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Smoothing of Time-Optimal Feedrates for Cartesian CNC Machines

  • Casey L. Boyadjieff
  • Rida T. Farouki
  • Sebastian D. Timar
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3604)

Abstract

Minimum-time traversal of curved paths by Cartesian CNC machines, subject to prescribed bounds on the magnitude of acceleration along each axis, usually involves a “bang-bang” control strategy in which the acceleration bound is realized by one or another of the machine axes at each instant during the motion. For a path specified by a polynomial parametric curve and prescribed acceleration bounds, the time-optimal feedrate may be expressed in terms of a C 0 piecewise-rational function of the curve parameter. This function entails sudden changes in either the identity of the limiting axis, or the sign of acceleration on a single limiting axis, incurring demands for instantaneous changes of motor torque that may not be physically realizable. A scheme is proposed herein to generate smoothed C 1 (slightly sub-optimal) feedrate functions, that incur only finite rates of change of motor torque and remain consistent with the axis acceleration bounds. An implementation on a 3-axis CNC mill driven by an open-architecture software controller is used to illustrate this scheme.

Keywords

Tool Path Switching Point Traversal Time Axis Acceleration Acceleration Constraint 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Casey L. Boyadjieff
    • 1
  • Rida T. Farouki
    • 1
  • Sebastian D. Timar
    • 1
  1. 1.Department of Mechanical and Aeronautical EngineeringUniversity of CaliforniaDavisUSA

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