AN ANALYTICAL AND EXPERIMENTAL STOCHASTIC MODELLING OF THE RESULTANT FORCE SYSTEM IN BTA DEEP-HOLE MACHINING AND ITS INFLUENCE ON THE DYNAMICS OF THE MACHINE TOOL WORKPIECE SYSTEM.

摘要

This investigation examines in detail the interaction between the cutting tool and the workpiece in BTA machining. Equations to represent the mean and periodic cutting forces are derived using the thin shear plane model. The equations representing the periodic cutting forces can be used when a chatter analysis of the machine tool system has to be carried out. In this investigation, the region of interest in the non-chatter zone. A theoretical approach to describe the resultant force system, consisting of an axial force and torque, is quite complex and impractical. Moreover, the characteristics of the randomly varying resultant force system can only be determined by performing a series of experiments. Hence, a set of experiments are performed to establish a mathematical model for the resultant force system. These are carried out using a piezo-electric transducer, mounted on a specially designed dynamometer. The data recorded from the dynamometer are analyzed, and a mathematical model is established to represent the resultant force system.;The effect of the resultant force system on the dynamics of the machine tool is obtained by the derivation of a system model using Lagrange's equation and assumed modes method. The solutions to these equations are combined using vector addition, to obtain an expression which describes the tool tip motion, for the case of a rotating cutting tool-stationary workpiece system. Based on the tool tip motion, a recommendation is made on the development of a microprocessor based adaptive control unit. Also, an index to define the roundness error is presented. The roundness error obtained from this index for certain machining conditions, is compared with a set of experimental values obtained under the same conditions and it is conjectured that the resultant force system is not completely balanced at the pads.