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.
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Boyadjieff, C.L., Farouki, R.T., Timar, S.D. (2005). Smoothing of Time-Optimal Feedrates for Cartesian CNC Machines. In: Martin, R., Bez, H., Sabin, M. (eds) Mathematics of Surfaces XI. Lecture Notes in Computer Science, vol 3604. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11537908_6
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DOI: https://doi.org/10.1007/11537908_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-28225-9
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