# 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
Figure 13: Transmission errors under different schemes. The maximum equivalent stress data of the intermediate tooth flank are extracted and processed in order to obtain the variation in the maximum equivalent stress of a single pair of teeth from the pre-engagement phase to the post-disengagement phase. In the figure, Zone A corresponds to the pre-engagement phase, Zone B corresponds to the toe contact phase, Zone C corresponds to the full-tooth contact phase, Zone D corresponds to the heel contact phase, and Zone E corresponds to the post-disengagement phase. In Zone A and Zone E, the maximum equivalent stress is observed to be relatively low, with minimal variation. In Zone B and Zone D, the maximum equivalent stress exhibits a notable increase, accompanied by a considerable degree of fluctuation. In Zone C, the maximum equivalent stress is observed to be lower than that in Zone B and Zone D, and the fluctuation amplitude also demonstrates a relatively stable state. In each stage from the post-engagement phase to the pre-disengagement phase (illustrated in the figure as Zone B, Zone C, and Zone D), two-tooth and three-tooth meshing occurs in each zone. Figure 16 illustrates the maximum equivalent stress of the pinion and gear with and without the segmented parabolic modification of the beveloid gear. The black line represents the change without modification, while the red line represents the change with modification. Figures 17 and 18 depict the distribution of the integrated equivalent stress of the tooth flank of the pinion and gear with and without modification. Figure 19 illustrates the distribution of the integrated root stress of the tooth flank of the pinion and gear. The red gridline represents the root stress state without modification, while the green gridline represents the root stress state with modification. Figure 15: Trend of contact area and maximum equivalent stress of the beveloid gear pair. Figure 16: Variation trend of maximum equivalent stress. (**a**) Pinion; (**b**) gear. Figure 17: Comprehensive equivalent stress distribution without modification. (**a**) Pinion; (**b**) gear. Figure 18: Comprehensive equivalent stress distribution with modification. (**a**) Pinion; (**b**) gear. As illustrated in the figures, the post-modification pinion tooth flank stress is reduced by approximately 20% during the heel contact phase compared to the pre-modification. Furthermore, in the full-tooth contact stage, the post-modification gear tooth flank stress is reduced by approximately 30% compared to the pre-modification. Additionally, the degree of fluctuation is more stable compared to the pre-modification. The gear of the beveloid gear pair, in its unmodified state, continues to exhibit a significant edge load and root stress bias phenomenon during the meshing process. In contrast, the modification has been observed to reduce the edge load by approximately 90% and effectively mitigate the effects of unbalanced loads. This demonstrates that the modification can enhance the meshing performance of the beveloid gear and improve the smoothness during the transmission process.