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

作　　者：魏齐 陶建峰[1,2] 孙浩 徐爽[1,2] 刘成良 WEI Qi;TAO Jianfeng;SUN Hao;Xu Shuang;LIU Chengliang(Institute of Mechatronics&Logistics Equipment,Shanghai Jiao Tong University,Shanghai 200240;State Key Laboratory of Mechanical System and Vibration,Shanghai Jiao Tong University,Shanghai 200240)

机构地区：[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

出　　处：《机械工程学报》2025年第4期323-332,共10页Journal of Mechanical Engineering

基　　金：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);上海市浦江人才计划(21PJ1407100)资助项目。

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0.0234 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。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 0.0234 mm and an average saving of 99.89%of the solution time.

关 键 词：机构动力学 摩擦模型 代理模型 快速计算 

分 类 号：TH113[机械工程—机械设计及理论]