Dynamic simulation of a rigid-flexible coupling positioning stage base on modified floating frame of reference formulation

Abstract

A rigid-flexible coupling positioning stage (RFCPS) is proposed in this study for long-stoke-high-precision (LSHP) positioning, and its dynamic model is established. The structure of the RFCPS contains three parts: the working stage, the frame and the flexure hinge group. The flexure hinges can provide micro deformation to compensate the positioning error cause by the friction of the mechanical bearing. In order to consider the deformation of the flexure hinges, the flexible multi-body system dynamic analysis method is adopted to establish the dynamic model of the RFCPS. The investigation of the principle model demonstrates that the floating frame of reference formulation (FFRF) has higher accuracy than the absolute nodal coordinate formulation (ANCF) for the deformation analysis of the RFCPS. Sequentially, a finite element based model (FE model) is established by using the FFRF. Numerical simulation results shown that the results of the FE model is consistent to the analytical solution, and the deformation of the flexure hinges is effectively obtained. The establishment of the dynamic model lays the foundation for structural optimization and control system design of the RFCPS.