Angle and frequency domain force models for a roughing end mill with a sinusoidal edge profile

This paper presents analytical force models for a cylindrical roughing end mill with a sinusoidal edge profile in both the angle and frequency domains. Starting from a general expression for the chip thickness model, it is shown that under normal feed conditions, there exists only one cutting point at any axial position for an N-flute roughing end mill with its chip thickness N times that of a regular end mill, while the effective axial depth of cut is only 1/Nth that of a regular end mill. Based on the chip load model, the analytical force model is subsequently established through convolution integration of the elemental cutting function with the cutting edge geometry function in the angular domain, followed by Fourier analysis to obtain the frequency domain force model. Distinctive features of the milling forces for a roughing end mill are illustrated and compared with a regular end mill in the frequency as well as in the angular domain. The effects of the geometric parameters of a roughing end mill on the chip load distribution and on the features of milling force are discussed. The force models in both the frequency and angular domains are finally verified through milling experiments.