# Determining the Best Dressing Parameters for External Cylindrical Grinding Using MABAC Method
## 4 Results and Discussions  
From the calculated results (Tables 4 and 5), the following remarks were given:  
* The 3 rd 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), \(n_{f}=2\), \(n_{0}=2\), and \(S_{d}=1\) (m/min.). * 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 (\(\upmu\)m) 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 3 rd alternative has a long wheel life as well as a low surface roughness and roundness. * 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 [PERSON] et al. in 1993 [PERSON] et al. (1993). The MARCOS method was chosen because it is a very new method. It was proposed in 2020 by [PERSON], [PERSON] et al. (2020). 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. (2020). The steps to apply TOPSIS and MARCOS methods to solve the MCDM problem are shown in (2020). The priority index and ranking of alternatives when using the MABAC, TOPSIS, and MARCOS methods are shown in Table 6 when using the entropy method and in Table 7 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 3 rd 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. * To compare the degree of association between ranks obtained using various MCDM methods, the [PERSON]'s rank correlation coefficient (\(R\)) was used. This coefficient is calculated as follows (2019): \[R=1-\frac{6\cdot\sum_{i=1}^{n}D_{i}^{2}}{n\cdot(n^{2}-1)}\] (17) In which \(n\) is the number of alternatives, and \(D\) is the rank difference. The [PERSON]'s rank correlation coefficient for rankings obtained using various methods is shown in Table 8.  
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 (2019) and 0.83 in (2020). Figure 3: Wheel topography after dressing [40]. (a) After rough dressing; (b) after fine dressing; (c) after non-feeding dressing.