Machining of free-form surfaces. Part I: Analytical chip load

In the machining simulations of 3D free-form surfaces with ball-end mill, determinations of instantaneously changing tool-workpiece engagement regions and chip load play very critical roles in force and surface quality predictions. Cutting force models for ball-end milling are based on the undeformed chip load. Undeformed chip load can be constructed from the boundaries of instantaneous engagement region between the ball-end mill and workpiece. In order to predict the cutting forces accurately, precise determination of the varying engagement regions is important. In the literature, there are two main engagement region constructing methods; one is the Z-mapping and the other one is using solid modeler based on Boolean operation method. Both methods construct the engagement region within accuracy limits, on the other hand the computational time for these methods are long such that it is not possible to calculate the forces at the same time of CL-point construction. This paper presents development of a new analytical method for fast and accurate determination of the instantaneous engagement regions in the 3D machining of monotonic free-form surfaces. The analytical tool is grid size independent, thus it is much faster than discretization and Boolean methods. In addition to that, the analytical tool gives the most precise and exact engagement regions.