Collocation Method for Finite Length Squeeze Film Dampers With Variable Clearance

1988 ◽  
Vol 110 (4) ◽  
pp. 685-692 ◽  
Author(s):  
N. K. Arakere ◽  
H. D. Nelson
Keyword(s):  
Finite Difference ◽  
Collocation Method ◽  
Finite Length ◽  
Squeeze Film ◽  
Eccentricity Ratio ◽  
Static And Dynamic Analysis ◽  
Damping Coefficients ◽  
Highly Nonlinear ◽  
Secant Stiffness ◽  
Stiffness And Damping

The Collocation method is used to study the characteristics of a finite length Squeeze Film Damper (SFD) with variable clearance. The secant stiffness and damping coefficients of the SFD for centered circular orbits is compured by solving Reynolds equation for a finite bearing, using the collocation method. A significant disadvantage with a conventional SFD is the highly nonlinear variation of secant stiffness and damping coefficients with eccentricity ratio. It is shown in this paper that by suitably varying the parameters α and λ, which control the nature of clearance variation, the secant stiffness and damping coefficient variation with eccentricity; ratio can be altered to better suit specific design needs. Nonlinear transient analysis of a single journal in a finite SFD is carried out, and, periodic journal center orbits due to unbalance response for uncentered finite SFD’s are also obtained. The centered circular orbit response for different unbalance values and speeds is obtained. Results from the Collocation method show excellent agreement with finite difference results. The Collocation method is shown to be an efficient and viable technique that is an order of magnitude computationally faster than the finite difference method, for static and dynamic analysis of finite length SFD’s.

An Interior Collocation Method for Static and Dynamic Analysis of Finite Length Gas Journal Bearings

1988 ◽  
Vol 110 (3) ◽  
pp. 456-461 ◽  
Author(s):  
N. Arakere ◽  
H. D. Nelson
Keyword(s):  
Differential Equation ◽  
Finite Difference ◽  
Dynamic Analysis ◽  
Collocation Method ◽  
Finite Length ◽  
Journal Bearings ◽  
Computational Domain ◽  
Static And Dynamic Analysis ◽  
Order Of Magnitude ◽  
Governing Differential Equation

The general Reynolds equation for self-acting, finite length gas-lubricated journal bearings is solved using an interior collocation method. The method assumes an approximate solution to the governing differential equation in the form of a series of trial functions, wn, with n unknown coefficients. The coefficients are evaluated by substituting the assumed solution in the governing differential equation, and forcing the residual (error) at n collocation points in the computational domain to be zero. The effectiveness of the collocation method is demonstrated by using the technique for the static and dynamic analysis of a journal supported by a plane gas bearing. The results from the collocation method agree very well with those obtained from a finite difference technique. Periodic orbit plots for a single journal in a finite bearing are presented for various journal unbalances and speeds. The collocation method is shown to be an order of magnitude computationally faster than the finite difference method. The method can be extended to other bearing types such as slider, hydrostatic and tilting pad bearings.

scholarly journals Journal Bearing Impedance Descriptions for Rotordynamic Applications

1977 ◽  
Vol 99 (2) ◽  
pp. 198-210 ◽  
Author(s):  
D. Childs ◽  
H. Moes ◽  
H. van Leeuwen
Keyword(s):  
Finite Length ◽  
Reaction Force ◽  
Squeeze Film ◽  
Damping Coefficients ◽  
Analytic Expressions ◽  
Complete Set ◽  
Impedance Vector ◽  
Force Components ◽  
Stiffness And Damping ◽  
Vector Magnitude

Bearing impedance vectors are introduced for plain journal bearings which define the bearing reaction force components as a function of the bearing motion. Impedance descriptions are developed directly for the approximate Ocvirk (short) and Sommerfeld (long) bearing solutions. The impedance vector magnitude and the mobility vector magnitude of Booker are shown to be reciprocals. The transformation relationships between mobilities and impedance are derived and used to define impedance vectors for a number of existing mobility vectors including the finite-length mobility vectors developed by Moes. The attractiveness and utility of the impedance-vector formulation for transient simulation work is demonstrated by numerical examples for the Ocvirk “π”, and “2π” bearing impedances and the cavitating finite-length-bearing impedance. The examples presented demonstrate both bearing and squeeze-film damper application. A direct analytic method for deriving a complete set of (analytic) stiffness and damping coefficients from impedance descriptions is developed and demonstrated for the cavitating finite-length-bearing impedances. Analytic expressions are provided for all direct and cross-coupled stiffness and damping coefficients, and compared to previously developed numerical results. These coefficients are used for stability analysis of a rotor, supported in finite-length cavitating bearings. Onset-speed-of-instability results are presented as a function of the L/D ratio for a range of bearing numbers. Damping coefficients are also presented for finite-length squeeze-film dampers.

Ball bearing turbocharger vibration management: application on high speed balancer

2020 ◽  
Vol 21 (6) ◽  
pp. 619
Author(s):  
Kostandin Gjika ◽  
Antoine Costeux ◽  
Gerry LaRue ◽  
John Wilson
Keyword(s):  
Dynamic Behavior ◽  
High Speed ◽  
Internal Combustion Engines ◽  
Ball Bearing ◽  
Squeeze Film ◽  
Design And Technology ◽  
Squeeze Film Damper ◽  
Damping Coefficients ◽  
Bearing Loads ◽  
Stiffness And Damping

Today's modern internal combustion engines are increasingly focused on downsizing, high fuel efficiency and low emissions, which requires appropriate design and technology of turbocharger bearing systems. Automotive turbochargers operate faster and with strong engine excitation; vibration management is becoming a challenge and manufacturers are increasingly focusing on the design of low vibration and high-performance balancing technology. This paper discusses the synchronous vibration management of the ball bearing cartridge turbocharger on high-speed balancer and it is a continuation of papers [1–3]. In a first step, the synchronous rotordynamics behavior is identified. A prediction code is developed to calculate the static and dynamic performance of “ball bearing cartridge-squeeze film damper”. The dynamic behavior of balls is modeled by a spring with stiffness calculated from Tedric Harris formulas and the damping is considered null. The squeeze film damper model is derived from the Osborne Reynolds equation for incompressible and synchronous fluid loading; the stiffness and damping coefficients are calculated assuming that the bearing is infinitely short, and the oil film pressure is modeled as a cavitated π film model. The stiffness and damping coefficients are integrated on a rotordynamics code and the bearing loads are calculated by converging with the bearing eccentricity ratio. In a second step, a finite element structural dynamics model is built for the system “turbocharger housing-high speed balancer fixture” and validated by experimental frequency response functions. In the last step, the rotating dynamic bearing loads on the squeeze film damper are coupled with transfer functions and the vibration on the housings is predicted. The vibration response under single and multi-plane unbalances correlates very well with test data from turbocharger unbalance masters. The prediction model allows a thorough understanding of ball bearing turbocharger vibration on a high speed balancer, thus optimizing the dynamic behavior of the “turbocharger-high speed balancer” structural system for better rotordynamics performance identification and selection of the appropriate balancing process at the development stage of the turbocharger.

Dynamical Behaviors of Hybrid Squeeze Film Damper for Rotor System Vibration Control

1995 ◽  
Author(s):  
Zhu Changsheng
Keyword(s):  
Rotor System ◽  
Squeeze Film ◽  
Radial Clearance ◽  
Rigid Rotor ◽  
Squeeze Film Damper ◽  
Damping Coefficients ◽  
Dynamical Behaviors ◽  
System Vibration ◽  
Stiffness And Damping ◽  
Film Stiffness

Abstract The behaviors of oil film stiffness and damping coefficients of the deep multi-recessed hybrid squeeze film damper (HSFD) with the orifices compensated are first analysed in this paper. The control ability of the HSFD on the rotor system vibrations is studied theoretically and experimentally with a rigid rotor system supported on the HSFD, and compared with that of the conventional squeeze film damper (SFD). Investigation shows that the HSFD not only can significantly improve the high nonlinearity of the SFD, but also can effectively control the rotor vibrational amplitudes, especially for larger rotor unbalance levels and radial clearance ratios, as compared with the SFD.

Hermetically Sealed Squeeze Film Damper for Operation in Oil-Free Environments

2018 ◽  
Vol 141 (2) ◽  
Author(s):  
Bugra Ertas ◽  
Adolfo Delgado
Keyword(s):  
Excitation Frequency ◽  
Squeeze Film ◽  
Force Density ◽  
Viscous Damping ◽  
Squeeze Film Damper ◽  
Open Flow ◽  
Damping Coefficients ◽  
End Plate ◽  
Stiffness And Damping ◽  
Gas Bearing

The following work advances a new concept for a hermetically sealed squeeze film damper (HSFD), which does not require an open-flow lubrication system. The hermetically sealed concept utilizes a submersed plunger within a contained fluidic cavity filled with incompressible fluid and carefully controlled end plate clearances to generate high levels of viscous damping. Although the application space for a hermetic damper can be envisioned to be quite broad, the context here will target the use of this device as a rotordynamic bearing support damper in flexibly mounted gas bearing systems. The effort focused on identifying the stiffness and damping behavior of the damper while varying test parameters such as excitation frequency, vibration amplitude, and end plate clearance. To gain further insight to the damper behavior, key dynamic pressure measurements in the damper land were used for identifying the onset conditions for squeeze film cavitation. The HSFD performance is compared to existing gas bearing support dampers and a conventional open-flow squeeze film dampers (SFD) used in turbomachinery. The damper concept yields high viscous damping coefficients an order of magnitude larger than existing oil-free gas bearing supports dampers and shows comparable damping levels to current state of the art open-flow SFD. The force coefficients were shown to contribute frequency-dependent stiffness and damping coefficients while exhibiting amplitude independent behavior within operating regimes without cavitation. Finally, using experimentally based force density calculations, the data revealed threshold cavitation velocities, approximated for the three end seal clearance cases. To complement the experimental work, a Reynolds-based fluid flow model was developed and is compared to the HSFD damping and stiffness results.

Modal Analysis of Rotor on Piecewise Linear Journal Bearings Under Seismic Excitation

1999 ◽  
Vol 121 (2) ◽  
pp. 190-196 ◽  
Author(s):  
B. J. Gaganis ◽  
A. K. Zisimopoulos ◽  
P. G. Nikolakopoulos ◽  
C. A. Papadopoulos
Keyword(s):  
Modal Analysis ◽  
Dynamic Properties ◽  
Piecewise Linear ◽  
Computer Time ◽  
Seismic Excitation ◽  
Damping Coefficients ◽  
Highly Nonlinear ◽  
Rotor Bearing ◽  
Stiffness And Damping ◽  
Bearing System

A rotor bearing system is expected to exhibit large vibration amplitudes when subjected to a large seismic excitation. It is possible that these vibrations can lead to large values the eccentricity of the bearings. Then the bearing is operated in highly nonlinear region because the stiffness and the damping coefficients are nonlinear as functions of the eccentricity. To solve this problem numerical integration must be performed with high cost in computer time. The idea of this paper was to divide the nonlinear area into more areas where the stiffness and damping coefficients could be considered to be constants. In other words the bearing coefficients are considered to be piecewise constant. The excitation due to the earthquake is modelled as a movement of the base of the bearings using the El Centro data for the acceleration. Then a simplified modal analysis for each of these piecewise linear regions can be performed. The equation of motion of the rotor contains rotational speed depended terms, known as gyroscopic terms, and terms due to base excitation. The response and the variation of the dynamic properties of this complicated rotor bearing system are investigated and presented.

Optimized Short Bearing Theory for Squeeze Film Dampers

2009 ◽  
Author(s):  
Stephen L. Edney
Keyword(s):  
Closed Form ◽  
Correction Factor ◽  
Closed Form Solution ◽  
Squeeze Film ◽  
Radial Clearance ◽  
Positive Pressure ◽  
Damping Coefficients ◽  
Lubrication Equation ◽  
Squeeze Film Dampers ◽  
Stiffness And Damping

It is well established that classical short bearing theory can be applied to assess squeeze film dampers whirling in circular centered orbits. This theory yields accurate values for the stiffness and damping coefficients for designs with small length-to-diameter (L/D) ratios (typically less than 0.5) whirling at amplitudes of less than half the damper radial clearance. For L/D ratio designs above 0.5 and/or whirling amplitudes approaching the damper radial clearance, the short bearing theory increasingly overestimates the stiffness and damping coefficients that stretch its applicability for some designs. There are two limitations with the classical theory that compromise the solution at high L/D ratios and large whirling amplitudes. The first is that as the L/D ratio increases, the unrestricted end flow assumption that forms the basis of the short bearing theory introduces increasingly larger errors. The second is that as the whirling amplitude approaches the damper radial clearance, the stiffness and damping coefficients approach infinity much more rapidly than those from a full solution of the governing lubrication equation. The ideal method for determining more exact values is to numerically solve the full lubrication equation, although not everyone has access to such a code. An alternative approach is to use the expressions presented in this paper that are derived from an optimized solution of the short bearing theory that appreciably reduces the errors introduced at high L/D ratios and whirling amplitudes approaching the damper radial clearance. The optimized solution yields a simple closed form correction factor based on Galerkin’s method that minimizes these errors over the positive pressure region of the oil film. This analytic correction factor increases the accuracy of the short bearing theory for all whirling amplitudes and extends the applicability of the closed form solution to larger L/D ratio damper designs. The simple closed form expressions presented herein apply to a damper whirling in a circular centered orbit for both a partial pi-film cavitated model and a full-film uncaviated model. Examples are given that demonstrate the optimized solution yields stiffness and damping values that are significantly closer to the numerical solution for L/D ratio designs up to 1.0 and/or whirling amplitudes approaching the damper radial clearance.

Study of Transient Characteristic of a Simple Rigid Rotor Supported on a Squeeze Film Damper With Valvular Metal Rubber Squeeze Film Ring

2007 ◽  
Author(s):  
Yanhong Ma ◽  
Jie Hong ◽  
Dayi Zhang ◽  
Hong Wang
Keyword(s):  
High Speed ◽  
Squeeze Film ◽  
Impact Loads ◽  
Rigid Rotor ◽  
Squeeze Film Damper ◽  
Damping Coefficients ◽  
Metal Rubber ◽  
Stiffness And Damping ◽  
Film Stiffness ◽  
Blade Loss

An efficient oil film damper known as a squeeze film damper with valvular metal rubber squeeze film ring (SFD/VMR) was developed for more effective and reliable vibration control, and especially for improving the blade loss dynamics of high-speed rotors based on the conventional squeeze film damper (SFD). The immobile squeeze film ring of the SFD was replaced by the elastic squeeze film ring with the valvular metal rubber subassembly (VMR) of the SFD/VMR. The squeeze film force properties of the SFD/VMR was improved, because it can passively adjust the squeeze film clearance by taking advantage of the elastic deformation of the VMR and can control the squeeze film clearance in a suitable range. The characteristics of squeeze film stiffness and damping coefficients, as well as the steady-state unbalance response of a simple rigid rotor supported on SFD/VMR and SFD, were reported in a previous literature[1]. In this paper, the transient response of the rigid rotor supported on SFD/VMR and SFD subjected to sudden unbalance of blade loss are inverstigated. Time transient simulation and experimental results indicated that SFD/VMR can operate effectively under much greater unbalance compared with SFD, especially under relative large impact loads of blade loss. The SFD/VMR can suppress the occurrence of the nonlinear vibration phenomenon markedly, such as the bistable jump up phenomenon. Furthermore, the effective eccentricities of SFD/VMR with small transfer ratio (T<1.2) extend to two times of SFD, and optimum film stiffness and damping distribution within the whole film clearance can be achieved.

Hermetically Sealed Squeeze Film Damper for Operation in Oil-Free Environments

2018 ◽  
Author(s):  
Bugra Ertas ◽  
Adolfo Delgado
Keyword(s):  
Excitation Frequency ◽  
Squeeze Film ◽  
Force Density ◽  
Viscous Damping ◽  
Squeeze Film Damper ◽  
Open Flow ◽  
Damping Coefficients ◽  
End Plate ◽  
Stiffness And Damping ◽  
Gas Bearing

The following work advances a new concept for a hermetically sealed squeeze film damper (HSFD), which does not require an open-flow lubrication system. The hermetically sealed concept utilizes a submersed plunger within a contained fluidic cavity filled with incompressible fluid and carefully controlled end plate clearances to generate high levels of viscous damping. Although the application space for a hermetic damper can be envisioned to be quite broad, the context here will target the use of this device as a rotordynamic bearing support damper in flexibly mounted gas bearing systems. The effort focused on identifying the stiffness and damping behavior of the damper while varying test parameters such as excitation frequency, vibration amplitude, and end plate clearance. To gain further insight to the damper behavior, key dynamic pressure measurements in the damper land were used for identifying the onset conditions for squeeze film cavitation. The HSFD performance is compared to existing gas bearing support dampers and a conventional open-flow squeeze film dampers (SFD) used in turbomachinery. The damper concept yields high viscous damping coefficients an order of magnitude larger than existing oil-free gas bearing supports dampers and shows comparable damping levels to current state of the art open-flow SFD. The force coefficients were shown to contribute frequency dependent stiffness and damping coefficients while exhibiting amplitude independent behavior within operating regimes without cavitation. Finally, using experimentally based force density calculations the data revealed threshold cavitation velocities, approximated for the three end seal clearance cases. To complement the experimental work, a Reynolds based fluid flow model was developed and is compared to the HSFD damping and stiffness results.

Rotordynamic Performance of Finite Length Squeeze Film Dampers

2003 ◽  
Author(s):  
A. El-Shafei ◽  
A. S. El-Kabbany
Keyword(s):  
Finite Length ◽  
Reynolds Equation ◽  
Squeeze Film ◽  
Rigid Rotor ◽  
Damping Coefficients ◽  
At Resonance ◽  
R Ratio ◽  
Squeeze Film Dampers ◽  
Current Design ◽  
Analytical Formulae

A recently developed finite length model of squeeze film dampers is extended and used in predicting the behavior of a rigid rotor supported by squeeze film dampers (SFDs). The model is based on a perturbation solution of Reynolds’ equation. The finite length SFD damping coefficients are presented for various L/R ratios. The effect of damper finite length is studied. Simulations of the behavior of a rigid rotor with the finite length SFDs illustrate the response of the roto-rbearing system. The accuracy of the finite damper model is shown for cases comparable to short and long dampers models. The short damper and long damper models are generally accepted to be valid for L/D < 1/4, and for L/D > 4, respectively. The capability of the finite length damper model to capture the main essence of the L/R ratio on the rotor response at resonance is illustrated. Analytical formulae for damping estimates are provided for finite length dampers. It is shown that the finite length damper actually provides less damping than either the short or the long damper models, which means that current design practices actually overestimate the SFD damping capabilities.

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