Milling force convolution modeling for identification of cutter axis offset

This paper discusses the application of a convolution integral force model to the identification of the geometry of cutter axis offset in milling operations. This analysis builds upon the basis of linear decomposition of elemental local cutting forces into a nominal component and an offset-induced component. The convolution of each elemental local cutting force component with the chip width density in the context of cutter angular position provides an integral expression for the total cutting forces. By virtue of the convolution integration property, the total cutting forces in the frequency domain can be derived as closed-form functions of the cutting pressure constants, various cutting conditions, as well as the cutter offset geometry. Subsequently, the magnitude and phase angle of cutter axis offset are shown to be algebraic and explicit functions of the Fourier series coefficients of cutting forces at the spindle frequency. Following the theoretical analysis, experimental study is discussed to illustrate the implementation procedure for offset identification, and frequency domain data are presented to verify the analytical results. Potential industrial applications of this work include the real-time monitoring of dynamic cutter runout and the in-process compensation for the loss of tolerance or finish using automatic controls based on the feedback information of offset magnitude and phase angle.