循环式行星滚柱丝杠副环状牙离散化修形

doi:10.3901/JME.260238

机械工程学报 ›› 2026, Vol. 62 ›› Issue (5): 204-214.doi: 10.3901/JME.260238

• 机器人及机构学 • 上一篇

扫码分享

循环式行星滚柱丝杠副环状牙离散化修形

张子豪¹, 姚琴^1,2,3, 陈志荣¹, 孙俊贤¹, 黄佳乐¹

1. 苏州科技大学机械工程学院苏州 215009;
2. 南京理工大学机械工程学院南京 210094;
3. 苏州亚太精睿传动科技股份有限公司苏州 215132

收稿日期:2025-04-27 修回日期:2025-07-24 发布日期:2026-04-23
作者简介:张子豪,男,2004年出生。主要研究方向为行星滚柱丝杠副承载机理。E-mail:zhangzihao@post.usts.edu.cn
姚琴(通信作者),女,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副可靠性分析与结构优化设计。E-mail:yaoqin@usts.edu.cn
基金资助:
国家自然科学基金(52305273)和中国博士后科学基金(2023M742572)资助项目。

Discrete Modification of Annular Teeth in Recirculating Planetary Roller Screw Mechanism

ZHANG Zihao¹, YAO Qin^1,2,3, CHEN Zhirong¹, SUN Junxian¹, HUANG Jiale¹

1. School of Mechanical Engineering, Suzhou University of Science and Technology, Suzhou 215009;
2. School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing 210094;
3. Suzhou Asia-Pacific Intelligent Transmission Technology Co. Ltd., Suzhou 215132

Received:2025-04-27 Revised:2025-07-24 Published:2026-04-23

摘要/Abstract

摘要： 为提高循环式行星滚柱丝杠副的传动性能，需开展关键零件结构修形研究。针对传统线性补偿修形策略精度不足的问题，建立环状牙-螺纹牙载荷分布数学模型。基于变形协调关系和刚度矩阵，获得滚柱环状牙离散化修形量。进一步结合修形量的分布特征，构建拟合函数模型，并采用Levenberg-Marquardt算法优化拟合系数，以获得最优修形曲线。在此基础上，综合考虑丝杠、滚柱和螺母的牙型半角以及滚柱牙型轮廓半径对接触应力极值的影响，提出多参数耦合的协同修形策略。通过有限元分析，对比修形前后载荷分布与接触应力峰值的变化，验证了所建理论模型的有效性。结果表明，基于二次多项式模型构建的修形曲线使螺母侧和丝杠侧的载荷分布系数分别收敛至0.998～1.001和0.995～1.003，协同修形策略在保持载荷均匀性的同时，使滚柱两侧的平均接触应力分别降低35.55%和32.93%。

关键词: 循环式行星滚柱丝杠副, 离散化修形量, Levenberg-Marquardt算法, 协同修形

Abstract: To improve the transmission performance of the recirculating planetary roller screw mechanism (RPRSM), structural modification of key components is essential. Addressing the accuracy limitations of conventional linear compensation strategies, a mathematical model of load distribution between the annular teeth of the roller and the threads of the screw and nut is established. Based on the deformation compatibility and the stiffness matrix, the discrete modification values of the roller’s annular teeth are derived. A fitting function model is then constructed according to the distribution characteristics of these values, and the Levenberg-Marquardt algorithm is employed to optimize the fitting coefficients and obtain the optimal modification curve. Furthermore, a multi-parameter coupled cooperative modification strategy is proposed, considering the effects of the flank angles of the screw, roller, and nut, as well as the profile radius of the roller tooth, on the peak contact stress. The theoretical model is validated by comparing the load distribution and peak contact stress before and after modification through finite element analysis. The results indicate that the modification curve, based on a quadratic polynomial model, causes the load distribution coefficients on the nut and screw sides to converge to 0.998-1.001 and 0.995-1.003, respectively. Moreover, the cooperative modification strategy significantly reduces the average contact stress on both sides of the roller by 35.55% and 32.93%, while maintaining uniform load distribution.

Key words: recirculating planetary roller screw mechanism, discrete modification values, Levenberg-Marquardt algorithm, cooperative modification

中图分类号:

TH156

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.

ZHANG Zihao, YAO Qin, CHEN Zhirong, SUN Junxian, HUANG Jiale. Discrete Modification of Annular Teeth in Recirculating Planetary Roller Screw Mechanism[J]. Journal of Mechanical Engineering, 2026, 62(5): 204-214.

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.260238

http://www.cjmenet.com.cn/CN/Y2026/V62/I5/204

参考文献

[1] CHU L，ZHU P，CHANG C. Research on full brake-by-wire system and clamping force estimation strategy based on redundant drive motors[J]. IEEE Access，2023，11:124098-124113.
[2] IYAGHIGBA S D，ALI F，JENNIONS I K. A review of diagnostic methods for hydraulically powered flight control actuation systems[J]. Machines，2023，11(2):165.
[3] MAMAEV I M，MOROZOV V V，FEDOTOV O V，et al. Precision of a roller screw actuator transmission for a radio telescope[J]. Russian Engineering Research，2015，35(12):919-923.
[4] ZHENG F Y，LIU J Y，HAN X H，et al. A new workspace estimation method for heavy-load parallel kinematic machine considering mechanism deformation and motor loading performance[J]. Robotica，2024:1-23.
[5] DONG X L，ZHU H Y，LIU Q Y，et al. Design of downhole robot actuator system and mechanical behavior analyses of the PRSM by considering elastic errors and radial loads[J]. Processes，2022，10(8):1520.
[6] YAO Q，ZHANG M C，MA S J. Structural design for planetary roller screw mechanism based on the developed contact modelling[J]. Tribology International，2022，171:107570.
[7] FU X J，LIU G，MA S J，et al. A comprehensive contact analysis of planetary roller screw mechanism[J]. Journal of Mechanical Design，2016，139(1):012302.
[8] CAI W，FU X J，MA S J，et al. Meshing characteristics analysis of planetary roller screw mechanism with misalignment[J]. Proceedings of the Institution of Mechanical Engineers，Part C:Journal of Mechanical Engineering Science，2023，238(9):3794-3806.
[9] FU X J，LIU G，LI X，et al. Dynamic modeling of the double-nut planetary roller screw mechanism considering elastic deformations[J]. Journal of Computational and Nonlinear Dynamics，2021，16(5):051003.
[10] MO S，WU S Y，HUANG X，et al. Nonlinear dynamics of planetary roller screw mechanism[J]. Chaos:An Interdisciplinary Journal of Nonlinear Science，2024，34(7):073110.
[11] XING M C，LIU S，CUI Y，et al. A comprehensive sliding wear prediction method for planetary roller screw mechanism[J]. Wear，2024，558-559:205536.
[12] CHENG Z W，ZU L，XING M C，et al. Effects of eccentric errors on sliding velocity and accumulative wear depth of planetary roller screw mechanism[J]. Journal of Tribology，2024，146(8):081703.
[13] XIE Z J，WANG Y，ZHAN H，et al. Calculation model of contact load and axial stiffness of planetary thread roller bearing based on direct stiffness method[J]. Advanced Theory and Simulations，2023，6(7):2300126.
[14] 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.
[15] ZHANG W J，LIU G，MA S J，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] DU X，CHEN B K，ZHENG Z D. Investigation on mechanical behavior of planetary roller screw mechanism with the effects of external loads and machining errors[J]. Tribology International，2021，154:106689.
[17] DENG P，XING M C，LIN J G，et al. A mathematical model for load distribution of planetary roller screw with pitch deviation[J]. Journal of the Brazilian Society of Mechanical Sciences and Engineering，2023，45(10):547.
[18] 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.
[19] MIAO J C，DU X，LI C Y，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.
[20] MENG J J，DU X，LI Y M，et al. A multiscale accuracy degradation prediction method of planetary roller screw mechanism based on fractal theory considering thread surface roughness[J]. Fractal and Fractional，2021，5(4):237.
[21] ZHANG W J，LIU G，TONG R T，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.
[22] 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.
[23] YAO Q，ZHANG M C，LIU Y S，et al. Multi-objective optimization of planetary roller screw mechanism based on improved mathematical modelling[J]. Tribology International，2021，161:107095.
[24] DU X，LU S Y，TANG R，et al. An efficient method for designing high-performance planetary roller screw mechanism with low contact stress[J]. Tribology International，2023，187:108709.
[25] HU R，WEI P T，ZHOU P L，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):1-20.
[26] CASTELANI E V，DURAN E，LOPES R，et al. A multi-step algorithm based on Levenberg-Marquardt method for solving LOVO problems[J]. Operations Research Forum，2025，6(2):45-45.
[27] QIAO G，LIAO R，GUO S J，et al. Design and dynamic analysis of the recirculating planetary roller screw mechanism[J]. Chinese Journal of Mechanical Engineering，2022，35(1):87.

循环式行星滚柱丝杠副环状牙离散化修形

Discrete Modification of Annular Teeth in Recirculating Planetary Roller Screw Mechanism

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 1

编辑推荐

Metrics

本文评价