Mathematical modeling of the rotor's dynamic of a turbomachine on gas foil bearings under the exposure of vibration

BACKGROUND: Turbomachines on gas foil bearings are a promising direction of the turbomachinery due to their economy, autonomous and durability. However, gas foil bearings have lower load capacity than other types of bearings. At the same time, turbomachines are complicated dynamic systems which must meet high standards of safety, sustainability and durability against external mechanical factors vibration, shock and etc. 
AIM: development of a mathematical model of rotor dynamics suitable for predicting displacement of the rotor in foil bearings under the exposure of vibration for exclude contact of the rotor with the housing. 
METHODS: In this paper, mathematical model of dynamic of stiff rotor on gas foil bearings taking into account flexibility of bearings housings supports and flexibility of housing of all turbomachine. Stationary and transient modes of operation and transient modes with random vibration exposure are simulated. The system of equations in ordinary derivatives, describing the mathematical model, was solved by the Rado IIA method. Random vibration was modeled by digital filter of Fourier transformation. Results of modeling were analyzed by discrete Fourier transformation and short-time Fourier transformation. 
RESULTS AND CONCLUSIONS: Rotors movement trajectories are obtained on. Results are compared with authors previously experimental data. Upper bound was obtained. Maximal values of rotor displacement are allowed set up optimal values of blade tip gaps.