] studied optimal burnishing parameters for surface hardness of AA 7178 aluminum alloy using Taguchi method. Dweiri et al. [18] optimized the surface roughness roller burnished nonfer rous component using fuzzy model. In this paper, surface hardness was estimated as a function of four factors, namely, burnishing speed, feed rate, burnishing force and number of passes. ANOVA was conducted to analyze the effect of control factors on surface hardness. Additionally, obtained results from Taguchi method, regression analysis and fuzzy logic model for surface hardness in ball burnishing process were compared and analyzed to each other.
2. Experimental Details
In this study, AA 7075 aluminum alloy was used as the workpiece material and its chemical composition given in Table 1. It was extensively used in defense and aerospace industry, rubber and plastic molds, rivet and nuclear applications. In experiments, the workpiece was taken in the shape of bars, diameter of 30 mm and length of 100 mm as a three part each having a length of 20 mm. The experimental set-up for the ball burnishing tests was shown in Figure 1. Distinct ball burnishing parameters were carried out on each part. Table 1. Chemical composition of AA 7075 aluminum alloy Chemical structure w/%
Stainless steel ball with hardness of 60 HRc and a diameter of Ø18 mm was used in the burnishing process. The experiments were carried out by using Doosan Puma 240 type industrial CNC lathe. The workpieces were assembled between the chuck and tailstock center on the lathe. Throughout burnishing process, there was no used coolant. Before burnishing process was conducted, the workpieces were cleaned with alcohol. To preserve any particles from ingress the surface of touch between the test apparatus and the workpiece, a ball cleaning process was conducted throughout the ball burnishing process. Vickers hardness test was implemented using ZHVμ series Zwick micro hardness tester. These workpieces were tested and appraised for their microhardness. During the hardness test, a load of 5kgf was conducted with a loading duration 10 seconds. The indenter was performed the distinct places on the workpiece to avoid surface effects and overlap. Three reasonable measurements were acquired from overall workpieces.
Figure 1. Expe rimental set up of the ball burnishing process
3.1. Prediction of surface hardness using Taguchi Method
The Taguchi method developed by Genuchi Taguchi is a statistical method used to enhance the product quality. It is generally used in engineering analysis. This method drastically reduces the quantity of trials by using orthogonal arrays [19-21]. Moreover, it ensures a basic, fruitful and systematic approach to identifying the optimum ball burnishing parameters [22]. The Taguchi method utilizes a loss function to establish the quality characteristics. Loss function values are also transformed to a signal-to-noise (S/N) ratio [23]. In usually, there are three distinct quality characteristics in S/N ratio analysis, the lower-the-better, the nominal-thebest and the higher-the-better, respectively. For each level of control factors, S/N ratio is calculated based on S/N analysis. The aim of this work was to maximize hardness. Thus, the higher-the-better quality characteristic was used as indicated in Equation (1): ƞ=
where, n is the number of experiments and y is the experimental data [24]. Burnishing speed, burnishing force, feed rate and number of passes were used as control factors and surface hardness was regarded as output factor. Control factors and their levels were given in Table 2. The most proper orthogonal array L25 (45) was selected to define the optimal burnishing parameters and to analyze the effects of control factors. Table 2. Control factors and their levels Symbol Bs Fr Bf Nop
Factors Burnishing speed Feed rate Burnishing force Number of passes
Consequently, the higher-the-better was utilized as offered in the Equation (1). The average of the S/N ratio for each level of burnishing process parameters was computed and given in Table 3. Table 3. S/N values for surface hardness Levels Level 1 Level 2 Level 3 Level 4 Level 5
Control factors Fr Bf 45.38 45.09 45.60 45.30 45.52 45.71 45.52 45.85* 45.80 45.73*
The highest S/N values indicated the optimal level of each process parameters. Therefore, it was shown that in Table 3 that the second level of Bs, the fifth level of Fr, the fourth level of Bf, and the fifth level of Nop were higher and thus the combination of parameters was Bs2Fr5Bf4Nop5. ANOVA was used to analyze the influences of burnishing process parameters on surface hardness. ANOVA which is a statistical method used for detecting individual interactions of all input parameters and their interactions. ANOVA was executed for a confidence grade of 95%. The ANOVA results for the surface hardness was displayed in Table 4. Burnishing force and number of passes were established as a significant factor since their p values are less than 0.05. Table 4. Results of ANOVA for the surface hardness Variance Source Bs Fr Bf Nop Error Total
According to Table 4, the percent contributions of the Bs, Fr, Bf and Nop factors on the surface hardness were found to be 4.60%, 6.30%, 45.45% and 30.23%, respectively. Therefore, the most significant factor on surface hardness was burnishing force (Bf, 45.45%). In the Taguchi method, Equation (2) was used for the prediction of surface hardness. 𝑇ℎ value displays the surface hardness value acquired from the experimental work (Table 5). As a result of the computations, the 𝑇ℎ value was found to be 189.72 HV. 𝐻𝑎𝑟𝑑𝑛𝑒𝑠𝑠𝑝𝑟𝑒𝑑𝑖𝑐𝑡 = (𝐵𝑠𝑛 − 𝑇ℎ ) + (𝐹𝑟𝑛 − 𝑇ℎ ) + (𝐵𝑓𝑛 − 𝑇ℎ ) + (𝑁𝑜𝑝𝑛 − 𝑇ℎ ) + 𝑇ℎ where, n is the level value of the factors for the predict hardness value to be calculated.
Control factors Bs Fr Bf Nop Level 1 188.6 186.2 179.8 185.6 Level 2 193.4 190.8 184.2 183.4 Level 3 187.2 189.0 193.0 187.6 Level 4 189.2 189.0 196.2 195.0 Level 5 190.2 193.6 195.4 197.0 𝑇ℎ (surface hardness total mean value) = 189.72 HV
3.2. Prediction of surface hardness using fuzzy logic model
In fuzzy inference system, model is in the shape of If-Then rules in place of a mathematical equation. A fuzzy inference system is consisted of a fuzzifier, an inference engine, a database, a rule base and a defuzzifier (Figure 2). To predict output data, the Mamdani fuzzy inference system was chosen. The burnishing speed (𝑥1 ), feed rate (𝑥2 ), burnishing force (𝑥3 ) and number of passes (𝑥4 ) were utilized as input parameters and surface hardness (𝑦1 ) was used as the output parameter. Fuzzy logic model was indicated in Figure 3.
Figure 2. Structure of fuzzy logic system with four inputs and one output In fuzzy logic, the range of input/output parameters are detected initially. Then, to acquire fuzzy sets, triangular membership function was used for fuzzification. In fuzzification, numerical input and output values are transformed into linguistic terms like lowest, low, medium, high, highest, etc. The range of input parameters and membership functions were shown in Figure 4, while the range of output parameter and membership function were shown in Figure 5. Eventually, triangular membership function was utilized to defuzzify it to acquire the outputs. Defuzzification is the process of transformation of fuzzy amount into exact amount. Centroid defuzzification method which computed the centroid of the area under the membership function was conducted in this work [25].
Figure 3. Fuzzy inference system The equation (3) of the triangular membership function was offered below: 0 𝑥≤𝑎 𝑥−𝑎 𝑎≤𝑥≤𝑏 𝑡𝑟𝑖𝑎𝑛𝑔𝑙𝑒(𝑥; 𝑎, 𝑏, 𝑐) = 𝑏−𝑎 𝑐−𝑥 𝑏≤𝑥≤𝑐
𝑐 ≤ 𝑥} {0 where a, b, c means the triangular fuzzy triplet which defines the x coordinates of the three corners of the underlying triangular membership function [26]. Linguistic expression used to describe the relation between the inputs and outputs were referred to fuzzy rules. These rules can be shown as: Rule 1: if 𝑥1 is 𝐴1 and 𝑥2 is 𝐵1 and 𝑥3 is 𝐶1 , and 𝑥4 is 𝐷1 then 𝑦1 is 𝐸1 else Rule 2: if 𝑥1 is 𝐴1 and 𝑥2 is 𝐵2 , and 𝑥3 is 𝐶2 , and 𝑥4 is 𝐷2 then 𝑦1 is 𝐸2 else . . Rule n: if 𝑥1 is 𝐴𝑛 and 𝑥2 is 𝐵𝑛 , and 𝑥3 is 𝐶𝑛 , and 𝑥4 is 𝐷𝑛 then 𝑦1 is 𝐸𝑛 else The fuzzy sets are symbolized by membership functions which were exemplified by Figure 4 and Figure 5. Five fuzzy sets were selected for the variables of inputs (VL, L, M, H, VH), and eleven fuzzy sets were utilized for the surface hardness (VVVVL, VVVL, VVL, VL, L, M, H, VH, VVH, VVVH, VVVVH). The number of fuzzy rules was adjusted according to the Taguchi L25 orthogonal array. Hence, numerical values were replaced with linguistic values.
Output variable: Surface hardness Figure 5. Membership function of output parameter The relation between input parameters and output parameter variables was improved by fuzzy rules. In overall 25 rules were shown in Figure 6. Figure 7 indicated the twenty-five rule and dispersion utilized in the suggested Taguchi based fuzzy logic modelling.
3.3. Prediction of surface hardness using regression analysis
Regression analysis is a statistical technique for predicting the relation among variables which have reason and result relationship. It establishes the correlation between a continuous dependent variable and continuous or discrete independent variables [27]. Mathematical models based on burnishing parameters were acquired from regression analysis to estimate surface hardness. Regression analysis was performed through Minitab 17 software. Hardness values were modeled as second order regression model. Equation (4) improved for surface hardness was as follow: 𝐻𝑎𝑟𝑑𝑛𝑒𝑠𝑠 = 149.5 + 0.167𝐵𝑠 + 62.8𝐹𝑟 + 0.177𝐵𝑓 + 2.18𝑁𝑜𝑝 + 0.00037𝐵𝑠 2 + 2𝐹𝑟 2 − 0.000456𝐵𝑓 2 + 0.928𝑁𝑜𝑝2 − 0.563𝐵𝑠𝐹𝑟 + 0.00036𝐵𝑠𝐵𝑓 − 0.0496𝐵𝑠𝑁𝑜𝑝 − 4.87𝐹𝑟𝑁𝑜𝑝 (4)
3.4. Performance comparison of different predictive models
The experimental results and predicted distinct three models were shown in Table 6, which indicated that the Mean Absolute Percentage Error (MAPE) was 1.570 % for Taguchi method, 1.617 % for regression model, and 0.764 % for Fuzzy logic model.
Table 6. Experimental and predicted surface hardness values Trial No
Experimental
value 165 179 190 197 212 181 203 205 194 184 196 195 178 179 188 189 193 187 188 189 200 184 185 187 195
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 (%) MAPE
Method
Regression Model 166.730 179.588 191.087 201.226 210.005 182.121 193.676 203.871 190.263 182.088 199.696 187.591 189.644 179.731 190.466 190.347 192.456 180.806 191.597 190.940 198.700 185.313 186.158 188.807 190.095
Fuzzy Logic Model 167 177 192 197 211 182 202 207 192 182 197 197 177 177 187 187 192 187 187 187 202 182 187 187 197
Distinct performance parameters can be utilized to appraise the convergence of experimental values to estimated values. The Mean Absolute Deviation (MAD), Mean Square Error (MSE), the Root Mean Square Error (RMSE), MAPE and correlation coefficient (R 2) were used to search the convergence between the target values and the output values [28]. In this paper, equation (5-9) were used as performance parameter to compare three distinct models: 𝑀𝐴𝐷 = 𝑀𝑆𝐸 =
where 𝑡 is target value, 𝑜 is output value and 𝑛 is total number of data. Performance values of three different models were given in Table 7. According to results of the MAD, MSE, RMSE and MAPE, the fuzzy logic model produced the best estimation for surface hardness, followed by Taguchi method and then the second order regression model.
Table 7. Performance values of predictive models Taguchi Method Regression Model Fuzzy Logic Model 2.938 3.076 1.440 12.627 17.338 2.560 3.553 4.164 1.600 1.570 1.617 0.764 86.58 % 81.58 % 97.52 %
Scatter plots for the experimental and estimated values with Taguchi method, regression analysis and fuzzy logic model were shown in Figure 8. The efficiency of the developed models was appraised by R2 values. In Taguchi method, regression analysis and fuzzy logic model, R 2 values for the surface hardness were found as 86.58 %, 81.58 % and 97.52 %, respectively. The estimated values acquired with Taguchi method, regression analysis and fuzzy logic modelling were compared with experimental values and results were plotted as demonstrated in Figure 8. It was monitored from Figure 8 that the diversities between experimental and estimated values were low. It was accomplished that Taguchi method, regression analysis and fuzzy logic model could be used for forecasting the surface hardness in ball burnishing of AA 7075 aluminum alloy.
Experimental values Taguchi Method Regression Model Fuzzy Logic Model
Number of experiment Figure 8. Comparison of experimental and predicted values for surface hardness
4. Conclusion
In this survey, surface hardness values obtained in ball burnishing process of AA 7075 aluminum alloy were modeled using multiple approach, including, Taguchi method, regression and fuzzy logic. The main results were as follows:
The optimal level of the control factors to acquire better surface hardness were (level 2) 50 m/min burnishing speed, (level 5) 0.45 mm/rev feed rate, (level 4) 200 N burnishing force and (level 5) 5 number of passes. According to ANOVA results, the most important factor on surface hardness was burnishing force with contribution of 45.45 %, following number of passes with contribution of 30.23 %. Based upon the acquired values of performance parameters (MAD, MSE, RMSE, MAPE), the fuzzy logic model performed the best estimation of surface hardness, followed by the predict Taguchi method, and then the second order regression model. Fuzzy logic model is the best proper for estimating surface hardness. This model can produce an accurate relation between burnishing process parameters and surface hardness. Thus, fuzzy logic can be used to estimate surface hardness even before the ball burnishing process, which will be very much near to values and has acquired after burnishing process. Correlation coefficient (R2) was obtained 86.58 %, 81.58 % and 97.52 % for Taguchi method, the second order regression model and fuzzy logic model, respectively. This means that the predicted results of fuzzy logic model are very near to actual experimental results.
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BAŞAR, G.; KAHRAMAN, F. Prediction of Surface Hardness in a Burnishing Process Using Taguchi Method Fuzzy Logic Model and Re. Sigma Journal of Engineering and Natural Sciences 2018, Vol. 36, pp. 1283-1295. https://doi.org/10.62051/ytu.sigma-journal-of-engineering-and-natural-sciences-prediction-of-surface-hardness-in-a-burnishing-process-using-taguchi-method-fuzz