Novel Feedrate Optimization Method for NURBS Tool Paths Under Various Constraints

A good feedrate profile for NURBS tool paths should be able to consider both machining efficiency and motion limits. In other words, the feedrate profile can lead to the machining time as small as possible and can satisfy various path and axis motion constraints. However, owing to the complicated relationship between trajectory motion and axes, it is difficult and time-consuming to check axis motion constraints (e.g., axis velocity, axis acceleration, axis jerk). In addition, the path length is not easy to calculate, so the machining time cannot be accurately estimated. This paper presents a feedrate profile planning method that can easily include, delete or organize the constraints and minimize the machining time for NURBS tool paths. The key idea is to use the same parameter
$u$
to represent both NURBS tool path and feedrate profile. When designing the feedrate profile with
$u$
, an analytical form of machining time can be obtained, and the constraints are converted into functions of
$u$
(including feedrate, tangential acceleration, tangential jerk, axis velocity, axis acceleration, axis jerk, chord error, and centripetal acceleration), which can be quickly checked. Particle swam optimization algorithm is employed to eliminate the solutions with long machining time or do not meet the constraints, and gradually optimize the feedrate profile. In the simulation, a star-shaped NURBS curve is selected to demonstrate the effectiveness of the proposed method. The results show that the proposed method can achieve not only smooth and high-speed machining under various constraints, but also high accuracy with the minimization of position error at the final interpolation point.