## 6 Conclusions  
In this study, grind-hardening tests were designed based on the response surface methodology, theoretical analysis was conducted and the prediction model for the surface roughness of grind-hardening was developed. The following conclusions have been obtained:  
Figure 11: BP neural network training process curve.  
Figure 12: Test values compared with the predictions.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multicolumn{3}{c}{**Ginding Parameters**} & \multicolumn{1}{c}{**Test Values**} & \multicolumn{1}{c}{**Predictions \(Ra^{\prime}\)**} & \multicolumn{1}{c}{**Absolute**} & \multicolumn{1}{c}{**Relative Errors**} \\ \(v_{w}\) **(m\(\cdot\)min\({}^{-1}\))** & **(m\(\cdot\)s\({}^{-1}\))** & **(m\(\cdot\)s\({}^{-1}\))** & **\(Ra\) (\(\mu\)m)** & **(\(\mu\)m)** & **Errors (\(\mu\)m)** & **(\%)** \\
**X1** & **X2** & **X3** & & & & & \\ \hline
0.4 & 0.4 & 30 & 2.15 & 2.0750 & \(-\)0.075 & 3.49\% \\
0.2 & 0.2 & 35 & 1.75 & 1.8957 & 0.1457 & 8.33\% \\
0.4 & 0.3 & 25 & 2.23 & 2.2165 & \(-\)0.0135 & 0.61\% \\ \hline \hline \end{tabular}
\end{table}
Table 8: Test values of grind-hardening compared with the predictions of BP neural network.  
1. Uneven morphology exists on the surface after grinding, which can be roughly divided into the cutting-in, middle and cutting-out areas. In the cutting-in area, the grinding texture is clearer, with much bonding and trace damage. In the middle area, the surface is relatively flat, with a small amount of bonding and some damage. In the cutting-out area, the grinding texture is coarse, with more microcracks and grinding damage.
2. Under the conditions in this test, the surface roughness tends to increase with the increase of cutting depth and workpiece feed speed, while the variation over the grinding line speed is not significant.
3. The effects of grinding parameters (grinding line speed, workpiece feed speed and cutting depth) on grinding surface roughness in order of significance are cutting depth > workpiece feed speed > grinding line speed.
4. It was not possible to build a response surface regression prediction model. The response surface methodology-BP neural network-based surface roughness prediction model for grind-hardening is established, which has a mean relative error of 2.38% (only one has an error of 10.86%) thus, it can be used to predict the surface roughness after grind-hardening. This study could provide a theoretical and experimental basis for the engineering applications and grinding surface quality improvement of grind-hardening.  
Conceptualization, G.W., C.S. and C.W.; methodology, C.W. and C.S.; software, C.W.; validation, C.S. and C.W.; formal analysis, C.W.; investigation, C.W.; resources, C.W.; data curation, C.W.; writing--original draft preparation, C.W.; writing--review and editing, G.W. and C.S.; visualization, C.W. and C.S.; supervision, G.W.; project administration, G.W.; funding acquisition, G.W. All authors have read and agreed to the published version of the manuscript.  
This study was supported by the National Natural Science Foundation of China (No.50275066) and the National Major Science and Technology Project (No.2013 ZX04009-030).  
Not applicable.  
The authors declare that they have no conflict of interest.