A generalized dynamic model taking into account coupled vibrations of a rotor-fluid-foundation system, linear eccentricity, damping, and rolling bearing nonlinearity is developed. The nonlinear equations of motion are formulated and analysed. Forced and free vibrations of the system are investigated. Peculiarities of the dynamic behaviour are revealed, including properties of vibration frequencies and amplitudes. The obtained results have the potential to be implemented in the optimal design of modern industrial devices.
A method for calculating amplitudes and constructing frequency characteristics of forced and self-excited vibrations of a rotor-fluid-foundation system on rolling bearings with a non-linear characteristic based on the method of complex amplitudes and harmonic balance has been developed. Non-linear equations of motion of the rotor-fluid-foundation system are derived, and analytical methods of their solution are presented. Frequencies of fundamental and ultra-harmonic resonances are determined. The intervals between self-oscillation frequencies are estimated. The dependence of amplitudes on the amount of fluid in the rotor cavity, the mass of the foundation, linear imbalance, the value of the stiffness coefficient, and the damping coefficient is shown.
The paper considers a rotor system with a nonlinear characteristic. Its equations of motion are a kind of Duffing class equations with multiple degrees of freedom. The paper shows the advantage of using the method of elliptic functions for solving problems of this type. This method enables us to take into account not only vibrations of the rotor installed in elastic nonlinear supports, but also vibrations of the foundation. A comparative analysis of application of the method of elliptic functions proposed by the authors is carried out by comparing the derived equations of motion of the system, as well as by comparing the obtained amplitude-frequency characteristics with the results obtained by the numerical Runge–Kutta–Fehlberg’s 4-order method and the approximate analytical Van der Pol method. The regions of resonant frequencies for superharmonic oscillations and bifurcation regimes are determined. It is concluded that the method proposed by the authors is a more accurate and general case than the previously used approximate methods.
The self-oscillation in the vertical rotor system mounted on elastic supportsIn this paper, we study the causes of self-excited oscillations (self-oscillations) and their further behavior, since these oscillations are the main cause of instability of vertical rotor systems mounted on sliding bearings. The cause of the self-excited oscillations are hydrodynamic forces arising from the lubricating layer between the bearing and its spike. Based on the classical methods of the theory of oscillations and the Sommerfeld hypothesis of a lubricating layer in sliding bearings, nonlinear equations of motion of a vertical rotor system were obtained. The obtained nonlinear differential equations of rotor motion and supports do not have an exact solution. The study is carried out by numerical methods. The dependences of the amplitudes of the rotor and bearings on the viscosity of the oil in the bearing, on the size of the gap, on the mass of the bearings, on the stiffness and on the damping coefficients are obtained. The results of the study of this work allow us to accurately determine and predict all the necessary characteristics of the working process of this system. The results of the work confirm the physical meaning of the process considered in the problem, which can justify the use of this mathematical model in the design of vertical rotor systems on sliding bearings.
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