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Dynamic characteristics of self-acting gas bearing–flexible rotor coupling system based on the forecasting orbit method

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Abstract

This paper studies the nonlinear dynamic characteristics of a flexible rotor supported by self-acting gas bearings theoretically. The multiple degree freedom model of flexible rotor is established by the finite element method and analyzed coupled with the transient gas lubricated Reynolds equation by employing the forecasting orbit method. The Reynolds equation is solved by the alternating direction implicit method and the dynamic response of the rotor is calculated by the Newmark integral method. To settle the problem that the two kinds of transient solving processes (transient Reynolds equation for bearing and transient equation of motion for rotor) cannot be solved simultaneously, which arises from the fact that they need each other’s results as their initial values, the multi-field coupling algorithm based on the forecasting method is proposed and applied in this paper. By employing the numerical method, the rotor trajectory diagram, phase diagram, frequency spectrum, power spectrum, bifurcation diagram, and vibration mode diagram were obtained. It is to note that the dynamic characteristics of self-acting gas bearing–rotor system and whirling instability of the system could be depicted successfully. This would establish the foundation for contributing to a further understanding of the gas bearing–flexible rotor system.

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Abbreviations

c :

average air film thickness

e :

eccentricity

e x ,e y :

eccentricity in x, y direction

h :

air film thickness

l T :

the length of the rotor element

p :

air film pressure

p a :

atmospheric pressure

t :

time

x,y,z :

coordinates

A :

the section area of the rotor

F x ,F y :

the gas film forces act on the rotor

F n ,F n+1 :

the gas film forces at time n and n+1

H :

dimensionless air film thickness

H n :

gas film thickness function at time n

\(H_{\mathrm{forecast}}^{n + 1}\) :

gas film thickness function at time n+1 by forecasting

I y :

moment of the inertia for rotor

L :

the length of the bearing

NX :

the mesh number of circumferential direction

NZ :

the mesh number of bearing length direction

P :

dimensionless pressure

P n+1 :

dimensionless pressure at time n+1

Q :

the square of the P; Q=P 2

R :

radius of the bearing

W :

load capacity

ε :

the eccentricity ratio

η :

the dynamic viscosity of air

θ :

the angular coordinate

θ 0 :

attitude angle

ξ :

the dimensionless coordinates in length direction

ρ :

the air density under arbitrary pressure

ρ a :

the air density under atmospheric pressure

ρ r :

the density of the rotor

τ :

the dimensionless time

φ :

the attitude angle

ω :

rotating angular speed of the shaft

Λ :

the bearing number

Φ s :

shear factor for the rotor

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Authors and Affiliations

  1. School of Energy Science and Engineering, Harbin Institute of Technology, Harbin, China

    Guang-hui Zhang, Zhan-sheng Liu, Min Zhang & Jia-jia Yan

  2. School of Astronautic, Harbin Institute of Technology, Harbin, China

    Yi Sun

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  1. Guang-hui Zhang
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  2. Yi Sun
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  3. Zhan-sheng Liu
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  4. Min Zhang
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  5. Jia-jia Yan
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Correspondence to Guang-hui Zhang.

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Zhang, Gh., Sun, Y., Liu, Zs. et al. Dynamic characteristics of self-acting gas bearing–flexible rotor coupling system based on the forecasting orbit method. Nonlinear Dyn 69, 341–355 (2012). https://doi.org/10.1007/s11071-011-0268-z

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