Force model of freeform surface multi-axis machining with fillet end mill based on analytical contact analysis

In the multi-axis machining of freeform surface, compared with ball end mill, the fillet end mill has higher machining efficiency under the same residual height and has been widely used. As the most important physical quantity in machining process, milling force has always been the focus of research. In this paper, the contact geometry between fillet end mill and freeform surface is analyzed by analytical method, and then the milling force prediction model of multi-axis machining is established. Based on differential discretization, the cutter location point of multi-axis machining of freeform surface is approximate to multi-axis machining of oblique plane, which simplifies the research object. The inclination angle is defined to describe the relationship among cutter axis, feed, and workpiece in cutter coordinate system. The space range of the cutting edge element participating in material cutting is constructed by the swept surface of previous tool path, the to-be machined surface and the feed direction surface, and the in-cut cutting edge is determined by judging the cutting edge element one by one. Considering cutter run-out, the element cutting forces on the cylindrical and fillet surfaces of fillet end mill are derived, and all the element forces within in-cut cutting edge are summed by vector to obtain the overall milling force of fillet end mill. Simulation results show that, compared with the solid method, this contact analysis method between cutter and workpiece can take both efficiency and accuracy into account. In the machining experiment, the measured force and predicted force are consistent in trend and amplitude, which verifies the effectiveness of the milling force prediction model.