Toward the complete practicability for the linear-equation dwell time model in subaperture polishing.

This study intends to address several problems that are still obstructing the complete practicability of the linear equation dwell time model (LEDTM) used in deterministic subaperture polishing, including memory cost, time cost, arbitrary boundary, and arbitrary tool path. For a large-scale surface error matrix, the memory cost and time cost are two major problems of concern. Here, we present a method that uses the operation of a sparse matrix to build and store the coefficient matrix of the linear equation, which can reduce the memory cost and time cost tens to hundreds of times, thus making LEDTM readily deal with a large-scale surface error matrix on a common personal computer, with a time cost of ∼1-6  s for a surface error matrix with a scale of 300×300 to 600×600. The compatibility for an arbitrary surface error boundary and tool path is also addressed. Using the proposed method, we believe the LEDTM reaches a complete practicability in engineering.