Force predictive model for five-axis ball end milling of sculptured surface

As a high precision and high efficiency cutting method, CNC milling of five axis is the first choice for manufacturing parts with complex sculptured surface. Milling force is one of the most important physical parameters in machining which affects the cutting vibration, cutting deformation, cutting heat, and surface quality directly. Aiming at the five-axis ball end milling of sculptured surface, a force predictive model with arbitrary cutter axis vector and feed direction is established. The conditions of micro-cutting edge of three-axis ball end mill involved in cutting are determined by space region limitation at the first. Then, after space rotation transformation, an analytic in-cut cutting edge (ICCE) method for five-axis ball end milling of oblique plane is proposed by judging micro-cutting edge one by one. Based on the idea of differential discretization, the machining of general complex surface can be regarded as a combination of a series of tiny oblique planes. Drawing on the idea to sculptured surface and combining micro-element milling force model and undeformed chip thickness model that is suitable for five-axis ball end milling with arbitrary feed direction, a milling force predictive model for five-axis ball end milling of sculptured surface is established. The results of simulations and experiments show that the ICCE determined by the space region limitation is consistent with the traditional Z-map method and the solid modeling method with high efficiency and precision. The measured force and the predictive force of the five-axis milling on sculptured surface are in good agreement in amplitude and trend, which proves the effectiveness of the milling force predictive model of five-axis ball end milling of sculptured surface.