计及铰链间隙的机械臂动力学建模与仿真

Modeling and Simulation of a Mechanical Arm with Joint Clearance

工程中的机械多体系统都存在铰链间隙问题,铰链间隙使系统的约束条件、自由度数目和拓扑结构发生变化.根据Hertz接触定律和Coulomb摩擦定律,建立了含间隙平面旋转铰的力学模型;采用几何变形约束法和模态缩聚技术描述了柔性机械臂的非线性变形;同时考虑两个旋转铰的间隙特性和柔性臂的弹性,最终采用Kane方程建立了含铰链间隙的刚-柔机械臂系统的动力学模型.以Mathematica软件为编程工具.对含两个铰链间隙的双刚性臂系统进行了仿真计算,得到了更加真实的动力学响应.

Joints are usually treated as ideal ones in traditional mechanical multibody dynamics. But in engineering, joint clearance exists in mechanical multibody systems. The constraint conditions, degree of freedom, topological structures of the mechanical system are affected by joint clearance. In some cases, it is important to consider joint clearance and its effects on the dynamic responses. A two-beam mechanical ann with one rigid beam and one flexible beam is studied. Based on Hertz＇s contact law and Coulomb＇s friction law, mechanical model of the planar revolute joint with clearance is built. And the elastic distortion of the flexible beam is described by geometrical deformation constraint method and modal condensation. According to Kane＇s equation, complete dynamic model of the mechanical arm considering two planar revolute joints with clearance is built. Computer code is developed by Mathematica software and simulation of a mechanical arm with two rigid beams and two joint clearance is made. The simulation results show that the clearance has great influence on the angular acceleration, but it has little influence on the angular displacement. The theory and method presented in this paper can be further applied to studying the dynamic accuracy, abrasion and vibration of mechanical multibody systems with joint clearance.