COMBINATION OF TAGUCHI METHOD, MOORA AND COPRAS TECHNIQUES IN MULTI-OBJECTIVE OPTIMIZATION OF SURFACE GRINDING PROCESS

This study presentes a combination method of several optimization techniques and Taguchi method to solve the multi-objective optimization problem for surface grinding process of SKD11 steel. The optimization techniques that were used in this study were Multi-Objective Optimization on basis of Ratio Analysis (MOORA) and Complex Proportional Assessment (COPRAS). In surface grinding process, two parameters that were chosen as the evaluation creterias were surface roughness (Ra) and material removal rate (MRR). The orthogonal Taguchi L16 matrix was chosen to design the experimental matrix with two input parameters namely workpiece velocity and depth of cut.  The two optimization techniques that mentioned above were applied to solve the multi-objective optimization problem in the grinding process. Using two above techniques, the optimized results of the cutting parameters were the same. The optimal workpiece velocity and cutting depth were 20 m/min and 0.02 mm. Corresponding to these optimal values of the workpiece velocity and cutting depth, the surface roughness and material removal rate were 1.16 µm and 86.67 mm3/s. These proposed techniques and method can be used to improve the quality and effectiveness of grinding processes by reducing the surface roughness and increasing the material removal rate.


INTRODUCTION
In the machining methods, grinding method are the most common method to machine the surfaces that requires high precision and high surface gloss. The efficiency of the grinding process is evaluated through many parameters such as surface roughness, material removal rate (MRR), cutting forces, cutting heat, system vibrations, ... Many studies have been done to determine the optimum value of the machining parameters to achieve one or more objectives. Mahajan et al. [1] determined the optimal value of wheel grit size, the grinding wheel speed, the feed rate per revolution, and depth of cut in surface grinding process of D2 steel. Taguchi method was applied to design and optimize the machining surface roughness and material removal rate. To obtain the minimum value of surface roughness, the optimal value of wheel grit size, the grinding wheel speed, the feed rate per revolution, and depth of cut were 46 (mesh), 2300 (rev/min), 0.834 (mm/rev), and 0.05 (mm), respectively. Besides, to obtain the maximum value of MRR, the optimal value of wheel grit size, the grinding wheel speed, the feed rate per revolution, and depth of cut were 36 (mesh), 1650 (rev/min), 0.834 (mm/rev), and 0.075 (mm), respectively. However, this method has not yet given a set of values of input parameters to ensure simultaneously the minimum value of surface roughness and maximum value of MRR. Rai et al. [2] used Taguchi method to optimize the sur-face grinding process of AISI410 steel. The wheel grit size, the feed rate per revolution, and depth of cut were chosen the input parameters to design the experimental matrix. The aim of this study was determination of the input parameters to ensure the average surface roughness and mean square of surface roughness having the minimum values. Using this method, the average surface roughness and mean square of surface roughness have also the minimum values when the wheel grit size, the feed rate per revolution, and depth of cut were 54 (mesh), 0.5 (mm/rev), and 0.06 (mm), respectively. Atish et al. [3] used Taguchi to optimize the surface grinding process of the mild steel. The aim of this study was determination of values of the depth of cut, the workpiece velocity, and cross feed rate to achieve the minimum value of surface roughness and maximum of MRR. This study found that to obtain the minimum of surface roughness, the depth of cut, the workpiece velocity, and cross feed rate were 0.1 (mm), 20 (strokes/min), and 10 (strokes/min), respectively. To obtain the maxinmum of MRR, the depth of cut, the workpiece velocity, and cross rate were 0.1 (mm), 30 (strokes/min), and 30 (strokes/ min), respectively. Aravind et al. [4] combined the Taguchi method and response surface method (RSM) to optimize the surface grinding process of ASIS 1035 steel. The wheel grain size, the grinding wheel speed, depth of cut, and feed rate were selected as the input parameters to design the experimental matrix. This study showed that to obtain the minimum values of both Ra and Rz, the wheel grain size, the grinding wheel speed, depth of cut, and feed rate were 54 (mesh), 0.05 (mm), and 0.45 (mm/stroke), respectively. Hamid Reza FAZLI SHAHRI et al. [5] combined Taguchi method and regression analysis to optimize the surface grinding process of AISI 1045 AISI 1045. This study showed that to achieve the maximum of machining surface hardness, the grinding wheel must be fine dressed, and the optimal values of depth of cut, cutting velocity, workpiece velocity, cross feed were 0.03 (mm), 32 (m/s), 10 (m/min), and 5 (mm/rev), respectively. Prashant et el. [6] combined the Taguchi method and grey relational analysis (GRA) technique to optimize the surface grinding process of EN8 steel. The parameters that were selected as the input parameters were depth of cut, type of lubricant, feed rate, grinding wheel speed, coolant flow rate, and nanoparticle size. This study showed that to obtain the minimum of surface roughness, the type of lubricant was the water containing the CuO particles with the grain size of 100 (nm), concentration of 2%, and flow of 5 (ml/min), and the depth of cut, feed rate, grinding wheel speed were 5 (µm), 2000 (mm/ min), and 35(m/s), respectively. Luu Anh Tung et al. [7] also combined Taguchi method and GRA to determine the optimal values of the grinding wheel dressing parameters in grinding process of 9CrSi tool steel. The purpose of this study was assurance of the minimum value of machining surface roughness and minimum value of the flatness tolerance. In this study, the optimal values of the dressing parameters were determined including: The coarse dressing depth was 0.025 (mm), the coarse dressing times were 3 times, the fine dressing depth was 0.005 (mm), the fine dressing times were 2 times, and the dressing feed rate was 1.6 (m/min). In other study, the multi-objective optimization in surface grinding process of 90CrSi tool steel was also performed by Nguyen Thi Hong et al. [8]. This study aimed to determine the dressing parameters to simultaneously ensure the minimum values of surface roughness and tangential cutting force, and maximum value of tool life. In this study, Taguchi method and GRA were combined to determine the optimal values of dressing parameters as following. The coarse dressing depth was 0.015 (mm), the coarse dressing times were 2 (times), the fine dressing depth was 0.005 (mm), the non-feeding dressing times were 3 (times), and the dressing feed rate was 1.6 (m/ min). The combination of Taguchi method and GRA was also applied to solve the multi-objective optimization problem in the surface grinding process of AISI D2 steel [9]. In this study, three different coolant conditions were applied in surface grinding process including dry conditions, flood cooling condition, and minimum quantity lubrication (MQL) condition. This study showed that to simultaneously ensure the minimum values of machining surface roughness, cutting heat, and normal cutting forces, the grinding process was performed with a cutting depth of 15 (µm), a workpiece velocity of 3 (m/min), cutting velocity of 25 (m/s), and with flow rate 250 (mL/h) of MQL condition. Prashant J. Patil et al. [10] also combined Taguchi method and GRA to solve the multi-objective optimization problem in surface grinding process of EN-24 steel in MQL condition. The input parameters that were selected in this study included the nanoparticles in the lubricating solution (Al2O3, CuO, water), the concentration of particles, particle size, flow rate of solution, depth of cut, feed rate, and cutting velocity. The obtained results showed that to simultaneously achieve the minimum values of mormal cutting force, tangential cutting force, and cutting heat, the grinding process must be performed in the lubricating solution using CuO nanoparticle with a concentration of 2%, a nanoparticle size of 100 (nm), a coolant flow rate of 5 (ml/minute), and with a cutting depth of 5 (µm), a feed rate of 2000 (mm/min), and a grinding wheel speed 35 (m/s). The combination of Taguchi method and GRA to solve the multi-objective optimization problem in grinding process of OCR12VM material was performed by Hendri Jumianto et al. [11]. This study showed that to ensure the minimum values of system vibrations, the cutting velocity, workpiece velocity, and cross feed rate were 3000 (rpm), 11 (mm/s), and 5 (mm/stroke), respectively. From above studies, it shows that the Taguchi method has been successfully applied in solving the optimization of the surface grinding process in many specific cases. Among published studies, the cutting parameters are often chosen as the input parameters for the experimental process. This issue could be explained that the adjustment of these parameters during machining is more easily done by the operator than by adjusting other parameters such as the rigidity of the machine system, the vibrating factors transmitted into the system, etc. However, with each specific case about the machining material, the optimal values of cutting parameters were different. So, for each machining material and each specific machining condition, the experimental and optimization studies must be performed under specific conditions. Besides, if only using Taguchi method, only one evaluation criteria is optimized (the single objective optimization), if the multi-objective optimization problem is solved, the Taguchi method must be combined with other methods or techniques. MOORA and COPRAS are two of the famous optimization methods that were applied into different research fields. Gadakh [12] combined Taguchi and MOORA technique to optimize the cutting parameters of the milling process. The purpose of this study was determination of the optimal values of spindle speed, feed rate per flute, tool diameter, tool nose radius, and the machining time to ensure the minimum of the tool wear, and to ensure the maximum of MRR. Mesran et al. [13] applied the MOORA technique to in-Nhu-Tung Nguyen, et al. -Combination of taguchi method, moora and copras techniques in multi-objective optimization of surface grinding process vestigate the division of the students into each class when entering the universities. This study proposed the best method to divide the students into the class based on the parameters of each student (UN Average Score, Psychotest Value, IPA Value, Mathematics Value, Interview Value). Nguyen et al. [14] used the MOORA to optimize the Powder mixed electrical discharge machining (PMEDM). The aim of this study to determine the optimal values of the workpiece material, tool material, polarity, peak current, pulse-on-time, pulse-off-time, and titanium powder concentration to ensure the minimum values of surface roughness and electrode wear. Tran et al. [15] applied MOORA and COPRAS techniques to determine the optimal values of the materials (straw, corn cobs, sawdust, rice bran, and CaCO3) for growing mushrooms, and so on. However, up to now, there have not been any published studies on the application of these two techniques to solve the multi-objective optimization problem in the machining process in general or the surface grinding processes in particular. Surface roughness has a significant influence on the workability and life of the product. While MRR is a parameter that reflects machining productivity, energy consumption, grinding wheel consumption, so the efficiency of grinding process also can be evaluated through this parameter. Therefore, these two parameters are often chosen as indicators of evaluating the efficiency of grinding processes in general and the surface grinding process in particular. In this study, SKD11 steel was grinded on a surface grinder. The experiments were designed according to the Taguchi method including 16 experiments. In which, the workpiece velocity and cutting depth were selected as the input parameters for each experiment. The surface roughness and MRR were chosen as the two output parameters. Two techniques MOORA and COPRAS have been applied to solve the multi-objective optimization problem. The results showed that these techniques have determined the same set of values of workpiece velocity and depth of cut to ensure the minimum value of surface roughness and maximum value of MRR. The two techniques MOORA and COPRAS not only successfully applied in solving the multi-objective optimization problem of the surface grinding process in this study, but also opened up a very potential research direction in multi-objective optimization of other machining processes.

Experimental system
The experiments were conducted in the surface grinding APSG-820/2A machine. The grinding wheel aluminum oxide APSG-820/2A was used in this study. The workpiece material that was used in the experimental process was heat treated SKD11 with the hardness of 60 HRC. The length, width, and height of workpiece were 80 (mm), 40 (mm), and 10 (mm), respectively. The surface roughness tester SJ-301 (Japan) was used to measure the surface roughness of machining parts. Each experiment, the surface roughness was measured at least three consecutive times. The average value of surface roughness was used for evaluation and analysis process. The material removal rate RMM was calculated by equation MRR =v w ×b×t (mm 3 /s). Where v w , b, and t are the workpiece velocity (m/s), the width of the grinding wheel (mm), and the depth of cut (mm), respectively.

Experimental design
The Taguchi method was applied to design the experimental matrix. The cutting parameters that were chosen as the input parameters were workpiece velocity and depth of cut. The orthogonal L 16 matrix with 16 experiments was used and listed in Table 1.

Grinding conditions
The experiments were conducted with the controllable factors in Table 1 and with the grinding conditions as following: -The cutting velocity: 26 m/s. -The dressing depth of cut: 0.01 mm.

Multiple-Criteria Decision Making (MCDM)
The multiple criteria decision making -MCDM can be used to select the best solution from the solutions A= {A 1 ,A 2 ,…,A m } based on the criterias C= {C 1 ,C 2 ,…,C n }.
In this study, in the MOORA and COPRAS techniques, the weights were calculated using measurement of Entropy, because this method can get the high accuracy. The steps of the weight calculation process will be performed as following [17, 18]: Step 1: Calculating the values p ij with i = 1, 2, …, m and j = 1, 2, …, n using Eq. (1).
Step 2: Calculating the measurement entropy e j of each criterion C j with j = 1, 2, …, n by Eq.
Step 3: Calculating the weight w j of each criterion C j with j = 1, 2, …, n by Eq. . This multi-objective optimization technique can be successfully appliec to solve the complex decision problems in the production environment with the together conflicting objectives. The MOORA technique includes the steps as following: Step 1: Calculating the values p ij with i = 1, 2, …, m and j = 1, 2, …, n using Eq. (1).
Step 3: Calculating the weight w j of each criterion C j with j = 1, 2, …, n by Eq. (3).
where B and NB are the set of benefit criteria and the set of non-beneficial criteria with i = 1, 2, …, m.

COPRAS technique
COPRAS technique was introduced by Zavadskas et al.
Step 2: Calculating the measurement entropy e j of each criterion C j with j = 1, 2, …, n by Eq. (2).
Step 3: Calculating the weight w j of each criterion C j with j = 1, 2, …, n by Eq. (3).
Step 8: Ranking the solutions A k > A i if Q k < Q i with i, k = 1, 2, …, m.

Experimental results
The experiments were conducted according to the experimental matrix in Table 1. The experimental results were listed in Table 2. To facilitate for the using of the mathematical symbols when optimizing according to MOORA and COPRAS techniques, the surface roughness criterion and the MRR criterion were set as C1 and C2 as presented in Table 3.

The optimized results using MOORA technique
From the data in Table 3, MOORA technique was used to calculate the values as following: Step 1: Calculating the values p ij by Eq. (1). The calculated results were listed in Table 4.
Step 2: Calculating the values e j by Eq. (2). The calculated results were listed in Table 5.
Step 3: Calculating the values w j by Eq. (3). The calculated results were also listed in Table 5.
Step 4: Calculating the matrix X = [X ij ] m×n by Eq. (4). The calculated results were listed in Table 6.
Step 5: Calculating the matrix W by Eq. (5). The calculated results were listed in Table 7.
Step 6: Calculating the values P and Ri by Eq. (6) and Eq. (7). The calculated results were listed in Table 8.
Step 7: Calculating the values Q i by Eq. (8). The calculated results were also listed in Table 8. The calculated results from Table 8 showed that the solution A 16 was the best solution in 16 solutions. If considering only the surface roughness criteria or only the MRR, A 16 is not the best solution (Table 2). However, when considering the two parameters of surface roughness and MRR at the same time, this solution was considered to be the best solution.

The optimized results using COPRAS technique
From the data in Table 3, COPRAS technique was applied according to the steps in above section. The results were calculated and listed in Table 9, Table 10, and Table  11. The calculated results from Table 11 also showed that the solution A16 was the best solution in 16 solutions. The ranking order of the solutions in Table 11 also co-incided with the ranking order of solutions in Table 8. Thus, in this case, the MOORA and the COPRAS techniques gave a unified result when determining the optimal solution. That further confirms the correctness of the implemented methods. So, in surface grinding process of KSD11 steel, to ensure the minumum value of surface roughness and maximum value of material removal rate, the optimal values of the workpiece velocity and cutting depth were 20 m/min and 0.02 mm.

CONCLUSIONS
This study was performed using Taguchi method, MOO-RA and COPRAS techniques to solve the multi-objective optimization problem for surface grinding process of SKD11 steel. The conclusions of this study were drawn as following: • Taguchi method, MOORA and COPRAS techniques were successfully applied to solve the multi-objec-tive optimization problem for surface grinding process of SKD11 steel. Using these above techniques, the optimized results of the cutting parameters were the same. • The optimal workpiece velocity and cutting depth were 20 m/min and 0.02 mm. Corresponding to these optimal values of the workpiece velocity and cutting depth, the surface roughness and material removal to improve the quality and effectiveness of grinding processes by reducing the surface roughness and increasing the material removal rate.