RESONANT PHENOMENA IN NONLINEAR VERTICAL ROTOR SYSTEMS

Ospan T.M. Kydyrbekuly A.B. Ibrayev G.E.
2021 al-Farabi Kazakh State National University

KazNU Bulletin. Mathematics, Mechanics, Computer Science Series
2021 #112 Issue 4 57 - 68 pp.

In this paper, the study of the dynamics of a rotor system mounted on an elastic foundation rotating in rolling bearings is considered. To describe the bearing model, the Hertz theory was used, linking radial loads acting on the bearing and deformation at the points of contact between the movable foundation and the bearing rings. In the bearing model, it is assumed that there are no types of sliding of bodies and rolling surfaces. The obtained differential equations of the rotor and the foundation do not have a common solution. Therefore, the study was conducted using numerical methods. In order to simplify the problem and increase the accuracy in solving the obtained differential equations, dimensionless quantities were used. With the increase and decrease of dimensionless quantities, the amplitudes of the rotor and the foundation are constructed. As a result, two resonances were formed: the main resonance and the second resonance. The work is connected with the physical meaning of the process considered in the problem the results obtained are the basis for the application of this mathematical model in the design of a rotary system rotating in rolling bearings.

rotor-foundation system , Hertz theory , nonlinear rotary system , numerical methods , rolling bearings

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Al-Farabi Kazakh National University, Almaty, Kazakhstan

Al-Farabi Kazakh National University

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