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The article describes the features of the interaction between the cutting part of the tool and the part when processing deep holes. The description of the motion of the executive body is based on the second-order Lagrange equation. The differential equations of motion for five generalized coordinates derived. At the first stage of the study, only longitudinal and torsional oscillations were considered. With the use of Laplace images, a transfer function is obtained, taking into account the relationship between longitudinal and torsional oscillations. Graphically the relationship between the marked oscillations is shown. For an example, the frequency characteristic of a gun drill is brought.

On the question of the relationship between longitudinal and torsional vibrations in the manufacture of holes in the details