Efficient high-speed cornering motions based on continuously-variable feedrates. II. Implementation and performance analysis

Abstract

A novel high-speed cornering strategy for piecewise-linear motions is proposed, based on the G 2 continuous Pythagorean-hodograph (PH) rounding segments and continuously-variable feedrates described in Part I of this two-part paper. This strategy employs an accelerationlimited approach to feedrate scheduling, including smooth deceleration and acceleration profiles along linear segments entering and leaving the rounded segments. A G-code part program parsing software package has been developed, that automatically identifies toolpath corners and inserts appropriately-sized PH quintic corner rounding segments, with associated feedrate suppression ratios. The method has been tested on a three-axis CNC mill with an openarchitecture controller incorporating real-time interpolators that realize smoothly varying feedrates along the PH corner curves. Tests on a representative selection of toolpaths yield substantial savings (up to 40 %) in execution times, compared to the traditional "full stop" strategy for unmodified sharp corners.

Optimization of Corner Blending Curves

“…The rounding of sharp corners in piecewise-linear loci has been considered by many authors, most frequently in the context of ensuring smoother execution of G code part programs in CNC machining [2,6,8,21,27,28,29,36]. The emphasis in these studies is mainly on ensuring smooth (G 1 or preferably G 2 ) junctures of corner curves with the linear segments they connect, to preclude velocity or acceleration discontinuities.…”

“…In consumer products design, for example, rounded corners are often preferred to satisfy aesthetic or ergonomic considerations, and in the design of load-bearing mechanical components, the rounding or "filleting" of sharp corners is essential in minimizing stress concentration and thereby enhancing fatigue life. In CNC machining, sharp corners in piecewise-linear toolpaths must be rounded to permit accurate high-speed execution without incurring excessive decelerations and accelerations [2,8,18,19,21,25,26,27,28,29]. An analogous concern occurs in the layout of highways or railways, wherein precise control of the curvature of transition curves is required to guarantee compatibility with prescribed safe vehicle traversal speeds [1,17,23,24].…”

Efficient high-speed cornering motions based on continuously-variable feedrates. I. Real-time interpolator algorithms

“…The companion paper [11] presents a detailed experimental performance analysis for this corner-rounding strategy, including the acceleration-limited selection of feedrate parameters for the rounded corner curves and the linear segments between them, through implementation on a 3-axis CNC machine with an open-architecture controller. This implementation demonstrates the significant practical benefits of the proposed cornering scheme over the simple "full stop" method for exact execution of sharp corners.…”

“…The present paper develops the mathematical formulations and algorithms required for the construction and analysis of the G 2 PH quintic corner curves, and real-time interpolator algorithms for representative feedrate variations. A companion paper [11] presents detailed results from an implementation on a 3-axis CNC milling machine with an open-architecture contoller.…”

“…Finally, Section 7 analyzes the accelerations of the individual machine axes incurred by the cornering strategies (with an emphasis on the first feedrate function), while Section 8 recapitulates the main points of this study and directs the reader to the companion paper [11].…”