Determining the Best Dressing Parameters for External Cylindrical Grinding Using MABAC Method

Abstract

Multi-criteria decision making (MCDM) is a research area that entails analyzing various available options in a situation involving social sciences, medicine, engineering, and many other fields. This is due to the fact that it is used to select the best solution from a set of alternatives. The MCDM methods have been applied not only in economics, medicine, transportation, and the military, but also in mechanical processing processes to determine the best machining option. In this study, determining the best dressing mode for external grinding SKD11 tool steel using an MCDM method—the MABAC (multi-attributive border approximation area comparison) method—was introduced. The goal of this research is to find the best dressing mode for achieving the minimal surface roughness (RS), the maximum wheel life (T), and the minimal roundness (R) all at the same time. To perform this work, an experiment was carried out with six input parameters: the fine dressing depth, the fine dressing passes, the coarse dressing depth, the coarse dressing passes, the non-feeding dressing, and the dressing feed rate. In addition, the Taguchi method and an L16 orthogonal array were used to design the experiment. Furthermore, the MEREC (method based on the removal effects of criteria) and entropy methods were used to determine the weight of the criteria. The best dressing mode for external cylindrical grinding has been proposed based on the results. These findings were also confirmed by comparing them to the TOPSIS (technique for order of preference by similarity to ideal solution) and MARCOS (measurement of alternatives and ranking according to compromise solution) methods.

1. Introduction

As technology advances, machining processes must meet ever-increasing demands for mechanical product quality and productivity. Grinding is a type of machining that uses hard abrasive particles as the cutting medium. It is often the key to achieving the required quality [1], so it is widely used for finishing and semi-finishing machine parts. It accounts for approximately 20 to 25 percent of the total industry spent on mechanical parts [2].

In practice, the grinding wheel wears while working, affecting the process’s quality and productivity. As a result, the dressing process is required to ensure the grinding wheel’s original specification. The dressing process impacts the profile, topography, and wear behavior of the grinding wheel. Therefore, it has a significant influence on the grinding process’s efficiency and accuracy. For those reasons, researchers are always interested in improving the quality and productivity of grinding process as well as determining the best grinding mode.

A. Daneshi et al. [3] conducted a study to identify appropriate dressing strategies for dressing in internal cylindrical grinding. In this study, two different types of wheels, including CBN (cubic boron nitride) and corundum wheels, and three separate dressing rollers, including an electroplated, a vitrified bond form roller, and a cup-dresser were used. Yueming Liu et al. [4] used kinematic simulations to predict surface roughness in grinding. Three different abrasive grain shapes (sphere, truncated cone, and cone) and a single-point diamond dressing model were investigated in their study. In addition, the proposed surface roughness model was experimentally validated with a difference of 7–11 percent. F. Klocke and B. Linke [5] investigated the mechanisms resulting in the formation of grinding wheel topography by dressing. The effect of kinematical dressing factors on wheel wear behavior has been computed in this work. Christian Walter et al. [6] discussed the dressing and truing of hybrid bonded (metal-vitrified) CBN grinding wheels using a short-pulsed fiber laser. Several studies have been conducted to determine the optimum dressing mode. Optimal dressing parameters have been suggested for cylindrical grinding [7,8,9], surface grinding [10,11,12], and internal grinding [13,14]. L.M. Kozuro et al. [15] proposed the following dressing mode for external grinding to achieve the surface roughness Ra = 0.32–1.25 (μm); a longitudinal feed rate of 0.4 (m/min); dressing four passes with a dressing depth of 0.03 (mm); and four passes non-feeding dressing.

Difficult-to-cut materials are becoming more popular as materials engineering advances. According to their application fields, difficult-to-cut materials are required to go through the grinding process. However, due to the complexity of the grinding process, several challenges are encountered while grinding these materials. These difficulties can be mitigated by employing effective lubricating techniques and selecting appropriate process parameters. Furthermore, a proper wheel dressing mode guarantees a reduction in these challenges during the grinding operation. As a result, many researchers are interested in grinding these materials. Manish Mukhopadhyay and Pranab Kumar Kundu [16] conducted an experimental study of grinding Ti-6Al-4V using an alumina wheel. In their study, the simple and inexpensive RQL (restricted quantity lubrication) technique was shown to be significantly efficient in expanding Ti-6Al-4V grindability than both dry and flood cooling. It also greatly reduces coolant consumption when compared to flood cooling. Manish Mukhopadhyay et al. [17] noted that using grinding fluid via the SQL (small quantity cooling and lubrication) technique results in better grinding results. In this study, alkaline soap water is discovered to be more efficient than conventional grinding fluid in the grinding of titanium alloy Ti-6Al-4V. Manish Mukhopadhyay and Pranab Kumar Kundu [18] introduced an economical and environmentally friendly drop by drop delivery technique for improving the grindability of Ti-6Al-4V. The effective use of the environment-friendly unconventional fluids when machining Ti-6Al-4V has also been reported when using an alumina wheel [19,20] and a SiC wheel [21]. Berend Denkena et al. [22] investigated the wear-adaptive optimization of in-process conditioning factors during the face plunge grinding of PcBN. It was noted that the optimal input factors allow the process of in-process conditioning to dramatically reduce grinding tool wear without increasing the process time or non-productive time. Dung Hoang Tien et al. [23] presented the results of a multi-target optimization study to find the optimum input factors for getting the minimum surface roughness and maximum material removal rate when external grinding SCM440 steel. When grinding GH4169 alloy with a ceramic bonded CBN grinding wheel, a multi-information fusion recognition model and experimental study of grinding wheel wear status were reported in [24]. G. Xiao and S. Malkin [25] conducted online-optimizing, the internal grinding process, and the dressing parameters to reduce the production time while maintaining part quality requirements. The optimum process parameters when grinding Ti-6Al-4 V using a CBN grinding wheel was introduced in [26]. The Taguchi method and gray relational analysis (GRA) were applied to find the optimum dressing parameters when processing the SKD11 tool steel in surface grinding to increase the material removal rate and to reduce the roundness tolerance of the ground parts [11].

Table 1. Several previous research results on optimization of dressing process.

Grinding Type	Wheel Type	Dressing Tool	Workpiece Material	Method	Objective	Optimum Parameters	Reference
Surface grinding	Alumina	Single-point diamond dresser	Ti–6Al–4V	- Experimental	- Grinding ratio - Grinding surface	- Dressing infeed	[27,28,29]
Surface grinding	Silicon carbide	Multi-point diamond dresser	90CrSi	- Experimental - Taguchi and GRA	- Surface roughness - Flatness tolerence	- Dressing feed rate - Coarse dressing depth - Coarse dressing times - Fine dressing depth - Fine dressing times - Non-feeding dressing	[30]
Cylindrical plunge grinding	Bronze-bonded diamond	Laser tool	Alumina ceramic	- Experimental	- Wheel surface - Grinding force	- Laser power density - Pulse overlap ratio - Scanning cycle number	[31]
Cylindrical plunge grinding	Aluminium oxide	Unclear	AISI 52100	- Experimental	- Production time	- Dressing interval	[25]
Surface grinding	Silicon carbide	Multi-point diamond dresser	SKD11	- Experimental - Taguchi and GRA	- Material removal rate - Flatness tolerence	- Dressing feed rate - Coarse dressing depth - Coarse dressing times - Fine dressing depth - Fine dressing times - Non-feeding dressing	[11]
Cylindrical plunge grinding		Multi-point diamond dresser	EN-31	- Experimental - TOPSIS and AHP	- Surface finish	- Dressing feed rate - Dressing depth - Width of diamond dresser - Dresser drag angle	[32]
Plunge face grinding	Diamond cup	Vitrified cup dresser, white corundum	PCBN	- Experimental	- Wheel wear - Grinding power	- Dressing feed rate - Dressing depth	[22]
Cylindrical plunge grinding	Vitrified CBN	Synthetic diamond disc	AISI 52100		- Surface roughness - Grinding force	- Number of dressing passes	[7]
Cylindrical plunge grinding	Aluminium oxide	Diamond roller	150Cr14	- Experimental - Multi-objective optimization	- Production rate	- Dressing feed ratio - Radial infeed	[8]

presents a brief overview of some previous studies on the dressing process of different types of grinding. In this table, the specifications of the grinding type, wheels, dresser, workpiece material, the objective of study, and the output optimum factors presented in these studies are indicated. This table helps to determine the ultimate optimal parametric combination for all methods considered.

From the above analyses and

Table 2. Input factors.

No.	Input Factors	Symbol	Unit	Levels
				1	2	3	4
1	Coarse dressing depth	ar	mm	0.03	0.04	-	-
2	Coarse dressing passes	nr	-	1	2	3	4
3	Fine dressing depth	af	mm	0.005	0.01	0.015	0.02
4	Fine dressing passes	nf	times	0	1	2	3
5	Non-feeding dressing	n0	-	0	1	2	3
6	Dressing feed rate	Sd	m/min	1	1.5	-	-

, it can be noted that so far, there have been quite a few studies on the dressing mode and on the determination of the optimum or reasonable wheel dressing mode. Besides, different dressing modes such as coarse dressing, fine dressing, and non-feeding dressing influence the efficiency of the dressing process. However, to date, there has been no research on determining the best dressing mode among many different dressing setups for external grinding SKD11 tool steel using an MCDM method. Therefore, finding the best dressing mode in external cylindrical grinding SKD11 tool steel using an MCDM method has been taken into considered.

Multi-criteria decision making (MCDM) is a common problem when it is necessary to analyze multiple options to choose the best one. Numerous studies on MCDM have been conducted for various mechanical machining processes such as milling, turning, grinding, electrical discharge machining (EDM), etc. [33]. This is because the machining process is frequently required to meet many criteria, such as the maximal material removal rate (MMR), the minimal surface roughness (SR), or the minimal tool wear rate. So far, several studies have been conducted to determine the best dressing mode using MCDM methods. Santonab Chakraborty and Shankar Chakraborty [34] presented a scoping review on the applications of MCDM methods for the parametric optimization of machining processes. In this paper, more than 120 scientific papers are reviewed while investigating the implementations of various MCDM techniques in solving parametric optimization problems of turning, drilling, and milling processes. This review paper would serve as a knowledge base for determining the best experimental design plan to be deployed (Taguchi’s L9, L18, or L27 orthogonal array); difficult-to-cut advanced engineering materials to be machined (composites, aluminum, titanium, and their alloys); input parameters for turning, drilling, and milling processes, and corresponding responses to study their interaction effects, MCDM tools, and subjective and objective criteria weighting techniques to be used; and the possibility of integrating with other mathematical tools to deal with an uncertain decision-making environment. Ritwika Chattopadhyay et al. [35] presented the results of a study conducted to determine the best supplier of gearboxes in the Indian iron and steel industry. In this study, a design of experiments (DoE)-based metamodel is developed to connect the computed MABAC scores to the criteria under consideration. Competing suppliers are ranked using a rough-MABAC-DoE-based metamodel, which also simplifies the computational steps when new suppliers are added to the decision-making process. Sanjay S. Patil and Yogesh J. Bhalerao [32] used the TOPSIS (technique for order of preference by similarity to ideal solution) method to select levels of dressing parameters for a better surface finish in cylindrical angular grinding of En-31 parts. In this study, four input parameters, including the dressing cross feed rate, the dressing depth of cut, the width of the diamond dresser, and the drag angle of the dresser were investigated. However, only three solutions with a surface finish criterion are provided for the MCDM problem. H.Q. Nguyen et al. [33] carried out a comparison study on MCDM for the dressing process when internal grinding SKD11 steel. Four MCDM methods, TOPSIS, MARCOS (measurement of alternatives and ranking according to compromise solution), EAMR (evaluation by an area-based method of ranking), and MAIRCA (multi-attributive ideal–real comparative analysis), as well as two weight calculation methods, entropy and MEREC, were used in this study. It can be recognized from the above analysis, that while there have been various applications of MCDM methods for different mechanical machining processes, no studies have been conducted to determine the best dressing mode for external cylindrical grinding.

This paper, hence, presents a study on MCDM for the dressing process in cylindrical external grinding. In this work, three criteria were chosen for the investigation: RS, wheel life T, and roundness Rn. In addition, to solve the MCDM problem, the MABAC method was selected. Furthermore, the MEREC and entropy methods were used to determine the weights of the criteria. As a result, the MABAC method has been successfully used to determine the best dressing mode in external cylindrical grinding. This result is also verified by using TOPSIS and MARCOS methods for comparison.

2. Materials and Methods

2.1. MABAC Method for MCDM

The MABAC method was introduced by Pamucar and Cirovic in 2015. This method has the following characteristics [36]: This is one of the compensatory methods; the attributes are unrelated to one another; the qualitative attributes are transformed into quantitative attributes. This method is commonly used in railway station evaluation, wind farm location selection, and site energy generation technology [36]. In practice, solving this MCDM problem can completely use other MCDM methods such as TOPSIS, MARCOS, etc. However, in this work, the MABAC method was applied to solve the MCDM problem both to determine the best dressing mode for cylindrical external grinding and to compare this method with many used ways in mechanical processing (TOPSIS and MARCOS method).

The steps to solve the MCDM problem by the MABAC method are as follows [36]:

Step 1: Generating the initial matrix by:

$$\mathrm{X}=\left[\begin{array}{c}{r}_{11 }\cdots r_{1j}\cdots r_{1n}\\ ⋮ \ddots ⋮ \ddots ⋮\\ r_1 \cdots r_{ij }\cdots r_{in}\\ ⋮ \ddots ⋮ \ddots ⋮\\ r_{m1} \cdots r_{mj}\cdots r_{mn}\end{array}\right]$$

(1)

In which, m is the alternative number; n is the number of criteria.

Step 2: Determining the normalized values $r_{ij}^{*}$ by:

$$r_{ij}^{*}=\frac{r_{ij}-r_i^{-}}{r_i^{+}-r_i^{-}}$$

(2)

$$r_{ij}^{*}=\frac{r_{ij}-r_i^{+}}{r_i^{-}-r_i^{+}}$$

(3)

In which, i = 1, 2, …, m and j = 1, 2, …, n. In addition, Equation (2) is used if the criterion j is as bigger as better and Equation (3) is used if the criterion j is as smaller as better. In addition, $r_i^{+}=max\left(r_1,r_2,\dots ,r_m\right)$ and $r_i^{-}=min\left(r_1,r_2,\dots ,r_m\right)$.

Step 3: Finding the elements of weighted matrix by:

$$v_{ij}=w_j+w_j\times r_{ij}^{*}$$

(4)

Step4: Calculating the border approximation area matrix:

$${\mathrm{g}}_j={\left({\displaystyle \prod }_{i=1}^m{v}_{ij}\right)}^{1/m}$$

(5)

where in, j = 1, 2, …, n.

Step5: Calculating the distance between the alternatives and the border approximation area by the following Equation:

$$q_{ij}=v_{ij}-{\mathrm{g}}_i$$

(6)

In Equation (6), i = 1, 2, …, m and j = 1, 2, …, n.

Step6: Estimating the total distances of each alternative from the approximate border area:

$$S_i={{\displaystyle \sum }}_{j=1}^n{q}_{ij} i=1, 2,\dots , m$$

(7)

Step7: The order of alternatives is determined by maximizing S.

2.2. Method for Calculation of the Criterion Weight

The weight of the criteria in this study is determined by two methods: MEREC and Entropy. This section explains how to use these methods.

2.2.1. The Entropy Method

When using the entropy method to calculate the weight of the criteria, the following steps should be followed [37]:

Step 1: Computing indicator normalized values.

$$p_{\mathrm{ij}}=\frac{x_{\mathrm{ij}}}{m+{{\displaystyle \sum }}_{i=1}^m{x}_{\mathrm{ij}}^2}$$

(8)

Step 2: Calculating the indicator entropy values.

$$m{e}_j=-{{\displaystyle \sum }}_{i=1}^m\left[p_{ij}\times ln\left(p_{ij}\right)\right]-\left(1-{{\displaystyle \sum }}_{i=1}^m{p}_{ij}\right)\times ln\left(1-{{\displaystyle \sum }}_{i=1}^m{p}_{ij}\right)$$

(9)

Step 3: Determining the criation weight.

$$w_j=\frac{1-m{e}_j}{{{\displaystyle \sum }}_{j=1}^n\left(1-m{e}_j\right)}$$

(10)

2.2.2. The MEREC Method

The MEREC method can be used by following the steps below [38]:

Step 1: Set up the initial matrix as described in step 1 of the MABAC method.

Step 2: Calculating the normalized values by:

$$h_{ij}=\frac{min{x}_{ij}}{x_{ij}} \mathrm{if} \mathrm{the} \mathrm{criterion} j \mathrm{is} \mathrm{as} \mathrm{bigger} \mathrm{as} \mathrm{better}$$

(11)

$$h_{ij}=\frac{x_{ij}}{max{x}_{ij}} \mathrm{if} \mathrm{the} \mathrm{criterion} j \mathrm{is} \mathrm{as} \mathrm{smaller} \mathrm{as} \mathrm{better}$$

(12)

Step 3: Finding the alternative performance S_i by the following Equation [38]:

$$S_i=ln\left[1+\left(\frac{1}{n}{\displaystyle \sum }_j\left|ln\left(h_{ij}\right)\right|\right)\right]$$

(13)

Step 4: Estimating the performance of ith alternative $S_{ij}^{\prime }$ by [38]:

$$S_{ij}^{\prime }=Ln\left[1+\left(\frac{1}{n}{\displaystyle \sum }_{k, k\ne j}^{}\left|ln\left(h_{ij}\right)\right|\right)\right]$$

(14)

Step 5: Finding the removal effect of the jth criterion E_j by:

$$E_j={\displaystyle \sum }_i\left|S_{ij}^{\prime }-S_i\right|$$

(15)

Step 6: Calculating the criation weight by:

$$w_j=\frac{E_j}{{{\displaystyle \sum }}_k{E}_k}$$

(16)

2.3. Method for Determining the Best Dressing Mode for External Grinding SKD11 Tool Steel

2.3.1. Method for Determining the Best Dressing Mode for External Grinding SKD11 Tool Steel

The process to determine the best dressing mode for external grinding SKD11 tool steel is as follows: First, design and conduct an experiment to determine the best dressing mode for external grinding when processing SKD11 tool steel. Because the dressing process has many input parameters, there will be many experiments to determine the best dressing mode. The experimental number is the number of dressing mode solutions. Then, select the best dressing mode by applying an MCDM method (in this case, the MABAC method).

2.3.2. Experimental Work

To solve the MCDM problem, an experiment was performed. The model of the experiment was presented in Figure 1. According to this model, the input parameters of the experiment are the input factors of the dressing process and the grinding process. The input parameters of the dressing process and their levels are described in Table 2. These factors will affect the grinding process, which is characterized by the cutting force, the thermal, the wheel topography, the wheel wear, and the vibration. The grinding process results are shown through the output responses, including the surface roughness, the machining accuracy, the material removal rate, and the wheel life. In this experiment, the surface roughness Ra, the roundness Rn (represents for the accuracy), and the wheel life are selected for the experimental responses.

The experiment was designed according to the Taguchi method with the design L16 orthogonal array (4⁴ × 2²). The experimental matrix is shown in

Table 3. Experimental matrix and output results.

No.	Input Parameters						Output Results
	ar	nr	af	nf	n0	Sd	Ra (μm)	T (min)	Rn (μm)
1	0.025	1	0.005	0	0	1	0.3652	0.9186	0.0127
2	0.03	1	0.01	1	1	1	0.2137	1.0413	0.0087
3	0.025	1	0.015	2	2	1.2	0.1948	1.1215	0.0037
4	0.03	1	0.02	3	3	1.2	0.2417	1.1111	0.0050
5	0.03	2	0.005	1	2	1.2	0.1850	1.2459	0.0090
6	0.025	2	0.01	0	3	1.2	0.2477	1.2667	0.0090
7	0.03	2	0.015	3	0	1	0.2520	1.1782	0.0023
8	0.025	2	0.02	2	1	1	0.2167	1.2251	0.0043
9	0.03	3	0.005	2	3	1	0.3064	1.4878	0.0093
10	0.025	3	0.01	3	2	1	0.3239	1.3724	0.0057
11	0.03	3	0.015	0	1	1.2	0.3406	1.2709	0.0080
12	0.025	3	0.02	1	0	1.2	0.3541	1.1988	0.0050
13	0.025	4	0.005	3	1	1.2	0.3179	1.2273	0.0107
14	0.03	4	0.01	2	0	1.2	0.3126	1.2647	0.0110
15	0.025	4	0.015	1	3	1	0.3259	1.1247	0.0050
16	0.03	4	0.02	0	2	1	0.3634	1.1898	0.0080

. Figure 2 describes the setup of the experimental in which the following equipment was used: the grinding machine: CONDO-Hi-45 HTS (Made in Japan); the grinding wheel: Ct80MV1-G 400x40x203 35 m/s (Made in Vietnam); the dresser: 3908-0088C type 2 (Made in Russia); the surface roughness tester: Mitutoyo 178-923-2A, SJ-201 (Made in Japan). The order of the experiment is as follows: First, the wheel dressing experiment is performed. After dressing, the grinding wheel is used to process the samples with the grinding mode as follows: the workpiece material: SKD11 tool steel; the grinding wheel speed: 29.3 (m/s); the longitudinal feed rate: 1.8 (m/min); the total depth of cut: 0.05 (mm), and the depth of cut: 0.005 (mm/stroke). During the experiment, the SR (in this case is Ra (μm)) and the roundness Rn (μm) are measured after conducting experiments. Besides, the wheel life is determined as stated in [39], specifically as follows: For each wheel dressing mode, the external grinding process is carried out with the above grinding mode. After each experimental run, the grinding time is recorded and the surface roughness of the machined part is measured. The above process is repeated continuously until the surface roughness of the machined part exceeds the allowable value (in this study, 0.5 μm). At this time, the total grinding time of all machined parts is the wheel life T with the given dressing mode. The output responses (Ra, T, and Rn) are given in the three left columns in Table 3.

3. Determining the Best Alternative in Dressing Process for External Grinding

In this section, the MABAC method was applied to solve the MCDM problem with the calculation of the criterion weights using the MEREC method.

3.1. Calculating the Weights for the Criteria

When using the entropy method, the following steps are used to calculate the weight of the criteria (see Section 2.2.1): Equation (8) is used to calculate the normalized values $p_{\mathrm{ij}}$; Equation (9) is used to calculate the entropy value for each indicator $m{e}_j$, and Equation (10) is used to calculate the weight of the criteria w_j (10). The weights of Ra, T, and Rn are 0.4368, 0.3212, and 0.2419, respectively.

When using the MEREC method, the following steps (see Section 2.2.2) can be taken to calculate the weights for the criteria: calculating the normalized values h_j using Equations (11) and (12); Determining Si and $S_{ij}^{\prime }$ using Equations (13) and (14); Calculating the criterion removal effect using Equation (15), and finding the weight of the criteria w_j using Equation (16). In addition, Ra, T, and Rn were found to have weights of 0.3062, 0.4402, and 0.2536, respectively.

3.2. Finding the Best Alternative by Using MABAC Method

The following are the steps to perform MCDM using the MABAC method (see Section 2.1): The initial matrix is generated using Equation (1); after that, the normalized values of $r_{ij}^{*}$ are determined using formula (2) if the criterion j is “the wheel life”and formula (3) if the criterion j is“the surface roughness” or “the roundness”. Next, the normalized weighted values v_ij are calculated using a formula (4). The border approximation area matrix is then computed using Equation (5). After that, using the formula (6), the distance between the alternatives and the border approximation area q_ij is computed. Finally, the total distances between each alternative and the approximate border area S are then determined using a formula (7). S is maximized to determine the ranking of alternatives. Several calculated parameters and ranking of alternatives are presented in

Table 4. Calculated results when using MABAC and entropy methods.

Trial.	vij			gij			qij			Si	Rank
	Ra	T	R	Ra	T	R	Ra	T	R
1	0.437	0.363	0.242	0.601	0.390	0.360	0.164	0.027	0.119	−0.310	16
2	0.505	0.351	0.336	0.601	0.390	0.360	0.096	0.039	0.025	−0.160	15
3	0.677	0.642	0.453	0.601	0.390	0.360	0.076	0.253	0.092	0.421	1
4	0.578	0.333	0.421	0.601	0.390	0.360	0.023	0.057	0.061	−0.019	9
5	0.656	0.385	0.328	0.601	0.390	0.360	0.055	0.005	0.033	0.017	8
6	0.594	0.373	0.328	0.601	0.390	0.360	0.007	0.017	0.033	−0.057	11
7	0.694	0.353	0.484	0.601	0.390	0.360	0.094	0.037	0.123	0.180	3
8	0.621	0.366	0.437	0.601	0.390	0.360	0.020	0.024	0.077	0.072	5
9	0.595	0.500	0.320	0.601	0.390	0.360	0.005	0.110	0.040	0.064	6
10	0.677	0.422	0.406	0.601	0.390	0.360	0.077	0.032	0.045	0.154	4
11	0.592	0.376	0.351	0.601	0.390	0.360	0.009	0.014	0.009	−0.033	10
12	0.621	0.359	0.421	0.601	0.390	0.360	0.020	0.031	0.061	0.050	7
13	0.591	0.352	0.289	0.601	0.390	0.360	0.010	0.038	0.072	−0.120	14
14	0.566	0.403	0.281	0.601	0.390	0.360	0.035	0.013	0.079	−0.101	13
15	0.679	0.438	0.421	0.601	0.390	0.360	0.078	0.048	0.061	0.187	2
16	0.591	0.321	0.351	0.601	0.390	0.360	0.010	0.069	0.009	−0.088	12

when using the MABAC and entropy methods and in

Table 5. Calculated results when using MABAC and MEREC methods.

Trial.	vij			gij			qij			Si	Rank
	Ra	T	R	Ra	T	R	Ra	T	R
1	0.306	0.497	0.254	0.421	0.534	0.378	0.115	0.037	0.124	−0.276	16
2	0.354	0.481	0.352	0.421	0.534	0.378	0.067	0.054	0.026	−0.147	15
3	0.475	0.880	0.474	0.421	0.534	0.378	0.053	0.346	0.097	0.496	1
4	0.405	0.456	0.442	0.421	0.534	0.378	0.016	0.078	0.064	−0.031	9
5	0.460	0.528	0.344	0.421	0.534	0.378	0.038	0.007	0.034	−0.003	8
6	0.416	0.511	0.344	0.421	0.534	0.378	0.005	0.023	0.034	−0.062	11
7	0.487	0.484	0.507	0.421	0.534	0.378	0.066	0.050	0.129	0.145	4
8	0.435	0.501	0.458	0.421	0.534	0.378	0.014	0.033	0.080	0.061	6
9	0.417	0.685	0.335	0.421	0.534	0.378	0.004	0.151	0.042	0.104	5
10	0.475	0.579	0.425	0.421	0.534	0.378	0.054	0.044	0.048	0.145	3
11	0.415	0.515	0.368	0.421	0.534	0.378	0.006	0.020	0.010	−0.036	10
12	0.435	0.492	0.442	0.421	0.534	0.378	0.014	0.043	0.064	0.036	7
13	0.414	0.482	0.303	0.421	0.534	0.378	0.007	0.053	0.075	−0.135	14
14	0.397	0.552	0.294	0.421	0.534	0.378	0.024	0.018	0.083	−0.090	12
15	0.476	0.600	0.442	0.421	0.534	0.378	0.055	0.065	0.064	0.184	2
16	0.414	0.440	0.368	0.421	0.534	0.378	0.007	0.094	0.010	−0.111	13

when using the MABAC and MEREC methods.

4. Results and Discussions

From the calculated results (Table 4 and Table 5), the following remarks were given:

-

The 3rd alternative has provided the largest index. That means it is the best alternative and the optimum dressing parameters are: n_r = 3, a_r = 0.04 (mm), a_f = 0.005 (mm), n_f = 2, n₀ = 2, and S_d = 1 (m/min.).

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The proposed optimal dressing mode has all three components: coarse dressing, fine dressing, and non-feeding dressing. That proves the role of fine dressing and non-feeding dressing. This can be explained with the illustration of Figure 3 as follows: after rough dressing, the wheel surface is very undulating, and the wheel topography is unstable (Figure 3a). When grinding with this mode, the wheel will wear quickly, and the surface roughness and the roundness are high (see Table 3—alternative 1). However, the wheel surface is less undulating, and the wheel topography is more stable after fine (Figure 3b) and non-feeding dressing (Figure 3c). As shown in Figure 3b, after fine dressing, the wheel topography was noticeably flatter than that after rough dressing (Figure 3a). In addition, after non-feeding dressing (Figure 3c), although the grinding wheel surface has the same maximum protrusion height of abrasive grains of 64 (µm) as after fine dressing (Figure 3b), the wheel topography was significantly flatter than that after fine dressing. So, non-feeding dressing reduces the wear of the grinding wheel. As a result, the 3rd alternative has a long wheel life as well as a low surface roughness and roundness.

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To verify the results of applying the MABAC method, two methods, TOPSIS and MARCOS, were used. The TOPSIS method was selected as it is a very old method. This method was presented by Ching-Lai Hwang et al. in 1993 [41]. The MARCOS method was chosen because it is a very new method. It was proposed in 2020 by Stević, Ž. et al. [42]. In addition, both mentioned methods have been applied to determine the best solution for mechanical machining processes such as turning, milling, grinding, electrical discharge machining, etc. [43]. The steps to apply TOPSIS and MARCOS methods to solve the MCDM problem are shown in [33]. The priority index and ranking of alternatives when using the MABAC, TOPSIS, and MARCOS methods are shown in

Table 6. Priority index and ranking when the weight calculation by entropy method.

Trial.	MABAC		TOPSIS		MARCOS
	Si	Rank	Ri	Rank	f(Ki)	Rank
1	−0.3097	16	0.0494	16	0.0204	16
2	−0.1599	15	0.3368	13	0.0228	15
3	0.4209	1	0.8882	1	0.0435	1
4	−0.0194	9	0.5878	7	0.0273	9
5	0.0172	8	0.3952	11	0.0307	6
6	−0.0566	11	0.3592	12	0.0266	11
7	0.1804	3	0.7214	2	0.0425	2
8	0.0724	5	0.6530	4	0.0312	5
9	0.0639	6	0.3954	10	0.0297	8
10	0.1541	4	0.6325	5	0.0353	4
11	−0.0326	10	0.4276	8	0.0269	10
12	0.0504	7	0.6166	6	0.0302	7
13	−0.1200	14	0.2461	14	0.0254	14
14	−0.1012	13	0.2290	15	0.0255	13
15	0.1866	2	0.6821	3	0.0365	3
16	−0.0876	12	0.4086	9	0.0255	12

when using the entropy method and in

Table 7. Priority index and ranking when the weight calculation by MEREC method.

Trial.	MABAC		TOPSIS		MARCOS
	Si	Rank	Ri	Rank	f(Ki)	Rank
1	−0.27647	16	0.0367	16	0.0211	16
2	−0.14691	15	0.3405	13	0.0229	15
3	0.49609	1	0.8889	1	0.0438	1
4	−0.03072	9	0.6180	7	0.0266	9
5	−0.00262	8	0.4585	9	0.0290	8
6	−0.06243	11	0.4011	12	0.0259	11
7	0.144716	4	0.7842	2	0.0398	2
8	0.061298	6	0.6963	4	0.0302	5
9	0.104289	5	0.4131	11	0.0302	6
10	0.145346	3	0.6815	5	0.0335	4
11	−0.03564	10	0.4623	8	0.0263	10
12	0.035771	7	0.6609	6	0.0291	7
13	−0.13474	14	0.3034	14	0.0245	13
14	−0.08992	12	0.2681	15	0.0255	12
15	0.183893	2	0.7283	3	0.0348	3
16	−0.11064	13	0.4500	10	0.0244	14

when using the MEREC method for calculating the weight of the criteria. Figure 4 also shows a comparison of the results obtained using the three MCDM methods with the two mentioned weight calculation methods. From the figure and these tables, it is obvious that all three methods agree on the same result—the 3rd alternative is the best—which proves that the MABAC method can be applied to solve the MCDM problem in the dressing process for external grinding. Furthermore, the MEREC and the entropy method can be used to calculate the weight of criteria when using the MABAC method.

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To compare the degree of association between ranks obtained using various MCDM methods, the Spearman’s rank correlation coefficient (R) was used. This coefficient is calculated as follows [27]:

$$R=1-\frac{6·{{\displaystyle \sum }}_{i=1}^n{D}_i^2}{n·\left(n^2-1\right)}$$

(17)

In which n is the number of alternatives, and D is the rank difference.

The Spearman’s rank correlation coefficient for rankings obtained using various methods is shown in

Table 8. Spearman’s rank correlation coefficient.

Spearman’s Rank Correlation Coefficient
Using Entropy Method		Using MEREC Method
MABAC and TOPSIS	MABAC and MARCOS	MABAC and TOPSIS	MABAC and MARCOS
0.995	0.999	0.996	0.999

.

According to Table 8, the highest correlation coefficient is 0.999 for MARBAC and MARCOS when both the entropy and MEREC methods were used for calculating the weights of the criteria, and the lowest is 0.995 for MABAC and TOPSIS when the weights of the criteria were calculated by entropy method. The correlations obtained between these methods are generally very good, compared to 0.96 in [28] and 0.83 in [29].

5. Conclusions

The results of an MCDM study on identifying the appropriate dressing mode for external grinding SKD11 tool steel using the MABAC method were presented in this study. In the study, the entropy and MEREC methods were used to calculate the weight of the criteria. Besides, six process factors, including the coarse dressing depth, the coarse dressing passes, the fine dressing depth, the fine dressing passes, the non-feeding dressing, and the dressing feed rate were chosen for the exploration. Moreover, for the experimental design, the Taguchi method with L16 orthogonal array (4⁴ × 2²) was chosen. The following conclusions can be drawn from the study results:

• The results of using the MABAC method to solve the MCDM problem in the dressing process for external grinding SKD11 tool steel have been investigated for the first time.
• To verify the results of applying the MABAC method, two methods, TOPSIS and MARCOS were used. As a result, all three methods identified that option three is the best for the dressing process.
• The Spearman’s rank correlation coefficient has been found to be extremely useful in assessing the correlation between various ranking methods.
• The optimal wheel dressing parameters to achieve the minimum surface roughness, the maximum wheel life, and the minimum roundness simultaneously are: n_r = 3, a_r = 0.04 (mm), a_f = 0.005 (mm), n_f = 2, n₀ = 2, and S_d = 1 (m/min.).