# The Simulation Analysis of Cutting Characteristics and Chip Formation Mechanism in Gear Skiving
## 4 Finite Element Analysis of the Gear Skiving Cutting Process  
This study simulates the gear skiving cutting process through the use of the SPH method in LS-DYNA software. The SPH method is based on the Lagrangian formula, which discretizes continuous objects into movable particles that have the same physical properties as objects. The core is the interpolation algorithm, and the interaction between the particles is described by an interpolation function. Through the calculation of the interpolation function, the core estimation value of each particle can be obtained, and then the differential form is converted into the integral form by using the conservation law of  
Figure 6: Tool inclination angle, tangential cutting speed, and normal cutting speed in gear skiving.  
continuum dynamics; thus the mechanical behavior of the whole system is obtained [17]. The units used in this simulation are Kg, mm, ms, KN, and GPa.  
The parameters of the skiving tool and internal gear are shown in Table 1. Modeling the actual number of teeth for the simulation would require substantial computation time. Due to the periodic nature of the geometries of the skiving tool and the gear workpiece, this simulation uses a single-tooth structure for both the tool and the workpiece. The workpiece material is 45 steel, it is modeled using the Johnson-Cook material model with the parameters listed in Table 2, and the friction coefficient is set to 0.2. The tool material is cemented carbide, and the elastic model is selected for the tool material in the simulation, with the parameters listed in Table 3.  
The SPH method differs significantly from traditional finite element simulation methods and offers advantages in many situations, especially in addressing large deformation problems of metal materials. Thus, the SPH method is increasingly used in the field of cutting processing. The chip formation process in gear skiving involves significant deformations, making it difficult to form chips using traditional mesh methods due to the large deformations in the workpiece material, which can lead to mesh failure.  
Due to the periodic nature of the geometries of the skiving tool and the gear workpiece, only one tooth of the tool and one tooth slot of the workpiece are considered in this analysis to reduce computational load. The 3D models of the skiving tool and workpiece are imported into LS-PREPOST for meshing, which is an advanced pre-processing and post-processing program that is compatible with LS-DYNA. The tool uses a tetrahedral mesh with a mesh size of 0.1 mm. The workpiece uses an SPH mesh with a particle distance of 0.1 mm.  
During the simulation of the gear skiving process, the freedoms of the workpiece tooth in \(\mathrm{X_{w}}\), \(\mathrm{Y_{w}}\), \(\mathrm{Z_{w}}\) and its rotations around \(\mathrm{X_{w}},\mathrm{Y_{w}}\) are constrained, allowing rotation only around the \(\mathrm{Z_{w}}\) axis. Similarly, the freedoms of the tool tooth in \(\mathrm{X_{c}}\), \(\mathrm{Y_{c}}\), \(\mathrm{Z_{c}}\) and its rotations around \(\mathrm{X_{c}}\), \(\mathrm{Y_{c}}\) are constrained, allowing rotation only around the \(\mathrm{Z_{c}}\) axis, as shown in Figure 7. The rotational speeds of the tool and workpiece are set according to the transmission ratio to simulate the gear skiving process. The gear rotating speed is 500 rpm, and the feed rate per revolution is 1 mm.  
\begin{table}
\begin{tabular}{l l} \hline \hline
**Parameter** & **Value** \\ \hline Density (kg/mm\({}^{3}\)) & \(7.85\times 10^{-6}\) \\ Shear Modulus (GPa) & 78.5 \\ Young’s Modulus (GPa) & 206 \\ Poisson’s Ratio & 0.3 \\ A (GPa) & 0.507 \\ B (GPa) & 0.32 \\ N & 0.28 \\ C & 0.064 \\ M & 1.06 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Workpiece material parameters.  
\begin{table}
\begin{tabular}{l l} \hline \hline
**Parameter** & **Value** \\ \hline Density (kg/mm\({}^{3}\)) & \(7.85\times 10^{-6}\) \\ Shear Modulus (GPa) & 210 \\ Poisson’s Ratio & 0.3 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Tool material parameters.