## 4 Performance Indicator Analysis  
To analyze the impact of the number of finishing operations on the performance indicator \(G\), it is necessary to express the components in the Equation (21). To ensure that there are no traces of previous processing on the grinding surface, it is necessary to remove a layer of metal from the part \(\Omega\) (Figure 5):  
\[\Omega=10^{-3}\cdot(C_{0}\cdot Ra_{0}-C_{1}\cdot Ra_{1}) \tag{26}\]  
Abrasive grain size \(l_{0}\) is not the only factor determining the roughness of the surface of the part after grinding, so the relationship between them cannot be presented in an unambiguous form. Reducing the roughness of the surface of the part is possible:  
1. Through reduction of the depth of penetration of single grains into the metal at the same granularity as that of the wheel, \(l_{0}=const\);
2. By changing the grain size of the wheel, the bundle, and/or the grinding mode, and changing the composition of the coolant. At the same time, the dependence \(l_{0}\) from \(Ra\) can be expressed by the equation: \[l_{0}=a_{0}\cdot R_{a}^{a_{1}}\] (27) where \(a_{0}\) and \(a_{1}\) are regression coefficients. Consider the effect of surface roughness after grinding on the performance indicator when \(l_{0}=const\) and \(l_{0}=25.5\cdot R_{a}^{0.72}\) (Figure 6). In the calculations in accordance with the experimental data, the values of the coefficients were assumed to be equal: \(K_{Q}=2\); \(K_{b}=0.65\); \(K_{R}=0.8\); and \(C_{0}=C_{1}=2\). The radius of rounding of abrasive grains was assumed to be equal to: \(\rho=0.077\cdot l_{0}\) um [12]. Figure 5: Scheme of surface roughness before and after grinding with a fine-grained wheel. The analysis of Figure 6 shows that the productivity indicator decreases with a decrease in surface roughness after grinding. Higher values of the performance indicator correspond to the case when the reduction of roughness is achieved by reducing the grain size of the wheel, the grinding mode, and the composition of the coolant. Therefore, the use of fine-grained wheels is a more effective method of reducing roughness than nursing. Considered dependencies \(\Omega\) and \(l_{0}\) on the preliminary and required roughness make it possible to calculate the performance indicator during grinding of parts, not only with one finishing operation, but also with two, three, or more operations. When grinding in several operations, the performance indicator can be determined by the equation:  
\[G=\frac{1}{\frac{1}{C_{1}}+\frac{1}{C_{2}}+...+\frac{1}{C_{n}}} \tag{28}\]  
where \(n\) is number of finishing grinding operations; \(G_{1}\)... \(G_{n}\) is the performance indicator of each individual operation. Expressing the performance indicator of individual operations by the Formula (21) we obtain:  
\[G=\frac{103}{\frac{\Omega_{0}\cdot l_{0}^{2}}{K_{Q}\cdot(1-K_{b})\cdot f_{cp} \cdot V_{K}\cdot\left(1+\frac{V_{0}}{60V_{K}}\right)\cdot\sqrt{K_{k}\cdot R_{ 1}}}+...+\frac{\Omega_{0n-l_{0}^{2}}}{K_{Q}\cdot(1-K_{b})\cdot f_{cp}\cdot V _{K}\cdot\left(1\pm\frac{V_{0}}{60V_{K}}\right)\cdot\sqrt{K_{k}\cdot R_{1}}}} \tag{29}\]  
When substituting the values into Equation (29)--\(f_{cp}\) from Equation (12), \(\Omega\) from Equation (26), and \(l_{0}\) from Equation (27)--we obtain:  
\[G=\frac{187.5}{\frac{Ra_{0}-Ra_{01}}{Ra_{01}^{2}}+\frac{Ra_{01}-Ra_{02}}{Ra_{0 2}^{2}}+...+\frac{Ra_{0n-1}-Ra_{1}}{Ra_{1}^{18}}} \tag{30}\]  
where \(Ra_{01}\), \(Ra_{02}\),..., \(Ra_{0n}\)--surface roughness after the first, second, etc. operations. Consider the example of grinding a part to obtain surface roughness (\(Ra_{1}=0.025\) um; \(Ra_{0}=0.50\) um), the effect on the performance indicator of the number of operations and surface roughness after each operation.