Bifurcations and Chaos in the Response of a Rigid Rotor Supported by Eccentric Squeeze-Film Dampers

2001 ◽  
Author(s):  
Jawaid Iqbal Inayat-Hussain ◽  
Hiroshi Kanki ◽  
Njuki W. Mureithi
Keyword(s):  
Period Doubling ◽  
Squeeze Film ◽  
Response Analysis ◽  
Rigid Rotor ◽  
Chaotic Motions ◽  
Practical Applications ◽  
Squeeze Film Dampers ◽  
Order Of Magnitude ◽  
Type 3 ◽  
Rigid Rotors

Abstract In the unbalance response analysis of rotors supported by squeeze-film dampers with centering springs, the fluid-film forces are usually computed based on the assumption that the rotor exhibits a circular centered whirl orbit motion. The validity of this assumption is, however, limited to the ideal case of squeeze-film dampers with centering springs that are perfectly adjusted to offset the gravitational force. In most practical applications, eccentric operation of these dampers is almost unavoidable since precise setting of the centering springs in a real environment is usually not possible. In this paper the bifurcations in the response of a rigid rotor in eccentric squeeze-film dampers are investigated. The values of the bearing parameter (B), gravity parameter (W) and spring parameter (S) are respectively fixed at 0.015, 0.05 and 0.3, while the unbalance parameter (U) is varied from 0.05 to 0.8. The results indicated that the rotor might lose its stability due to period-doubling and saddle node bifurcations. Chaotic response of the rotor was also observed for 0.365 < U < 0.367 and 0.381 < U < 0.392. The transitions to chaos in these two regimes were respectively via the period-doubling and type 3 intermittency routes. The levels of rotor unbalance where non-synchronous and chaotic motions were observed in this study are only an order of magnitude higher than the specified levels for rigid rotors. Such levels of unbalance may easily occur in practice due to in-service erosion or in the event of a partial or an entire blade loss.

Routes to Chaos in Squeeze-Film Dampers

2004 ◽  
Author(s):  
Jawaid I. Inayat-Hussain ◽  
Njuki W. Mureithi
Keyword(s):  
Period Doubling ◽  
Squeeze Film ◽  
Saddle Node Bifurcation ◽  
Chaotic Vibrations ◽  
Saddle Node ◽  
Highly Nonlinear ◽  
Squeeze Film Dampers ◽  
Route To Chaos ◽  
Type 3 ◽  
Period Doubling Bifurcations

This work reports on a numerical study undertaken to investigate the imbalance response of a rigid rotor supported by squeeze-film dampers. Two types of damper configurations were considered, namely, dampers without centering springs, and eccentrically operated dampers with centering springs. For a rotor fitted with squeeze-film dampers without centering springs, the study revealed the existence of three regimes of chaotic motion. The route to chaos in the first regime was attributed to a sequence of period-doubling bifurcations of the period-1 (synchronous) rotor response. A period-3 (one-third subharmonic) rotor whirl orbit, which was born from a saddle-node bifurcation, was found to co-exist with the chaotic attractor. The period-3 orbit was also observed to undergo a sequence of period-doubling bifurcations resulting in chaotic vibrations of the rotor. The route to chaos in the third regime of chaotic rotor response, which occurred immediately after the disappearance of the period-3 orbit due to a saddle-node bifurcation, was attributed to a possible boundary crisis. The transitions to chaotic vibrations in the rotor supported by eccentric squeeze-film dampers with centering springs were via the period-doubling cascade and type 3 intermittency routes. The type 3 intermittency transition to chaos was due to an inverse period-doubling bifurcation of the period-2 (one-half subharmonic) rotor response. The unbalance response of the squeeze-film-damper supported rotor presented in this work leads to unique non-synchronous and chaotic vibration signatures. The latter provide some useful insights into the design and development of fault diagnostic tools for rotating machinery that operate in highly nonlinear regimes.

Eccentric Operation and Blade-Loss Simulation of a Rigid Rotor Supported by an Improved Squeeze Film Damper

1995 ◽  
Vol 117 (3) ◽  
pp. 490-497 ◽  
Author(s):  
J. Y. Zhao ◽  
E. J. Hahn
Keyword(s):  
Outer Ring ◽  
Squeeze Film ◽  
Rigid Rotor ◽  
Cavitation Model ◽  
Squeeze Film Damper ◽  
Constant Stiffness ◽  
Flexible Support ◽  
Squeeze Film Dampers ◽  
Stiffness And Damping ◽  
Blade Loss

This paper outlines an improved squeeze film damper which reduces significantly the dependence of the stiffness of conventional squeeze film dampers on the vibration amplitudes. This improved damper consists of a conventional squeeze film damper with a flexibility supported outer ring. This secondary flexible support is considered to be massless, and to have a constant stiffness and damping. Assuming the short bearing approximation and the ‘π’ film cavitation model, the performances of this damper in preventing bistable operation and sub-synchronous and nonsynchronous motions are theoretically demonstrated for a rigid rotor supported on a squeeze film damper. Blade-loss simulations are carried out numerically.

Electric-Hydraulic Actuator Design for a Hybrid Squeeze-Film Damper-Mounted Rigid Rotor System With Active Control

2005 ◽  
Vol 128 (2) ◽  
pp. 176-183 ◽  
Author(s):  
Her-Terng Yau ◽  
Chieh-Li Chen
Keyword(s):  
Dynamical Behavior ◽  
Rotor System ◽  
Squeeze Film ◽  
Rigid Rotor ◽  
Loop Gain ◽  
Hydraulic Actuator ◽  
Squeeze Film Damper ◽  
Chaotic Vibration ◽  
Squeeze Film Dampers ◽  
Actuator Design

When a squeeze-film damper-mounted rigid rotor system is operated eccentrically, the nonlinear forces are no longer radially symmetric and a disordered dynamical behavior (i.e., quasi-periodic and chaotic vibration) will occur. To suppress the undesired vibration characteristics, the hybrid squeeze-film damper bearing consisting of hydrostatic chambers and hydrodynamic ranges is proposed. In order to change the pressure in hydrostatic chambers, two pairs of electric-hydraulic orifices are used in this paper. The dynamic model of the system is established with the consideration of the electric-hydraulic actuator. The complex nonsynchronous vibration of squeeze-film dampers rotor-bearing system is demonstrated to be stabilized by such electric-hydraulic orifices actuators with proportional-plus-derivative (PD) controllers. Numerical results show that the nonchaotic operation range of the system will be increased by tuning the control loop gain.

scholarly journals Effects of Fluid Inertia and Turbulence on the Force Coefficients for Squeeze Film Dampers

1986 ◽  
Vol 108 (2) ◽  
pp. 332-339 ◽  
Author(s):  
L. San Andre´s ◽  
J. M. Vance
Keyword(s):  
Squeeze Film ◽  
Fluid Inertia ◽  
High Eccentricity ◽  
Small Eccentricity ◽  
Inertia Effects ◽  
Force Coefficients ◽  
Inertia Coefficient ◽  
Squeeze Film Dampers ◽  
Order Of Magnitude ◽  
Large Eccentricity

The effects of fluid inertia and turbulence on the force coefficients of squeeze film dampers are investigated analytically. Both the convective and the temporal terms are included in the analysis of inertia effects. The analysis of turbulence is based on friction coefficients currently found in the literature for Poiseuille flow. The effect of fluid inertia on the magnitude of the radial direct inertia coefficient (i.e., to produce an apparent “added mass” at small eccentricity ratios, due to the temporal terms) is found to be completely reversed at large eccentricity ratios. The reversal is due entirely to the inclusion of the convective inertia terms in the analysis. Turbulence is found to produce a large effect on the direct damping coefficient at high eccentricity ratios. For the long or sealed squeeze film damper at high eccentricity ratios, the damping prediction with turbulence included is an order of magnitude higher than the laminar solution.

Optimal Design of Centered Squeeze Film Dampers

1993 ◽  
Vol 115 (2) ◽  
pp. 210-215 ◽  
Author(s):  
C. Nataraj ◽  
H. Ashrafiuon
Keyword(s):  
Optimal Design ◽  
Nonlinear System ◽  
Circular Orbit ◽  
Design Variable ◽  
Optimization Process ◽  
Squeeze Film ◽  
Rigid Rotor ◽  
Variational Stability ◽  
Squeeze Film Dampers ◽  
Two Degree Of Freedom

A two degree-of-freedom model, consisting of a rigid rotor supported on rigid bearings which are in turn supported on squeeze film dampers, is considered. Isotropic centering springs are assumed resulting in a steady synchronous centered circular response for the rotor. The resulting nonlinear system is modeled in nondimensional form. The transmissibility ratio of the system as well as the power dissipated are minimized for various values of unbalance and at several speeds, with the squeeze film bearing parameter as the primary design variable. Expressions are derived for linear variational stability of the circular orbit, and are imposed as constraints in the optimization process. The dependence of the optimal configuration on speed and unbalance is discussed.

Stability and bifurcation of a rigid rotor in cavitated squeeze-film dampers without centering springs

2001 ◽  
Vol 34 (10) ◽  
pp. 689-702 ◽  
Author(s):  
Jawaid Iqbal Inayat-Hussain ◽  
Hiroshi Kanki ◽  
Njuki W. Mureithi
Keyword(s):  
Squeeze Film ◽  
Rigid Rotor ◽  
Stability And Bifurcation ◽  
Squeeze Film Dampers

The Effect of Fluid Inertia in Squeeze Film Damper Bearings: A Heuristic and Physical Description

1983 ◽  
Author(s):  
John A. Tichy
Keyword(s):  
Hydrodynamic Lubrication ◽  
Turbulence Models ◽  
Squeeze Film ◽  
Squeezing Flow ◽  
Fluid Inertia ◽  
Inertia Effects ◽  
Practical Applications ◽  
Viscous Forces ◽  
Squeeze Film Dampers ◽  
Inertia Forces

Fluid inertia forces are comparable to viscous forces in squeeze film dampers in the range of many practical applications. This statement appears to contradict the commonly held view in hydrodynamic lubrication that inertia effects are small. Upon closer inspection, the latter is true for predominantly sliding (rather than squeezing) flow bearings. The basic equations of hydrodynamic lubrication flow are developed, including the inertia terms. The appropriate orders of magnitude of the viscous and inertia terms are evaluated and compared, for journal bearings and for squeeze film dampers. Exact equations for various limiting cases are presented: low eccentricity, high and low Reynolds number. The asymptotic behavior is surprisingly similar in all cases. Due to inertia, the damper force may shift 90° forward from its purely viscous location. Inertia forces are evaluated for typical damper conditions. The effect of turbulence in squeeze film dampers is also discussed. On physical grounds it is argued that the transition occurs at much higher Reynolds numbers than the usual lubrication turbulence models predict.

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