Research On Rotor Dynamics Of Foil Hydrodynamic Gas Bearing Based On Modal Method

In this paper,modal method is used to study the rotor dynamics of bump foil gas bearings.Most previous studies have considered the corrugated foil as a spring model without considering the interaction between the bumps.In this paper,the bump foil is equivalent to the modal model,fully consider the interaction between bumps,and the dynamic problem of the foil bearing rotor is solved simultaneously.The key of the modal method is to use a limited number of modes to calculate the deformation of the corrugated foil.In this paper,the modal model of the corrugated foil is established by the finite element method and the natural frequency and modal vector of the corrugated foil are obtained.The formula for calculating the foil deformation of the bump foil caused by air film force is established by using the method of modal superposition in the circumferential direction.The calculation formulas of gas film thickness and film force is derived according to the structure of bump foil gas bearing.and the corresponding state equations such as Reynolds equation and rotor dynamics equation are established.The finite difference method is used to solve the aeroelastic coupling state equation.The calculation results of modal method are compared with those in literature,and the correctness of modal method is verified.Compared with the results of the traditional spring model,the results show that the stiffness and deformation of the foil calculated by considering the interaction between the bumps are larger than that of the spring model,and the trajectory of the rotor is closer to the bearing center.In order to further verify the modal method,the foil deformation is calculated by radial mode superposition and frequency response function method respectively and compared with the modal superposition results in the circumferential direction.The results show that the three methods have good consistency.The influence of rotor speed,rotor mass and air film gap on rotor stability is further analyzed.The dynamic characteristics of the rotor considering the cone whirl are solved.The film thickness equation and the moment balance equation are derived.The variation of the rotor trajectory and deflection angle with time is obtained after solving the equations using the finite difference method,.The results show that the cone whirl of rotor is more significant when the initial deflection angle is not zero.Under certain rotor mass,the cone whirl of rotor decreases gradually,and the rotor only makes cylindrical whirl.The natural frequency test of corrugated foil and the dynamics experiment of corrugated foil bearing rotor are carried out.The natural frequency of the corrugated foil is tested by the hammer method,and the natural frequency of the corrugated foil is obtained.The experimental results show that the rotor vibration has multiple frequency components.When the rotor displacement response exceeds a certain speed,a relatively large low frequency component will appear,which is more consistent with the theoretical simulation results.