| The ball-end milling process is one of the most widely used machining processes in the manufacture of parts with 3-D sculptured surfaces such as dies and molds. The need to select the machining conditions on the basis of a rational optimization procedure provides the motivation of the present study. Two system models, the rigid system model and the flexible system model, have been developed for the prediction of cutting forces and the resulting machining errors in the ball-end milling process. The steps used in developing these models are based upon the empirical mechanistic principles of metal cutting. The basic strategy is to partition the 3-D cutting edges into a series of small axial cutting edge elements. The instantaneous cutting forces acting on the ball-end mill are obtained by considering the contributions of all the cutting edge elements engaged in the cut along the axis of the cutter. The resulting machining errors are then evaluated from the associated cutting system deflections and the surface generation mechanism of the ball-end mill.;For the rigid system model, the cutting forces are calculated with an assumption of a completely rigid machining system. The factors considered include the cutter specification, the cut geometry, the cutter runout, and the three-dimensional cutter feed motion. For the flexible system model, the feedback effect of the cutting system deflections on the cutting forces are considered. The predictions of cutting forces and cutting system deflections are achieved by using an iterative procedure to balance the cutting forces and the associated cutting system deflections at any instant.;Due to the empirical nature of the proposed models, an individual set of experiments was performed to evaluate the empirical parameters incorporated in the model formulations for the particular workpiece/cutter combination. Model verification experiments were also conducted to validate the capability of the developed system models. It is shown that the flexible system model gives significantly better predictions of the cutting forces than the rigid system model. Good agreement between the predicted and measured machining errors is demonstrated for the simple surfaces generated by horizontal cuts. |
