High efficiency simulation of five-axis cutting force based on the symbolically solvable cutting contact boundary model

Abstract

In the optimization process of five-axis cutting direction and cutter orientation, the cutter/workpiece engagement (CWE) region and cutting forces vary with different machining parameters; the prediction of CWE region is still a challenge especially for bullnose end mills. This paper presents a method to model the CWE boundaries of bullnose end cutters as a function of the five-axis parameters: the lead angle, the tilt angle, the cutting depth, and the path interval. In this method, the CWE boundaries are determined by three boundary curves: the characteristic of the envelope, the intersection of the envelop and the workpiece surface, and the projective of the previous characteristic curve in the feed direction. Based on the symbolically solvable CWE boundary model, margin height method to determine the in-cutting edge is proposed, which is validated obviously much faster than Z-map method. Using margin height method to calculate the upper and lower limits of the cutting edge, the algebraic method to predict cutting force is described and validated by five-axis machining experiment for a bullnose end cutter. The cutting force is simulated without discretizing along the cutter axis, and the calculating efficiency is improved largely comparing with the traditional method that accumulated the differential forces element by element. The symbolically solvable CWE model and margin height method-based cutting force model are very suitable for optimizing cutting direction and cutter orientation in five-axis machining.