An identification model of cutting force coefficients for five-axis ball-end milling

Five-axis ball-end milling is widely used in energy, ship, aerospace, and other fields. As one of the difficulties in milling research, milling force is often critical to the processing efficiency and quality of part. For predicting the milling force of the five-axis ball-end milling better, this paper presents a cutting force coefficients identification model which is related to the instantaneous chip layer thickness and axial position angle considering the cutter run-out. For five-axis ball-end milling of the oblique plane, the relationship of feed direction, cutter axis vector, and machined surface is parameterized. The boundary curves of cutter workpiece engagement (CWE) are determined by intersecting spatial surfaces. The boundary curves are discretized, and an algorithm of in-cut cutting edge (ICCE) is proposed by defining the distance between discrete points and the cutting edge. Combining the instantaneous chip thickness considering arbitrary feed direction and cutter run-out, the five-axis milling force model of ball-end mill is established. Based on the undetermined coefficient method and the instantaneous average milling force of teeth, the cutting force coefficients identification model corresponding to the instantaneous chip layer thickness and the axial position angle is established. Furthermore, cutter run-out parameters are obtained combined with instantaneous measured milling force of single tooth. The experimental and simulation examples demonstrate that the CWE determined by the spatial surfaces is consistent with the experimental results. The ICCE is in good agreement with the simulation results based on the solid modeling method. A large number of milling experiments under different processing parameters show that the cutting force coefficients and cutter run-out parameters identification model can be effectively applied to five-axis ball-end milling.