Lapping trajectories analysis and experimental study of the miniature balls lapping process using a plate with discontinuous sectors of fixed abrasives

To address the high process efficiency and quality requirements for the ultra-precision machining of miniature balls used in small bearings, a new lapping method is proposed using an upper plate with discontinuous sectors of fixed abrasives (PDSFA) in which the spin angle of the miniature ball changes periodically in an abrupt manner so that the lapping trajectories can fully envelop the ball surface to generate a uniform machining process. A kinematic model is developed for the PDSFA lapping process, which introduces a coefficient of slip ratio between the ball surface and the lapping plate and generates the lapping trajectories and the variations of the spin angle of the miniature ball. The effect of the slip ratio coefficient on the distribution of lapping trajectories and the fluctuations of the spin angle are discussed. A dynamic simulation study is then undertaken using the commercial ADAMS software to generate lapping trajectories for the PDSFA lapping process, which is used to assess the effectiveness of the kinematic model predictions and verified by lapping experiment. An experiment is finally performed with three types of PDSFA plates for three slip ratio coefficients to assess the developed models and the viability of the new lapping process. The effects of process parameters on the roundness and surface roughness of miniature balls are also apply discussed. It shows that when the eccentric V-groove lower lapping plate rotates at 40 rpm under the lapping pressure of 0.3 N/ball, the roundness and surface roughness of the balls lapped using resin-bonded silicon carbide as the abrasive material in the fixed abrasive sectors outperform the other abrasive materials considered in the work, in which both the ball roundness and surface roughness reduce monotonically from the initial 1.03 μm (RON_t) and 0.119 μm (R_a), respectively, to 0.10 μm (RON_t) and 0.008 μm (R_a) within 5 h of lapping and 3 h polishing.