New algorithm for calibration of instantaneous cutting-force coefficients and radial run-out parameters in flat end milling

It is well recognized that the cutter run-out appearing in the milling process will cause an uneven redistribution of the instantaneous uncut chip thickness through the cutter flutes and thereby will generate an irregular distribution of the cutting forces in different tooth periods. This work aims to develop a new approach able to identify the cutter radial run-out and cutting-force coefficients in the flat end milling. It is shown that the total cutting forces can be considered as the sum of a nominal component that is independent of the run-out plus a perturbation component induced by the run-out. Mathematical formulations of both components are developed, accounting for the cutting geometry and the radial run-out parameters. Firstly, to calibrate the cutting-force coefficients, a generic procedure is proposed using the instantaneous value of the nominal component instead of the average value. Secondly, considering the fact that the perturbation component of the cutting force depends non-linearly upon the run-out parameters, the identification of run-out parameters is carried out by solving the linearized equation. In the identification procedure, some key techniques such as the calculation of the immersion boundary at any cutting instant and the reasonable selection of the depth of cut are discussed in detail. Finally, based on simulation and experimental results, the validity of the identification approach is demonstrated.