一种含间隙并联机构动力学仿真与混沌响应分析

Dynamicsimulation and chaotic responses analysis of a parallel mechanism with clearance

以自主提出的一种两转动一移动解耦并联机构为研究对象,考虑机构虎克铰中间隙,应用拉格朗日法建立机构动力学模型,根据Lankarani-Nikravesh接触力模型计算法向接触力,采用AMBROSIO提出的修正的Coulomb摩擦力法则计算切向接触力,并借助MATLAB软件予以数值求解;绘制机构相轨迹图,基于wolf法计算最大Lyapunov指数并据此定量判别机构的混沌运动,分析间隙对机构位移、速度、加速度及接触力的影响,并研究不同间隙大小及输入速度对机构混沌运动状态的影响。研究内容对机构进一步的动力学参数设计及混沌运动控制具有一定的指导意义。

A two rotational and one translational decoupled parallel mechanism was taken as the research object, considering the clearance existing in the Hookejoint of the mechanism, the dynamic model of the mechanism was established by using Lagrange method. Lankarani-Nikravesh contact force model was used to calculate the normal contact force, and the modified Coulomb friction force model proposed by Coulomb was used to calculate the tangential contact force. The equations were solved by MATLAB software, and the phase trajectory of the mechanism was plotted. The largest Lyapunov index method was calculated with wolf method, which is the basis to distinguish the chaotic motion of the mechanism quantitatively. The influence of the clearance on the mechanism displacement, velocity, acceleration and contact force was analyzed, and the influence of different clearance values and input speeds on the chaotic motion status of the mechanism was analyzed. The research contents possesscertain theoretical guidance significance for the further dynamic parameter design and chaotic control of the mechanism.