Linear programming feedrate optimization Adaptive path sampling and feedrate override

Abstract

This paper focuses on two aspects of feedrate optimization via linear programming methods. Namely, the effect of curve sampling on time optimality of the resultant feedrate profile and a method of feedrate profile adaptation in response to a feedrate override command. A comparison of three distinct curve sampling approaches (uniform in parameter, uniform in arc length and curvature adaptive) is performed on a series of standard tool path curves. Results show that the curvature-adaptive sampling approach leads to substantial machining time reduction for tool path curves displaying high degree of curvature variation. Secondly, a method by which a new feedrate profile can be calculated in response to a feedrate override command is developed. The method formulates a new set of boundary conditions on the control point sequence of the feedrate curve in such a way that the resulting profile is guaranteed to coincide with the currently active profile up to the moment of override command, while minimizing the arc length necessary for transition to the newly commanded feedrate.