变压强研磨数学力学原理与去除效率分析

The effect of varied lapping pressure on the material removal rate of optics lapping

提出了大型光学镜面变压强的高效研磨方法.传统研磨中普遍采用常压研磨的方式,很大程度上阻碍了去除率与收敛率的进一步提高.大量实验表明去除效率与压强之间并非线性关系,本文从研磨盘、磨粒与工件的几何学关系推导变压强条件下有效磨粒的分布规律,进而建立压强、磨粒运动形式与材料去除方式的映射关系,研究变压强条件下材料去除机理以及磨粒运行轨迹的微分几何描述,进而推导变压强条件下的非线性去除函数;通过音圈电机驱动的变压强研磨工具,利用机器人研磨平台实现了大型光学镜面的变压强高效研磨.

SiC and Zerodur are materials often used in spacing optics. This material is hard and brittle, difficult to manufacture. With the increasing size of optics, the effectiveness of optics manufacture has become a key problem in optics system. As an important part in optics manufacturing process, lapping in computer controlled optics surfacing （CCOS） use time-invariant tool influence function （TIF） and features with low removal rate and edge effect, this had a bad impact on the subsequent process. The structure of lathe is no longer suit for optics lapping as the size become larger. The high effective lapping method for large optics is an extreme important problem in optics manufacturing. Invariant pressure in conventional lapping restricts further advancement in material removal rate and convergence rate. This paper presents material removal mechanism with varied lapping pressure for an intelligent lapping pressure schedule to match the geometric properties of the error surface. Relationship between pressure and statistical distribution of abrasive status is established based on the geometrical and mechanical properties of the workpiece, abrasive and lapping pad. Removal mechanism and nonlinear removal rate with varied lapping pressure is deduced through the collective removal behavior of abrasive. Furthermore, to better match the error surface, material removal along freeform curve is developed through the differentiation of trajectory. The results of lapping a SiC optics with varied pressure demonstrated superior material removal rate and convergence rate over constant pressure. Lapping with varied pressure is proposed to increase the efficiency. With varied lapping pressure, the transforming distance between the pad and workpiece changes the abrasive number participating in lapping, as well as the pressure on each abrasive. It results in varied proportion of movement pattern of abrasive and corresponding removal pattern. Removal mechanism and nonlinear removal rate with varied lapping pressure distinct from Preston＇s equation is deduced through the collective removal behavior of abrasive. Bio-inspired from handwork lapping, surface characteristics of error profile and pressure distribution along the trajectory is obtained. The results point out that pressure-variant lapping contributes to further decrease the process time, and thus to make a computer controlled lapping process more efficient. The platform for large optics robot lapping is established. Varied pressure is realized through voice coil motor. The reduction of the process time was observed to approximately 30% using a combination of the dwell time method with pressure-variant tool influence function compared to stable pressure lapping.