Physical constraints on feedrates, feed accelerations along curved tool paths

To achieve a desired fixed or variable speed (feedrate) along a given curved path, CNC machines employ independent motors to drive each of their axes in a time-coordinated manner. There are physical limits to the torque and power that the motors can supply, and the machine performance is compromised if the demands of overcoming machine inertia, cutting forces, and friction exceed these limits. Assuming fixed upper bounds on the motor torque and power available to each axis, we develop analytical tools that can be employed in a pre-processing capacity to identify the maximum safe fixed feedrate along a curved path, and safe rates of increase of feedrate with time or arc length. It is shown that, for the PH curves, determining the largest safe constant feedrate can be reduced to computing the maxima of rational functions over [0,1], and identifying safe feed acceleration rates can be phrased in terms of finding the smallest width τ of an interval [0, τ ] over which certain polynomials remain root-free.  2000 Elsevier Science B.V. All rights reserved.