Unbalance Response of a Jeffcott Rotor Incorporating Short Squeeze Film Dampers

1989 ◽  
Author(s):  
A. El-Shafei
Keyword(s):  
Fast Algorithm ◽  
Vibration Isolation ◽  
Squeeze Film ◽  
Fluid Inertia ◽  
Unbalance Response ◽  
Squeeze Film Dampers ◽  
Jeffcott Rotor ◽  
Second Mode ◽  
Parametric Studies ◽  
Inertia Forces

The steady state unbalance response of a Jeffcott rotor incorporating short squeeze film dampers executing circular centered whirl is obtained by a fast algorithm. Savings in execution time of the order of fifty times are gained over numerical integration. Fluid inertia forces are included in the model of the squeeze film dampers. The fast algorithm allows parametric studies to be performed. It is shown that fluid inertia results in the excitation of a second mode for the Jeffcott rotor, decreases the possibility of jump resonance, and decreases the useful range of vibration isolation of the dampers. It is also shown that a squeeze film damper with no centering spring (or a very soft spring) may be advantageous with regards to the unbalance response and the vibration isolation capability of the dampers.

Unbalance Response of a Jeffcott Rotor Incorporating Short Squeeze Film Dampers

1990 ◽  
Vol 112 (4) ◽  
pp. 445-453 ◽  
Author(s):  
A. El-Shafei
Keyword(s):  
Fast Algorithm ◽  
Vibration Isolation ◽  
Squeeze Film ◽  
Fluid Inertia ◽  
Unbalance Response ◽  
Squeeze Film Dampers ◽  
Jeffcott Rotor ◽  
Second Mode ◽  
Parametric Studies ◽  
Inertia Forces

The steady-state unbalance response of a Jeffcott rotor incorporating short squeeze film dampers executing circular centered whirl is obtained by a fast algorithm. Savings in execution time of the order of fifty times are gained over numerical integration. Fluid inertia forces are included in the model of the squeeze film dampers. The fast algorithm allows parametric studies to be performed. It is shown that fluid inertia results in the excitation of a second mode for the Jeffcott rotor, decreases the possibility of jump resonance, and decreases the useful range of vibration isolation of the dampers. It is also shown that a squeeze film damper with no centering spring (or a very soft spring) may be advantageous with regards to the unbalance response and the vibration isolation capability of the dampers.

Unbalance Response of a Jeffcott Rotor Incorporating Long Squeeze Film Dampers

1991 ◽  
Vol 113 (1) ◽  
pp. 85-94 ◽  
Author(s):  
A. El-Shafei
Keyword(s):  
Vibration Isolation ◽  
Fluid Velocity ◽  
Resonance Phenomenon ◽  
Squeeze Film ◽  
Fluid Inertia ◽  
Unbalance Response ◽  
Squeeze Film Dampers ◽  
Jeffcott Rotor ◽  
Second Mode ◽  
Inertia Forces

The steady state unbalance response of a Jeffcott rotor incorporating long squeeze film dampers executing circular centered precession is obtained. Fluid inertia forces are included in the model of the squeeze film dampers, using an energy approximation. The fluid velocity profiles are assumed not to change much due to fluid inertia, and the kinetic coenergy of the fluid is calculated. The fluid inertia forces are then obtained by Lagrange’s equations in conjunction with Reynolds transport theorem. The unbalance response of the rotor is obtained by assuming circular centered precession, and it is shown that fluid inertia results in the excitation of a second mode for the Jeffcott rotor and decreases the useful range of vibration isolation of the dampers. It is also shown that the second mode can exhibit the jump resonance phenomenon.

Observations on the Nonlinear Fluid Forces in Short Cylindrical Squeeze Film Dampers

1993 ◽  
Vol 115 (4) ◽  
pp. 692-698 ◽  
Author(s):  
J. Zhang ◽  
J. Ellis ◽  
J. B. Roberts
Keyword(s):  
Theoretical Work ◽  
Squeeze Film ◽  
Navier Stokes ◽  
Fluid Inertia ◽  
Navier Stokes Equation ◽  
Fluid Forces ◽  
Recent Theoretical Work ◽  
Starting Point ◽  
Squeeze Film Dampers ◽  
Inertia Forces

Recent theoretical work by Tichy and Bou-Said (1991) and El-Shafei and Crandall (1991) has resulted in new theoretical expressions for the nonlinear inertia forces for both short and long cylindrical squeeze film dampers (SFDs). This paper provides alternative derivations for the short cylindrical SFD using as a starting point a simplified two-dimensional Navier-Stokes equation. The resulting expressions for the fluid inertia forces are similar to the Tichy and Bou-Said/El-Shafei and Crandall expressions except for differences in certain numerical constants which can be explained by the different averaging methods used within the squeeze-film thickness. The analyses give additional insight into the temporal and convective origins of the various coefficients. The theoretical results are compared with published theoretical and experimental work involving nonlinear cylindrical SFD behavior. The paper highlights the importance of convective inertia terms when cylindrical SFDs operate at large values of eccentricity ratio.

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.

The Nonlinear Response of Multimode Rotors Supported on Squeeze Film Dampers

2000 ◽  
Vol 123 (4) ◽  
pp. 839-848 ◽  
Author(s):  
R. Y. Yakoub ◽  
A. El-Shafei
Keyword(s):  
Differential Equations ◽  
Computer Time ◽  
Squeeze Film ◽  
Fast Method ◽  
State Behavior ◽  
Unbalance Response ◽  
Analysis Theory ◽  
Squeeze Film Dampers ◽  
Modal Force ◽  
Parametric Studies

This paper describes the development of an extremely fast method to obtain the unbalance response of multiple mode rotors supported on squeeze film dampers (SFDs). Planar modal analysis theory is used to model the rotor-SFD system. Undamped critical speed analysis is performed to obtain the rotor eigenvalues and eigenvectors. The SFD nonlinear forces are included in the modal force vector. The system differential equations are constructed and are uncoupled using the orthogonal properties of modal vectors. Assuming circular orbit, consistent with planar modes, the differential equations are converted into algebraic ones. A polynomial in speed is obtained through algebraic manipulations. This polynomial represents the steady-state behavior of the rotor-SFD system. The full unbalance response is directly obtained by finding the roots of the polynomial for each particular orbit. This method is extremely fast compared to numerical integration and to iterative methods. The developed method is useful in performing parametric studies and optimum design of SFDs. Twenty-five orders of magnitude computer time savings are reported. Parametric studies of an aircraft gas turbine fan rotor supported by an SFD are presented. The parametric studies show the possibility of appropriately locating the SFD, to dampen the rotor modes. In addition, parametric studies are also used to determine the effect of the SFD parameters on the AGTFR unbalance response.

A Fast Method to Obtain the Nonlinear Response of Multi-Mode Rotors Supported on Squeeze Film Dampers Using Planar Modes: Part II — Parametric Studies

1998 ◽  
Author(s):  
R. Y. Yakoub ◽  
A. El-Shafei
Keyword(s):  
Fast Algorithm ◽  
Nonlinear Response ◽  
Computer Time ◽  
Squeeze Film ◽  
Fast Method ◽  
Rotor Speed ◽  
Squeeze Film Dampers ◽  
Parametric Studies ◽  
Time Savings ◽  
Multi Mode

This paper is a continuation of Part I, where the advantages of the fast algorithm to obtain the nonlinear response of multi-mode rotors supported on Squeeze Film Dampers (SFDs) are exploited. In Part I, the fast algorithm which relies on planar modal analysis and circular orbits to obtain a polynomial in rotor speed, is described. The advantages of the algorithm showing twenty five orders of magnitude computer time savings are discussed. In this paper, the fast algorithm is used to perform parametric studies on an aircraft gas turbine fan rotor (AGTFR). The parametric studies show the possibility of appropriately locating the SFD, to dampen the rotor modes. In addition, parametric studies are also used to determine the effect of the SFD parameters on the AGTFR unbalance response.

A Fast Method to Obtain the Nonlinear Response of Multi-Mode Rotors Supported on Squeeze Film Dampers Using Planar Modes: Part I — Theory

1998 ◽  
Author(s):  
R. Y. Yakoub ◽  
A. El-Shafei
Keyword(s):  
Differential Equations ◽  
Squeeze Film ◽  
Fast Method ◽  
State Behavior ◽  
Unbalance Response ◽  
Analysis Theory ◽  
Squeeze Film Dampers ◽  
Modal Force ◽  
Parametric Studies ◽  
Multi Mode

This paper describes the development of an extremely fast method to obtain the unbalance response of multiple mode rotors supported on Squeeze Film Dampers (SFDs). Planar modal analysis theory is used to model the rotor-SFD system. Undamped critical speed analysis is performed to obtain the rotor eigenvalues and eigenvectors. The SFD nonlinear forces are included in the modal force vector. The system differential equations are constructed for the system and are uncoupled using the orthogonal properties of modal vectors. Assuming circular orbit, consistent with planar modes, the differential equations are converted into algebraic ones. A polynomial in speed is obtained through algebraic manipulations. This polynomial represents the steady state behavior of the rotor-SFD system. The full unbalance response is directly obtained by finding the roots of the polynomial for each particular orbit. This method is extremely fast compared to numerical integration and to iterative methods. The developed method is useful in performing parametric studies and optimum design of SFDs. Twenty five orders of magnitude computer lime savings are reported. Part II of the paper presents parametric studies of an aircraft gas turbine fan rotor supported by an SFD.

The influence of fluid inertia forces on the sudden unbalance responses of squeeze-film damper supported rotors

1998 ◽  
Vol 212 (5) ◽  
pp. 353-357 ◽  
Author(s):  
G Meng ◽  
Y-C Guo ◽  
E. J. Hahn
Keyword(s):  
Transient Process ◽  
Vibration Amplitude ◽  
Constant Speed ◽  
Squeeze Film ◽  
Flexible Rotor ◽  
Fluid Inertia ◽  
Transient Vibration ◽  
Squeeze Film Damper ◽  
Squeeze Film Dampers ◽  
Inertia Forces

The influence of fluid inertia on the sudden unbalance response of a flexible rotor supported on centralized and uncentralized squeeze-film dampers is investigated. Whether the rotor is at constant speed or accelerating, it was generally found that fluid inertia shortens the transient process and decreases the transient vibration amplitude. Qualitatively, the effect of fluid inertia is similar to increased damping.

Fluid Inertia Forces in Squeeze Film Dampers

1991 ◽  
Author(s):  
A. El-Shafei ◽  
S. M. Crandall
Keyword(s):  
Reynolds Number ◽  
Velocity Profiles ◽  
Squeeze Film ◽  
Fluid Inertia ◽  
Eccentricity Ratio ◽  
Number Range ◽  
Squeeze Film Dampers ◽  
Energy Approximation ◽  
Inertia Forces ◽  
Good Agreement

Abstract Fluid inertia forces in Squeeze Film Dampers (SFDs) are obtained for short and long dampers using an energy approximation based on the assumption that the velocity profiles with inertia are the same as those for an inertialess fluid. It is shown that the inertia forces thus obtained are proportional to the usual radial, centripetal, tangential and Coriolis accelerations of the journal, plus an additional nonlinear acceleration. The inertia coefficients of the dampers are obtained, for both uncavitated and cavitated dampers, and are plotted versus the eccentricity ratio for centered, nearly circular whirl. The inertia forces obtained by the energy approximation are compared to an exact linearized solution for centered, circular whirl, and good agreement is found for both short and long dampers in the Reynolds number range of ordinary SFD application.

scholarly journals Unbalance Response of a Multi-Mode Rotor Supported on Short Squeeze Film Dampers

1996 ◽  
Author(s):  
R. Youssef ◽  
A. El-Shafei
Keyword(s):  
Steady State ◽  
Differential Equations ◽  
Linear Part ◽  
Mode Shapes ◽  
Squeeze Film ◽  
Unbalance Response ◽  
Analysis Technique ◽  
Squeeze Film Dampers ◽  
Parametric Studies ◽  
Multi Mode

This paper describes a fast algorithm to obtain the steady state unbalance response of a multi-mode rotor supported on short squeeze film dampers (SFDs). The presented algorithm is developed based on planar modal theory. Undamped critical speed analysis is first performed to obtain the rotor critical speeds and their associated mode shapes. The modal analysis technique is then applied to the linear part of the rotor-SFD assembly to obtain the system differential equations. The rotor is assumed to execute circular centered orbits, hence all differential equations are reduced to algebraic ones. The resulting equations are manipulated algebraically to form a polynomial in rotor rotational speed. The roots of the polynomial are found and the full unbalance response is obtained. A conventional rotor is used to describe the developed algorithm numerically. Results show that the proposed algorithm gives accurate response in comparison to that obtained by integrating the system differential equations numerically. The great advantage of the proposed algorithm is the saving in the execution time which is extremely dramatic with respect to numerical integration, in addition to other advantages such as the possibility of obtaining all solutions occurring in regions of multiple steady state. Accuracy and speed of execution are quite advantageous regarding parametric studies on multi-mode rotors. These parametric studies can help in the optimization of SFDs design.

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