Performance analysis of CNC interpolators for time-dependent feedrates along PH curves

Abstract

Virtually any desired time variation V(t) of the feedrate along a curved path can be realized by real-time CNC interpolator algorithms for the Pythagorean-hodograph (PH) curves: the only stipulation is that V(t) should admit a closed-form indefinite integral F(t). Different feedrate variations V(t) can be accommodated with minimal modifications to the core algorithm by employing a modular function call to define F(t). Such time-dependent feedrate capability is invaluable in high-speed machining applications, where it can ensure smooth acceleration and deceleration control of a CNC machine under extreme torque or power demands on the axis drives. Empirical results from implementations of these time-dependent feedrate interpolators on an open-architecture 3-axis mill are presented, highlighting their exceptional performance and versatility. These results also furnish a compelling illustration of a basic defect of “traditional” (piecewise-linear/circular) G code path descriptions—namely, the fundamental conflict between geometrical path accuracy (which entails use of many short G code segments) and the accurate and smooth maintenance of rapid commanded feedrates.