GENERALIZED MATHEMATICAL MODEL OF VIBRATIONS OF A VERTICAL AXIS ROTARY SYSTEM

Abstract

The rotor’s response to dynamic actions depends on its physical parameters and the parameters of the supporting structure. The vibration measured on the bearings or on the rotor shaft, in addition to the physical properties of the rotor, also depends on the value of the unbalance, its distribution along the rotor axis, as well as on the rotational speed. These factors influence the choice of the balancing method. This article proposes a dynamic model of a rotary machine with a vertical axis of rotation and six degrees of freedom. Differential equations of free and forced oscillations of the rotor system are compiled. It is shown that when considering the general case of oscillations of the rotor system, there is a high connectivity of oscillations along all generalized coordinates. Based on the analysis of differential equations, ways of reducing vibration activity and connectivity of machine vibrations are shown, which provide for: reduction of the center of mass of the platform to the axis of rotation of the rotor; alignment of the center of stiffness of the elastic support system with the center of gravity of the platform, and the main axes of stiffness and constant viscous friction of dampers with the main central axes of inertia of the platform; the use of vertical suspensions for the oscillating system in the construction of the machine; replacement of the elastic sealing diaphragm of the rotor with a non-rigid one. The above measures to reduce the connectivity of vibrations and vibration activity do not completely eliminate the vibrations of the machine caused by stochastic, variable imbalances. Therefore, a further decrease in the vibration activity of the machine can be associated with the use of auto-ballasting devices, which make it possible to reduce the disturbing forces by reducing the magnitude of the stochastic imbalances of the rotary machine.