Nonsynchronous vibrations of turbomachinery bladed discs

The stability and bifurcation of the unbalance response of a squeeze film damper-mounted flexible rotor are investigated based on the assumption of an incompressible lubricant together with the short bearing approximation and the “π” film cavitation model. The unbalanced rotor response is determined by the trigonometric collocation method and the stability of these solutions is then investigated using the Floquet transition matrix method. Numerical examples are given for both concentric and eccentric damper operations. Jump phenomenon, subharmonic, and quasi-periodic vibrations are predicted for a range of bearing and unbalance parameters. The predicted jump phenomenon, subharmonic and quasi-periodic vibrations are further examined by using a numerical integration scheme to predict damper trajectories, calculate Poincare´ maps and power spectra. It is concluded that the introduction of unpressurized squeeze film dampers may promote undesirable nonsynchronous vibrations.

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Numerical and Experimental Studies on Nonlinear Dynamic Behaviors of a Rotor-Fluid Film Bearing System With Squeeze Film Dampers

Journal of Vibration and Acoustics ◽

10.1115/1.1368119 ◽

2000 ◽

Vol 123 (3) ◽

pp. 297-302 ◽

Cited By ~ 2

Author(s):

Jun Hua ◽

Fangyi Wan ◽

Qingyu Xu

Keyword(s):

Finite Element ◽

Structural Parameters ◽

Experimental Studies ◽

Element Model ◽

Mapping Method ◽

High Order ◽

Squeeze Film ◽

Dynamic Behaviors ◽

Squeeze Film Dampers ◽

Nonsynchronous Vibrations

In this paper, the nonlinear oil film forces of bearings and dampers with free boundary conditions are determined by the finite element method (FEM) and the complementary solution for variational inequalities. The mode synthesis technique is used to reduce the linear degrees of the high order finite element model. The periodic solution of the system and its stability are determined by the Poincare´ mapping method and the Floquet theory, respectively. The results of experiment show that squeeze film dampers (SFDs) can effectively prevent subsynchronous and nonsynchronous vibrations and some structural parameters have significant effects on the dynamic behaviors of the system. Comparing the numerical results with those of experiment, it is shown that the above theories and schemes are feasible and efficient in analyzing nonlinear behaviors of the high-order dynamic system with local nonlinearities.

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A Simple Stability Analysis for Flexible Rotors in Tilting Pad Bearings

Journal of Mechanical Design ◽

10.1115/1.3453881 ◽

1978 ◽

Vol 100 (1) ◽

pp. 165-172 ◽

Cited By ~ 1

Author(s):

E. A. Bulanowski

Keyword(s):

Stability Analysis ◽

Free Vibrations ◽

Damping Factor ◽

Quick Method ◽

Flexible Rotors ◽

Tilting Pad ◽

Rotor Bearing ◽

Single Mass ◽

Tilting Pad Bearings ◽

Nonsynchronous Vibrations

A simplified stability analysis for flexible rotors in tilting pad bearings is developed which provides a convenient and practical approach for the consideration of nonsynchronous vibrations during the design phase of rotor bearing systems. It is known that the synchronous unbalance response of a single mass Jeffcott rotor in linear isotropic bearings is identical in form to the response of a simple spring-mass-damper system excited by a rotating unbalance. This paper demonstrates that the free vibrations, and hence the system damping factor, of a distributed mass flexible rotor in tilting pad bearings may be analyzed using a single mass, two tier spring-damper model. The relationship between the system damping factor and rotor stability is discussed. Non-synchronous tilting pad bearing characteristics are incorporated into the expression for the damping factor, and nondimensional curves are presented which establish values of the damping factor as a function of operating speed, critical speed, bearing clearance and Sommerfeld number. The subject curves provide a quick method for establishing stability guidelines during rotor design and for comparing existing rotor bearing systems.

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Dynamic Analysis of a Flexible Rotor Supported on Two Turbulent Model Journal Bearings with Micropolar Fluid Lubrication

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.592-594.1386 ◽

2014 ◽

Vol 592-594 ◽

pp. 1386-1390

Author(s):

Sushant Bhatia ◽

Jaideep Gupta

Keyword(s):

Dynamic Analysis ◽

Micropolar Fluid ◽

Reynolds Equation ◽

Journal Bearings ◽

Flexible Rotor ◽

Wide Range ◽

Dimensional Parameters ◽

Rotor Center ◽

Nonsynchronous Vibrations ◽

Tangential Directions

This paper presents the complex dynamic analysis of a flexible rotor–bearing system supported by two turbulent micropolar fluid film journal bearings under nonlinear suspension. The Modified Reynolds equation based on the assumptions of turbulent flow and the micropolar parameters has been considered. The system considers Short bearing approximation to simplify the numerical computations. The pressure distribution thus obtained is used to find out the resulting forces about the journal center in the radial and tangential directions. The Non-dimensional dynamic equations are derived considering appropriate non dimensional parameters and solved using MATLAB for a wide range of non-dimensional speed ratios. Plots of the journal center trajectories and rotor center trajectories are obtained. The results show that the system undergoes undesirable nonsynchronous vibrations due to bearing center displacement. Micropolar fluid is found to stabilize the system even when the flow of the system becomes turbulent. The study presented enhances the understanding of the nonlinear dynamics of turbulent journal bearings with respect to dimensionless parameters.

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Effect of Tip Clearance on the Prediction of Nonsynchronous Vibrations in Axial Compressors

Journal of Turbomachinery ◽

10.1115/1.4006401 ◽

2012 ◽

Vol 135 (1) ◽

Cited By ~ 10

Author(s):

Martin Drolet ◽

Huu Duc Vo ◽

Njuki W. Mureithi

Keyword(s):

Operating Temperature ◽

Axial Flow ◽

Tip Clearance ◽

Turbine Engine ◽

Tip Clearance Flow ◽

Background Theory ◽

Proposed Model ◽

Clearance Flow ◽

Flow Compressor ◽

Nonsynchronous Vibrations

This work investigates the effect of tip clearance size and operating temperature on the predictions of the critical rotor speed at which nonsynchronous vibrations (NSV) can be encountered in a turbine engine axial flow compressor. It has been proposed that the tangential tip clearance flow, observed at high blade loading near stall, can act as an impinging resonant jet on the upcoming blades and could be the underlying physics behind NSV. A model, in the form of an equation to predict the critical blade tip speed at which NSV can occur, was proposed based on the Jet-Core Feedback Theory and was experimentally verified by Thomassin et al. (2008, “Experimental Demonstration to the Tip Clearance Flow Resonance Behind Compressor NSV,” Proceedings of GT2008: ASME Turbo Expo Power for Land, Sea and Air, Berlin, Germany, Jun. 9–13, Paper No. GT2008-50303). In the equation, a factor k that was called the “tip instability convection coefficient” was measured experimentally and found to be influenced by the tip clearance size and operating temperature. This factor has a significant impact on the accuracy of the NSV predictions obtained using the proposed model. This paper propose a numerical experiment to determine the effect of tip clearance size and temperature on k, in order to improve the critical NSV tip speed predictions using the proposed model. A review of the NSV model is presented along with the relevant background theory on the subject. Two different blade geometries are simulated to provide a generic approach to the study. The leakage flow velocity is calculated to estimate k and a correlation is proposed to model the behavior of the k parameter as a function of the tip clearance size. The latter was found to significantly improve the critical NSV speed predictions. The effect of operating temperature on k is also discussed. Finally, the variation of k with the aerodynamic loading is assessed and compared with available data in the literature to strengthen the generic nature of the results.

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Blade Tip Clearance Flow and Compressor Nonsynchronous Vibrations: The Jet Core Feedback Theory as the Coupling Mechanism

Journal of Turbomachinery ◽

10.1115/1.2812979 ◽

2008 ◽

Vol 131 (1) ◽

Cited By ~ 22

Author(s):

Jean Thomassin ◽

Huu Duc Vo ◽

Njuki W. Mureithi

Keyword(s):

High Speed ◽

Feedback Mechanism ◽

Tip Clearance ◽

Coupling Mechanism ◽

Blade Vibration ◽

Potential Core ◽

Tip Clearance Flow ◽

Clearance Flow ◽

Blade Tip ◽

Nonsynchronous Vibrations

This paper investigates the role of tip clearance flow in the occurrence of nonsynchronous vibrations (NSVs) observed in the first axial rotor of a high-speed high-pressure compressor in an aeroengine. NSV is an aeroelastic phenomenon where the rotor blades vibrate at nonintegral multiples of the shaft rotational frequencies in operating regimes where classical flutter is not known to occur. A physical mechanism to explain the NSV phenomenon is proposed based on the blade tip trailing edge impinging jetlike flow, and a novel theory based on the acoustic feedback in the jet potential core. The theory suggests that the critical jet velocity, which brings a jet impinging on a rigid structure to resonance, is reduced to the velocities observed in the blade tip secondary flow when the jet impinges on a flexible structure. The feedback mechanism is then an acoustic wave traveling backward in the jet potential core, and this is experimentally demonstrated. A model is proposed to predict the critical tip speed at which NSV can occur. The model also addresses several unexplained phenomena, or missing links, which are essential to connect tip clearance flow unsteadiness to NSV. These are the pressure level, the pitch-based reduced frequency, and the observed step changes in blade vibration and mode shape. The model is verified using two different rotors that exhibited NSV.

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Subharmonic and Quasi-Periodic Motions of an Eccentric Squeeze Film Damper-Mounted Rigid Rotor

Journal of Vibration and Acoustics ◽

10.1115/1.2930436 ◽

1994 ◽

Vol 116 (3) ◽

pp. 357-363 ◽

Cited By ~ 59

Author(s):

J. Y. Zhao ◽

I. W. Linnett ◽

L. J. McLean

Keyword(s):

Numerical Integration ◽

Least Square ◽

Harmonic Series ◽

Squeeze Film ◽

Maximum Speed ◽

Rigid Rotor ◽

Squeeze Film Damper ◽

Squeeze Film Dampers ◽

The Stability ◽

Nonsynchronous Vibrations

When a squeeze-film damper is operated eccentrically, the nonlinear damper forces are no longer radially symmetric and subharmonic and quasi-periodic vibrations may be excited by the rotor unbalance. In this study, the unbalance response of a rigid rotor, supported on an eccentric squeeze film damper, is first approximated by a harmonic series whose coefficients are determined by the collocation method, together with a nonlinear least-square regression. The stability of the resulting periodic solution is then examined using the Floquet transition matrix method. For sufficiently large values of the unbalance and the damper static radial misalignment, it is shown that the approximate harmonic motion loses its stability and bifurcates into a stable subharmonic motion and a quasi-periodic motion at speeds above twice the system critical speed. This analytical finding is verified by a numerical integration in forms of the Poincare´ map, the rotor trajectory, the bifurcation diagram, and the power spectrum. It is suggested that stability analysis and numerical integration should always be incorporated into an approximate analytical method to achieve an adequate approximation. The results of this study show that the introduction of squeeze-film dampers may give rise to the undesirable nonsynchronous vibrations, which limits the maximum speed at which dampers should be used.

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