Method of Reducing the Number of DOF in the Machine Tool-Cutting Process System from the Point of View of Vibrostability Analysis

Abstract

The model of the mass-damping-spring (MDS) system of a machine tool is multi-degree of freedom model. The model of the cutting process (CP) has to correspond structurally to the MDS system model constituting the machine tool-cutting process (MT-CP) system model. This is often a model of time-variant parameters. Therefore, forecasting the vibrostability, i.e. resistance to the occurrence of self-excited vibrations, in the MT-CP system is a complicated task. To simplify analysis it is justified to reduce the number of degrees of freedom. The method presented simplifies significantly the computational model while the interpretation of the results applies to the whole construction. The reduced model carries information concerning vibration modes that determine vibrostability loss. The paper presents the mathematical fundamentals of the reduction of the machine tool MDS system model, analysis and selection of vibration modes considered in the reduced model and analysis of reduction errors.