Damping Of Bearings Research Articles

Inertia Effects in Squeeze-Film Damper Bearings Generated by Circumferential Oil Supply Groove

The dynamic properties of an industrial Squeeze-Film Damper (SFD) bearing design are described using the well-known perturbation approach, where the reaction forces induced by small movements away from the position of equilibrium are expanded into a Taylor series in terms of displacement, velocity, and acceleration. Although generally negligible, the acceleration term can become significant in SFD bearings when inertia effects in the damper lands are enhanced by the flow in a central circumferential oil supply groove. By using a bulk flow approximation in the oil supply groove an explicit expression is derived for the acceleration term. Experimental results confirm the significance of the oil supply groove geometry and appear to validate the bulk flow approximation.

An investigation into the non-linear dynamics of an unbalanced flexible rotor running in an unsupported squeeze-film damper bearing

The non-linear dynamics of a multimodal flexible rotor running in an unsupported squeeze-film damper (SFD) bearing are investigated analytically and experimentally. The main aim is to assess the ability to predict and explain the non-linear performance using an integrated analytical technique and a standard model for the SFD. A fast harmonic balance method that uses receptance functions is used to determine periodic solutions. A modal-based approach is used for the analysis of the stability and bifurcation of these solutions, as well as the analysis of aperiodic motion. Non-synchronous motion with combination frequencies and subharmonic motions are correctly predicted. It is also shown that such an SFD introduces subcritical superharmonic resonance when it is apparently inactive. It is concluded that, despite the economy in design, the benefits of using an unsupported SFD in a flexible rotor-rigid bearing housing system are dubious.

Optimal Rotor-Dynamic Design Based on Experimental Design Methodology. Optimal Design Methodology for Rotor Systems Supported by Damper Bearings.

When designing rotor systems, development costs and the number of trial production runs must be minimised. To do so, the optimum structure must be found by combining CAE optimisation tools during the initial stages of development. We propose a low-response magnification design method for process compressor rotor systems supported by damper bearings. The effectiveness of this method is demonstrated by experiment. The main elements of our system are (1) a variance analysis of the contribution rate of design variables and mutual actions, (2) an assignment of the design variables to the orthogonal array, (3) a rational parameter survey of this array, and (4) an understanding of solution space from multiple points of view gained by using an approximation method for a response surface model.

Stability Analysis and Testing of a Train of Centrifugal Compressors for High Pressure Gas Injection

This paper describes the rotor dynamic stability analysis and the PTC-10 Class 1 test of a three body centrifugal compressor train for high pressure natural gas injection service. This train had a full load full pressure string test on hydrocarbon gasses to a final discharge pressure of 500 BAR (7250 PSIA). Each compressor is of the back to back configuration, and is equipped with tilting pad seals, damper bearings, and a honeycomb labyrinth at the division wall with shunt holes. The driver is a gas turbine.

Double Disk Rotor Model Analysis of Dynamical Property of Damper Bearing.

The double disk rotor model is used to analyse the second bending vibration mode generated by unbalance in a damper bearing-supported process compressor. First, a Q-factor map of the model is discussed. It has been shown that this type of map is a highly useful tool in selecting the most suitable parameter sets for rotor design. Secondly, a Q-factor map numerically generated by FEM is used to evaluate the model. The shapes of the Q-factor maps are classified according to vibration mode type. From this classification, the features of each vibration mode are extracted and the cause of the vibration can be analysed. The double disk rotor model is also used to decide on parameters for FEM calculation. The results suggest that the model provides a powerful tool for the simple creation of Q-factor maps.

Fluid forces in short squeeze-film damper bearings

This paper has studied influences of fluid inertia on fluid velocity profiles and provided an axial inertia velocity profile for short squeeze film damper bearings (SFDs) using as a starting point a simplified Navier–Stokes equation. The velocity profile reasonably represents influences of fluid inertia on fluid flow. From the inertia velocity profile, present work develops new theoretical models for fluid forces in cylindrical short SFDs. Published experimental work confirms that the new models for fluid forces are better than traditional short-SFD theory, especially for tangential force. The new models show that the damping coefficient for 2 π film is related to fluid inertia.

Simulations of Vibration for Squeeze Film Dampers. Rotor System Subjected to Earthquake with Vertical Shock. 1st Report. A Rigid Rotor System.

The present study deals with vibration in the case of a high-speed rotary machine that is subjected to earthquake with vertical shock. We derived the equations of motion in the case of a rigid rotor that was supported by squeeze film dampers and subjected to vertical base excitation, and developed programs that can carry out dynamic analyses. It is assumed that damper journals do not collide with damper bearings even if the rotor is oscillated by basic excitation and unbalance of the rotor. Dynamic characteristics of a model rotor were investigated by eigenvalue analysis. Time history responses in the case of the model rotor subjected to a vertical sine wave were calculated. Validities of the equations and the programs developed here were confirmed by comparing calculated results with those for an elastic rotating shaft system shown in the previous reports.

Simulations of Vibration for Squeeze Film Dampers. Rotor System Subjected to Earthquake with Vertical Shock. 2nd Report. A Flexible Rotor System, the Case of Being Subjected to the Great Hanshin Earthquake.

In this report, we developed programs for calculations of time history response in the case of a flexible rotor system that is subjected to base excitation such as earthquake with vertical shock. A finite element method was used in the equations of a flexible rotating shaft. As an analytical model of a SFD, the same one as that in the 1st report was used. A program was also developed for calculating time history responses even if damper journals collide with damper bearings due to vibration caused by a large base excitation. We calculated the natural frequencies and modes of vibration for the rotor system modeled in the dimensions near those of an existing turbine, and investigated the dynamic characteristics of the rotor system. Furthermore, we calculated the time history response in the case of the rotor system that was oscillated by a vertical seismic wave that was observed in Kobe City when the Great Hanshin Earthquake occurred.

A Theoretical and Experimental Investigation of a Gas-Operated Bearing Damper for Turbomachinery: Part I—Theoretical Model and Predictions

This is the first (Part I) of two papers describing recent results of the research program directed at developing a vibration damper suitable for high-temperature turbomachinery applications. It is expected that such dampers will replace squeeze-film dampers, which use oil as the working fluid and have limitations at higher temperatures. A novel gas-operated bearing damper has been evaluated analytically and experimentally for its damping characteristics. A theory based on the isentropic assumptions predicts the damper performance characteristics reasonably well. A maximum damping level of 2311 N-m/s (13.2 lb-s/in.) at a frequency of 100 Hz was measured with a single actuator of the gas damper. Since many such actuators could be placed circumferentially around the squirrel cage, considerable damping levels can be realized. The study also shows that significantly higher damping levels can be achieved by modifying the current design. Part I describes the theoretical model that has been developed based on isentropic assumptions. This model is an improved version of the previous theory (Vance et al., 1991) and includes the supply groove effects, dynamic area changes of the inlet feeding holes, and the effects of flow choking on damper behavior. The governing equations are derived and theoretical predictions using these equations have been made for two hardware designs that were experimentally investigated (see Part II for experimental results).

Parametric Study of the Unbalance Response of an Eccentric Sueeze Film Damper-Mounted Rigid Rotor.

This paper presents a limited parametric study of the unbalanced response of a rigid rotor supported by an eccentric squeeze film damper bearing. The rotor unbalance response is approximated by a trigonometric series whose coefficients are determined by the collocation method. The results indicate that for small static misalignments and unbalances, nonsynchronous components are negligible and the rotor response is an offset ellipse. Nonsynchronous components increase as both the unbalance and the static misalignment are increased. However, the amplitude of the rotor response is independent of the static misalignment direction. There is a tendency for the rotor to self-center in the vicinity of the resonance. This self-centering effect is more pronounced as the unbalance is increased and it is reduced as the static misalignment is increased. For large unbalances and static misalignments, both main resonant jump and secondary resonant jump are predicted at speeds above twice the system critical speed.

Nonlinear Vibration of Horizontal Jeffcott Rotors Supported by Oil Film Damper Bearings Having No Centering Springs : Calculation of Nonlinear Imbalance Response and Forced Damped Natural Frequency

In this paper, nonlinear imbalance response and forced damped natural frequency are calculated for horizontal Jeffcott rotors supported by oil film damper bearings having no centering springs. The former calculation reveals that there exists four types of synchronous imbalance responses. In one of the four types, the vibration amplitide can become infinitely large, and this dangerous type of vibration can appear easily with increasing imbalance. The latter calculation reveals that the stability margin, which is determined from the calculated complex eigenvalues, greatly depends on the type of synchronous response that happens to appear.

Fundamental dynamic performance of fluid-pivot and squeeze-film damper bearings

Due to the increase in rotational speeds and performance of modern turbomachinery the rotordynamic stability of such machinery has reduced. In order to improve rotordynamic stability, fluid-pivot and squeeze-film damper bearings have been developed. By using a simple analytical model to predict the unbalance response of a single mass rotor and by modelling the above bearings as a two-mass-spring and damper system the fundamental performance of these types of bearings has been determined. The results are that these bearings can significantly improve rotordynamic performance over a certain frequency range. This is mainly due to the ability of these bearings to reduce the effective bearing stiffness and hence improve the damping efficiency of the bearings. These auxiliary damped bearings increase the bearing damping efficiency rather than increase the bearing damping.

A Gas-Operated Bearing Damper for Turbomachinery

A gas-operated bearing damper for turbomachinery has been designed, analyzed, and experimentally investigated in the laboratory. The damper utilizes air bled off from the compressor to power an actuator through orifices with area modulated by the vibratory displacement at the bearing support. The design objective for this passive device is to make the actuating dynamic gas pressure phase lead the vibratory displacement by 90 deg. Several variations of the basic concept have been tested. An analysis was performed to guide the experiments. All of the designs tested to date can produce positive damping, and one particular design has produced a damping coefficient of 8756 N-s/m (50 lb-sec/in.) with a power penalty of 5.2 kW (7 hp) at 310 KPa (45 psi). This design was installed on a laboratory rotor with flexibly supported ball bearings, and significant damping of the critical speed response was demonstrated. The experimental results to date suggest that further research can produce significant improvements in performance, and the device appears to be especially adaptable to high-temperature applications for aircraft engines.

Development of Porous Squeeze Film Damper Bearings for Improving the Blade Loss Dynamics of Rotor-Support Systems

An efficient oil film damper known as porous squeeze film damper (PSFD) is developed based on conventional squeeze film damper (SFD) for more effective and reliable rotor vibration control and especially for improving the blade loss dynamics for rotor support system. The permeability of the outer race of PSFD could remarkably improve the squeeze film damping properties. The transient response of a simple rigid rotor and flexible Jeffcott’s rotor supported on PSFD and SFD subjected to sudden unbalance of blade loss are investigated. Time transient simulation show that PSFD could operate effectively under much greater unbalance as compared with SFD, especially under relative large impact loading of blade loss. Furthermore, the effective eccentricities of PSFD with small transmissibilities (T<1.0) extend to a range of ε<0.9, and optimum film stiffness and damping distribution within the whole film clearance could be achieved.

Optimum Design of Damper Bearing for Cylindrical Bearing-Rotor System.

Optimum Design of Damper Bearing for Cylindrical Bearing-Rotor System.

A Density Correlation for a Two-Phase Lubricant and its Effect on the Pressure Distribution©

Air entrainment in squeeze film damper bearings results in a type of cavitation that is considerably different from the cavitation traditionally assumed for hydrodynamic bearings. The fluid lubricant in this case is highly compressible and results in a drastic influence on the pressure distribution. This describes and experimental procedure for determining the density correlation for and oil-air mixture. This correlation is then utilized in the Reynolds equation to determine the influence lubricant compressibility has on the pressure distribution in a squeeze film damper bearing.

Unbalance Response of Flexible Rotors Coupled With Torsion

The effect of coupling with torsion on the unbalance response of flexible rotors, supported by isotropic flexible and damped bearings is investigated. Flexural vibrations of the shaft-disk system are coupled with torsional oscillations through mass eccentricity. The governing equations of motion of the continuous system are solved numerically with a modified Myklestad-Prohl method without the necessity of considering an equivalent lumped system. The cases of constant or harmonic torque applied to the disk are considered. Gyroscopic, rotary inertia, shear deformation, external and internal damping effects are taken into account.

An Experimental Study on the Behaviour of Damper Bearing Plane Stiffness in Squeeze Film Mounted Rotor Systems

The stiffness values of externally pressurized squeeze film dampers were evaluated from the results of direct measurements of transmitted force, damper ring displacement, and the phase difference between them. The parameters that could control the flexible support stiffnes of the damper bearing plane, the external oil supply pressure (OSP), bearing length to diameter (BL-D) ratio, film thickness (FT), and unbalance (UB), were varied in tests of two geometries of damper rings at different values of the excitation frequencies (EFs). It was found that the variation in OSP affected stiffness more at the lower EFs than at higher EF values. The stiffness increased at higher values of BL-D ratio, increased UB and upon the increase of FT from 150 to 250 microns, but stiffness values fell rapidly at the further increase of FT to 500 microns. Variations of the undamped critical speed of the rotor in the range of the stiffness values encountered in the study and damped critical speeds are presented graphically. (I.S.)

Experimental Measurement of the Dynamic Pressure Distribution in a Squeeze-Film Bearing Damper Executing Circular-Centered Orbit

A review of previous experimental measurements of squeeze film damper (SFD) forces is given. Measurements by the authors of SFD pressure fields and force coefficients, for circular centered orbits with epsilon = 0.5, are described and compared with computer predictions. For Reynolds numbers over the range 2-6, the effect of fluid inertia on the pressure fields and forces is found to be significant.

The effect of fluid inertia in hydrodynamic lubrication studied by a linearization method: Two useful applications

In several recent articles a linearization method was presented to study the effect of fluid inertia in fluid film bearings. Very accurate results are obtained in closed form which were previously amenable only to numerical analysis or asymptotic analysis (e.g. very weak inertia effects). Two applications presently studied are: (a) the one-dimensional journal bearing; and (b) the squeeze film damper bearing. The solutions are applicable at arbitrary modified Reynolds number and eccentricity ratio, provided the flow is laminar and the film is thin.