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Bifurcation and chaos for porous squeeze film damper mounted rotor–bearing system lubricated with micropolar fluid

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Abstract

This study presents a dynamic analysis of a flexible rotor supported by two porous squeeze micropolar fluid-film journal bearings with nonlinear suspension. The dynamics of the rotor center and bearing center are studied. The analysis of the rotor–bearing system is investigated under the assumptions of non-Newtonian fluid and a short bearing approximation. The spatial displacements in the horizontal and vertical directions are considered for various nondimensional speed ratios. The dynamic equations are solved using the Runge–Kutta method. The methods of analysis employed in this study are inclusive of the dynamic trajectories of the rotor center and bearing center, power spectra, Poincaré maps, and bifurcation diagrams. The maximum Lyapunov exponent analysis is also used to identify the onset of chaotic motion. The numerical results show that the stability of the dynamic system varies with the nondimensional speed ratios, the nondimensional parameter, and permeability. The modeling results obtained by using the method proposed in this paper can be employed to predict the dynamics of the rotor–bearing system, and the undesirable behavior of the rotor and bearing centers can be avoided.

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Abbreviations

c 1 :

damping coefficient of the supported structure

c 2 :

viscous damping of the rotor disk

e :

\({=}\sqrt{X^{2}+Y^{2}}\)

F :

fluid-film force

f e , f φ :

components of the fluid-film force in radial and tangential directions

F x , F y :

components of the fluid-film force in X and Y directions

g :

acceleration of gravity

k 1, k 2 :

stiffness of the springs supporting the bearing housings

k s :

stiffness of the shaft

L :

bearing length

m, m 1 :

masses lumped at the rotor midpoint and bearing housing midpoint

O 1, O 2, O 3 :

geometric centers of the bearing, rotor and journal

p :

pressure distribution in the fluid film

R :

inner radius of the bearing housing

r :

radius of the journal

X, Y, Z :

horizontal, vertical, and axial coordinates

x 1, y 1, x 2, y 2 :

=X 1/c,Y 1/c,X 2/c,Y 2/c

ρ :

mass eccentricity of the rotor

φ :

rotational angle (φ=ωt)

ω :

rotational speed of the shaft

φ :

attitude angle

c :

radial clearance =R−r

θ :

the angular position

μ :

oil dynamic viscosity

ε :

=e/c

s 2 :

\({=}\frac{\omega ^{2}}{\omega _{n}^{2}}\)

ω 2 n :

=k s /m

β :

=ρ/c

\(f{\kern 1pt}\) :

\({=}\frac{mg}{ck_{s}}\)

ξ2 :

\({=}\frac{c_{2}}{2\sqrt{K_{s}m}}\)

\({\kern 1pt}C_{om}\) :

\({=}\frac{m_{1}}{m}\)

c p :

\({=}\frac{k_{s}}{k_{1}}\)

s 21 :

=c om c p s 2

\({\kern 1pt}\xi_{1}\) :

\({=}\frac{c_{1}}{2\sqrt{k_{1}m_{1}}}\)

α :

\({=}\frac{k_{2}c^{2}}{k_{s}C_{om}}\)

ψ :

permeability

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Authors and Affiliations

  1. Department of Mechanical and Automation Engineering, I-Shou University, 1, Section 1, Hsueh-Cheng Rd., Ta-Hsu Hsiang, Kaohsiung County, 840, Taiwan

    Cai-Wan Chang-Jian

  2. Graduate Institute of Greenergy Technology, National University of Tainan, Tainan, 700, Taiwan

    Jenn-Kun Kuo

Authors
  1. Cai-Wan Chang-Jian
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  2. Jenn-Kun Kuo
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Correspondence to Cai-Wan Chang-Jian.

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Chang-Jian, CW., Kuo, JK. Bifurcation and chaos for porous squeeze film damper mounted rotor–bearing system lubricated with micropolar fluid. Nonlinear Dyn 58, 697–714 (2009). https://doi.org/10.1007/s11071-009-9511-2

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  • DOI: https://doi.org/10.1007/s11071-009-9511-2

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