### Numerical Simulation Process Analysis and Scheme Formulation of Warm Forging-Finishing  
The main process parameters affecting the forming quality of spiral bevel gear forging are the forging striking speed, die preheating temperature, friction factor and workpiece heating temperature. According to the principle of the single variable, three different groups of forging striking speed, die preheating temperature, friction factor and workpiece heating temperature were set, and the differences of numerical simulation results under different combinations of process parameters were studied and analyzed, so as to find out the influence law of various process parameters on the forging-forming quality of spiral bevel gears. The reasonable combination of process parameters is determined to guide the warm forging of spiral bevel gears, providing theoretical support for the warm-forging precision-forming process of spiral bevel gears.  
Combined with the practical production experience, a reasonable range of process parameter values was selected to better analyze the influence law of the parameter in the warm-forging process of spiral bevel gear. According to the relevant data, the temperature of warm forging of 45 steel is 923-1073 K, and the heating temperatures of workpieces are 923 K, 1023 K and 1073 K, respectively. The forging striking speed of the die-forging hydraulic press is generally 1-to-50 mm/s, and the forging striking speeds are 10 mm/s, 20 mm/s and 30 mm/s, respectively. Considering the heat transfer performance between the blank and the die, the preheating temperature range of the warm-forging-finishing die is usually 423-573 K, so the preheating temperature of the die is 473 K, 523 K and 573 K, respectively. Lubricant materials in warm-forging-finishing are graphite, MoS2, PbO, etc., and the friction coefficient is 0.008-0.2, so the friction factors are selected to be 0.1, 0.15 and 0.2, respectively.  
The numerical simulation process scheme formulated in this paper is shown in Table 2.  
At the same time, the specific process parameter combinations of 12 kinds of process schemes used in the numerical simulation were determined. In addition, the forging die used in the simulation experiment in this paper adopts the semi-closed forging die structure, and the forging simulation geometry is shown in Figure 5. Due to the influence of the gear mold structure, the forging flying edge of the finished gear is distributed in the direction of the gear back cone, as shown in Figure 6.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Experimental Scheme**} & \multicolumn{4}{c}{**Process Parameters**} \\ \cline{2-5}  & **Forging Striking** & **Die Preheating** & **Friction** & **Workpiece Heating** \\  & **Speeds (mm/s)** & **Temperature (K)** & **Factor** & **Temperature (K)** \\ \hline \hline \multirow{3}{*}{Scheme I} & \multirow{3}{*}{20} & \multirow{3}{*}{523} & \multirow{3}{*}{0.15} & 923 \\  & & & & 1023 \\ \cline{1-1}  & & & & 1073 \\ \hline \hline \multirow{3}{*}{Scheme II} & \multirow{3}{*}{20} & \multirow{3}{*}{523} & \multirow{3}{*}{0.15} & \multirow{3}{*}{1023} \\  & & & & 0.2 \\ \cline{1-1}  & & & & 0.2 \\ \hline \hline \end{tabular}
\end{table}
Table 2: The numerical simulation process scheme.