A STOCHASTIC CHARACTERIZATION OF THE MACHINE TOOL WORKPIECE SYSTEM IN BTA OEEP HOLE MACHINING Part I: Mathematical Modelling and Analysis

A three dimensional model of the BTA deep-hole machining system is presented by modelling each of the components separately and later combining to represent the total system. A model for the interaction between the workpiece and the cutting tool is also included. Such a model can determine the response of any component of the machine tool as well as the individual influence on the system performance. Based on this, physical models representing the three working methods in the BTA process can be studied, from which stochastic differential equations are derived to represent the resultant force system on the machine tool

A physical model for the stationary workpiece and rotating cutting tool working method is developed. The assumed modes method along with the Lagrange' equation is used to obtain the stochastic differential equation to represent the influence of axial force and torque, in order to obtain the response of the system under the action of the axial force and torque to predict the stability behaviour.