(untitled) (Journal of Mathematics Mechanics and Computer Science, 2020)
In this pap er, we study the causes of self-excited oscillations (self-oscillations) and their further b ehavior, since these oscillations are the main cause of instability of vertical rotor systems mounted on sliding b earings. The cause of the self-excited oscillations are hydro dynamic forces arising from the lubricating layer b etween the b earing and its spike. Based on the classical metho ds of the theory of oscillations and the Sommerfeld hyp othesis of a lubricating layer in sliding b earings, nonlinear equations of motion of a vertical rotor system were obtained. The obtained nonlinear differential equations of rotor motion and supp orts do not have an exact solution. The study is carried out by numerical metho ds. The dep endences of the amplitudes of the rotor and b earings on the viscosity of the oil in the b earing, on the size of the gap, on the mass of the b earings, on the stiffness and on the damping co efficients are obtained. The results of the study of this work allow us to accurately determine and predict all the necessary characteristics of the working pro cess of this system. The results of the work confirm the physical meaning of the pro cess considered in the problem, which can justify the use of this mathematical mo del in the design of vertical rotor systems on sliding b earings.