## 4 Analysis of Surface Morphology and Surface Roughness after Grind-Hardening
### Formation and Variations of Surface Roughness in Grind-Hardening  
The above grinding surface morphology analysis revealed a certain unevenness in the surface after grind-hardening. Therefore, five measurements were taken in the cutting-in area, middle area and cutting-out area of the specimens during surface roughness measurement and analysis under the OLYMPUS-DSX500 optical digital microscope. To reduce the measurement error, the maximum and minimum values of each area were removed and the mean of the remaining measurement data was taken as the roughness measurement result. The test matrix and surface roughness measurements are presented in Table 6.  
The influence patterns of each interaction term in the grinding parameters on the surface roughness were obtained through the Box-Behnken response surface analysis, as shown in Figures 6-8. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Samples** & **1** & **2** & **3** & **4** & **6** & **7** & **8** & **9** \\ \hline \(Ra(\mu\text{m})\) & 1.87 & 1.56 & 2.39 & 2.29 & 2.03 & 2.32 & 2.3 & 1.28 \\ \hline
**Samples** & **10** & **11** & **12** & **13** & **15** & **16** & **17** & \\ \hline \(Ra(\mu\text{m})\) & 1.81 & 1.85 & 2.54 & 1.85 & 1.95 & 1.91 & 2.1 & \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Surface roughness \(Ra\) measurements of the test based on response surface methodology. Figure 8: Grinding line speed–workpiece feed speed response surface and contour map. Figure 6: Cutting depth–workpiece feed speed response surface and contour map. Figure 7: Cutting depth–grinding line speed response surface and contour map. Figure 6 shows the response surface and contour map of the surface roughness \(Ra\) after grind-hardening at a cutting depth \(a_{p}\) and workpiece feed speed \(v_{w}\) when the grinding speed is at the zero level, i.e., \(v_{s}\) = 30 m\(\cdot\)s\({}^{-1}\). As can be observed from the response surface plot, the surface roughness tends to increase gradually with the increase of cutting depth and workpiece feed speed. According to the grinding mechanism, the increases in cutting depth and workpiece feed speed increase the number of effective dynamic grinding edges and the maximum undeformed chip thickness, which, in turn, increases the depth of the grinding marks, the grinding force and the grinding heat. As a result, the plastic deformation and stress of the material increase, thus rendering the surface increasingly rough and uneven, i.e., the surface roughness \(Ra\) increases. According to the contour map, the effect of the cutting depth on surface roughness is greater than that of the workpiece feed speed under the parameters in this test. Figure 7 shows the response surface and contour map of surface roughness after grinding at different cutting depths and grinding line speed when the workpiece feed speed is at the zero level, i.e., \(v_{w}\) = 0.4 m/min. Figure 8 shows the response surface and contour map of surface roughness after grinding at different grinding line speeds and workpiece feed speeds when the cutting depth is at the zero level, i.e., \(a_{p}\) = 0.3 mm. As can be observed, with the increase in grinding speed, the surface roughness shows a firstly decreasing and then increasing trend. However, the changes are slight, and the influence is not significant. The reason for this is that as the grinding speed increased, the per-unit-of-time grinding edge density on the contact surface between the workpiece and the grinding wheel increased, and the maximum undeformed chip thickness of the abrasive grains decreased. As a result, the grinding force decreased and the surface roughness tended to decrease. However, due to the dimensional effect, the chip strain increased and the grinding temperature tended to rise. Thus, the plastic deformation increased, increasing the surface roughness instead. Therefore, the effect of grinding speed on surface roughness is not significant under the parameters of this test.