Comprehensive Stiffness Modeling and Posture Optimization of Robotic Bonnet Polishing System

Abstract

The introduction of a metal rubber vibration damper into a robotic bonnet polishing system can effectively dissipate high-frequency chatter energy and significantly improve the machined surface quality of optical components. However, its inherent porous elastic characteristics inevitably introduce a series compliance link at the end-effector, leading to a decrease in the macroscopic normal static stiffness of the system. This makes it highly susceptible to trajectory deviation and insufficient deformation resistance under polishing contact forces. To seek the optimal balance between "microscopic dynamic vibration reduction" and "macroscopic static high stiffness", this paper investigates comprehensive stiffness modeling and posture optimization methods considering end-effector compliance. First, based on the classical joint stiffness model of industrial robots, the vibration damper is equivalently transformed into a spatial compliance matrix to construct a comprehensive static stiffness analytical model of the polishing system. The anisotropic characteristics of the spatial stiffness at the end-effector are thoroughly analyzed using the compliance ellipsoid theory, and an evaluation index for maximizing normal stiffness oriented to actual processes is proposed. Second, taking redundant posture angles such as the bonnet precession angle as optimization variables, a posture optimization mathematical model based on Particle Swarm Optimization (PSO) is established. This aims to actively compensate for the loss of end-effector stiffness by adjusting the posture of the robot body. Finally, finite element simulations and dwell-spot polishing experiments are carried out. The results demonstrate that the optimization algorithm effectively mobilizes the optimal stiffness direction of the robot body, successfully overcoming the weakness of static deformation while fully leveraging the vibration reduction advantages of the metal rubber. Under the optimized posture, the surface roughness of quartz glass in spot polishing is significantly reduced from 0.101 μm in the conventional posture to 0.025 μm, representing a reduction of 68.3%. This study provides a new perspective for the collaborative control of "vibration reduction and stiffness enhancement" for low-stiffness robots in the field of precision polishing.