考虑构件弹性的电动Stewart并联机构刚度建模与仿真

Stiffness modeling and simulation for an electric stewart parallel mechanism considering elasticity of components

基于集总解析建模方法和构件有限元分析建立包含驱动副、被动万向铰链和运动杆件弹性变形以及预载作用下的Stewart机构刚度矩阵模型。采用添加虚拟铰链等效构件弹性的方式,将分支等效为一系列刚性构件经由主、被动副以及虚拟铰链连接的形式,给出了运动关节和虚拟铰链变量对机构末端位姿的运动学Jacobian矩阵的数值计算方法,应用虚功原理得到静平衡方程,最终建立了机构无预载以及预载下的刚度矩阵模型。该模型不仅考虑了控制环路刚度,还将构件柔性的有限元分析结果与解析建模相结合,在降低计算成本的同时保证了精度。通过一机构分析实例,考察了两种模型下刚度分布的差异。

Based on lumped modeling and finite element analysis, the stiffness model of a Stewart mechanism was established considering elastic deformations of driving joints, passive universal joints and moving components and the effect of preloading. By adding virtual joints to describe the elasticity of components, a branch was equivalent to a series of rigid components connected with active, passive and virtual joints. The numerical method for moving and virtual joints＇ kinematic Jacobian matrix was developed. The static balance equation was obtained by applying the principle of virtual work, and the stiffness matrices of the mechanism without/under preloading were established. The proposed model considered the control loop stiffness, and combined the result of the finite element analysis with the analytical modeling. The computation cost was reduced while the accuracy was ensured. The stiffness distribution differences between the with/ without preloading two models were examined with an example.