## 3 Results and Discussion  
### Analysis of the Means and S/N Ratios of the Results  
Polishing efficiency and torque were measured by the Taguchi design of experiments for the different factors as shown in Table 3. In order to minimize the error, each experiment is repeated four times. The total polishing time (\(T_{p}\)) for polishing of one workpiece was 60 s. Optimization of the control factors is performed by the calculated S/N ratios for the \(PE\) and \(T\). The highest \(PE\) and the lowest \(T\) values are desirable for better system performance on lower production costs. Therefore, S/N condition higher the best for \(PE\) and lower the best for the \(T\) is used as in Equations (3) and (2) respectively. Table 4 shows the response tables of the average response of the S/N ratios, which analyze the effect of the control factors (\(T_{g}\), \(\omega\), \(F_{z}\), and \(V_{f}\)) on the response of \(PE\) and \(T\). It reveals all the levels based on the S/N ratios for the control factors that provides highest \(PE\) as \(T_{g}\) at level 1 (S/N = \(-\)2.451), \(\omega\)  
at level 3 (\(S\!/N=-2.066\)), \(F_{z}\) at level 3 (\(S\!/N=-1.312\)), and \(V_{f}\) at level 1 (\(S\!/N=-2.642\)). Similarly, for the lowest \(T\), the best factor levels and \(S\!/N\) ratios are \(T_{g}\) at level 1 (\(S\!/N=9.049\)), \(\omega\) at level 1 (\(S\!/N=9.398\)), \(F_{z}\) at level 1 (\(S\!/N=12.278\)), and \(V_{f}\) at level 3 (\(S\!/N=9.160\)). Delta and the rank determine which of these four factors has the greatest impact on the response. Delta measures the magnitude of the impact by subtracting the lowest average response value of a factor from its highest value. Rank assigns the order number to the factors in highest to lowest impact depending on the delta values. For \(PE\), \(F_{z}\) has highest impact (delta: \(S\!/N=3.447\), and rank = 1) and \(V_{f}\) has lowest impact (delta: \(S\!/N=0.246\), and rank = 4). Likewise, for the \(T\), \(F_{z}\) also has the highest impact (delta: \(S\!/N=6.164\), and rank = 1), however \(T_{g}\) has the lowest impact (delta: 0.018, \(S\!/N=0.357\), and rank = 4). The graphical representation (main effects plot) of the levels of the factors in Table 4 is shown in Figures 6 and 7. These main effect plots show the optimum values of the control factors to achieve the highest \(PE\) and lowest \(T\). The main effect is called the difference in the means due to various levels within a factor. If the graph line is horizontal then there is no main effect present for the levels of a factor but the line with higher slop or difference between vertical points will have a higher main effect. For both polishing efficiency and torque, normal force shows the graphical lines with higher slopes, and therefore it has the highest main effect. The main goal of the experimentation is to find the control factor levels that minimize the noise factors on the responses. Optimal polishing parameters of the control factors for maximize the \(PE\) and minimizing the \(T\) can be easily determined from these graphs. The best level for each control factor was found according to the highest \(S\!/N\) ratio in the levels of those input parameters (control factors). The control factors range in the experiments for the \(T_{g}\) is 0.019-0.02 Nm, for \(\omega\) is 3500-4500 rpm, for \(F_{z}\) is 8-16 N, and for \(V_{f}\) is 5-15 mm/s. \(T_{g}\), 0.019 Nm; \(\omega\), 4500 rpm; \(F_{z}\), 16 N, and \(V_{f}\), 5 mm/s are best for the polishing efficiency and \(T_{g}\), 0.019 Nm; \(\omega\), 3500 rpm; \(F_{z}\), 8 N, and \(V_{f}\), 15 mm/s. The most significant factor is a force for both responses.