Arc-Length Parameterized NURBS Tool Path Generation and Velocity Profile Planning for Accurate 3-Axis Curve Milling

In modern industrial CNC (Computer Numerical Control) machining processes, the pursuing of higher accuracy and efficiency has always been one of the most important tasks to be discussed and studied. A lot of proposed algorithms are developed in order to optimize the machining performance in either of the above focused domains. Nevertheless, there is forever a trade-off between gaining less machining error and providing higher feed rate. As for machining a free-shaped curve (e.g., Bezier curves, B-splines and NURBS) in a three-dimensional space, a better manner to balance out the aforementioned trade-offs turns out to be even more critical and essential. The conventional iterative function used for tool path generation could cause feed rate fluctuation during the actual machining, and it thus might lead to failure on constraining the error within the machining accuracy requirement. Another potential problem occurs when the machining process comes across into a relatively high curvature segment with the prescribed high feed rate, due to the machine axial acceleration limit, the machine may not be able to maintain the tool tip trajectory within the error tolerance. Therefore, a new approach to NURBS tool path generation for high feed rate machining is proposed. In this work, several criterions are set for checking the viability of the prescribed feed rate and adjusting it according to the actual shape of the objective curve and the capability of the machine. After the offline feed rate viability check and readjustment, a new iterative algorithm based on the arc-length re-parameterized NURBS function would be implemented to calculate the tool path in real-time. By using this proposed method, the feed rate fluctuation is diminished and the overall efficiency of the machining process would have been optimized under the condition of accuracy guaranteed.