行星滚柱丝杠副主曲率计算与接触特性分析

doi:10.3901/JME.2020.21.140

机械工程学报 ›› 2020, Vol. 56 ›› Issue (21): 140-148.doi: 10.3901/JME.2020.21.140

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行星滚柱丝杠副主曲率计算与接触特性分析

乔冠¹, 刘更², 马尚君²

1. 内蒙古工业大学机械工程学院呼和浩特 010051;
2. 西北工业大学陕西省机电传动与控制工程实验室西安 710072

收稿日期:2019-11-17 修回日期:2020-08-10 出版日期:2020-11-05 发布日期:2020-12-19
作者简介:乔冠(通信作者),男,1990年出生,讲师。主要研究方向为行星滚柱丝杠副传动。E-mail:qiaoguan@imut.edu.cn 刘更,男,1961年出生,博士,教授,博士研究生导师。主要研究方向为机械系统动力学、机械传动、接触力学和机电作动系统。E-mail:npuliug@nwpu.edu.cn 马尚君,男,1980年出生,副研究员。主要研究方向为行星滚柱丝杠副传动和机电作动系统设计。E-mail:mashangjun@nwpu.edu.cn
基金资助:
国家自然科学基金(51875458,51905428)、内蒙古自然科学基金(2020BS05003)和内蒙古工业大学科学研究(ZZ201903,BS2020014)资助项目。

Principal Curvature Calculation and Contact Characteristics Analysis of the Planetary Roller Screw Mechanism

QIAO Guan¹, LIU Geng², MA Shangjun²

1. School of Mechanical Engineering, Inner Mongolia University of Technology, Huhhot 010051;
2. Shaanxi Engineering Laboratory for Transmissions and Controls, Northwestern Polytechnical University, Xi'an 710072

Received:2019-11-17 Revised:2020-08-10 Online:2020-11-05 Published:2020-12-19

摘要/Abstract

摘要： 根据丝杠、滚柱和螺母螺旋滚道曲面特点,建立了通用化的法截面内零件的轮廓方程和滚道螺旋曲面方程。通过将滚道截面的原点定义在对应零件的中心轴上,避免了现有模型中将滚道截面原点定义在螺纹牙轮廓中心而带来的繁琐坐标变换问题。其次,利用微分几何原理推导了丝杠-滚柱接触侧和螺母-滚柱接触侧在相应接触位置的主曲率,与传统的基于等效球法计算行星滚柱丝杠副主曲率进行了对比。利用赫兹接触理论求解了滚柱与滚道间的主曲率差、接触椭圆面积及最大接触应力,并讨论了行星滚柱丝杠副结构参数对接触特性的影响规律。结果表明:丝杠和螺母滚道在某一主平面内的主曲率不是零,使用等效球模型计算主曲率会带来较大误差;增大螺纹螺距使得滚柱两接触侧的主曲率差变大,但几乎不影响接触椭圆的面积和滚柱螺纹曲面两接触侧的最大接触应力;增大法向牙侧角会使两接触侧的主曲率差和接触面积同时减小,但过大的法向牙侧角会导致接触应力和摩擦力增大。

关键词: 行星滚柱丝杠副, 法截面, 螺旋曲面方程, 主曲率, 赫兹接触

Abstract: The generalized contour equation and spiral surface equation of the screw, roller and nut are developed, based on their structural characteristics. By defining the origin of raceway section on the central axis of the corresponding part, the tedious coordinate transformation caused by defining the origin of raceway section on the contour center of the thread tooth in the existing model is avoided. Besides, the principal curvatures at the corresponding contact positions on the screw-roller contact interface and the nut-roller contact interface are deduced using the principle of differential geometry, and then compared with the traditional method based on the equivalent ball model. The main curvature difference, contact ellipse area and maximum contact stress are solved by using Hertzian contact theory, and the influence of the structural parameters on the contact characteristics are discussed. The results show that the main curvatures of the screw/nut raceway in a principal plane are not zero, which means the equivalent ball model when calculating the principal curvature would bring a large error. Increasing the pitch of planetary roller screw mechanism increases the main curvature difference on the two contact interfaces of the roller, but hardly affects the contact ellipse area and the maximum contact stress. Increasing the normal flank angle of thread causes the main curvature difference and the contact area to decrease simultaneously, but a big normal flank angle of thread leads to an increased contact stress and thus friction.

Key words: planetary roller screw mechanism, normal section, spiral surface equation, principal curvature, Hertzian contact

中图分类号:

TH132

乔冠, 刘更, 马尚君. 行星滚柱丝杠副主曲率计算与接触特性分析[J]. 机械工程学报, 2020, 56(21): 140-148.

QIAO Guan, LIU Geng, MA Shangjun. Principal Curvature Calculation and Contact Characteristics Analysis of the Planetary Roller Screw Mechanism[J]. Journal of Mechanical Engineering, 2020, 56(21): 140-148.

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行星滚柱丝杠副主曲率计算与接触特性分析

Principal Curvature Calculation and Contact Characteristics Analysis of the Planetary Roller Screw Mechanism

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