基于ease-off的弧齿锥齿轮齿面高阶接触分析方法  

High-order contact analysis method of spiral bevel gear tooth surface based on ease-off

作　　者：陈鹏 王三民[1] 李飞 CHEN Peng;WANG Sanmin;LI Fei(School of Mechanical Engineering,Northwestern Polytechnical University,Xi’an 710072,China)

机构地区：[1]西北工业大学机电学院,西安710072

出　　处：《航空动力学报》2024年第6期238-247,共10页Journal of Aerospace Power

摘　　要：为应对弧齿锥齿轮二阶接触分析方法的不足与其高阶接触理论实现的复杂问题,基于ease-off拓扑曲面方程与弧齿锥齿轮齿面方程的结合以及传动误差与接触迹线和ease-off之间的解析关系,提出以传动比高阶导数和接触迹线短程曲率为高阶接触参数的离散齿面的高阶接触分析方法,并建立基于有限差分的简便计算方法。结果表明,高阶齿面的传动比高阶导数波动值分别为0.0031、0.0019与0.001,数值反映齿面形貌的全局特性;接触线短程曲率波动值分别为0.0000769、0.000586和0.000127,说明沿接触迹线的齿面接触过程的复杂性。结果不仅验证了离散齿面高阶接触分析方法的正确性与有效性,而且说明该方法降低了高阶接触参数的计算难度,为齿面全局设计提供了可能。In order to deal with the shortcomings of the second-order contact analysis method of spiral bevel gears and the complex problems of its high-order contact theory realization,based on the combination of ease-off topological surface equation and tooth surface equation of spiral bevel gears and the analytical relationship between transmission error and contact trace and ease-off,a high-order contact analysis method for discrete tooth surfaces with high-order contact parameters of high-order derivative of transmission ratio and short-range curvature of contact trace was proposed,and a simple calculation method based on finite difference was established.The results showed that the fluctuation values of the high-order derivative of the transmission ratio of the high-order tooth surface were 0.0031,0.0019 and 0.001,respectively,which reflected the global characteristics of the tooth surface morphology.The short-range curvature fluctuation values of the contact line were 0.0000769,0.000586 and 0.000127,respectively,indicating the complexity of the tooth surface contact process along the contact trace.The results not only verified the correctness and effectiveness of the discrete tooth surface high-order contact analysis method,but also showed that the method reduced the calculation difficulty of high-order contact parameters,providing the possibility for the global design of tooth surface.

关 键 词：弧齿锥齿轮 ease-off 高阶接触分析 有限差分法 全局接触问题 

分 类 号：V232.8[航空宇航科学与技术—航空宇航推进理论与工程] TH132.41[机械工程—机械制造及自动化]