Angle Domain Analytical Model for End Milling Forces

This paper presents the development of an explicit expression of cutting force wave forms in end milling with helical multi-flute cutters. From the relationship of elemental cutting forces and chip load, the net cutting forces are analytically formulated based on the integration of elemental cutting forces in the feed, cross feed, and axial directions. This formulation leads to a solution of force waveforms as algebraic functions of tool geometry, machining parameters, cutting configuration, and work piece material properties. The closed-form nature of the resulting model facilitates force estimation and process optimization without resorting to numerical iterations. The theoretical error of prediction due to the truncation of higher frequency terms is analyzed. It provides a guideline for choosing the model size for given error tolerance. It also offers an understanding of upper bound of prediction error for a known number of approximating terms used in the model. In the paper end milling experimental results were examined over a range of conditions to verify the analytical model in the context of waveform, power spectrum, and model size effect.