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The article presents equivalent mathematical models of a boring bar designed for deep boring, in a distributed and a discrete idealizations. A mathematical model describing coupled torsional and lateral vibrations of a boring bar is constructed in the form of a set of differential equations with lagging of the cutting process dynamics. A methodology for studying stability in small of the deep boring process using a characteristic quasi-polynomial is presented. The numerical-analytical results of the studies made it possible to discern stability regions in the parameter space of the model and to obtain relations for maximal cutting depth as a function of geometrical and technological parameters (stiffness, cutting velocity, feeding etc.) of the boring bar considered. It is noted that the obtained numerical-analytical results are in good agreement with experimental data.

On the self-excitation of vibrations of a boring bar in the process of deep boring