Beschreibung
Machine tool vibrations are one of the major limitations with respect to material removal rates and productivity. From the engineering point of view, an assessment of operating points supports the selection of suitable parameters in order to decrease tool wear, increase surface quality, and avoid damage of entire machine tools. The tendency to self-excited vibrations in machining systems bases essentially on surface regeneration. Mathematical modeling yields delay-differential equations, which can exhibit highly non-smooth, time-periodic coefficients. Time discretization enables the estimation of Floquet multipliers.
In order to obtain robust stability lobe diagrams or stabilizability diagrams, numerical continuation is applied using analytical derivatives and exploiting piecewise smoothness of eigenvalues and the spectral radius. In doing so, smooth parameter dependence of the Floquet matrix is essential and the main task in modeling and time discretization. In addition, parameter-dependent structural dynamics can be maintained by parametric model-order reduction with matrix interpolation which is an excellent approach in modeling of in-process workpiece dynamics.
