Vibrostability of a Multidimensional Machine Tool-Workpiece-Tool System, Part I: Modeling the Mechanical Structure and Cutting Process

Abstract

Predicting the vibrostability of machine tools requires mathematical models for the elements that form a multidimensional dynamic machine tool-workpiece-tool system (i.e., mass-damping-spring system, cutting process, friction process, processes of driving motors, and the control system). This article presents the principles of modeling this system using the rigid finite element method. The result is a mathematical model that is useful in analyzing dynamic properties of a machine, including the vibrostability (dynamic stability) analysis. Part I describes the modeling of the multidimensional mass-damping-spring system of a machine tool and cutting process. This enables the designer to construct an entire model of the system and to analyze its dynamic properties during designing, including predicting the vibrostability.