# Simulation of Surface Topography Considering Cut-in Impact and Tool Flank Wear
## 7 Results  
The cutting impact vibration with the cutting parameters (Test 1) in the the \(x\) and \(y\) directions are shown in Figure 9.  
The simulation results of maximum cutting vibration values with/without impact vibration are compared with the experimental results for cutting parameters (Test 1-5) as shown in Figure 10. The maximum cutting vibration values in the \(x\) direction were changed into absolute values. As seen in Figure 10, the simulation results of cutting vibration considering impact vibration (Simu.2) are more precise. The simulation error of cutting vibration in the \(x\) direction can be reduced by 33.13% in maximum (Test 5). The simulation error of cutting vibration in the \(y\) direction can be reduced by 25.02% at the maximum (Test 2). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Test No.** & **Spindle Speed** & **Cutting Depth** & **Cutting Width** & **Feed per Tooth** \\  & **(r/min)** & **(mm)** & **(mm)** & **(mm/tooth)** \\ \hline
1 & 5000 & 0.25 & 0.3 & 0.1 \\
2 & 5000 & 0.3 & 0.25 & 0.10 \\
3 & 4000 & 0.25 & 0.2 & 0.12 \\
4 & 4000 & 0.25 & 0.25 & 0.1 \\
5 & 4000 & 0.3 & 0.3 & 0.15 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The experimental scheme. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Workpiece** & \(K_{tc}\) **(N/mm\({}^{2}\))** & \(K_{rc}\) **(N/mm\({}^{2}\))** & \(K_{tc}\) **(N/mm)** & \(K_{rc}\) **(N/mm)** \\ \hline Cr12 MoV & 1842.2 & 1842.2 & 1842.2 & 134.9 \\ hardened steel & 1842.2 & 1842.2 & 1842.2 & 134.9 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The cutting force coefficients. Figure 8: Ball-end milling cutters with different wear states (**a**) VB = 0; (**b**) VB = 87 um; (**c**) VB = 121 um; (**d**) VB = 164 um. VB—the tool wear. The simulation results of total cutting vibration with cutting parameters (Test 1) in the \(x\) and \(y\) directions are shown in Figure 11a,c. Cutting vibration obtained from cutting experiments is shown in Figure 11b,d. It can be found from Figure 11 that the vibration signal obtained by simulation and experiment has a good consistency in both trend and value. Therefore, the vibration simulation data can be used to simulate the dynamic characteristics of the machining process, which lays a foundation for studying the influence of milling vibration on the surface morphology. The simulation and experimental results of surface morphology and roughness for cutting parameters (Test 1) are shown in Figure 12.  
Figure 10: Simulation (Simu.1 and Simu.2) and experiment (Exe.) of cutting vibration: Simu.1-cutting vibration without impact vibration; Simu.2-cutting vibration with impact vibration; cutting vibration (**a**) \(x\) direction, (**b**) \(y\) direction; error (**c**) \(x\) direction, (**d**) \(y\) direction. Figure 9: Impact vibration. Figure 11: Simulation and experiment of cutting vibration. (**a**) simulation in the \(x\) direction; (**b**) experiment in the \(x\) direction; (**c**) simulation in the \(u\) direction; (**d**) experiment in the \(u\) direction. Figure 12: Surface morphology (**a**) experiment (Ra = 0.273 um); (**b**) without cutting vibration (Ra = 0.221 um); (**c**) without impact vibration (Ra = 0.240 um); (**d**) with cutting vibration (Ra = 0.247 um)  
It can be seen from Figure 12 that the dynamic characteristics of the cutting system affect the texture structure of the machined surface. Due to the influence of cutting system vibration, the cutting contour of adjacent surface topologies in the feed direction is different, which is caused by the slight up-down displacement of the two edges of the ball-end milling cutter, as shown in Figure 12a. A is the surface profile formed when the vibration of the cutting system is maximum, and B is the surface profile formed when the vibration of the cutting system is minimum. It can be seen from Figure 12 b-d that, when the vibration of cutting system is considered, the surface topography obtained by simulation is closer to that obtained by actual machining process.