Application of maximum entropy principle in plane lapping

With technology developing, there are increasing demands for the high-quality optical elements, as well as the related processing techniques and equipments. The plane lapping tool uses a rotating tool which overlaps the workpiece surface. By accurately controlling processing parameters, a prescribed amount of material may be removed at each point on the surface. Thus the key for us to increase lapping accuracy of optical elements is to select the optimal processing parameters. In this study, the technique of ultra-precision plane lapping is the subject. A method based on maximum entropy principle is presented to express the lapping effect and optimize processing parameters in plane lapping. We aim to provide valuable scientific foundation for improving present processing techniques and equipments and finally to increase machining accuracy and efficiency. In this paper, mathematic formulation and corresponding physical explanations for the lapping entropy are established. Moreover, the processing parameters in eccentric plane lapping are computed. The computational results show that in eccentric plane lapping the same rotational speed of the workpiece and lapping tool should be selected to remove material equably, and that a rather large eccentricity ratio should be selected to increase lapping efficiency. To reduce the influence of the wear on lapping accuracy, the lapping tool should be refaced on real time. The optimization method we have used possesses advantages of simplicity, intuition and generality. Using the optimized parameters, we have successfully fabricated a SiC workpiece whose flatness error has reduced from 1.9 μm to 0.18 μm in a short time.