无理数转速比下的平面研磨轨迹均匀性研究

Analytical study on uniformity of path distribution with irrational rotational speed ratio in plan lapping process

平面研磨过程中磨粒与工件的相对运动轨迹分布对工件表面质量有重要影响。针对有理数转速比下的研磨加工过程中磨粒轨迹重复的问题,对磨粒相对工件的运动轨迹进行了研究,分析了典型的定偏心式主驱动方式平面研磨过程中磨粒轨迹对抛光均匀性的影响,提出了一种无理数转速比的平面研磨加工方法,利用Matlab工具对无理数转速比平面研磨加工进行了运动学仿真,理论分析了基于螺旋线磨粒排布的研磨盘在无理数转速比下的磨粒轨迹均匀性。仿真结果表明,无理数转速比下的磨粒轨迹线是开放的,其在均匀性方面优于有理数;对于不同无理数转速比,研磨轨迹均匀性随着转速比的增大而提高,但随着研磨时间的增加其均匀性趋于相同。该研究为无理数转速比平面研磨抛光设备的研制提供理论依据。

The distribution of particle sliding trajectories on wafer surface possessed great importance in the machined work-piece surface quality. Aiming at the problem that particle sliding trajectories with rational rotational speed ratio was periodic, the trajectory simulations were carried out based on the kinematic analysis. Numerical simulations of particle sliding trajectories were performed to examine the influ- ence of the kinematic parameters on the polishing uniformity of typical rotary-type lapping equipment. A method of plane lapping with irra- tional rotational speed ratio was presented. The kinematic analysis and numerical calculation were used to discuss the effect of the rotating speed ratio on the trajectory uniformity by using Matlab and the lapping plate with preferred helix arrangement of fixed particle was selected. The results indicate that the trajectory distribution with irrational rotational speed ratio is more intensive and complicate than that with rational rotational speed ratio. For different irrational rotational speed ratio, the uniformity of trajectory distribution increases with increasing of rota- tional speed ratio gradually but it is more uniform with increasing of lapping time. The research provides theoretical guide to the design and development of new plan lapping equipment with condition of irrational rotating speed ratio.