Geometry Optimisation for 2D Cutting: A Quadratic Programming Approach

Abstract

A novel approach to geometry optimisation in the field of 2D cutting is presented in this paper. Set point generation inside of state of the art CNCs is divided in the preparation of the geometry and the feed rate generation. The feed rate generation is influenced by parametric derivatives of the given geometry. Due to this fact, the shaping of a B-Spline is carried out by optimisation of the weighted sum of parametric derivatives while the given manufacturing tolerances are maintained. For the sake of robustness, the arising optimisation problem is formulated as a quadratic program with linear constraints, one which can be solved with great efficiency by using an interior point method. In contrast to state of the art methods, the discrete formulation of the problem allows for a pointwise specification of the manufacturing tolerance. Depending on the manufacturing process, the given manufacturing tolerance is shared by different axes, which is shown for a 2D cutting geometry. An application example shows that the geometry optimisation leads to an increase in machining productivity over state of the art methods.