Journal
INTERNATIONAL JOURNAL OF ADVANCED MANUFACTURING TECHNOLOGY
Volume 58, Issue 1-4, Pages 327-338Publisher
SPRINGER LONDON LTD
DOI: 10.1007/s00170-011-3394-3
Keywords
CNC machine; High-speed machining; Feedrate; Contour error; Cornering; Path modification; Constrained optimization; Linear programming
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To exactly execute a sharp corner in the toolpath, the feedrate of a CNC machine must instantaneously drop to zero at that point. This constraint is problematic in the context of high-speed machining, since it incurs very high deceleration/acceleration rates near sharp corners, which increase the total machining time, and may incur significant path deviations (contour errors) at these points. A strategy for negotiating sharp corners in high-speed machining is proposed herein, based upon a priori toolpath/feedrate modifications in their vicinity. Each corner is smoothed by replacing a subset of the path that contains it with a conic splice segment, deviating from the exact corner by no more than a prescribed tolerance I mu, along which the square of the feedrate is specified as a Bernstein-form polynomial. The problem of determining the fastest traversal of the conic segments under known axis acceleration bounds can then be formulated as a constrained optimization problem, and by exploiting some well-known properties of Bernstein-form polynomials this can be approximated by a simple linear programming task. Some computed examples are presented to illustrate the implementation and performance of the high-speed cornering strategy.
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