Two-stage LP/NLP feedrate optimization for spline toolpaths

Abstract

Feedrate optimization is an inherently nonlinear and complex problem, but also critical to enhancing the productivity of multi-axis machining operations. This paper presents a new approach to utilize linear programming (LP) alongside nonlinear programming (NLP) in a dual windowing configuration, for optimizing the feed profile for long spline toolpaths. LP is able to handle kinematic constraints of limiting axis velocity, acceleration, and jerk. NLP, afterwards, solves the minimum time problem subject to less conservative, albeit nonlinear, motor torque and servo error constraints. While NLP adds nearly an order of magnitude computation time, in the simulation case studies conducted, it was seen to improve motion time by typically 30 %. The optimized trajectory was also tested on a 3-axis router.