MPCC-Based Set Point Optimisation for Machine Tools

Abstract

Numerical control code is typically used for manufacturing a workpiece using machine tools. Most state-of-the-art approaches decouple the set point optimisation into two steps: the geometry and the feed rate optimisation that does not necessarily result in time-optimal set points for the desired geometry. Given the originally programmed geometry through the numerical control code, dynamic constraints of the machine tool, and maximum permissible contour error for the optimisation, a model predictive contouring control based set point optimisation approach is developed to generate time-optimal set points for machine tools globally. A suitable error definition and its linearisation are used whereby the optimisation problem can be represented by a quadratic programming problem with linear constraints. Compared to most state-of-the-art methods, a direct approach is presented and no previous geometry optimisation step is required. Depending on the demands of accuracy, different maximum contour error constraints and penalisation as well as various maximum permissible axis velocities and accelerations are presented and tested on a test bench. The method is shown to be adaptable to different demands on the set points, and the contour errors can be affected by either the constraints or penalising factors.