Kinematics and trajectory in processing precision balls with eccentric plate and variable-radius V-groove

Abstract

A fine processing method for precision balls is developed based on eccentric plate and variable-radius V-groove (EPVV) method. The ball-spin angle is a key kinematical parameter affecting the generation of spherical surface. The geometry and kinematics of workpiece was theoretically analyzed, and then ball-spin angles θ and γ and trajectory on the spherical surface can be obtained. The standard deviation (SD) of trajectory density is used to quantitatively evaluate the trajectory distribution. Under the condition of equal rotation speeds of upper and lower plates, the ball-spin angles θ and γ can vary continuously within a range of 0°–180° and the trajectory can be distributed over the entire spherical surface after a processing cycle, which was proved by an experimental observation. From the result of polishing experimental in which the deviation of surface roughness (Ra) at different positions on single ball surface decreased from 38 to 11 nm, the trajectory distribution of EPVV method was demonstrated to be improved. The effects of polar radius of V-groove curve, eccentricity, and V-groove half-angle on the ball-spin angles θ and γ and trajectory distribution were also investigated.