High speed CNC system design. Part I: jerk limited trajectory generation and quintic spline interpolation

Abstract

Reference trajectory generation plays a key role in the computer control of machine tools. Generated trajectories must not only describe the desired tool path accurately, but must also have smooth kinematic profiles in order to maintain high tracking accuracy, and avoid exciting the natural modes of the mechanical structure or servo control system. Spline trajectory generation techniques have become widely adopted in machining aerospace parts, dies, and molds for this reason; they provide a more continuous feed motion compared to multiple linear or circular segments and result in shorter machining time, as well as better surface geometry. This paper presents a quintic spline trajectory generation algorithm that produces continuous position, velocity, and acceleration profiles. The spline interpolation is realized with a novel approach that eliminates feedrate fluctuations due to parametrization errors. Smooth accelerations and decelerations are obtained by imposing limits on the first and second time derivatives of feedrate, resulting in trapezoidal acceleration profiles along the toolpath. Finally, the reference trajectory generated with varying interpolation period is re-sampled at the servo loop closure period using fifth order polynomials, which enable the original kinematic profiles to be preserved. The proposed trajectory generation algorithm has been tested in machining a wing surface on a three axis milling machine, controlled with an in house developed open architecture CNC.