Bisector optimal ball-end tool orientation

For five-axis CNC machining with ball-end tool, smooth variation of tool orientation is desirable for stable rotary axes movement with constant inclination angle between surface normal and tool axis so as to obtain constant cutting speed. According to the Darboux frame, the orientation for a ball-end tool can be decomposed into two components, one of which along the surface normal is fixed and the other on the tangent plane is undetermined for possible optimization. Based on geometrical analysis for the latter component, a novel bisector optimization approach is proposed to optimize variation of the tool orientation. Simulations are conducted and the bisector optimization approach has exhibited smoother variation of tool orientation along the whole path.