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 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.

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.

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.

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.

scholarly journals Steady-State Unbalance Response of a Three-Disk Flexible Rotor on Flexible, Damped Supports

1978 ◽  
Vol 100 (3) ◽  
pp. 563-573 ◽  
Author(s):  
R. E. Cunningham
Keyword(s):  
Ball Bearing ◽  
Squeeze Film ◽  
Flexible Rotor ◽  
Frequency Range ◽  
Lateral Bending ◽  
Damping Coefficients ◽  
The Third ◽  
Unbalance Response ◽  
Squeeze Film Damping ◽  
Squeeze Film Dampers

Experimental data are presented for the unbalance response of a flexible, ball bearing supported rotor to speeds above the third lateral bending critical. Values of squeeze film damping coefficients obtained from measured data are compared to theoretical values obtained from short bearing approximation over a frequency range from 5000 to 31,000 cycles/min. Experimental response for an undamped rotor is compared to that of one having oil squeeze film dampers at the bearings. Unbalances applied varied from 0.62 to 15.1 gm-cm.

Stability and Unbalance Response of Centrally Preloaded Rotors Mounted in Journal and Squeeze Film Bearings

1979 ◽  
Vol 101 (2) ◽  
pp. 120-128 ◽  
Author(s):  
E. J. Hahn
Keyword(s):  
Steady State ◽  
Vibration Isolation ◽  
Journal Bearings ◽  
Squeeze Film ◽  
State Behavior ◽  
Unbalance Response ◽  
Radial Stiffness ◽  
Rolling Element ◽  
Orbit Eccentricity ◽  
Vertical Bearing

The unbalance response and stability of centrally preloaded symmetric rigid rotors are investigated. Steady state solutions for unbalance transmissibilities, orbit eccentricity radii, and stability are presented for rotors running in hydrodynamic journal bearings and in rolling element bearings which are supported in squeeze film bearings. The Ocvirk and Warner approximations are used to evaluate the fluid film forces, rendering the data applicable to any length/diameter ratio. Both pressurized (2π film) and unpressurized (π film) oil supply are considered. Pressurization has a far reaching influence on the steady state behavior of both journal and squeeze film bearings. For unpressurized bearings, conditions of multistable operation and for stability are depicted, with journal bearings exhibiting ‘half frequency whirl’ possibilities as well. The error involved in predicting vertical bearing behavior by assuming an equivalent unidirectional load equal to the unbalance load is demonstrated. For pressurized bearings multistable operation is eliminated but both squeeze film and journal bearings are unstable for most length/diameter ratios in the absence of external radial stiffness. The stabilizing effect of superimposed external radial stiffness on pressurized bearings is clearly demonstrated. While pressurized journal bearings can run stably, they are less suited than pressurized squeeze film bearings for vibration isolation.

Chaos in the unbalance response of a rigid rotor in cavitated squeeze-film dampers without centering springs

2002 ◽  
Vol 13 (4) ◽  
pp. 929-945 ◽  
Author(s):  
Jawaid Iqbal Inayat-Hussain ◽  
Hiroshi Kanki ◽  
Njuki W. Mureithi
Keyword(s):  
Squeeze Film ◽  
Rigid Rotor ◽  
Unbalance Response ◽  
Squeeze Film 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.

scholarly journals Static Stiffness Parametric Studies of Newly Conceptualized Inter Shaft Squeeze Film Damper (ISSFD) Rings

2019 ◽  
Vol 4 (2) ◽  
pp. 77-84
Author(s):  
SHIVAPRASAD MALLAIAH HIRENALLUR ◽  
GIRIDHARA G GAIKWAD ◽  
ARUNKUMAR V
Keyword(s):  
Gas Turbine ◽  
Gas Turbine Engine ◽  
Squeeze Film ◽  
Static Stiffness ◽  
Current Effort ◽  
Turbine Engine ◽  
Squeeze Film Damper ◽  
Stiffness Evaluation ◽  
Squeeze Film Dampers ◽  
Parametric Studies

Most of the modern gas turbine engine designs requiring super critical operations will often have squeeze film dampers (SFDs) on the high pressure spool bearing as an inevitable feature. However, Squeeze Film Dampers are not very common for inter-shaft bearing applications and are still in the research and development stage. The current effort concentrates on static stiffness parametric studies based on newly conceptualized intershaft squeeze film damper (ISSFD) ring design suitable for space constrained intershaft bearing application of a typical two spool configured system. The work involves static stiffness evaluation of three and four grooves ISSFD rings by varying the groove angle/groove length/subtended angle of groove & hence the overlapping angle of grooves by conducting static tests on a dedicated static stiffness evaluation test rig designed and fabricated for the purpose. The pattern of circumferential variation of stiffness of each ring is studied and the results revealed a typical trend of decreasing stiffness in ISSFD ring with the increase in groove angle and hence the overlapping angle of grooves. The static stiffness parametric studies has resulted in developing an ideal profile of ISSFD ring having six grooves that exhibited axisymmetric pattern of circumferential variation of stiffness. When used in a space constrained intershaft bearing plane of a typical two spool gas turbine engine, the ideal ISSFD ring profile would exhibit the best damping performance.  Keywords: Inter Shaft Squeeze Film Damper (ISSFD), Gas Turbine Engine, Static stiffness, two spools, grooves.

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