High-speed cornering by CNC machines under prescribed bounds on axis accelerations and toolpath contour error

Original Article

Abstract

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 ϵ, 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.

Keywords

CNC machine High-speed machining Feedrate Contour error Cornering Path modification Constrained optimization Linear programming 

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Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

  1. 1.Department of Mechanical and Aerospace EngineeringUniversity of CaliforniaDavisUSA

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