The Algorithms of the Cross-Coupled Precompensation Method for Generating the Involute-Type Scrolls

Abstract

Cross-coupled precompensation method (CCPM) has been proven efficient in tracking nonlinear spatial curves. It requires a path generating algorithm derived from the mathematical equation of the target curve. This paper discussed the time base transform of target curve from a parametric form. The time based path generating algorithm for the extended involute scroll was then proposed. A comparison among three kinds of tool path generating algorithms were performed. The proposed path algorithms, along with other two algorithms, were implemented and tracked by four different control schemes, US (uncoupled-unprecompensated system), CCS (cross-coupled system), PPM (path precompensation method), and cross-coupled precompensation method (CCPM). The proposed path algorithm for extended involute scroll provided the best accuracy. The proposed algorithm tracked by CCPM achieved the most precise profile especially at high feedrates.