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.

Dynamic Analysis of Squeeze Film Damper Supported Rotors Using Equivalent Linearization

1994 ◽  
Vol 116 (3) ◽  
pp. 682-691 ◽  
Author(s):  
A. El-Shafei ◽  
R. V. Eranki
Keyword(s):  
Dynamic Analysis ◽  
Numerical Integration ◽  
Dynamic Characteristics ◽  
Nonlinear Dynamic Analysis ◽  
Squeeze Film ◽  
Equivalent Linearization ◽  
Squeeze Film Damper ◽  
Elliptic Orbits ◽  
Dynamic Programs ◽  
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 rotor-dynamic methods. Historically, it is customary to design SFDs for rotor-dynamic 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-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 rotor-dynamic programs to determine the rotor-dynamic characteristics through iteration. It is expected that for multirotor multibearing systems this technique will result in even more economical computation.

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.

A System to Measure the Response of a High-Speed Rotor to a Sudden Imbalance

1981 ◽  
Author(s):  
R. J. Trippett
Keyword(s):  
High Speed ◽  
Dynamic Test ◽  
Data Acquisition System ◽  
Squeeze Film ◽  
Sudden Increase ◽  
Test Rig ◽  
Dynamic Data ◽  
Squeeze Film Damper ◽  
Rotor Dynamic ◽  
Dynamic Data Acquisition

A unique rotor dynamic data acquisition system is described to control the gathering and display of rotor displacement data measured at rotor speeds up to 70 000 r/min. The first published results measured with this system are demonstrated with plots of measured transient shaft motion after a sudden increase in shaft imbalance at speeds up to 44 500 r/min. The displacements of the rotor in the forms of Lissajous plots with and without a squeeze film damper are presented at four axial shaft locations below and above the shafts critical speeds. The blade-loss, dynamic test rig is also described.

In Situ Estimation of the Dynamic Characteristics of an Uncavitated Squeeze-Film Damper

1988 ◽  
Vol 110 (1) ◽  
pp. 162-166
Author(s):  
C. R. Burrows ◽  
M. N. Sahinkaya ◽  
N. C. Kucuk ◽  
M. L. Tong
Keyword(s):  
Frequency Domain ◽  
Dynamic Characteristics ◽  
Estimation Algorithm ◽  
Squeeze Film ◽  
Oil Film ◽  
Squeeze Film Damper ◽  
Damping Coefficients ◽  
Theoretical Predictions

A modified form of the author’s frequency-domain estimation algorithm has been applied to estimate the inertia and damping coefficients of an uncavitated squeeze-film bearing. These estimates are obtained in situ from measurements on a specially designed rig. The experiments provided further evidence that oil-film inertia coefficients may be significant and showed that theoretical predictions are inadequate.

Static and dynamic characteristics of an orifice compensated three-pad hydrostatic squeeze film damper

2018 ◽  
Vol 70 (6) ◽  
pp. 1078-1085 ◽  
Author(s):  
Mahmoud Hammou ◽  
Ahmed Bouzidane ◽  
Marc Thomas ◽  
Aboubakeur Benariba ◽  
Mohamed Bouzit
Keyword(s):  
Dynamic Characteristics ◽  
Squeeze Film ◽  
Static And Dynamic Characteristics ◽  
Squeeze Film Damper

Equivalent Linearization of a Squeeze Film Damper

1986 ◽  
Vol 108 (4) ◽  
pp. 434-440 ◽  
Author(s):  
Songqi Chen ◽  
Shengpei Liu
Keyword(s):  
Squeeze Film ◽  
Equivalent Linearization ◽  
Cycle Period ◽  
Mean Square ◽  
Damping Force ◽  
Average Force ◽  
Squeeze Film Damper ◽  
Spring Force ◽  
The Difference ◽  
Mean Square Errors

In this paper, the equivalent linearization of an intershaft squeeze film damper in a two shaft engine system is investigated. The two shaft centers at the damper position are assumed to move in different elliptical offset orbits and at synchronous frequency with the unbalanced rotor (e.g., the high pressure rotor). The nonlinear damper force is resolved into two orthogonal components along the absolute coordinate directions and, in turn, each of these force components is supposed to be equivalent to the sum of an average force, a linear spring force, and a linear damping force in the corresponding direction. By using the method of equivalent linearization by harmonic balance, the six parameters of the equivalent forces, including two average forces, two equivalent spring coefficients, and two equivalent damping coefficients, are expressed analytically by the squeeze film forces and the assumed orbital motion of the two shaft centers at the damper position. The analytical expressions of the squeeze film forces are derived from an approximate solution of the basic Reynolds equation. The results obtained are verified by the method of equivalent linearization by minimum mean square errors. It shows that the six obtained parameters make the mean square errors minimum over a cycle period of motion, the errors being the difference between the equivalent forces and the actual nonlinear forces.

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