Cubic time-spline fitting and interpolation for five-axis CNC machining

Abstract

Abstract In CNC machining, G01 codes are widely used to represent the tool path. Directly interpolating these G01 codes is time-consuming and may cause discontinuities. In this paper, we propose a time-spline curve fitting method that combines tool path fitting and feedrate scheduling into a single step for five-axis CNC machining. The input for this method consists of a three-dimensional linear path of the tool tip in the workpiece coordinate system and two-dimensional tool orientations in the machine coordinate system (MCS). The output is a fitted tool path in the MCS represented by a five-dimensional smooth time-parametric B-spline curve, simply referred to as the time-spline curve. The time-spline curve provides not only position information but also kinematic information, including velocity, acceleration, and jerk for each axis, directly derived from the first, second, and third derivatives of the curve. To meet fitting error constraints and axial kinematic constraints, our objective is to find the time-spline curve that is time-optimal. We formulate the optimization problem as a nonlinear optimization model and design a recursive algorithm to solve it. The resulting time-spline curve demonstrates high accuracy and fully utilizes the machine’s kinematic capabilities. Along the tool path defined by the time-spline curve, exact interpolation points can be straightforwardly obtained according to the interpolation period. Simulations and experimental results indicate that the proposed method yields a time-optimal time-spline curve with the desired precision and kinematic constraints.