人形机器人用反向式行星滚柱丝杠副多滚柱载荷分布

doi:10.3901/JME.260163

机械工程学报 ›› 2026, Vol. 62 ›› Issue (15): 334-349.doi: 10.3901/JME.260163

• 机器人与机构学 • 上一篇

扫码分享

人形机器人用反向式行星滚柱丝杠副多滚柱载荷分布

周焕辉^1,2,3, 胡瑞^1,2,3, 汪淑君^2,3, 秦蕊丽^2,3, 施金芳^2,3, 魏沛堂¹, 朱才朝¹

1. 重庆大学高端装备机械传动全国重点实验室重庆 400044;
2. 杭州前进齿轮箱集团股份有限公司杭州 311203;
3. 浙江省全省高端智能装备齿轮传动系统重点实验室杭州 311203

收稿日期:2025-07-08 修回日期:2025-11-23 发布日期:2026-10-13
作者简介:周焕辉，男，1980年出生，博士研究生，高级工程师。主要研究方向为齿轮传动装置及粉末冶金关键技术。E-mail：zhouhh@chinaadvace.com;胡瑞，男，1994年出生，博士。主要研究方向为行星滚柱丝杠传动与驱动系统。E-mail：hurui2020@163.com;魏沛堂(通信作者)，男，1984年出生，教授，博士研究生导师。主要研究方向为行星滚柱丝杠传动与驱动系统。E-mail：peitangwei@cqu.edu.cn;朱才朝，男，1966年出生，教授，博士研究生导师。主要研究方向为高速重载齿轮传动系统。E-mail：cczhu@cqu.edu.cn
基金资助:
国家自然科学基金(52505055)和浙江省尖兵领雁研发攻关计划(2025C01015)资助项目。

Multi-roller Load Distribution of Inverted Planetary Roller Screw Mechanism for Humanoid Robot

ZHOU Huanhui^1,2,3, HU Rui^1,2,3, WANG Shujun^2,3, QIN Ruili^2,3, SHI Jinfang^2,3, WEI Peitang¹, ZHU Caichao¹

1. State Key Laboratory of Mechanical Transmission for Advanced Equipment, Chongqing University, Chongqing 400044;
2. Hangzhou Advance Gearbox Group Co., Ltd., Hangzhou 311203;
3. Zhejiang Key Laboratory of Gear Transmission Systems for Advanced Intelligent Equipment, Hangzhou 311203

Received:2025-07-08 Revised:2025-11-23 Published:2026-10-13

摘要/Abstract

摘要： 面向人形机器人对反向式行星滚柱丝杠副(IPRSM)功率密度的严苛要求，承载能力成为决定其性能的关键指标。安装误差不可避免，加剧载荷分布不均匀性，引发螺纹牙过度磨损甚至压溃，成为导致IPRSM提前失效的重要原因。针对安装误差与滚柱间的载荷分布关联规律不清的问题，提出了一种考虑安装误差的IPRSM多滚柱载荷分布计算方法。基于啮合原理计算了考虑安装误差的螺纹轴向接触间隙，利用等效接触理论获取了多滚柱的等效接触力和变形，建立了螺纹牙多点接触变形–力平衡关系，并开发了迭代算法求解滚柱上的载荷分布。通过与有限元仿真的对比分析，验证了其有效性。最后，开展了安装误差和外载荷对载荷分布的参数化影响分析。结果表明，越靠近轴线偏移误差方向，滚柱承担的总载荷增加，同时加剧滚柱上的载荷分布不均匀性。轴线倾斜误差增大会造成部分滚柱上的最大轴向接触力逐渐从一端向另一端转移。安装误差过大可能导致部分滚柱或螺纹牙脱离啮合。外载荷越小，滚柱间的载荷分布均匀性越差。

关键词: 人形机器人, 行星滚柱丝杠副, 安装误差, 载荷分布, 多滚柱

Abstract: Humanoid robots have placed stringent requirements on the power density of the inverted planetary roller screw mechanism (IPRSM), and the load-bearing capacity has become a key indicator that determines the performance of IPRSM. Installation errors are inevitable, exacerbating the uneven load distribution, leading to excessive wear or even crushing of the threads, which has become a significant cause of premature failure of IPRSM. Aiming at the problem that the correlation between installation error and load distribution among rollers is unclear, a multi-roller load distribution calculation method of IPRSM considering installation error is proposed. The axial contact clearance considering the installation error is calculated based on the meshing principle. The equivalent contact force and deformation of multiple rollers are obtained using the equivalent contact theory. The deformation-force balance relationship of multi-point contact of the thread is established, and an iterative algorithm is developed to solve the load distribution on the roller. The effectiveness of the established model is verified by comparative with finite element simulation. Finally, a parametric analysis of the influence of installation errors and external loads on load distribution is carried out. The results show that the closer to the axis offset error direction, the greater the total load borne by the roller, and the more uneven the load distribution on the roller. The increase in axis tilt error causes the maximum axial contact force on some rollers to gradually shift from one end to the other. Excessive installation errors may cause some rollers or threads to become disengaged. The smaller the external load, the worse the load distribution uniformity among rollers.

Key words: humanoid robot, planetary roller screw mechanism, installation error, load distribution, multi-roller

中图分类号:

TH132

周焕辉, 胡瑞, 汪淑君, 秦蕊丽, 施金芳, 魏沛堂, 朱才朝. 人形机器人用反向式行星滚柱丝杠副多滚柱载荷分布[J]. 机械工程学报, 2026, 62(15): 334-349.

ZHOU Huanhui, HU Rui, WANG Shujun, QIN Ruili, SHI Jinfang, WEI Peitang, ZHU Caichao. Multi-roller Load Distribution of Inverted Planetary Roller Screw Mechanism for Humanoid Robot[J]. Journal of Mechanical Engineering, 2026, 62(15): 334-349.

导出引用管理器 EndNote|Reference Manager|ProCite|BibTeX|RefWorks

链接本文: http://www.cjmenet.com.cn/CN/10.3901/JME.260163

http://www.cjmenet.com.cn/CN/Y2026/V62/I15/334

参考文献

[1] 刘更，付晓军，马尚君，等. 行星滚柱丝杠副啮合原理研究进展[J]. 机械传动，2015，39(7)：1-5. LIU Geng，FU Xiaojun，MA Shangjun，et al. Review on meshing theory of the planetary roller screw mechanism[J]. Journal of Mechanical Transmission，2015，39(7)：1-5.
[2] 刘更，马尚君，佟瑞庭，等. 行星滚柱丝杠副的新发展及关键技术[J]. 机械传动，2012，36(5)：103-108. LIU Geng，MA Shangjun，TONG Ruiting，et al. New development and key technology of planetary roller screw[J]. Journal of Mechanical Transmission，2012，36(5)：103-108.
[3] TANG L，LIANG D，GAO G，et al. Modeling and reinforcement learning-based locomotion control for a humanoid robot with kinematic loop closures[J]. Multibody System Dynamics，2024：1-27.
[4] HU R，WEI P，DU X，et al. Multi-objective optimization and accelerated experimental research on load distribution of planetary roller screw mechanism[J]. Tribology International，2024，199：110046.
[5] 杨家军，韦振兴，朱继生，等. 行星滚柱丝杠副载荷分布及刚度计算[J]. 华中科技大学学报，2011，39(4)：1-4. YANG Jiajun，WEI Zhenxing，ZHU Jisheng，et al. Calculation of load distribution of planetary roller screws and static rigidity[J]. Journal of Huazhong University of Science and Technology，2011，39(4)：1-4.
[6] RYŚ J，LISOWSKI F. The computational model of the load distribution between elements in a planetary roller screw[J]. Journal of Theoretical and Applied Mechanics，2014，52(3)：699-705.
[7] ABEVI F，DAIDIE A，CHAUSSUMIER M，et al. Static load distribution and axial stiffness in a planetary roller screw mechanism[J]. Journal of Mechanical Design，2016，138(1)：012301.
[8] JONES M H，VELINSKY S A. Stiffness of the roller screw mechanism by the direct method[J]. Mechanics Based Design of Structures and Machines，2014，42(1)：17-34.
[9] 张文杰，刘更，马尚君，等. 不同安装方式下行星滚柱丝杠副载荷分布研究[J]. 西北工业大学学报，2015，33(2)：229-236. ZHANG Wenjie，LIU Geng，MA Shangjun，et al. Load distribution of planetary roller screw mechanism with different installations[J]. Journal of Northwestern Polytechnical University，2015，33(2)：229-236.
[10] YAO Q，ZHANG M，LIU Y，et al. Multi-objective optimization of planetary roller screw mechanism based on improved mathematical modelling[J]. Tribology International，2021，161：107095.
[11] 乔冠，郝志鹏，廖荣，等. 反向式行星滚柱丝杠副的螺纹牙修形设计[J]. 机械传动，2024，48(4)：109-115. QIAO Guan，HAO Zhipeng，LIAO Rong，et al. Thread tooth modification of the inverted planetary roller screw mechanism[J]. Journal of Mechanical Transmission，2024，48(4)：109-115.
[12] 殷国富，宋俨轩，殷鸣，等. 反向式行星滚柱丝杠承载分布及寿命分析[J]. 工程科学与技术，2019，51(1)：222-228. YIN Guofu，SONG Yanxuan，YIN Ming，et al. Load distribution and life prediction of inverted planetary roller screw[J]. Advanced Engineering Sciences，2019，51(1)：222-228.
[13] ZHANG B，XING M，CUI Y，et al. A novel static model of planetary roller screw mechanisms based on an energy method[J]. Proceedings of the Institution of Mechanical Engineers，Part C：Journal of Mechanical Engineering Science，2024，238(22)：10889-10908.
[14] MIAO J，DU X，LI C，et al. Load distribution and radial deformations for planetary roller screw mechanism with axial load，radial load and turning torque[J]. Mechanics Based Design of Structures and Machines，2024，52(4)：1847-1873.
[15] ZHANG W，LIU G，MA S，et al. Load distribution over threads of planetary roller screw mechanism with pitch deviation[J]. Proceedings of the Institution of Mechanical Engineers，Part C：Journal of Mechanical Engineering Science，2019，233(13)：4653-4666.
[16] 刘柱，范元勋. 行星滚柱丝杠滚柱载荷差异分析与研究[J]. 组合机床与自动化加工技术，2020(5)：5-8. LIU Zhu，FAN Yuanxun. Study and research on load distribution of planetary roller screw[J]. Modular Machine Tool & Automatic Manufacturing Technique，2020(5)：5-8.
[17] DU X，CHEN B，ZHENG Z. Investigation on mechanical behavior of planetary roller screw mechanism with the effects of external loads and machining errors[J]. Tribology International，2021，154：106689.
[18] FU X，LI X，MA S，et al. A multi-roller static model of the planetary roller screw mechanism considering load sharing[J]. Tribology International，2022，173：107648.
[19] XING M，LIU S，CHENG Z，et al. Multi-rollers statics analysis of planetary roller screw mechanism based on explicit expression[J]. Tribology International，2024，197：109818.
[20] HU R，WEI P，LIU H，et al. Investigation on load distribution among rollers of planetary roller screw mechanism considering machining errors：Analytical calculation and machine learning approach[J]. Mechanism and Machine Theory，2023，185：105322.
[21] 付晓军，徐烨，刘更，等. 考虑滚柱偏斜的行星滚柱丝杠载荷分布计算方法[J]. 机械工程学报，2024，60(13)：247-256. FU Xiaojun，XU Ye，LIU Geng，et al. The calculation method for the load distribution in the planetary roller screw mechanism with the roller deviation[J]. Journal of Mechanical Engineering，2024，60(13)：247-256.
[22] 付晓军，刘更，马尚君，等. 考虑零件偏斜的行星滚柱丝杠副啮合特性研究[J]. 机械工程学报，2017，53(3)：25-33. FU Xiaojun，LIU Geng，MA Shangjun，et al. Meshing properties of planetary roller screw mechanism within misalignments[J]. Journal of Mechanical Engineering，2017，53(3)：25-33.
[23] HU R，WEI P，DU X，et al. Investigation of loaded contact characteristics of planetary roller screw mechanism based on influence coefficient method and machine learning[J]. Advanced Engineering Informatics，2023，58：102146.
[24] LITVIN F L，FUENTES A. Gear geometry and applied theory[M]. Cambridge University Press，2004.
[25] FU X，LIU G，MA S，et al. A comprehensive contact analysis of planetary roller screw mechanism[J]. Journal of Mechanical Design，2017，139(1)：012302.
[26] 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.
[27] ZHEN N，AN Q. Analysis of stress and fatigue life of ball screw with considering the dimension errors of balls[J]. International Journal of Mechanical Sciences，2018，137：68-76.
[28] ZHANG W，LIU G，TONG R，et al. Load distribution of planetary roller screw mechanism and its improvement approach[J]. Proceedings of the Institution of Mechanical Engineers，Part C：Journal of Mechanical Engineering Science，2016，230(18)：3304-3318.
[29] HU R，WEI P，ZHOU P，et al. A roller taper modification method for load distribution optimization of planetary roller screw mechanism[J]. Journal of Advanced Mechanical Design，Systems，and Manufacturing，2022，16(3)：JAMDSM0032.
[30] LI L，FU Y，ZHENG S，et al. Friction torque analysis of planetary roller screw mechanism in roller jamming[J]. Mathematical Problems in Engineering，2020，2020(1)：1392380.
[31] 郭辉，佟瑞庭，刘更，等. 面向行星滚柱丝杠副载荷均布的螺纹牙修形方法[J]. 西北工业大学学报，2018，36(4)：685-692. GUO Hui，TONG Ruiting，LIU Geng，et al. Thread modification method for load balance on planetary roller screw mechanism[J]. Journal of Northwestern Polytechnical University，2018，36(4)：685-692.
[32] 康新泓，魏沛堂，胡瑞，等. 行星滚柱丝杠副额定静载荷计算方法对比分析[J]. 机械传动，2022，46(11)：1-9. KANG Xinhong，WEI Peitang，HU Rui，et al. Comparison and analysis of calculation methods for rated static load of planetary roller screw mechanism[J]. Journal of Mechanical Transmission，2022，46(11)：1-9.

人形机器人用反向式行星滚柱丝杠副多滚柱载荷分布

Multi-roller Load Distribution of Inverted Planetary Roller Screw Mechanism for Humanoid Robot

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

编辑推荐

Metrics

本文评价

[1]	张子豪, 姚琴, 陈志荣, 孙俊贤, 黄佳乐. 循环式行星滚柱丝杠副环状牙离散化修形[J]. 机械工程学报, 2026, 62(5): 204-214.
[2]	邵士博, 林诚然, 杜国锋, 李俊年, 曹政才. 基于多评论家模仿学习的人形机器人运动技能生成方法[J]. 机械工程学报, 2026, 62(11): 191-200.
[3]	李常胜, 丁建军, 金雨生, 刘阳鹏, 王振翼, 刘昕东, 蒋庄德. 基于多传感数据融合与扩增补偿的圆光栅编码器测角误差抑制方法[J]. 机械工程学报, 2026, 62(10): 23-40.
[4]	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.
[5]	杜国锋, 邵士博, 李尚霖, 林诚然, 曹政才. 融合视觉语言模型与近端策略优化算法的人形机器人步态切换方法[J]. 机械工程学报, 2025, 61(21): 204-212.
[6]	陶永, 万嘉昊, 王田苗, 熊友军, 王柏村, 张文博, 邓昌义, 陶雨, 杨赓, 魏洪兴. 构建具身智能新范式：人形机器人技术现状及发展趋势综述[J]. 机械工程学报, 2025, 61(15): 121-147.
[7]	付晓军, 徐烨, 刘更, 李欣, 马尚君. 考虑滚柱偏斜的行星滚柱丝杠载荷分布计算方法[J]. 机械工程学报, 2024, 60(13): 247-256.
[8]	付晓军, 李欣, 马尚君, 王海伟, 刘更. 柱销式双螺母行星滚柱丝杠预紧机理研究[J]. 机械工程学报, 2023, 59(3): 122-132.
[9]	吕宏展, 王羽达, 王君政. 含安装误差的鼓形齿轮承载接触分析[J]. 机械工程学报, 2022, 58(21): 126-133.
[10]	黄健, 李朝阳, 陈兵奎. RV减速器用新型交错滚子主轴承承载能力分析与试验研究[J]. 机械工程学报, 2021, 57(7): 68-77.
[11]	路永婕, 张俊宁, 李皓玉, 马智喆. 基于非均匀接触的轮胎-道路系统耦合动力学研究[J]. 机械工程学报, 2021, 57(12): 87-98.
[12]	张进华, 方斌, 朱永生, 闫柯, 洪军. 基于球-滚道非完全接触状态下的球轴承载荷分布计算及刚度特性研究[J]. 机械工程学报, 2020, 56(9): 73-83.
[13]	袁冰, 常山, 刘更, 刘岚, 曹晓梅. 大齿宽齿轮耦合转子系统准静态接触分析及动态特性[J]. 机械工程学报, 2020, 56(3): 96-105.
[14]	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.
[15]	赵佳佳, 林明星, 宋现春, 骆伟超, 宋丽伟. 复合载荷下滚珠丝杠副全滚珠载荷分布建模与分析[J]. 机械工程学报, 2020, 56(17): 126-136.