Dynamic Behavior Analysis Of Spatial Parallel Mechanism With Clearance

The parallel mechanism has been widely used in space simulator,parallel robot manipulator,processing machinery,food packaging and medical field due to its advantages of large stiffness,high precision,strong bearing capacity,flexible to achieve spatial attitude and so on.The spherical pair is one of the common kinematic pairs in spatial parallel mechanism.The existence of clearances in spherical pairs is common phenomenon due to the errors in the process of manufacturing and assembly.The spherical pair clearances will lead to the collision between the spherical elements,which cause the vibration and noise,even deteriorate the dynamic performance of the mechanisn.Therefore,it is necessary to study the dynamic characteristics of spatial parallel mechanism with spherical clearance.In this paper,4-UPS.RPU spatial parallel mechanism is taken as the research object,and the dynamic modeling and dynamic behavior analysis of parallel mechanism with spherical clearance are systematically studied.The main contents are as follows:Firstly,kinematic model of 4-UPS-RPU parallel mechanism with spherical clearance was established.Based on the geometric relation of spherical pair clearance.the kinematic model of spherical pair with clearance is established.The normal contact force and tangential contact force are calculated by Lankarani-Nikravesh contact impact model and modified Coulomb friction model,respectively.The contact force between the spherical elements was embedded in the dynamic model with ideal spherical,and the dynamic model of the spherical with clearance was obtained.Then,the dynamic equation of the spatial parallel mechanism considering spherical pair clearance is solved based on the Runge Kutta method.The influences of different trajectories and different spherical pair clearance values on displacement,velocity,acceleration of the centroid point of moving platform and contact force were analyzed.The influences of different clearance values on center trajectory and embedding depth were both studied,and the chaotic characteristics of the parallel mechanism with spherical pair clearance were qualitatively and quantitatively analyzed by using phase trajectory-Poincare mapping and Lyapunov exponent.Finally,the basic theory of wear is expounded,and the Archard wear model and the Reye 's hypothesis wear model are compared and analyzed.Based on the Archard wear model,the model of three-dimensional wear depth of spherical pair with clearance is established from the perspectives of slip distance and contact velocity respectively.The three-dimensional wear characteristics of spatial parallel mechanisms with spherical pair clearance under different clearance values are compared and analyzed,which lays a good foundation for the research on the wear of the parallel mechanism with spherical pair clearance.