Hermite Quartic Splines for Smoothing and Sampling a Roughing Curvilinear Spiral Toolpath

Abstract

From an industrial point of view, the milling of 2.5D cavities is a frequent operation, consuming time and presenting optimization potential, especially through a judicious choice of the tool trajectory. Among the different types of trajectories, some have a general spiral-like aspect and can potentially offer a reduced machining time. They are called curvilinear trajectories and are obtained by interpolation between structure curves, which are the numerical solutions of a partial differential equation. In this case, the machine tool will connect points, and the trajectory will be made up of small segments. While these trajectories exhibit all the necessary qualities on a macroscopic level for rapid tool movement, the tangential discontinuities at a microscopic scale, inherent in the discretization, significantly increase the machining time. This article proposes a method to reparameterize the structure curves of the curvilinear spiral with a set of C2 connected Hermit quartic spline patches. This creates a smooth toolpath that can be machined at an average feedrate closer to the programmed one and will, de facto, reduce the machining time. This article shows that the proposed method increases on two representative geometries of cavities and toolpath quality indicators, and reduces the milling time from 10% to 18% as compared to the PDE curvilinear spiral generation method proposed by Bieterman and Sandström. In addition, the proposed method is suitable for any non-convex pocket, with or without island(s).