# The Simulation Analysis of Cutting Characteristics and Chip Formation Mechanism in Gear Skiving
## 2 Kinematic Model and Chip Morphology Analysis of Gear Skiving  
Gear skiving is a gear processing method with crossed axes and dual-degree-of-freedom meshing, known for its high production efficiency and precision. The efficiency of gear skiving mainly depends on the rotational speeds of the skiving tool and the gear workpiece, as well as the feed per revolution of the gear workpiece. Due to the high rotational speeds of both the tool and the workpiece during skiving, this characteristic ensures extremely high processing efficiency, significantly reducing processing costs. In practice, the main factor limiting the extensive application of gear skiving is the service life of the skiving tools. Improper use of the tools can severely affect their lifespan. Therefore, it is essential to deeply analyze the cutting characteristics of gear skiving to guide the design of the skiving process. The kinematic coordinate system of internal gear skiving is illustrated in Figure 1. In the figure, \(S_{c}(X_{c},Y_{c},Z_{c})\) and \(S_{w}(X_{w},Y_{w},Z_{w})\) represent the coordinate systems of the skiving tool and the workpiece. Their relative positions can be described by three parameters: \(\Sigma,\ a,\ L\). Figure 1: Schematic diagram of the gear skiving kinematic coordinate system. Here, '\(\Sigma^{\prime}\) represents the crossed axes angle, which is the angle between the axes of the tool and the workpiece; '\(a^{\prime}\) represents the center distance, which is the distance between the axes of the tool and the workpiece in the \(X_{w}\) direction; and '\(L^{\prime}\) represents the offset distance, which is the offset of the tool's origin relative to the workpiece's origin in the \(Y_{w}\) direction. For ease of subsequent analysis, the cutting edges of the skiving tool are named \(A\), \(T\), and \(R\), respectively. Cutting edge \(A\) is the approaching edge of the cutting tooth that first cuts into the workpiece in the rotational direction of the tool, \(R\) is the recessing edge that is the last edge that separates from the workpiece, and \(T\) is the top edge. The skiving cutting motion mainly includes three components: the workpiece rotates around its own axis with a velocity of \(\mathbf{\omega}_{w}\), the tool rotates around its own axis with a velocity of \(\mathbf{\omega}_{c}\), and the workpiece moves along its own axis with a feed velocity of \(\mathbf{f}\). The relationship among \(\mathbf{\omega}_{w}\), \(\mathbf{\omega}_{c}\), and \(\mathbf{f}\) can be expressed as:  
\[\mathbf{\omega}_{w}=\frac{Z_{c}}{Z_{w}}\cdot\mathbf{\omega}_{c}+\frac{\mathbf{f}}{p_{ z}}\cdot 2\pi \tag{1}\]  
where \(\mathbf{Z}_{w}\) and \(\mathbf{Z}_{c}\) are the number of teeth of the workpiece and the tool, and \(p_{z}\) is the lead of the workpiece. The cutting thickness of the tool is a crucial parameter affecting the cutting load, directly influencing tool wear. To study the variation law of cutting thickness during the gear skiving process, a simulation analysis of the undeformed chip geometry formation was conducted in UG. The basic parameters of the skiving tool and gear workpiece are shown in Table 1. The gear workpiece has an involute tooth profile. The cutting simulation results are illustrated in Figure 2. \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Skiving Tool** & **Gear Workpiece** \\ \hline Number of teeth & 56 & 113 \\ Module & 1.8 & 1.8 \\ Helix angle (\({}^{\circ}\)) & 0 & 14 \\ Rake angle (\({}^{\circ}\)) & 0 & / \\ Pressure angle (\({}^{\circ}\)) & / & 20 \\ Tip circle radius (mm) & 53.4 & 104.4 \\ Root circle radius (mm) & 48 & 108.5 \\ Center distance (mm) & & 44.822 \\ Crossed axes angle (\({}^{\circ}\)) & & 16.941 \\ Offset distance (mm) & & 114.139 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters of the skiving tool and gear workpiece. Figure 2: Undeformed chip geometry of gear skiving. The skiving tool and workpiece rotate relative to each other based on the transmission ratio, creating relative sliding between the cutting tooth and the workpiece, and thereby forming the cutting motion.