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Increase of the efficiency of using energy of parametric oscillations within the assembly of drilling string bottom by means of solving nonlinear-parametric equations of a "bit -drive motor -drilled-out rock" system to improve drilling indices.Methods. The paper applies the method of mathematical modeling of a mechanical system as well as impedance method to study oscillations. While modeling the system, a bit is considered to be an absolutely solid body; elastic elements are non-inertial, drive motor is ideal, and resistance in elastic relations is viscous. While modeling dynamic parameters of a drill string and its interaction with a near-bit system and bottom hole, mechanical system is represented in the form of blocks interacting with each other. Drill string in models is a sequential system of uniform rods.Findings. In the course of analytical studies, it has been proved that use of energy of parametric oscillations within the assembly of drilling string bottom makes it possible to increase axial load on a bit as well as rise mechanical velocity especially while drilling horizontal areas of inclined boreholes. Dynamic parameters of mechanical system of a drill string and its interaction with near-bit system and bottom hole have been substantiated. It has been determined that limitation of the amplitude of resonant vertical oscillations for a bit is possible at the expense of toothed surface of cone rollers in terms of periodical positioning from one tooth to two teeth, physical and mechanical properties of the drilled-out rocks, and features of correcting elements mounted above the bit.Originality. Innovative mathematical model describing dynamics of the operation of a "bit -drive motor -drilledout rock" mechanical system has been developed taking into consideration the effect of parametric oscillations. Practical implications. Limited amplitude of resonant vertical oscillations of a bit is the condition of efficient assembly operation and long service life of its components in the context of parametric excitations. The obtained results may be useful while designing drill rigs.