# Optimization of Replaced Grinding Wheel Diameter for Minimum Grinding Cost in Internal Grinding
## 4 Results and Discussion  
The influences of input parameters on the optimal replaced diameter are illustrated in Figure 4. From this figure, the optimal replaced diameter \(D_{e,op}\) is powerfully contingent on the original wheel diameter. Also, it depends on the dressing depth of cut \(a_{ed}\), the life of wheel \(T_{w}\), the cost of the grinding machine \(C_{m,h}\) and the grinding wheel cost \(C_{gw}\). In addition, \(\mathrm{D_{e,op}}\) is not affected by the width of wheel \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline
**StdOrder** & **RunOrder** & **CenterPt** & **Blocks** & \(\mathbf{D_{0}}\) & \(\mathbf{W_{gw}}\) & \(\mathbf{R_{ld}}\) & \(\mathbf{a_{ed}}\) & \(\mathbf{T_{w}}\) & \(\mathbf{W_{pd}}\) & \(\mathbf{C_{m,h}}\) & \(\mathbf{C_{gw}}\) & \(\mathbf{D_{e,op}}\) \\ \hline
97 & 1 & 1 & 1 & 10 & 8 & 1.2 & 0.05 & 10 & 0.03 & 10 & 0.3 & 7.84 \\
82 & 2 & 1 & 1 & 40 & 8 & 1.2 & 0.05 & 30 & 0.01 & 10 & 5 & 32.2 \\
51 & 3 & 1 & 1 & 10 & 40 & 1.2 & 0.05 & 30 & 0.03 & 4 & 5 & 5.33 \\
89 & 4 & 1 & 1 & 10 & 8 & 1.2 & 0.15 & 30 & 0.01 & 10 & 5 & 5.86 \\
108 & 5 & 1 & 1 & 40 & 40 & 1.2 & 0.15 & 10 & 0.03 & 10 & 5 & 25.69 \\
104 & 6 & 1 & 1 & 40 & 40 & 4 & 0.05 & 10 & 0.03 & 10 & 5 & 28.24 \\... & & & & & & & & & & & & \\
54 & 127 & 1 & 1 & 40 & 8 & 4 & 0.05 & 30 & 0.03 & 4 & 0.3 & 36.23 \\
9 & 128 & 1 & 1 & 10 & 8 & 1.2 & 0.15 & 10 & 0.01 & 4 & 5 & 3.23 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Experimental plans and output response. Figure 3: Creation of factorial design. \(\mathrm{W_{gw}}\), the ratio of the length to the diameter of work-piece \(\mathrm{R_{ld}}\) and the radial grinding wheel wear per dress \(\mathrm{W_{pd}}\). The Normal Plot of the standardized effects is described in Figure 5. From this graph it is known that the initial diameter of grinding wheel (factor A), the life of wheel (factor C), the cost of the grinding machine (factor G) and the interactions AE, GH, AG and EH have positive standardized effects. That means if their values increase, the optimal replaced diameter raises. Also, the cost of the wheel (factor H), the dressing depth of cut (factor D) and the interactions AH, AD, DH and EG have negative standardized effects. If their values grow, the optimum replaced diameter drops. Figure 6 presents the Pareto chart for the optimal replaced diameter. It can be seen from the figure that the reference line crosses characterized factors A (the initial diameter of wheel), H (the cost of the wheel), E (the life of wheel), G (the cost of the grinding machine), D (the dressing depth of cut) and the interactions AH, AE, EF, AE, GH, AG, EH, AD, DH and EG. Therefore, these parameters are significant with the optimum diameter. To find the significant effects on the optimum replaced diameter, the insignificant effects which have the P-values higher than 0.05 were ignored. Consequently, it can be found from the figure that the initial diameter of wheel \(D_{0}\), the dressing depth of cut \(a_{ed}\), the life of wheel \(T_{w}\), the cost of the grinding machine \(C_{m,h}\), the cost of the wheel \(C_{gw}\) and the interactions between \(D_{0}\) and \(a_{ed}\), \(T_{w}\), \(C_{m,h}\) and \(C_{gw}\); \(a_{ed}\) and \(C_{gw}\); \(T_{w}\) and \(C_{m,h}\) and \(C_{gw}\) and between \(C_{m,h}\) and \(C_{gw}\) have significant effects on the response (Figure 6). In addition, the following equation was proposed to calculate the optimum replaced wheel diameter:  
\[ \begin{array}{l}D_{op}=-0.58+0.814\cdot D_{0}+2.44\cdot a_{ed}-0.0004\cdot T_{w }-0.0692\cdot C_{mh}-0.8698\cdot C_{gw}-0.4021\cdot D_{0}\cdot a_{ed}+\\ +0.003865\cdot D_{0}\cdot T_{w}+0.01034\cdot D_{0}\cdot C_{mh}-0.03742\cdot D_{0 }\cdot C_{gw}-1.678\cdot a_{ed}\cdot C_{gw}-0.00339\cdot T_{w}\cdot C_{mh}+\\ +0.0164\cdot T_{w}\cdot C_{gw}+0.06769\cdot C_{mh}\cdot C_{gw}\end{array}  \tag{14}\]  
Figure 4: Main effects plot for optimum replaced grinding wheel diameter. Figure 5: Normal Plot for \(\mathrm{D_{e,op}}\).