Minimum-time cornering for CNC machines using an optimal control method with NURBS parameterization

Abstract

Speed and accuracy are conflicting demands that must be met by manufacturing machines. This conflict is very frequently encountered when executing sharp corners where, to achieve tight tolerances, machine axes have to slow down considerably thus sacrificing cycle time. The most common way of reducing this tradeoff between speed and accuracy is to smooth the corner using a pre-specified curve (e.g., a spline) that allows high-speed cornering subject to path tolerance and machine kinematic limits. This paper presents a different corner-smoothing approach where the smoothing curve is not specified a priori. Instead, an optimal control method is used to generate the best free-form curve that minimizes corner traversal time while adhering to path tolerance and kinematic constraints. The resulting optimal free-form curve is parameterized using an enhanced NURBS curve fitting process to allow its accurate execution in a CNC. Illustrative examples are presented to demonstrate the merits of the proposed approach.