渐开线斜齿轮进行适当修形后，可以有效地改善其啮合性能，降低噪音和延长齿轮的使用寿命。利用建立未修缘以及含不同齿廓修缘量的斜齿轮有限元模型，通过轮齿承载接触分析得到不同修缘量斜齿轮的静态传递误差和啮合刚度；在考虑齿顶修缘影响的基础上，建立了具有12个自由度的平行轴系斜齿轮转子系统动力学模型，将得到的时变啮合刚度应用于系统动力学模型中，研究不同修缘量对斜齿轮传动振动响应的影响规律。研究结果表明：在一定范围内，随着修缘量的增加，斜齿轮系统的径向振动和啮合力幅值明显降低，但当修缘量达到21 μm后其幅值有增大趋势。研究结果对确定斜齿轮的最优修形量和分析修形斜齿轮的振动特性具有重要意义。

Proper modification of the involute gear could effectively improve its meshing performance, lower the noise and extend its service life. A finite element model of helical gear pair in mesh with different amounts of tip relief was built by ANSYS parameter design language (APDL). Static transmission error and time-varying meshing stiffness with the different amounts of tip relief were calculated by loaded tooth contact analysis. Then, a 12-degree of freedom dynamic model of a parallel shaft helical gear meshing was established with considering the impact of tip relief. And the time-varying meshing stiffness was introduced into the dynamic model to research the influence of tip relief on the vibration response of helical gearing. The results show that the amplitude of radial vibration and meshing force of helical gear system decrease obviously with the increase of tip relief within a certain range, but it has an increase tendency when the tip relief reaches 21 μm. The results are significant to determine the optimal gear profile modification and analyze the vibration characteristics of repaired helical gears.

国家国际科技合作项目（2013DFA71330）。