考虑时变啮合刚度的行星滚柱丝杠动力学建模与振动特性分析

PDF(3573 KB)

振动与冲击 ›› 2025, Vol. 44 ›› Issue (11) : 119-128.

振动理论与交叉研究

考虑时变啮合刚度的行星滚柱丝杠动力学建模与振动特性分析

卢夏沁1，2，陈换过1，2，吴建伟*3，彭雨浩1，2，汤佳辉1，2

作者信息 +

Dynamic modeling and vibration characteristics analysis of planetary roller screw considering time-varying meshing stiffness#br#

LU Xiaqin1,2, CHEN Huanguo1,2, WU Jianwei*3, PENG Yuhao1,2, TANG Jiahui1,2

Author information +

文章历史 +

摘要

针对行星滚柱丝杠（Planetary Roller Screw Mechanism，PRSM）动态特性研究中的不足，特别是对传动副啮合刚度时变特性和非线性因数考虑不充分的问题，提出了一种考虑间隙、摩擦阻尼和时变啮合刚度的PRSM“扭转-平移-轴向”动力学建模方法。通过集中质量法构建动力学模型，基于达朗贝尔原理推导出运动微分方程；根据机构传动副特点，构建了齿轮副悬臂梁模型与螺纹副轴向刚度模型，结合势能法、直接刚度法和赫兹接触理论提取出啮合刚度参数。最后，采用Runge-Kutta数值积分法求解系统微分方程，通过与刚体动力学模型对比验证模型准确性，并获取了PRSM的振动特性。研究成果为PRSM的故障特性分析和智能诊断奠定了理论基础。

Abstract

Abstract: The study of the dynamic characteristics of Planetary Roller Screw (PRSM) revealed significant gaps, particularly regarding the time-varying meshing stiffness of drive pairs and nonlinear factors. A dynamic modeling method for PRSM is proposed, which considers friction damping and time-varying meshing stiffness, employing a 'torsional-translation-axial' approach. A dynamics model framework is established by using the lumped-mess method, with motion equations derived from D'Alembert's principle. A cantilever beam model for the gear pair and an axial stiffness model for the thread pair are constructed, integrating potential energy method, direct stiffness method and Hertz contact theory to obtain meshing stiffness parameters. Finally, the Runge-Kutta method is utilized to solve the motion equations, and the model's accuracy is validated against a rigid body dynamics model, further revealing PRSM's vibration characteristics. These findings provide a theoretical foundation for fault characteristic analysis and intelligent diagnosis of PRSM.

导出引用

卢夏沁1, 2, 陈换过1, 2, 吴建伟3, 彭雨浩1, 2, 汤佳辉1, 2. 考虑时变啮合刚度的行星滚柱丝杠动力学建模与振动特性分析[J]. 振动与冲击, 2025, 44(11): 119-128

LU Xiaqin1, 2, CHEN Huanguo1, 2, WU Jianwei3, PENG Yuhao1, 2, TANG Jiahui1, 2. Dynamic modeling and vibration characteristics analysis of planetary roller screw considering time-varying meshing stiffness#br#[J]. Journal of Vibration and Shock, 2025, 44(11): 119-128

参考文献

[1] 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: 205536-205536.
[2] 张宪,杨万强,刘富田,等. 风力发电机组振动状态监测及故障诊断分析 [J]. 科学技术创新, 2024, (18): 58-61.
ZHANG Xian, YANG Wan-qiang, LIU Fu-tian, et al. Vibration state monitoring and fault diagnosis analysis of wind turbine [J]. Scientific and Technological Innovation, 2024, (18): 58-61.
[3] Jones M H, Velinsky S A, Lasky T A. Dynamics of the Planetary Roller Screw Mechanism [J]. Journal of Mechanisms and Robotics: Transactions of the ASME, 2016, 8(1): 014503.
[4] Fu X J, Liu G, Tong R T, et al. A nonlinear six degrees of freedom dynamic model of planetary roller screw mechanism [J]. Mechanism and Machine Theory, 2017, (119):22-36.
[5] Fu X J, Liu G, Ma S J, et al. An efficient method for the dynamic analysis of planetary roller screw mechanism [J]. Mechanism and Machine Theory, 2019, 150
[6] Ma S J, Zhang T, Liu G, et al. Bond graph-based dynamic model of planetary roller screw mechanism with consideration of axial clearance and friction [J]. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2018, 232(16):2899-2911.
[7] 马尚君,刘更,周建星,等. 行星滚柱丝杠副运转过程动态特性分析 [J]. 振动与冲击, 2013, 32 (03): 167-171+187.
MA Shang-jun, LU Geng, ZHOU Jian-xing, et al. Dynamic characteristic analysis of a planetary roller screw in operating process [J]. Journal of Vibration and Shock, 2013, 32 (03): 167-171+187.
[8] 岳琳琳,王卫英,胡宝根. 基于有限元仿真的行星滚柱丝杠动态特性分析 [J]. 机械工程与自动化, 2014, (02): 16-18.
YUE Lin-lin, WANG Wei-ying, HU Bao-gen. Dynamic characteristic analysis based on finite element simulation for planetary roller screw [J]. Mechanical Engineering & Automation, 2014, (02): 16-18.
[9] 郭嘉楠,何鹏,黄洪雁,等. 行星滚柱丝杠动力学特性分析及试验研究 [J]. 推进技术, 2018, 39 (08): 1841-1848.
GUO Jia-nan, HE Peng, HUANG Hong-yan, et al. Theoretical investigation and experimental study on planetary roller screw dynamics [J]. Journal of Propulsion Technology, 2018, 39 (08): 1841-1848.
[10] Wu L P, Ma S J, Wan Q, et al. Dynamic Model of Planetary Roller Screw Mechanism with Considering Torsional Degree of Freedom [J]. MATEC Web of Conferences, 2020, 30601003.
[11] Wu L P, Ma S J, Deng P, et al. Research on the Modeling of Bending-Torsional Coupling and Vibration Characteristics of Planetary Roller Screw Mechanism [J]. Electronics, 2022, 11 (9): 1395-1395.
[12] 乔冠,张校民,刘付乐,等. 差动式行星滚柱丝杠副的运动特性与动力学分析 [J]. 机床与液压, 2024, 52 (13): 156-163.
QIAO Guan, ZHANG Xiao-min, LIU Fu-le, et al. Kinematics and dynamic characteristic analysis of the differential planetary roller screw mechanism [J]. Machine Tool & Hydraulics, 2024, 52 (13): 156-163.
[13] 万琦,刘更,乔冠,等. 机电作动器舵回路系统动态特性分析 [J]. 机械科学与技术, 2017, 36 (05): 805-810.
WAN Qi, LIU Geng, QIAO Guan, et al. Analyzing dynamic characteristics of rudder loop system for an electro-mechanical actuator [J]. Mechanical Science and Technology for Aerospace Engineering, 2017, 36 (05): 805-810.
[14] 桑萌. 基于耦合动力学的电机-3K行星齿轮系统动态特性及裂纹故障机电信号研究[D]. 合肥：合肥工业大学, 2022.
SANG Meng. Research on dynamic characteristics and cracking fault electromechanical signal of motor-3K planetary gear system based on coupling dynamics[D]. Hefei: Hefei University of Technology, 2022.
[15] 王家健. 行星滚柱丝杠设计[D]. 南京：南京理工大学, 2021.
WANG Jia-jian. Design of planetary roller screw[D]. Nanjing：Nanjing University of Science and technology, 2021.
[16] Huang Y H, Liu S J, Chen H G, et al. Dynamic behavior analysis method for the normal and faulty drivetrain of wind turbine under multi‐working conditions [J]. Energy Science & Engineering, 2023, 11(10):3619-3640.
[17] Liang X H, Zuo M J, Feng Z P. Dynamic modeling of gearbox faults: A review [J]. Mechanical Systems and Signal Processing, 2018, 98:852-876.
[18] 官鑫,董远德. 计入齿轮修形的时变啮合刚度计算模型研究 [J]. 机械设计与制造, 2024, (07): 57-64.
GUAN Xin, DONG Yuan-de. Study on calculation model of Time-varying meshing stiffness considering gear modification [J]. Machinery Design & Manufacture, 2024, (07): 57-64.
[19] 马腾龙,马尚君,吴林萍,等. 行星滚柱丝杠螺纹副-齿轮副同步啮合动态接触载荷特性 [J]. 西安交通大学学报, 2022, 56 (10): 11-21+30.
MA Teng-long, MA Shang-jun, WU Lin-ping, et al. Dynamic contact load characteristics of synchromesh between screw pair and gear pair in the planetary roller screw [J]. Journal of Xi'an Jiaotong University, 2022, 56 (10): 11-21+30.
[20] Juliette L, Loïc T, Emmanuel M, et al. Axial backlash of planetary roller screw mechanisms: Geometric modelling and Sobol's analysis of design parameters [J]. CIRP Annals - Manufacturing Technology, 2023, 72(1):113-116.
[21] 胡蛟,胡茑庆,沈建,等. 直升机主减典型部件故障动力学建模与仿真 [J]. 东北大学学报(自然科学版), 2022, 43 (12): 1732-1739+1747.
HU Jiao, HU Niao-qing, SHEN Jian, et al. Fault dynamic modeling and simulation for typical components of helicopter main reducers [J]. Journal of Northeastern University(Natural Science) , 2022, 43 (12): 1732-1739+1747.
[22] 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.
[23] 解志杰,张传伟,薛其河,等. 行星滚柱丝杠动态摩擦力矩和传动效率分析 [J]. 摩擦学学报, 2019, 39 (04): 489-496.
XIE Zhi-jie, ZHANG Chuan-wei, XUE Qi-he, et al. Analysis of dynamic friction torque and transmission efficiency of planetary roller screw [J]. Tribology, 2019, 39 (04): 489-496.
[24] 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.
[25] 高扬. 基于直接刚度法的行星滚柱丝杠刚度的研究[D]. 武汉：华中科技大学, 2016.
GAO Yang. The research of planetary roller screw stiffness based on direct method [D]. Wuhan:Huazhong University of Science & Technology, 2016.