一种弧齿锥齿轮时变啮合刚度和传动误差半解析计算方法

平 廖; 静 魏; 爱强 张; 卫青 张

doi:10.16578/j.issn.1004.2539.2019.12.009

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一种弧齿锥齿轮时变啮合刚度和传动误差半解析计算方法

设计计算 | 更新时间：2022-10-25

- 一种弧齿锥齿轮时变啮合刚度和传动误差半解析计算方法
- A Semi-analytical Calculation Method for Time-varying Meshing Stiffness and Transmission Error of Spiral Bevel Gear
- 机械传动 2019年43卷第12期页码：50-56
- 作者机构：
  
  1.重庆大学机械传动国家重点实验室，重庆 400044
  2.重庆理工大学汽车零部件先进制造技术教育部重点实验室，重庆 400054
- 作者简介：
  
  廖平（1993— ），男，江西赣州人，硕士研究生，从事机械传动理论及机械动力学研究。
  魏静（1978— ），男，江苏徐州人，博士，教授，从事机械传动理论及机械动力学研究。
- 基金信息：
  
  国家自然科学基金(51775058)
- DOI：10.16578/j.issn.1004.2539.2019.12.009
  中图分类号：
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廖平,魏静,张爱强等.一种弧齿锥齿轮时变啮合刚度和传动误差半解析计算方法[J].机械传动,2019,43(12):50-56.

Liao Ping,Wei Jing,Zhang Aiqiang,et al.A Semi-analytical Calculation Method for Time-varying Meshing Stiffness and Transmission Error of Spiral Bevel Gear[J].Journal of Mechanical Transmission,2019,43(12):50-56.
廖平,魏静,张爱强等.一种弧齿锥齿轮时变啮合刚度和传动误差半解析计算方法[J].机械传动,2019,43(12):50-56. DOI： 10.16578/j.issn.1004.2539.2019.12.009.

Liao Ping,Wei Jing,Zhang Aiqiang,et al.A Semi-analytical Calculation Method for Time-varying Meshing Stiffness and Transmission Error of Spiral Bevel Gear[J].Journal of Mechanical Transmission,2019,43(12):50-56. DOI： 10.16578/j.issn.1004.2539.2019.12.009.

摘要

弧齿锥齿轮时变啮合刚度传统计算方法大多采用有限元静态分析方法，但需计算多次，且采用节点弹性变形平均值计算的单齿啮合刚度存在较大误差。为此，改进了弧齿锥齿轮时变啮合刚度计算方法，在传统计算方法上引入单个节点啮合刚度，将工作齿面各个节点啮合刚度叠加，得到单齿啮合刚度，计算精度更高；基于有限元显式动态分析计算弧齿锥齿轮时变啮合刚度和传动误差，计算1次而不需要进行多次有限元分析，减少了整个计算时间周期。研究了不同负载转矩下时变啮合刚度和传动误差变化规律，分析了接触椭圆长轴长度、接触轨迹方向两个接触参数对时变啮合刚度和传动误差的影响。研究结果表明，时变啮合刚度和传动误差随负载转矩增大而增大，但时变啮合刚度峰-峰值和传动误差峰-峰值（PPTE）随负载转矩增大而变小；随着接触椭圆长轴长度增大，时变啮合刚度和传动误差呈增大趋势；随着接触轨迹方向增大，时变啮合刚度存在突增现象，而传动误差变化很小。

Abstract

The traditional method of calculating time-varying meshing stiffness of spiral bevel gears mostly adopted finite element static analysis method, but it needed to be calculated many times, also the single tooth meshing stiffness calculated by the mean value of the node elastic deformation has a large error. For this reason, a calculation method for time-varying meshing stiffness of spiral bevel gear is improved. The meshing stiffness of single node was introduced into the traditional calculation method, and the meshing stiffness of each node on the working tooth surface is superimposed to obtain single tooth meshing stiffness, the calculation accuracy is higher. The time-varying meshing stiffness and transmission error of spiral bevel gears are calculated based on explicit dynamic finite element analysis. The calculation time period is reduced by calculating once without repeating multiple finite element analysis. The variation law of time-varying meshing stiffness and transmission error under different load torques is researched. Also the influence of two contact parameters such as contact ellipse axis length and contact path direction on time-varying meshing stiffness and transmission error are analyzed. The research results show that the time-varying meshing stiffness and transmission error increase with the increase of load torque, but the peak-to-peak value of time-varying meshing stiffness and transmission error decrease with the increase of load torque. The time-varying meshing stiffness and the peak-to-peak value of transmission error (PPTE) are improved with the increase of contact ellipse long axis length. As the contact path increase, the time-varying meshing stiffness has a sudden increase, and the transmission error changes little.

关键词

弧齿锥齿轮时变啮合刚度传动误差接触椭圆长轴长度接触轨迹方向

Keywords

Spiral bevel gearTime-varying meshing stiffnessTransmission errorContact ellipse long axis lengthContact path direction

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