# Effect of Axial Modification on the Meshing Performance of Involute Developid Gear Pair
## 4 Meshing Performance Analysis of the Beveloid Gear Pair with Axial Modification
### Influence of Axial Modification on Dynamic Meshing Performance  
The objective of this study is to examine the meshing effect of the beveloid gear pair in the context of a single gear modification. Therefore, two additional schemes have been introduced: the ordinary pinion-modified gear meshing scheme and the modified pinion-ordinary gear meshing scheme. The aim is to assess the extent to which these schemes influence the transmission error of the beveloid gear pair. The modification amounts and modification lengths of the gear pair are presented in Table 4, which refers to Scheme 2. It should be noted that Scheme 7 employs the same parameters as Scheme 2. The calculation of the modified beveloid gear pair is performed in accordance with the transmission error calculation method described in the literature [26]. The transmission error of the beveloid gear pair during the transmission process was calculated using Equation (8). \[\varphi_{TE}=\left(\varphi_{g}-\varphi_{g}^{0}\right)-\left(\varphi_{p}-\varphi _{p}^{0}\right)\left(z_{1}/z_{2}\right), \tag{8}\]  
where \(\varphi_{TE}\) represents the transmission error, while \(\varphi_{p}\) and \(\varphi_{g}\) denote the actual rotational angles of the pinion and the gear, respectively. The variables \(\varphi_{p}{}^{0}\) and \(\varphi_{g}{}^{0}\) represent the initial rotational angles of the pinion and the gear, respectively, and \(z_{1}\) and \(z_{2}\) correspond to the number of teeth on the pinion and the gear. Figures 13 and 14 illustrate the comparative analysis of the transmission errors and the peak-to-peak values of the transmission error, both in the absence of modification and following the implementation of the three modification schemes. As illustrated in the figure, the transmission error is reduced to a certain extent following modification, with Scheme 7 demonstrating a greater reduction than Scheme 8 and Scheme 9; however, the peak-to-peak value of the transmission error remains relatively high. A comprehensive comparative analysis, based on the objective of reducing the transmission error of the beveloid gear and thus improving the driving condition, indicates that Scheme 7 is an optimal choice for optimising the meshing performance. \begin{table}
\begin{tabular}{c c c c} \hline
**Schemes** & **Modification Parameter** & **Pinion** & **Gear** \\ \hline \multirow{2}{*}{Scheme 4} & Amount (\(\mu\)m) & 10.0 & 10.0 \\  & Length (mm) & 5.2 & 4.8 \\ \hline \multirow{2}{*}{Scheme 5} & Amount (\(\mu\)m) & 0.0 & 20.0 \\  & Length (mm) & 0.0 & 4.8 \\ \hline \multirow{2}{*}{Scheme 6} & Amount (\(\mu\)m) & 20.0 & 0.0 \\  & Length (mm) & 5.2 & 0.0 \\ \hline \end{tabular}
\end{table} 
Table 4: Modification scheme group (3). Based on the aforementioned analysis, the modification of the beveloid gear is undertaken in accordance with the parameters delineated in Scheme 2. The ensuing investigation pertains to the alterations in the dynamic meshing performance of the beveloid gear pair, both before and after the modification. A drive simulation of the beveloid gear pair was conducted before and after modification. During the meshing process of the gear pair, the quantity of contact between the tooth flank grid cells is extracted. The alteration in the contact area of the gear pair can be reflected in the change in the contact number of grid cells, as illustrated in Figure 15. Given that the contact ratio of the beveloid gear pair is typically greater than 2, the lowest point in the number of contacts correlates with double-tooth meshing of the gear pair, while the highest point corresponds to triple-tooth meshing of the gear pair. As the model is non-full-tooth, single-tooth meshing occurs at the beginning and end of the entire mesh process, with a correspondingly small contact area. The result is not representative of the correct dynamic performance of the meshing; therefore, the following section is solely concerned with the intermediate tooth data. Figure 14: Peak-to-peak value of transmission error under different schemes.