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Artyunin A. I., Sumenkov O. Yu. Issledovaniye avtomaticheskoy balansirovki rotora v forme tsilindra, zhestko ustanovlennogo v korpuse na uprugikh oporakh [Research of the automatic balancing process of the cylindrical rotor, rigidly fixed in the housing on elastic supports]. Sovremennye tekhnologii. Sistemnyi analiz. Modelirovanie [Modern Technologies. System Analysis. Modeling], 2019. Vol. 64, No. 4. Pp. 13–19. DOI: 10.26731/1813-9108.2019.4(64).13-19

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The authors carried out the modeling process of the automatic balancing of an unstable rotor using four pendulums mounted in pairs on the rotating shaft on both sides of a cylindrical rotor. The rotor is rigidly fixed in the housing on elastic supports. Using the expressions for kinetic and potential energy, the Rayleigh dissipation function and the Lagrange equations of the second kind, differential equations are derived, describing the motion of our dynamic model both at acceleration and under stabilized conditions of the rotor motion. Numerical integration of the nonlinear differential equation system was implemented with the Runge-Kutta method of the forth order. But due to the insolvability of the top order equations with respect to top derivates, the calculation algorithm included matrix inversion at the each step of integration. Pendulum parameters and stability zones of the automatic balancing devices had been preliminarily calculated. The automatic balancing devices stability zones were artificially created by choosing the stiffnesses of the housing elastic supports so that the rotor operation speed was within the zone. The rotor and pendulum motion laws were derived, as well as laws of changing the angles of installation of the pendulums in relation to the imbalance. The authors demonstrated that in the selected zone the pendulums move apart and the rotor unbalance is compensated. The amplitudes of oscillations of the center of mass of the rotor with and without auto-balancer are compared. It has been established that the degree of compensation of the rotor imbalance by pendulums of the same mass and length substantially depends on the relative position of the center of the rotor mass, the center of the housing mass and the center of stiffness of the elastic supports of the housing and the distance between the pendulums in one pair. It is proved that automatic balancing can occur not only at rotational speeds higher than the critical rotor speed, but also in the resonance zones of the housing on elastic supports.

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