Three-wire measurement calculation method for pitch diameter of external threads in planetary roller screws

行星滚柱丝杠外螺纹中径三针测量计算方法

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

Received: 13 May 2025

Abstract

To improve the measurement accuracy of the external thread diameter in planetary roller screw mechanisms (PRSM) and to mitigate the influence of machining errors on the results of the traditional three-point measurement method, a contact equation between the measured thread and the measuring needle is established, using a set of calculation equations for the external thread diameter that incorporate machining errors, which are then solved. By considering the critical factors, including pitch deviation, half-thread thickness deviation and thread side angle deviation, contact points are predicted by using the assembly relationship between the thread and the measuring needle. The contact equation between the measured thread and the measuring needle is derived by using the principle of continuous surface tangency. The calculated values of the thread diameter in the three-point method, with and without considering machining errors, are solved separately, and the impact of thread machining errors on the correction values of the external thread diameter is investigated. The results reveal the following correlation between thread machining errors and the correction values of the diameter: the increase in pitch deviation results in a monotonically decreasing correction value; the increase in half-thread thickness deviation leads to a monotonically increasing correction value; under the simultaneous deviation of both thread side angles, the correction value exhibits a non-linear trend of initially decreasing and then increasing with the increasing of deviation angle; in asymmetric deviation conditions on one side, while maintaining a similar non-linear variation trend, the variation amplitude is significantly reduced.

摘要

为提高行星滚柱丝杠(PRSM)外螺纹中径的测量精度, 解决加工误差对传统三针法测量结果的影响, 建立被测螺纹与量针的接触方程和计入加工误差的外螺纹中径计算方程组并进行求解。综合考虑螺距偏差、半牙厚偏差及牙侧角偏差等关键因素, 通过螺纹-量针装配关系预测接触点。运用曲面连续相切原理推导出被测螺纹与测量量针的接触方程, 分别求解忽略/计入加工误差时的三针法中径计算值, 研究了螺纹加工误差对外螺纹中径修正值的影响。结果表明, 螺纹加工误差与中径修正值存在以下关联规律: 螺距偏差增大导致中径修正值单调递减; 半牙厚偏差增加导致修正值单调递增; 双侧牙侧角同步偏差条件下, 中径修正值随偏差角增大呈现先减小后增大的非线性变化趋势; 单侧非对称偏差工况中, 虽保持相似的非线性演变趋势, 但变化幅度显著下降。