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The article describes the results of an experimental study of the natural frequencies of oscillations of a mechanical system influence on the angular velocity of a pendulum mounted with the possibility of free rotation on a rotating shaft of an electric motor. It is established that at a constant moment of friction in the pendulum support, providing for a change in its mass moment of inertia, a mode of motion takes place in which the motor shaft rotates at a working angular velocity, and the angular velocity of the pendulum coincides with one of the natural frequencies of the oscillations of the mechanical system. The studies have also shown that there are ranges of the values of moments of inertia of the pendulum mass. For these moments of inertia, one can observe the establishment of a stable or unstable angular velocity of the pendulum, which is equal to one of the natural frequencies of the oscillations of the mechanical system.

Using the methods of the small parameter of nonlinear mechanics, the formulas for determining the parameters of the pendulum auto-balancer were obtained in the article. Conditions for the stability of the auto-balancing process of the unbalanced rotor, fastened in the housing on the elastic supports, were also found. It is established that the stable operation of the auto-balancer can be implemented in the angular velocity ranges of the rotor due to the choice of the stiffness characteristics of the elastic supports.

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The process of automatic balancing of an unbalanced rotor was simulated using four pendulums mounted in pairs on the shaft on both sides of the rotor. The rotor is rigidly fixed in the housing, which is mounted on elastic supports. Studies have shown that the pendulums partially or fully compensate the unbalance of the rotor within the range of its rotational frequencies. By selecting the stiffness characteristics of the housing supports and mass-and-inertia parameters of the housing, the rotor becomes a zone of stable operation of the auto-balancing device. It has been established that the degree of compensation for the rotor unbalance by pendulums of equal mass and length essentially depends on the relative position of the center of rotor masses, the center of the housing masses and the center of rigidity of the elastic supports of the housing and the distance between the pendulums in one pair.