高速柔性并联平台的动力学分析

Dynamic analysis of a high-speed flexible parallel manipulator

在考虑轴向力影响下,对刚柔耦合3-PRR平面柔性并联平台进行了动力学建模,分析了柔性并联平台的动力刚化问题和屈曲行为。柔性并联平台由动平台、静平台和三根对称的柔性梁组成,运用拉格朗日法和假设模态法对系统进行了刚柔耦合动力学建模,并建立了柔性梁振动频率和轴向力之间的函数关系。Matlab仿真结果表明:柔性梁受到的轴向力和动平台的速度及位形相关,当柔性梁受轴向拉力时,出现动力刚化现象,固有频率增加;当柔性梁受轴向压力时,出现动力柔化现象,固有频率减小;当轴向压力增加达到极限值时,柔性梁会发生屈曲行为。模态试验和不同速度下的轨迹控制实验验证了所建动力学模型和理论分析的正确性。

To investigate the dynamic stiffening and buckling behavior of a rigid-flexible coupled 3-PRR parallel manipulator under the effect of axial forces,a dynamic model of the manipulator is developed.The parallel manipulator is comprised of a moving platform connected to the static stage by three symmetric independent flexible links.Based on the Lagrange method and the assumed mode method,the overall rigid-flexible dynamic model and the functional relationship between the natural frequencies of the flexible links and the axial forces are obtained.Matlab simulation results show that：the axial forces of the flexible links are related to the speed and configuration of the moving platform,and the dynamic stiffening occurs when the flexible links are in tension;On the contrary,the dynamic softening occurs when the flexible links are in compression,and buckling happens for the flexible link when the moving platform reaches its limited speed.Modal testing and motion tracking experiments with different velocities are carried out,and the results validated the proposed dynamic model and theoretical analysis.