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In a systematic manner, this paper investigates the effects of harmonic force components on the regenerative stability of an end milling process. By representing the milling force pulsation in a Fourier series expansion form, the dynamic force components and the average forces due to bi-directional dynamic feed rates are both included in the generalized system dynamics formulation. In the resulting expression for the stability criterion, the spectral features of the milling forces are integrated with the dynamics of the structure, showing the significance or insignificance of the dynamic components of the milling forces in affecting the stability of the milling process. Key system parameters discussed include the magnitude of the average and harmonic forces, the cutter helix angle and the spindle speed. It is shown that a low helix angle and a smaller number of cutting flutes increase the effect of dynamic forces on the system stability. The significance of the harmonic forces is exemplified by the special cutting conditions where the average force becomes zero and the stability limits would be infinite as predicted by models using the average force alone. Improvements in the accuracy of stability lobes resulting from the inclusion of the dynamic forces and the validity of the presented model in general will be illustrated by numerical simulation and verified by experiments as well as by comparison with published results.Copyright © 2003 by ASME

For a generalized helical end mill, this paper presents a frequency domain force model considering the ploughing as well as the shearing mechanisms. The differential chip load and the corresponding cutting forces are first formulated through differential geometry for a general helical cutting edge. The differential cutting force is assumed to be a linear function of the chip load with a proportional shearing force and a constant ploughing force. The total milling force in the angle domain is subsequently composed through convolution integration and analyzed by Fourier analysis. The frequency domain model has the parameters of a general milling process all integrated in a single framework with their roles clearly defined so that Fourier coefficients of the milling force can be obtained for any analytically definable helical cutter. Applications are illustrated for three common helical cutters: the cylindrical, taper, and ball end mills. Furthermore, as an inverse application, a linear algebraic equation is formulated for the identification of six cutting constants from the average forces of two slot milling tests. Demonstration and verification of the milling force model as well as the identification of cutting constants are carried out through experiments with three types of milling cutters.Copyright © 2002 by ASME