Analysis of meshing characteristics of incomplete gear pair in planetary roller screw mechanism

行星滚柱丝杠不完整齿轮副啮合特性分析

School of Mechanical Engineering, Northwestern Polytechnical University, Xi'an 710072, China

Received: 12 March 2025

Abstract

Based on the roller thread equation, the spur tooth profile equation, and coordinate transformation relationships, the surface equations of the incomplete gear pairs in the planetary roller screw mechanism were established. Combining the gear meshing principle with the surface equations of incomplete gear pairs, a model for calculating the contact point positions and contact line lengths of incomplete gear pairs was proposed. A finite element model for incomplete gear pair was introduced to validate the correctness of the present model. The influence of the initial angle and width of the spur gear on the meshing characteristics of incomplete gear pairs was analyzed. The results show that under the same meshing radius, the maximum and minimum contact line lengths on each spur tooth structure are not affected by the initial angles of the roller's spur tooth profile and the roller's spur thread. The analysis shows that when the tooth width of the incomplete gear pair is an integer multiple of the roller thread lead, under the same meshing radius, the contact line lengths on any spur tooth structure are identical.

摘要

根据滚柱螺纹方程、直齿齿廓方程与坐标变换关系, 建立行星滚柱丝杠中不完整齿轮副曲面方程。基于齿轮啮合原理与不完整齿轮副曲面方程, 求解不完整齿轮副的接触点位置与接触线长度。建立不完整齿轮副的有限元模型, 验证了不完整齿轮副啮合模型的正确性。分析行星滚柱丝杠不完整齿轮副的啮合特性, 结果表明: 不完整齿轮副在同一啮合半径下, 各直齿结构上接触线长度的最大值与最小值不受滚柱直齿齿廓起始角度与滚柱直齿螺纹起始角度的影响; 当不完整齿轮副齿宽为滚柱螺纹导程的整数倍时, 同一啮合半径下, 任一直齿结构上的接触线长度均相同。