基于代理模型的含摩擦机构动力学快速求解方法

doi:10.3901/JME.2025.04.323

机械工程学报 ›› 2025, Vol. 61 ›› Issue (4): 323-332.doi: 10.3901/JME.2025.04.323

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基于代理模型的含摩擦机构动力学快速求解方法

魏齐^1,2, 陶建峰^1,2, 孙浩^1,2, 徐爽^1,2, 刘成良^1,2

1. 上海交通大学机电控制与物流装备研究所上海 200240;
2. 上海交通大学机械系统与振动国家重点实验室上海 200240

收稿日期:2024-04-02 修回日期:2024-08-20 出版日期:2025-02-20 发布日期:2025-04-14
作者简介:魏齐，男，1996年出生。主要研究方向为液压机器人的分析与控制。E-mail：v7sjtu@sjtu.edu.cn
陶建峰(通信作者)，男，1975年出生，博士，教授，博士研究生导师。主要研究方向为机电液系统动力学分析及控制。E-mail：jftao@sjtu.edu.cn
基金资助:
国家自然科学基金(52075320)、机械系统与振动国家重点实验室2020年度自主课题(MSVZD202006)和上海市浦江人才计划(21PJ1407100)资助项目。

Surrogate Model Based Fast Solution Method for Dynamics of Mechanisms with Friction

WEI Qi^1,2, TAO Jianfeng^1,2, SUN Hao^1,2, Xu Shuang^1,2, LIU Chengliang^1,2

1. Institute of Mechatronics & Logistics Equipment, Shanghai Jiao Tong University, Shanghai 200240;
2. State Key Laboratory of Mechanical System and Vibration, Shanghai Jiao Tong University, Shanghai 200240

Received:2024-04-02 Revised:2024-08-20 Online:2025-02-20 Published:2025-04-14

摘要/Abstract

摘要： 关节摩擦对机构的动力学行为有显著影响。在重载或机构中有球铰的场景中，构件间常用滑动关节连接，其关节摩擦力与约束力有关，因此约束力不能在广义坐标形式的动力学方程中被消去，导致机构正向动力学由一组微分-代数方程描述，未知中间变量过多，动力学的实时求解不容易实现。针对这一问题，提出基于代理模型的含摩擦机构动力学快速求解方法。首先利用约束力有关的连续Stribeck摩擦模型，构建光滑的机构动力学方程，对含摩擦机构进行物理建模；其次采用单隐层神经网络构建机构动力学的代理模型，将机构正向动力学方程简化为常微分方程，大大减少需要求解的未知中间变量。最后，通过管片拼装机的液压举升系统来验证所提出方法的有效性和优越性，最大误差为0.023 4 mm，平均节省了99.89%的求解时间，证明在含滑动摩擦的机构动力学分析中，所提出方法可以在保证精度的前提下显著提升计算效率。

关键词: 机构动力学, 摩擦模型, 代理模型, 快速计算

Abstract: Joint friction has a significant impact on the dynamical behavior of the mechanism. In scenarios where heavy loads or mechanisms have ball hinges, components are commonly connected by sliding joints, whose joint friction are related to the reaction force, and therefore the reaction force cannot be eliminated in the dynamical equations in generalized coordinate form. This leads to a forward dynamics described by differential-algebraic equations with too many unknown variables, and the real-time solution of the dynamical equations cannot be easily achieved. To address this problem, a surrogate model based fast solution method for dynamics of mechanisms with friction is proposed. Firstly, the smooth dynamical equations with continuous Stribeck friction model related to the reaction force are formulated. Secondly, the surrogate model is constructed by using a single hidden layer neural network to simplify the forward dynamics equations into ordinary differential equations, which greatly reduces the unknown variables that need to be solved. Finally, the effectiveness and superiority of the proposed method are verified by the hydraulic lifting system of the segment assembly robot. The numerical solutions prove that the proposed method significantly improves the calculation efficiency with guaranteed accuracy, with a maximum error of 0.023 4 mm and an average saving of 99.89% of the solution time.

Key words: mechanism dynamics, friction model, surrogate model, fast solution

中图分类号:

TH113

魏齐, 陶建峰, 孙浩, 徐爽, 刘成良. 基于代理模型的含摩擦机构动力学快速求解方法[J]. 机械工程学报, 2025, 61(4): 323-332.

WEI Qi, TAO Jianfeng, SUN Hao, Xu Shuang, LIU Chengliang. Surrogate Model Based Fast Solution Method for Dynamics of Mechanisms with Friction[J]. Journal of Mechanical Engineering, 2025, 61(4): 323-332.

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参考文献

[1] 王庚祥，刘宏昭，龚春园，等. 考虑关节摩擦效应的并联机构动力学分析[J]. 农业机械学报，2013，44(11):308-315. WANG Gengxiang，LIU Hongzhao，GONG Chunyuan，et al. Dynamics analysis of parallel mechanism with joint friction[J]. Transactions of the Chinese Society for Agricultural Machinery，2013，44(11):308-315.
[2] 段书用，李昌洛，韩旭，等. 机械臂动力学分析及关节非线性摩擦模型建立[J]. 机械工程学报，2020，56(9):18-28. DUAN Shuyong，LI Changluo，HAN Xu，et al. Forward-inverse dynamics analysis of robot arm trajectories and development of a nonlinear friction model for robot joints[J]. Journal of Mechanical Engineering，2020，56(9):18-28.
[3] LIU Dongyu，LIU Hong，HE Yu，et al. Research on flexible joint friction identification of space lab manipulator[C]//Proceedings of the 2018 IEEE International Conference on Mechatronics and Automation (ICMA)，2018:614-619.
[4] LIU Guanghui，LI Qiang，FANG Lijin，et al. A new joint friction model for parameter identification and sensor-less hand guiding in industrial robots[J]. Industrial Robot，2020，47(6):847-857.
[5] HE Y，WANG C，BAO S，et al. A joint friction model of robotic manipulator for low-speed motion[C]//Proceedings of the 2021 IEEE International Conference on Robotics and Biomimetics (ROBIO)，Sanya，China，2021:545-550.
[6] 张彦斐，金鹏，宫金良，等. 3-RPS并联机器人粘性摩擦工况动力学建模[J]. 农业机械学报，2018，49(9):374-381. ZHANG Yanfei，JIN Peng，GONG Jinliang，et al. Dynamic modeling of 3-RPS parallel robot considering joint friction[J]. Transactions of the Chinese Society for Agricultural Machinery，2018，49(9):374-381.
[7] GUO Feng，CHENG Gang，PANG Yusong. Explicit dynamic modeling with joint friction and coupling analysis of a 5-DOF hybrid polishing robot[J]. Mech Mach Theory，2022，167:104509.
[8] JAVANFAR A，BAMDAD M. Effect of novel continuous friction model on nonlinear dynamics of the mechanisms with clearance joint[J]. Proceedings of the Institution of Mechanical Engineers，Part C: Journal of Mechanical Engineering Science，2022，236(11):6040-6052.
[9] FRACZEK J，WOJTYRA M. On the unique solvability of a direct dynamics problem for mechanisms with redundant constraints and Coulomb friction in joints[J]. Mech Mach Theory，2011，46(3):312-334.
[10] SAHA S. Dynamics of serial multibody systems using the decoupled natural orthogonal complement matrices[J]. Journal of Applied Mechanics，1999，66(4):986-996.
[11] SCHIEHLEN W. Computational dynamics:Theory and applications of multibody systems[J]. European Journal of Mechanics A-Solids，2006，25(4):566-594.
[12] 陈根良，王皓，来新民，等. 基于广义坐标形式牛顿-欧拉方法的空间并联机构动力学正问题分析[J]. 机械工程学报，2009，45(7):41-48. CHEN Genliang，WANG Hao，LAI Xinmin，et al. Forward dynamics analysis of spatial parallel mechanisms based on the newton-euler method with generalized coordinates[J]. Journal of Mechanical Engineering，2009，45(7):41-48.
[13] SUSUKI Y. On koopman operator framework for semi-explicit differential-algebraic equations[J]. IFAC-PapersOnLine，2021，54(14):341-345.
[14] FABIANI G，GALARIS E，RUSSO L，et al. Parsimonious physics-informed random projection neural networks for initial-value problems of ODEs and index-1 DAEs[J]. Chaos，2023，33(4):043128.
[15] MOYA C，LIN G. DAE-PINN:A physics-informed neural network model for simulating differential algebraic equations with application to power networks[J]. Neural Computing and Applications，2022，35(5):3789-3804.
[16] STIASNY J，MISYRIS G S，CHATZIVASILEIADIS S. Physics-informed neural networks for non-linear system identification for power system dynamics[C]//Proceedings of the 2021 IEEE Madrid PowerTech，2021:1-6.
[17] 丁千，翟红梅. 机械系统摩擦动力学研究进展[J]. 力学进展，2013，43(1):112-131. DING Qian，QU Hongmei. The advance in researches of friction dynamics in mechanics system[J]. Advances in Mechanics，2013，43(1):112-131.
[18] SPECKER T，BUCHHOLZ M，DIETMAYER K. A new approach of dynamic friction modelling for simulation and observation[J]. IFAC Proceedings Volumes，2014，47(3):4523-4528.
[19] SCHWEIZER B，LI P. Solving differential-algebraic equation systems:Alternative index-2 and index-1 approaches for constrained mechanical systems[J]. Journal of Computational and Nonlinear Dynamics，2016，11(4):044501.
[20] MCKAY M D，BECKMAN R J，CONOVER W J. Comparison of three methods for selecting values of input variables in the analysis of output from a computer code[J]. Technometrics，1979，21(2):239-245.

基于代理模型的含摩擦机构动力学快速求解方法

Surrogate Model Based Fast Solution Method for Dynamics of Mechanisms with Friction

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