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

1994 ◽  
Vol 116 (3) ◽  
pp. 357-363 ◽  
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.

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.

Experiments on the Dynamic Behavior of a Supercritical Rotor

1982 ◽  
Vol 104 (2) ◽  
pp. 364-369
Author(s):  
M. Botman ◽  
M. A. Samaha
Keyword(s):  
Strain Energy ◽  
Squeeze Film ◽  
Maximum Speed ◽  
Stability Behavior ◽  
Squeeze Film Dampers ◽  
Rolling Element ◽  
Speed Range ◽  
In Series ◽  
The Stability ◽  
Desirable Effect

Tests have been performed on supercritical rotors to determine the sensitivity to unbalance and the suitability of balancing techniques. Results are presented for a rotor with an overhanging disk and supported on two rolling element bearings in series with squeeze-film dampers. The rotor has two flexural modes with high relative strain energy in the speed range up to 55,000 rpm. After completion of the balancing exercise the rotor could be run to maximum speed and was found to be stable and free from half-frequency whirl instability, depending on the oil inlet pressure of the dampers. Pressurization of the dampers and increasing the clearance of the dampers had a very desirable effect on the stability behavior and the unbalance response.

Feasibility of Applying Active Lubrication to Reduce Vibration in Industrial Compressors

2004 ◽  
Vol 126 (4) ◽  
pp. 848-854 ◽  
Author(s):  
Ilmar F. Santos ◽  
Rodrigo Nicoletti ◽  
Alexandre Scalabrin
Keyword(s):  
Load Condition ◽  
Squeeze Film ◽  
Design Solution ◽  
Maximum Speed ◽  
Stability Margins ◽  
Damping Coefficients ◽  
Squeeze Film Dampers ◽  
Tilting Pad ◽  
Tilting Pad Bearings ◽  
The Stability

In this paper the complete set of modified Reynolds’ equations for the active lubrication is presented. The solution of such a set of equations allows the determination of stiffness and damping coefficients of actively lubricated bearings. These coefficients are not just dependent on Sommerfeld number, as it would be the case of conventional hydrodynamic bearings, but they are also dependent on the excitation frequencies and gains of the control loop. Stiffness as well as damping coefficients can be strongly influenced by the choice of the control strategy, servo valve dynamics and geometry of the orifices distributed over the sliding surface. The dynamic coefficients of tilting-pad bearings with and without active lubrication and their influence on an industrial compressor of 391 Kg, which operates with a maximum speed of 10,200 rpm, are analyzed. In the original compressor design, the bearing housings are mounted on squeeze-film dampers in order to ensure reasonable stability margins during full load condition (high maximum continuous speed). Instead of having a combination of tilting-pad bearings and squeeze-film dampers, another design solution is proposed and theoretically investigated in the present paper, i.e., using actively lubricated bearings. By choosing a suitable set of control gains, it is possible not only to increase the stability of the rotor-bearing system, but also enlarge its operational frequency range.

scholarly journals Dynamic Analysis of Squeeze Film Damper Supported Rotors Using Equivalent Linearization

1993 ◽  
Author(s):  
A. El-Shafei ◽  
R. V. Eranki
Keyword(s):  
Dynamic Analysis ◽  
Numerical Integration ◽  
Dynamic Characteristics ◽  
Nonlinear Dynamic Analysis ◽  
Least Square ◽  
Squeeze Film ◽  
Equivalent Linearization ◽  
Squeeze Film Damper ◽  
Elliptic Orbits ◽  
Rotor Dynamic

The technique of equivalent linearization is presented in this paper as a powerful technique to perform nonlinear dynamic analysis of squeeze film damper (SFD) supported rotors using linear rotordynamic methods. Historically, it is customary to design squeeze film dampers (SFDs) for rotordynamic analysis by assuming circular centered orbits, which is convenient in making the nonlinear damper coefficients time independent and thus can be used in an iterative approach to determine the rotor dynamic characteristics. However, the general synchronous orbit is elliptic in nature due to possible asymmetry in the rotor support. This renders the nonlinear damper coefficients time dependent which would require extensive numerical computation using numerical integration to determine the rotor dynamic characteristics. Alternatively, it is shown that the equivalent linearization, which is based on a least square squares approach, can be used to obtain time independent damper coefficients for SFDs executing eccentric elliptic orbits which are nonlinear in the orbit parameters. The resulting equivalent linear forces are then used in an iterative procedure to obtain the unbalance response of a rigid rotor-SFD system. Huge savings over numerical integration are reported for this simple rotor. The technique can be extended to be used in conjunction with currently available linear rotordynamic programs to determine the rotor dynamic characteristics through iteration. It is expected that for multi-rotor multi-bearing systems this technique will result in even more economical computation.

Pressurized Oil Squeeze Film Dampers

1980 ◽  
Vol 102 (1) ◽  
pp. 41-47 ◽  
Author(s):  
A. Kent Stiffler
Keyword(s):  
Design Methodology ◽  
Squeeze Film ◽  
Rigid Rotor ◽  
Squeeze Film Damper ◽  
Supply Pressure ◽  
Squeeze Film Dampers ◽  
Stiffness And Damping ◽  
Film Stiffness

A pressurized oil squeeze film damper supporting a rigid rotor mounted in antifriction bearings is investigated. Orifice and inherent feed inlets are examined, and it is shown that the clearance determines the inlet resistance for a groove or slot. The film stiffness and damping forces are determined as a function of the restrictor coefficient, rotor unbalance speed and the supply pressure using the short bearing approximation. These forces are related to the system transmissibility. A design methodology for low transmissibilities is presented.

Perturbation Solutions for Eccentric Operation of Squeeze Film Damper Systems

1986 ◽  
Vol 108 (4) ◽  
pp. 619-623 ◽  
Author(s):  
Xuehai Li ◽  
D. L. Taylor
Keyword(s):  
Numerical Simulation ◽  
Experimental Results ◽  
Squeeze Film ◽  
Rigid Rotor ◽  
Squeeze Film Damper ◽  
Synchronous Motion ◽  
Squeeze Film Dampers ◽  
Large Speed ◽  
Good Agreement ◽  
Perturbation Solutions

The study focuses on the effect of a small unidirectional load such as comes from imperfect balance between preloading on centering springs and gravitational load on squeeze film dampers. A rigid rotor-squeeze film damper system is considered, and a thorough study of the synchronous motion of the system is performed. Two perturbation solutions are developed: one for large speed and one for small speed. The perturbation solutions are shown to be in good agreement with numerical simulation and published experimental results.

Time Transient Analysis of Horizontal Rigid Rotor Supported With O-Ring Sealed Squeeze Film Damper

2013 ◽  
Author(s):  
Saeid Dousti ◽  
Timothy W. Dimond ◽  
Paul E. Allaire ◽  
Houston E. Wood
Keyword(s):  
Transient Analysis ◽  
Reynolds Equation ◽  
Equations Of Motion ◽  
Excitation Frequency ◽  
Numerical Data ◽  
Operating Conditions ◽  
Squeeze Film ◽  
Rigid Rotor ◽  
Squeeze Film Damper ◽  
Squeeze Film Dampers

This study addresses the nonlinear dynamic behavior of O-ring seals as the retaining spring in squeeze film dampers (SFDs). An analytical model is developed to predict the restoring and hysteresis forces of elastomer O-rings based on experimental and numerical data. This model takes into account the temperature softening and excitation frequency hardening effects in O-rings as well as the installation conditions in the form of radial and vertical preloads, σ and γ, respectively. Long bearing assumption is adopted for the solution of Reynolds equation. The equations of motion of horizontal unbalanced rigid rotor are derived, and a dimensional analysis is conducted on them. The numerical results substantiates the synchronizing effects of bearing parameter, B and vertical preload, γ, and the asynchronizing effects of O-ring parameter, O and radial preload, σ. It is shown that the variation of temperature and rotational speed as operating conditions influence the rotor response significantly.

scholarly journals A Dynamical Study of a Rotor Supported by a Radial Journal Bearing Incorporating a Spherical Squeeze Film Damper

2021 ◽  
Vol 31 (5) ◽  
pp. 10-16
Keyword(s):  
Journal Bearing ◽  
Equations Of Motion ◽  
Spherical Shape ◽  
Squeeze Film ◽  
Dynamical Study ◽  
Squeeze Film Damper ◽  
Mechanical Waves ◽  
Squeeze Film Dampers ◽  
The Stability ◽  
Nonlinear Equations Of Motion

The reduction of noises, vibration, and mechanical waves transmitting through water from the shells of submarines is essential to their safe operation and travelling. Vibrations from the rotors of the engines are widely deemed as one of the main sources to which engineers have tried to attenuate with various designs. Squeeze-film dampers can be easily integrated into rotor-bearing structures in order to lower the level of vibrations caused by rotors out of balance. For this advantage, squeeze-film dampers are widely used in air-turbine engines. This paper presents preliminary results of a numerical simulation of a shaft running on a journal bearing integrated with a squeeze-film damper and evaluates the capacity in reducing vibrations concerning the stability of static equilibrium of the shaft journal center. The proposed damper is designed in spherical shape with self-aligning capacity. The results were obtained using finite difference method and numerical integration of the full nonlinear equations of motion.

The Effectiveness of Porous Squeeze Film Dampers for Suppressing Nonsynchronous Motions

1991 ◽  
Author(s):  
Shiping Zhang ◽  
Litang Yan ◽  
Qihan Li ◽  
Yoshihiko Kawazoe
Keyword(s):  
Time Domain ◽  
Squeeze Film ◽  
Rigid Rotor ◽  
Third Harmonic ◽  
Squeeze Film Damper ◽  
Outer Race ◽  
System Parameters ◽  
Highly Nonlinear ◽  
Squeeze Film Dampers ◽  
Force Characteristics

Abstract The rotor time domain orbits and the transmissibility trajectories of a rigid rotor supported on squeeze film damper (SFD) and porous squeeze film damper (PSFD) systems were investigated. Under certain system parameters, The SFD system with a centralising spring exhibits excessive nonsynchronous motions with approximate third harmonic frequencies and opposite whirling motions as well as severe transmitted forces. However, under same system parameters and with a porous permeable film outer race PSFD system could effectively attenuate the nonsynchronous motions with very small transmissibilities. The rigid rotor without a centering spring supported on SFD and PSFD systems were also investigated. The highly nonlinear film force characteristics take the major responsibility for the nonsynchronous motions of uncentralized SFD systems, and typical second and third harmonic orbits of SFD system were predicted. While under the same conditions, perfect synchronous orbits of PSFD system were resulted. PSFD through outer race permeability could provide more reasonable film force characteristics, and thus has the capability of suppressing nonsynchronous motions.

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