Previous  Next CONTACT

About | ECITTT | Conference Programme | Abstracts (9.)


Prof Rida T Farouki
Dept. of Mechanical and Aeronautical Engineering,
University of California, Davis, CA 95616.

The performance of modern CNC machines is severely constrained, especially in high-speed machining applications, by the need to approximate complex tool paths by numerous short linear/circular (G code) segments. Apart from the voluminous part programs such approximations entail, they incur a fundamental conflict between nominal geometrical accuracy and the ability to smoothly realize and maintain high feedrates and feed accelerations.

We describe a novel approach to circumventing this problem, based on the Pythagorean-hodograph (PH) curves. These polynomial curves, fully compatible with the standard Bezier/B-spline representations of CAD systems, are characterized by a special algebraic structure that makes them ideally suited to the problem of real-time interpolation at constant or variable feedrates on CNC machines. In particular, the "interpolation integral" for such curves admits a closed-form analytic reduction for feedrates that are constant or dependent on time, arc length, or curvature. The PH curves also have rational offsets, that can be executed directly by the interpolator.

The theoretical foundations for PH curves are briefly surveyed, and a variety of experimental results from the implementation of a suite of real-time PH curve interpolators on an open-architecture 3-axis CNC milling machine are presented. Compared to traditional linear/circular G code interpolators, the PH curve interpolators offer compact part programs; much smoother realization of commanded feedrates, and thus better surface finish; optimization of machining times through use of the variable-feedrate capability; control over machining force variations using curvature-dependent feedrates; and elimination of G code block-to-block feedrate fluctuations and the "block-look-ahead" problem in high speed machining.