Construction of Three-Workpiece Lapping Process

A new method, designated three-workpiece lapping, is proposed to produce flat surfaces of all the three workpieces prepared through some stages of reciprocation lapping, which is performed by a simple machine, by choosing appropriate combinations of upper, lower and waiting workpieces. Simulated and experimental results show that the parabolic shapes of the surfaces are maintained during lapping and two inherent properties exist in the change of profile parallel to the reciprocation, that is, (1) upper workpiece and lower one become concave and convex respectively as lapping proceeds and (2) they tend to fit each other, while only the second property is observed in the change of profile perpendicular to the reciprocation. Linear vector differential equations are introduced to represent the above properties and the stages required to get flat surfaces are deduced by constructing trajectories which express the changes of the shapes on the spaces where the differential equations are given.