2016 Volume 5 Issue 2 Pages 53-60
The key task performed by CNCs is the generation of the time sequence of set points for driving each physical axis of the machine tool during program execution. This interpolation of axes movement must satisfy a number of constraints on axes dynamics (velocity, acceleration, and jerk), and on process outcome (smooth tool movement and precise tracking of the nominal tool path at the desired feed rate). This paper presents an algorithm that aims at solving the axes interpolation problem by exploiting an optimal control problem formulation. Unlike other solutions proposed in the literature, the approach presented here employs an original approach by assuming a predefined path tracking tolerance—to be added to the constraints listed earlier—and calculating the entire trajectory (path and feed rate profile) that satisfies the given constraints. The proposed solution is used for preprocessing a milling part program and redefining the sequence of positioning commands to cope with the solution of the OC problem. The new part program is then executed by a state-of-the-art industrial CNC, and the effectiveness in reducing execution time and axes accelerations is experimentally tested and reported.