Semi-Continuous Interpolation Algorithm for Aspherical Surface Grinding

This paper proposed a tracking algorithm for the tool path of an aspherical surface in the grinding process. The algorithm is based on the concept that an operator simply puts in lens constants on the machine, and the grinding tool follows the lens surface. The ideal equation of a grinding tool path was derived from an aspherical lens equation. The path was sectioned by an arbitrary interval. The inputs of the algorithm, the acceleration and velocity, were determined from the position error at the beginning of the step. The velocity and the acceleration were updated by the position error and velocity of the previous step. This update smoothed the tool path and increased continuity. The algorithm was demonstrated on a 2-axis machine which had ball-screws and air-guide. The tool moved on both convex and concave surfaces by the proposed algorithm. Error was monitored by the change of the tool diameter. The maximum position error was under sub-micro level.