5-UPS/PRPU冗余驱动并联机床弹性动力学分析

Elastodynamics Analysis of a 5-UPS/PRPU Redundantly Actuated Parallel Machine Tool

结合有限元法和子结构法建立了5-UPS/PRPU冗余驱动并联机床的弹性动力学模型。首先,将系统划分为不同的子结构,根据空间柔性梁理论求出单元动力学方程,根据关节特点将各个梁单元组装成各个驱动分支;根据分支与动平台的运动学/动力学约束,将各个分支进行装配,从而得到系统动力学方程。以5-UPS/PRPU冗余驱动并联机床作为算例,求出其动平台中心的动态响应特性。通过比较5-UPS/PRPU冗余驱动并联机床及5-UPS/PRPU非冗余驱动并联机床动平台的动态响应,可以得到结论:冗余驱动可以明显改善该机床弹性动力学特性,从而减小因弹性变形引起的误差。研究结果为结构设计人员进行结构设计及优化提供可靠的依据。

An elastodynamics model of the 5-UPS / PRPU redundantly actuated PMT was derived by combining the finite element model and substructure synthesis techniques herein. Firstly,the overall system was divided into different substructures. According to the theory of spatial beam element,the dynamics equation of the spatial beam element was derived,and then assembling into different driving limbs; according to the dynamic constraints and kinematic constraints among the moving platform and each driving limbs,the dynamics equation of the overall system might be obtained by assembling the dynamics equation of the driving limbs. The 5-UPS /PRPU redundantly actuated PMT was set as an example to illustrate the derivation of the dynamic response of the moving platform. At last,by comparing the dynamic response of the redundantly actuated PMT and its non-redundant PMT,it can be concluded that： the elastodynamics performance of the PMT may be improved by the actuation redundancy,so that the errors caused by the driving limb deformations can be reduced as well. The research provides a theoretical reference of the structure design and optimization for the designers.