A novel method of calculating the engagement length of cutting edge in five-axis machining

Abstract

Determining the engagement length of cutting edge is a key to predict the cutting force in five-axis machining. During five-axis machining, the position and posture of the cutter relative to workpiece are constantly changing because of the complexity of motion. Therefore, solving the instantaneous engagement length of cutting edge is challenging. The current solutions to the problem mainly involve solving the cutter workpiece engagement (CWE) and then intersecting the boundary of the CWE with the cutting edge to obtain the engagement length. Traditional calculation methods do not consistently show high accuracy and high efficiency simultaneously. To enhance the accuracy and efficiency of the solution, this paper proposes a novel approach to directly calculate the engagement length of cutting edge based on spatial geometric modelling. When the cutting edge is in the engagement angle range, by solving the lowest and upper engagement points of the cutting edge, the engagement length can be calculated at any time. The lowest engagement point is solved by envelope theory, and the upper engagement point can be obtained by solving the intersection of the semi-finished workpiece surface and the instantaneous cutting edge curve. A hybrid method based on penalty function and Newton is used to solve the intersection of workpiece surface and instantaneous cutting edge curve. At the end of this paper, the influence of different cutting parameters on engagement length was studied. In order to verify the correctness of the calculation, the proposed algorithm was applied to the cutting force prediction of five-axis machining. The results show its correctness and availability of the algorithm.