Closed form formulation of cutting forces for ball and flat end mills

In this paper, a set of basis functions for the calculation of cutting forces in milling are introduced. It is shown that the cutting force at any tool position can be determined by the linear combination of the force basis functions. The method is based on the projection of the chip load area onto the reference coordinate planes. Due to the analytical integration of the cutting forces along the cutter edge, the developed closed form equations provide a fast means of calculating the cutting forces. The validity of the method is experimentally verified for both flat and ball end mills.