Comparison of different polynomial functions for predicting cutting coefficients in the milling process

Cutting coefficient identification plays a critical role in the calculation of cutting forces in the milling process. However, it is difficult to predict the cutting coefficients in the arc part of general end mills because of the various geometrical conditions along the cutting edge. This paper first introduces an improved identification model of specific cutting coefficients for the arc part of ball-end and bull-nose cutters. Then, the analytical expressions for the semi-empirical mechanistic identification of the cubic polynomial shear coefficients and constant edge coefficients are derived. In these expressions, elevation, axial immersion angle and local radius polynomial functions are used to describe the variation in the shear coefficients along the tool axis. Finally, the proposed identification model is applied to obtain the cutting coefficients for three end mills: a D12r6 ball-end cutter, a D12r3 bull-nose cutter, and a D16r3 bull-nose cutter. The matched validation cutting tests, which are slot millings with large cutting depths, are performed to compare the predictive ability of different polynomial functions. The results show that the local radius polynomial function covers all the geometric parameters and thus is more suitable for predicting the cutting coefficients of general end mills. Considering the differences in tool geometry, it is necessary to select the appropriate polynomial variable for predicting cutting coefficients outside the identified range of cutting depth.