考虑关节摩擦效应的并联机构动力学分析

Dynamics Analysis of Parallel Mechanism with Joint Friction

摘要:

分析了一种4-SPS/CU并联机构的运动学，将该机构的关节摩擦力视为非保守力。定量分析关节摩擦力对该机构动力学特性的影响，关键在于求出关节摩擦力对应的正压力。为了简化其动力学模型，将该机构驱动支链作为整体分析使其驱动力和驱动摩擦力视为内力，首先考虑该机构的恰约束从动关节的摩擦力，再以“库伦+粘性”摩擦模型为基础，利用牛顿-欧拉法分别对该机构的驱动支链、恰约束从动支链与上平台建立了含摩擦的动力学模型。在已知上平台运动轨迹的情况下，通过该动力学方程得到了该机构的关节约束反力/力矩。基于驱动支链正压力与各关节约束反力/力矩之间的关系，导出了该机构的驱动摩擦力模型，并成功地将驱动摩擦力引入到该机构的动力学模型中。为对该动力学模型进行有效的仿真计算，制定了其数值仿真迭代过程。仿真结果说明关节摩擦力的存在对该机构的驱动力产生显著的影响。

Abstract:

The kinematics of a 4-SPS/CU parallel mechanism was analyzed. In order to quantitatively analyze the influence of joint friction acted as non-conservative force on the mechanism dynamics, the calculation of the normal force corresponding to joint friction was important. For simplifying the dynamics model, the driving chain was treated as a rigid body so the driving friction could be seemed as internal force. Based on the “Coulomb + viscous” friction model, the dynamics model with joint friction of up platform, driving chain and driven chain were built respectively by using Newton-Euler formulation, which could obtain the joint constraint forces/torques with giving motion trajectory of the mechanism’s up platform. Subsequently, the driving friction models were established on account of the relationship between the driving chain’s normal forces and joint constraint reactions. The iterative procedure of complicated dynamics equations was formulated for the effective simulation. The research results showed that joint friction forces significantly impacted on the driving forces of the mechanism.