# Surface Quality Evolution Model and Consistency Control Method of Large Shaft Multi-Pass Grinding
## 4 Consistency Control Method of Surface Quality in Rough Machining  
### The Principle of Consistency Control Method of Surface Quality  
Since the surface quality is affected by actual grinding depth, a consistency control method of surface quality is proposed based on adjustment of actual grinding depth. Considering the grinding depth is quite small in practice, the adjustment of actual grinding depth is only performed in rough grinding.  
The principle of the adjustment of actual grinding depth is shown in Figure 9. The profile of the shaft before a grinding pass and the ideal profile after a grinding pass are shown in Figure 9a. The blue area is the tolerance range. The maximum and minimum values of the actual grinding depth allowed at \(z_{0}\) are \(\max(a_{p}(z_{0}))\) and \(\min(a_{p}(z_{0}))\), respectively.  
Figure 8: Prediction performance of surface quality evolution models: (**a**) surface roughness, (**b**) glossiness.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Models**} & \multirow{2}{*}{**Ginding Depth**} & \multirow{2}{*}{\begin{tabular}{c} **Previous Grinding** \\ **Surface Quality** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **Average Prediction Error** \\ **of Surface Roughness** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Average Prediction** \\ **Error of Glossiness** \\ \end{tabular} } \\ \hline Proposed model & Actual & Considered & 5.5\% & 5.1\% \\ Model 1 & Nominal & Considered & 12.4\% & 13.2\% \\ Model 2 & Actual & Ignored & 15.3\% & 16.8\% \\ Model 3 & Nominal & Ignored & 24.2\% & 25.3\% \\ \hline \hline \end{tabular}
\end{table}
Table 3: The prediction performance of different models for surface quality indexes.  
Therefore, the allowable range of the actual grinding depth along the \(z\)-direction can be obtained, as shown in Figure 9b.  
Several points \(z_{1}\), \(z_{2}\)...\(z_{n}\) are selected along the \(z\)-direction. According to the actual grinding depth range allowed at each point and the surface quality evolution model established in Section 4, the adjustable region of surface roughness and glossiness can be obtained as shown in Figure 10. The maximum values and minimum values of surface roughness and glossiness of the adjustable region are \(Ra_{0}\), \(Ra_{1}\), \(G_{0}\), and \(G_{1}\).  
The comprehensive index of surface quality, \(C\), is defined as:  
\[C=\frac{Ra_{0}-Ra}{2(Ra_{0}-Ra_{1})}+\frac{G-G_{1}}{2(G_{0}-G_{1})} \tag{6}\]  
The adjustable range of the comprehensive index of surface quality will have two situations, as shown in Figure 11. In Figure 11a, the minimum value of the upper bound of the adjustable region is completely contained within the adjustable region. Therefore, \(C\) of each point can reach \(C_{0}\) by adjusting the actual grinding depth. In Figure 11b, the minimum value of the upper bound of the adjustable region is not fully contained within  
Figure 10: The adjustable region of (**a**) surface roughness and (**b**) glossiness.  
Figure 9: The principle of the adjustment of actual grinding depth: (**a**) the profile of the shaft before a grinding pass and the ideal profile after a grinding pass, (**b**) the allowable range of the actual grinding depth.  
the adjustable region. Then, the points that can obtain \(C_{0}\) are adjusted to obtain \(C_{0}\), and the points that cannot obtain \(C_{0}\) are adjusted to the value closest to \(C_{0}\).  
The process of obtaining the desired comprehensive index \(C_{i}\) for point \(z_{i}\) by grinding depth adjustment is shown in Figure 12.  
In Figure 12, \(l\) is the iteration step length. After obtaining the actual grinding depth values of each point, the actual grinding depth curve along the \(z\)-direction is generated by B-spline interpolation.