Cutter Shape Determination and Tool Path Generation in CNC Flank Milling

We study cutter shape determination and tool path generation in 5-axis CNC flank milling. According to the fact that the cutting tool with a revolution surface is tangent to the target surface, we formulate the rigid motion of a cutter as a constrained optimization problem. We analyze this problem in details and give an algorithm to determine moving direction of cutting tool. The movement of the cutter gives a sequence of tool axes which forms a ruled surface. The least squares fitting to meridian curves of all revolution surfaces leads to a revolution surface which determines the shape of the cutting tool. By experiments, we show that the machined surface by the proposed method has small approximation error to the target surface.