Stability of Up-milling and Down-milling Operations with Variable Spindle Speed

In this article, a stability treatment is presented for up-milling and down-milling processes with a variable spindle speed (VSS). This speed variation is introduced by superimposing a sinusoidal modulation on a nominal spindle speed. The VSS milling dynamics is described by a set of delay differential equations with time varying periodic coefficients and a time delay. A semi-discretization scheme is used to discretize the system over one period, and the infinite-dimensional transition matrix is reduced to a finite-dimensional matrix over this period. The eigenvalues of this finite-dimensional matrix provide information on VSS milling stability with respect to control parameters, such as the axial depth of cut and the nominal spindle speed. The stability charts obtained for VSS milling operations are compared with those obtained for constant spindle speed milling operations, and the benefits of VSS milling operations are discussed.