Model of cutting forces prediction for gear milling considering the three-dimensional undeformed chip thickness, penetration curve and working angles

The cutting forces generated in gear milling are different from the cutting forces generated in milling and turning, due to the influence of the three-dimensional undeformed chip and penetration curve. To establish the cutting forces model to predict the cutting forces for gear milling, a mechanistic model considering three-dimensional undeformed chip thickness, penetration curve, and working angles is presented. In this paper, the calculation method for three-dimensional undeformed chip thickness is provided. In addition, the formula of penetration curve, a space curve of intersection of the sweep volume formed by the cutting edge and the outside cylinders of the workpiece, is obtained, which determines the machining zone. Moreover, the vector of resultant cutting speed is determined by vector analysis, on the basis of which, the working normal rake angle and working cutting edge inclination angle are determined. Furthermore, a gear milling cutter was used to carry out experiments to validate the cutting force model. The experimental results correlate in the predicted results and the errors of peak are around 20% in x-axis and y-axis. The main findings drawn from the experiments and simulations are that the peak of cutting forces of the down milling is higher than the peak of cutting forces of the up milling especially in the x-direction, due to the influence of the three-dimensional undeformed chip thickness.