Synchronization and sommerfeld effect as typical resonant patterns

Abstract

We analyze a classical problem of oscillations arising in an elastic base caused by rotor vibrations of an asynchronous driver near the critical angular velocity. The nonlinear coupling between oscillations of the elastic base and rotor takes place naturally due to unbalanced masses. This provides typical frequency-amplitude patterns, even let the elastic properties of the base be linear one. As the measure of energy dissipation increases, the effect of bifurcated oscillations can disappear. The latter circumstance indicates the efficiency of using vibration absorbers to stabilize the dynamics of the electromechanical system. The second section of this paper presents results of theoretical studies inspired by the problem of reducing the noise and vibrations by using hydraulic absorbers as dampers to dissipate the energy of oscillations in railway electric equipments. The results of experimental trials over this problem and some theoretical calculations, discussed in the text, are demonstrated the ability to customize the damping properties of hydraulic absorbers to save an electric power and to protect the equipment itself due to utilizing the synchronous modes of rotation of the rotors.

Bidirectional Controlled Multiple Synchronization of Unbalanced Rotors and Its Experimental Evaluation

“…ultra-low frequencies: 0 ω < 30 rad/s; 2. low frequencies: 30 ω < 50 rad/s; 3. medium frequencies: 50 ω < 70 rad/s; 4. high frequencies: 70 ω < 100 rad/s; 5. superior frequencies: ω 100 rad/s. At frequency ω ≈ 125 rad/s the Sommerfeld effect (Sommerfeld, 1902;Blekhman, 1988;Dimentberg et al, 1997;Blekhman and Fradkov, 2004;Kovriguine, 2012;Cvetićanin and Zukovic, 2015) manifests itself; the frequencies in this range and the upper one have not been experimentally studied in (Andrievsky et al, 2019;Fradkov et al, 2021) and are not considered in the present study. The control laws for frequency stabilization along with the prescribed phase shift between the rotors angular positions are proposed and experimentally studied on the mechatronic vibration setup SV-2M.…”

Sommerfeld effect characterization in rotors with non-ideal drive from ideal drive response and power balance

“…It is a very fast dynamics which produces no obvious change in the response except slowing down the simulations due to large differences in time constants. Moreover, motor armature inductance is small enough to influence the mechanical system's transient response [33][34][35]. Thus it has been dropped from the model.…”

Synchronous state of unbalanced rotors in a three-dimensional space and far-resonance system

“…[9][10][11] Meanwhile, Balthazar et al gave some short comments on synchronization in pre-resonance and resonance region between DC motors coupling with a flexible strut structure, and ''sommerfeld effect'' of self-synchronization of the proposed system is also analyzed by numerical simulations, 12,13 and then Kovriguine used theoretical and experimental calculation to demonstrate the synchronous rotations of motors, which are almost deenergized and do not need any high-powered energy set in the proposed mode. 14 Djanan et al focused on three motors operated in the common and opposite direction on a same plate, the synchronous rotation between the rotors is depended on frequency of the motors and structure parameter of the plate. 15,16 Sperling et al presented a two-plane automatic balancing device for equilibration of rigid-rotor unbalance, and it not only derives dynamic equations for the considered system but also gives the discussion of numerical computation, as well as determines the synchronous condition according to an analytical approximation.…”

“…gave some short comments on synchronization in pre-resonance and resonance region between DC motors coupling with a flexible strut structure, and “sommerfeld effect” of self-synchronization of the proposed system is also analyzed by numerical simulations, 12,13 and then Kovriguine used theoretical and experimental calculation to demonstrate the synchronous rotations of motors, which are almost deenergized and do not need any high-powered energy set in the proposed mode. 14 Djanan et al. focused on three motors operated in the common and opposite direction on a same plate, the synchronous rotation between the rotors is depended on frequency of the motors and structure parameter of the plate.…”