循环式行星滚柱丝杠副啮合机理与接触特性分析

doi:10.3901/JME.2025.05.202

机械工程学报 ›› 2025, Vol. 61 ›› Issue (5): 202-213.doi: 10.3901/JME.2025.05.202

• 机器人及机构学 • 上一篇

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循环式行星滚柱丝杠副啮合机理与接触特性分析

乔冠¹, 刘付乐¹, 唐术锋^1,2, 李宗学¹, 付晓军³

1. 内蒙古工业大学机械工程学院呼和浩特 010051;
2. 内蒙古自治区特殊服役智能机器人重点实验室呼和浩特 010051;
3. 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:2024-04-30 修回日期:2024-08-22 发布日期:2025-04-15
作者简介:乔冠，男，1990年出生，博士，副教授，硕士研究生导师。主要研究方向为行星滚柱丝杠传动设计与研制。E-mail：qiaoguan@imut.edu.cn;唐术锋(通信作者)，男，1981年出生，博士，教授，博士研究生导师。主要研究方向为动力学与控制、极端环境机电装备设计及系统集成技术、特殊服役机器人。E-mail：tangshufeng@imut.edu.cn
基金资助:
国家自然科学基金(52265009)、内蒙古自然科学基金（2024LHMS05009）、内蒙古自治区高等学校“青年科技英才支持项目”(NJYT24028)、自治区直属高校基本科研业务费项目(JY20220284, JY20230024)和中国博士后科学基金(2024M762956)资助项目。

Meshing Theory and Contact Characteristics Analysis of the Recirculating Planetary Roller Screw Mechanism

QIAO Guan¹, LIU Fule¹, TANG Shufeng^1,2, LI Zongxue¹, FU Xiaojun³

1. School of Mechanical Engineering, Inner Mongolia University of Technology, Hohhot 010051;
2. Inner Mongolia Key Laboratory of Special Service Intelligent Robotics, Hohhot 010051;
3. Shaanxi Engineering Laboratory for Transmissions and Controls, Northwestern Polytechnical University, Xi'an 710072

Received:2024-04-30 Revised:2024-08-22 Published:2025-04-15

摘要/Abstract

摘要： 根据循环式行星滚柱丝杠副滚柱无螺旋升角的结构特点，建立了丝杠、滚柱和螺母的螺旋滚道曲面方程和空间啮合模型，计算了循环式行星滚柱丝杠副的啮合点位置与轴向间隙，并讨论了牙侧角与螺距对啮合点位置与轴向间隙的影响规律。其次，根据微分几何原理推导了循环式行星滚柱丝杠副的主曲率计算公式，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，并讨论了牙侧角与螺距对接触特性的影响规律。结果表明：丝杠-滚柱侧的啮合点位置总是偏离丝杠与滚柱轴线之间的连线，丝杠和滚柱上的啮合点偏向螺纹牙顶；当滚柱与螺母的牙侧角相等时，滚柱-螺母侧的啮合点位置将位于二者螺纹中径的切点处。分析循环式行星滚柱丝杠副接触特性时，可用零件的名义半径代替啮合半径来近似计算主曲率；牙侧角增大时，滚柱两接触侧的主曲率差和接触椭圆面积逐渐减小，螺纹牙上的最大接触应力逐渐增大；螺距增大时，主曲率差增大，但接触椭圆面积和最大接触应力变化不明显。因此要实现循环式行星滚柱丝杠副的最优设计，不宜设置过大的牙侧角。

关键词: 循环式行星滚柱丝杠副, 螺旋曲面, 啮合机理, 接触特性

Abstract: According to the structural characteristics of the recirculating planetary roller screw mechanism that the rollers have no helix angle, the spiral raceway surface equations of the screw, roller and nut are established, and the spatial meshing model of recirculating planetary roller screw mechanism is calculated. The meshing point position and axial clearance are formulated, and the influence of the flank angle and the pitch on the meshing point position and axial clearance are discussed, respectively. Besides, the main curvature of the recirculating planetary roller screw mechanism is derived based on the principle of differential geometry. The Hertzian contact theory is used to solve the main curvature difference, contact ellipse area and maximum contact stress between the roller and the raceway, and the influence of the flank angle and the pitch on the contact characteristics are investigated. The results show that the meshing point position on the screw-roller interface always deviates from the line between the screw and roller axis, and the meshing point on the screw and roller is located toward the top of their thread. If the flank angles of the roller and the nut are equal, the meshing point position on the roller-nut interface will be located at the tangent point of the pitch diameter of the two threads. The nominal radius of the part can be used instead of the meshing radius to approximately calculate the principal curvature of the recirculating planetary roller screw mechanism. With the flank angle increases, the principal curvature difference and the contact ellipse area of the two contact interfaces simultaneously decrease, and the maximum contact stress on the thread teeth gradually increases. Increasing the pitch causes the principal curvature difference to increase gradually. However, the contact ellipse area and maximum contact stress do not change significantly. Therefore, in order to achieve the optimal design of the recirculating planetary roller screw mechanism, it is not advisable to set an excessively large flank angle.

Key words: recirculating planetary roller screw mechanism, helical surface, meshing mechanism, contact characteristics

中图分类号:

TH132

乔冠, 刘付乐, 唐术锋, 李宗学, 付晓军. 循环式行星滚柱丝杠副啮合机理与接触特性分析[J]. 机械工程学报, 2025, 61(5): 202-213.

QIAO Guan, LIU Fule, TANG Shufeng, LI Zongxue, FU Xiaojun. Meshing Theory and Contact Characteristics Analysis of the Recirculating Planetary Roller Screw Mechanism[J]. Journal of Mechanical Engineering, 2025, 61(5): 202-213.

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循环式行星滚柱丝杠副啮合机理与接触特性分析

Meshing Theory and Contact Characteristics Analysis of the Recirculating Planetary Roller Screw Mechanism

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