Analytical method to extract tool workpiece engagement from CAM data for five-axis machining stability prediction

Ball end milling cutters are commonly used for precision machining of complex curved parts in five axis CNC systems. To solve the problem of difficulty in adjusting the spindle speed to achieve stable milling during the five axis milling process of ball end cutters, this paper presents an analytical method for extracting the tool-workpiece engagement (TWE) from computer-aided manufacturing (CAM) data. This method extracts the TWE between the end portion of the ball-end mill and the surface of the workpiece during the processing of free-form surfaces, including slotting, first cutting, and following cutting. Further, the TWE extracted by this method is applied for constructing the cutting force model. The entry and exit angles for each of the micro-element cutting edges under different tool postures are obtained through the conversion matrix, and an efficient full discretization method is used for predicting the stability of the five-axis machining in the slotting mode. Finally, the accuracy and efficiency of the analytical method are verified through simulation and experimentation. The experimental results show that the efficiency of the proposed method increases by about 69% when compared to the arc-surface intersection method and that the predicted value of the five-axis machining stability shows good agreement with the experimental results.