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本文引用格式:邢航,郑旭东,王琪.基于LuGre模型非光滑柱铰链平面多体系统动力学的建模和数值方法[J].动力学与控制学报,2019,17(5):413~418;   Xing Hang,Zheng Xudong,Wang Qi.Modeling and simulation of planar multibody systems with frictional revolute joints based on LuGre friction model[J].Journal of Dynamics and Control,2019,17(5):413-418.
基于LuGre模型非光滑柱铰链平面多体系统动力学的建模和数值方法    点此下载全文
邢航  郑旭东  王琪
北京航空航天大学 航空科学与工程学院,北京 100083,北京航空航天大学 航空科学与工程学院,北京 100083,北京航空航天大学 航空科学与工程学院,北京 100083
基金项目:国家自然科学基金资助项目(11772021)
DOI:10.6052/1672-6553-2019-065
摘要:
      以含非光滑柱铰链平面多刚体系统为研究对象,将间隙充分小的柱铰链视为双边约束,用LuGre摩擦模型描述柱铰链内的摩擦;由第一类Lagrange方程导出该系统的动力学方程(微分 代数方程).铰链处的摩擦使得其动力学方程是关于Lagrange乘子的非线性代数方程组,由于LuGre摩擦模型具有很好的连续性,可将非线性代数方程组与常微分方程组的数值算法(如拟牛顿法和龙格 库塔法)相结合求解其动力学方程.最后,通过数值仿真算例说明了该算法的可行性和有效性,既能很好地反映柱铰链摩擦对系统动力学特性的影响,又能避免Coulomb干摩擦给方程求解带来的困难.
关键词:多体系统,柱铰链,Lagrange乘子,LuGre摩擦模型
Modeling and simulation of planar multibody systems with frictional revolute joints based on LuGre friction model    Download Fulltext
Xing Hang  Zheng Xudong  Wang Qi
Fund Project:
Abstract:
      This paper presented a method for modeling and simulating planar rigid multibody systems with non smooth revolute joints. The geometric constraints of the revolute joints were treated as bilateral constraints, and the tiny clearance sizes were neglected. The LuGre friction model was used to describe the tangential contact forces in the revolute joints. The dynamic equations (differential algebraic equations) were obtained by using Lagrange′s equations of the first kind. Due to the frictional forces in the revolute joints, the dynamic equations are nonlinear algebraic equations with respect to the Lagrange multipliers. Because of the perfect continuity of the LuGre friction model, numerical algorithms for nonlinear algebraic equations and differential equations,such as Quasi Newton method and Runge Kutta method, were combined to solve the dynamic equations. Finally, the feasibility and effectiveness of the method were verified by numerical examples, which showed that the method can consider the frictions in revolute joints, and at the same time also avoid the numerical difficulties caused by Coulomb dry friction model.
Keywords:multi-body system,revolute joint,Lagrange multiplier,LuGre friction model
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