On Parallel Hybrid Guide Bearings Under Combined Sliding and Small Amplitude Vibration

1994 ◽  
Vol 116 (1) ◽  
pp. 127-132 ◽  
Author(s):  
S. H. Chen ◽  
C. D. Mote
Keyword(s):  
Small Amplitude ◽  
Squeeze Film ◽  
Phase Lag ◽  
Fluid Inertia ◽  
Parallel Hybrid ◽  
Bearing Load ◽  
Hybrid Bearing ◽  
Unsteady Fluid ◽  
Saw Blade ◽  
Simultaneous Translation

An original hybrid bearing model, operating under constant volumetric incompressible lubricant supply rate Q*, is proposed for 2-D parallel hybrid guide bearings subject to simultaneous translation and small amplitude transverse vibration. The model may describe the typical fluid film constrained between a translating/rotating saw blade and a saw guide, where lubricant is fed directly into the oscillating film. The inner boundary, or recess, pressure is time varying and coupled to the external lubricant supply. Unsteady fluid inertia resulting from vibration is measured by the squeeze Reynolds’ number Res and modeled. A methodology for analytical solution is developed to predict the amplitude and phase of the dynamic bearing load Wt*. A sample hybrid bearing, used to demonstrate the film pressure generating mechanisms in hybrid squeeze film, generates a 1.1 to 7.1 percent larger Wt* with a 5 to 21 deg phase lag for 1 ≤ Q* ≤ 4 when compared to Wt* produced in a hydrodynamic squeeze film bearing at the same Res. This phase shift can be significant when bearings are used for vibration control purposes.

scholarly journals Squeeze Film Dampers Executing Small Amplitude Circular-Centered Orbits in High-Speed Turbomachinery

2016 ◽  
Vol 2016 ◽  
pp. 1-16 ◽  
Author(s):  
Sina Hamzehlouia ◽  
Kamran Behdinan
Keyword(s):  
Pressure Distribution ◽  
Small Amplitude ◽  
High Speed ◽  
Fluid Film ◽  
Distribution Model ◽  
Squeeze Film ◽  
Fluid Inertia ◽  
Inertia Effects ◽  
Squeeze Film Dampers ◽  
Reaction Forces

This work represents a pressure distribution model for finite length squeeze film dampers (SFDs) executing small amplitude circular-centered orbits (CCOs) with application in high-speed turbomachinery design. The proposed pressure distribution model only accounts for unsteady (temporal) inertia terms, since based on order of magnitude analysis, for small amplitude motions of the journal center, the effect of convective inertia is negligible relative to unsteady (temporal) inertia. In this work, the continuity equation and the momentum transport equations for incompressible lubricants are reduced by assuming that the shapes of the fluid velocity profiles are not strongly influenced by the inertia forces, obtaining an extended form of Reynolds equation for the hydrodynamic pressure distribution that accounts for fluid inertia effects. Furthermore, a numerical procedure is represented to discretize the model equations by applying finite difference approximation (FDA) and to numerically determine the pressure distribution and fluid film reaction forces in SFDs with significant accuracy. Finally, the proposed model is incorporated into a simulation model and the results are compared against existing SFD models. Based on the simulation results, the pressure distribution and fluid film reaction forces are significantly influenced by fluid inertia effects even at small and moderate Reynolds numbers.

Experimental Evaluation of Sector-Shaped Hydrodynamic Thrust Bearings Under Translation and Transverse Vibration

1994 ◽  
Vol 116 (3) ◽  
pp. 521-527 ◽  
Author(s):  
Y. K. Wang ◽  
C. D. Mote
Keyword(s):  
Reynolds Number ◽  
Transverse Vibration ◽  
Thrust Bearing ◽  
Lubrication Theory ◽  
Fluid Inertia ◽  
Thrust Bearings ◽  
Spring Force ◽  
Bearing Load ◽  
The Mean ◽  
Simultaneous Translation

The bearing load of a plane inclined sector-shaped hydrodynamic thrust bearing, under simultaneous translation and transverse vibration, is measured experimentally. The results are used to evaluate the lubrication theory solutions. Consequently, both the influences of the unsteady film inertia, measured by the squeeze Reynolds number Res, and the convective film inertia, measured by the modified Reynolds number Re*, on load amplitude and phase are investigated. It is found that the inertia-neglected lubrication solutions underestimate: (1) the oscillatory component of the bearing load by 6.5 percent at Res = 1.0 and by 1.4 percent at Re* = 1.0, and (2) the mean component of the bearing load by 0.7 percent at Res = 1.0 and by 2.0 percent at Re* = 1.0 Moreover, the fluid inertia induces an equivalent negative spring force component which shifts the phase of the bearing load by 9.5 deg at Res =1.0 and by 4 deg at Re* = 1.0 as compared to the lubrication theory predictions. Hence it can be an important consideration when designing bearings for vibration control purposes.

Dynamic Characterization of an Integral Squeeze Film Bearing Support Damper for a Supercritical CO2 Expander

2017 ◽  
Author(s):  
Bugra Ertas ◽  
Adolfo Delgado ◽  
Jeffrey Moore
Keyword(s):  
High Speed ◽  
Dynamic Performance ◽  
Mechanical Impedance ◽  
Squeeze Film ◽  
Fluid Inertia ◽  
Inertia Effects ◽  
Damping Behavior ◽  
Impedance Testing ◽  
Stiffness And Damping ◽  
Onset Of Cavitation

The present work advances experimental results and analytical predictions on the dynamic performance of an integral squeeze film damper (ISFD) for application in a high-speed super-critical CO2 (sCO2) expander. The test campaign focused on conducting controlled orbital motion mechanical impedance testing aimed at extracting stiffness and damping coefficients for varying end seal clearances, excitation frequencies, and vibration amplitudes. In addition to the measurement of stiffness and damping; the testing revealed the onset of cavitation for the ISFD. Results show damping behavior that is constant with vibratory velocity for each end seal clearance case until the onset of cavitation/air ingestion, while the direct stiffness measurement was shown to be linear. Measurable added inertia coefficients were also identified. The predictive model uses an isothermal finite element method to solve for dynamic pressures for an incompressible fluid using a modified Reynolds equation accounting for fluid inertia effects. The predictions revealed good correlation for experimentally measured direct damping, but resulted in grossly overpredicted inertia coefficients when compared to experiments.

Extended Finite Element Analysis of Journal Bearing Dynamic Forced Performance to Include Fluid Inertia Force Coefficients

2012 ◽  
Author(s):  
Luis San Andrés
Keyword(s):  
Finite Element ◽  
Test Data ◽  
Small Amplitude ◽  
Forced Response ◽  
Inertia Force ◽  
Fluid Inertia ◽  
Inertia Effects ◽  
Force Coefficients ◽  
Reaction Forces ◽  
Bearing Stiffness

Reynolds equation governs the generation of hydrodynamic pressure in oil lubricated fluid film bearings. The static and dynamic forced response of a bearing is obtained from integration of the film pressure on the bearing surface. For small amplitude journal motions, a linear analysis represents the fluid film bearing reaction forces as proportional to the journal center displacements and velocity components through four stiffness and four damping coefficients. These force coefficients are integrated into rotor-bearing system structural analysis for prediction of the system stability and the synchronous response to imbalance. Fluid inertia force coefficients, those relating reaction forces to journal center accelerations, are routinely ignored because most oil lubricated bearings operate at relatively low Reynolds numbers, i.e., under slow flow conditions. Modern rotating machinery operates at ever increasing surface speeds to deliver more power in smaller size units. Under these operating conditions fluid inertia effects need to be accounted for in the forced response of oil lubricated bearings, as recent experimental test data also reveal. The paper presents a finite element formulation to predict added mass coefficients in oil lubricated bearings by extending a basic formulation that already calculates the bearing stiffness and damping force coefficients. That is, a small amplitude perturbation analysis of the lubrication flow equations keeps the temporal fluid inertia effects and develops a set of equations to obtain the bearing stiffness, damping and inertia force coefficients. The method does not impose on the cost of the original formulation which makes it very attractive for ready implementation in existing software. Predictions of the computational model are benchmarked against archival test data for an oil-lubricated pressure dam bearing supporting large compressors. The comparisons show fluid inertia effects cannot be ignored for operation at high rotor speeds and with small static loads.

Squeeze Film Damper Suppression of Thermal Bow: Morton Effect Instability

2020 ◽  
Author(s):  
Dongil Shin ◽  
Alan B. Palazzolo ◽  
Xiaomeng Tong
Keyword(s):  
Squeeze Film ◽  
Viscous Heating ◽  
Fluid Inertia ◽  
Euler Beam ◽  
Nonlinear Simulation ◽  
Squeeze Film Damper ◽  
Morton Effect ◽  
Tilting Pad ◽  
Tilting Pad Journal Bearing ◽  
Rotor Model

Abstract The Morton Effect (ME) is a synchronous vibration problem in turbomachinery caused by the non-uniform viscous heating around the journal circumference, and its resultant thermal bow and ensuing synchronous vibration. This paper treats the unconventional application of the SFD for the mitigation of ME-induced vibration. Installing a properly designed squeeze film damper (SFD) may change the rotor’s critical speed location, damping and deflection shape, and thereby suppress the vibration caused by the ME. The effectiveness of the SFD on suppressing the ME is tested via linear and nonlinear simulation studies employing a 3D thermo-hydrodynamic (THD) tilting pad journal bearing, and a flexible, Euler beam rotor model. The example rotor model is for a compressor that experimentally exhibited an unacceptable vibration level along with significant journal differential heating near 8,000 rpm. The SFD model includes fluid inertia and is installed on the non-drive end bearing location where the asymmetric viscous heating of the journal is highest. The influence of SFD cage stiffness is evaluated.

Theory Versus Experiment for the Effects of Pressure Ratio on the Performance of an Orifice-Compensated Hybrid Bearing

1998 ◽  
Vol 120 (4) ◽  
pp. 930-936 ◽  
Author(s):  
P. Mosher ◽  
D. W. Childs
Keyword(s):  
High Speed ◽  
Stokes Equations ◽  
Load Capacity ◽  
Dynamic Stiffness ◽  
Pressure Ratio ◽  
Navier Stokes ◽  
Rotordynamic Coefficients ◽  
Wide Range ◽  
Bearing Load ◽  
Hybrid Bearing

This research investigates the effect of varying the concentric recess pressure ratio of hybrid (combination hydrostatic and hydrodynamic) bearings to be used in high-speed, high-pressure applications. Bearing flowrate, load capacity, torque, rotordynamic coefficients, and whirl frequency ratio are examined to determine the concentric, recess-pressure ratio which yields optimum bearing load capacity and dynamic stiffness. An analytical model, using two-dimensional bulk-flow Navier-Stokes equations and anchored by experimental test results, is used to examine bearing performance over a wide range of concentric recess pressure ratios. Typically, a concentric recess pressure ratio of 0.50 is used to obtain maximum bearing load capacity. This analysis reveals that theoretical optimum bearing performance occurs for a pressure ratio near 0.40, while experimental results indicate the optimum value to he somewhat higher than 0.45. This research demonstrates the ability to analytically investigate hybrid bearings and shows the need for more hybrid-bearing experimental data.

scholarly journals Squeeze-Film Damper Technology: Part 1 — Prediction of Finite Length Damper Performance

1983 ◽  
Author(s):  
J. W. Lund ◽  
A. J. Smalley ◽  
J. A. Tecza ◽  
J. F. Walton
Keyword(s):  
Finite Length ◽  
Gas Turbines ◽  
Squeeze Film ◽  
Fluid Inertia ◽  
Inertia Effects ◽  
Strongly Coupled ◽  
Squeeze Film Damper ◽  
Rotor Systems ◽  
Squeeze Film Dampers ◽  
Calculation Results

Squeeze-film dampers are commonly used in gas turbine engines and have been applied successfully in a great many new designs, and also as retrofits to older engines. Of the mechanical components in gas turbines, squeeze-film dampers are the least understood. Their behavior is nonlinear and strongly coupled to the dynamics of the rotor systems on which they are installed. The design of these dampers is still largely empirical, although they have been the subject of a large number of past investigations. To describe recent analytical and experimental work in squeeze-film damper technology, two papers are planned. This abstract outlines the first paper, Part 1, which concerns itself with squeeze-film damper analysis. This paper will describe an analysis method and boundary conditions which have been developed recently for modelling dampers, and in particular, will cover the treatment of finite length, feed and drain holes and fluid inertia effects, the latter having been shown recently to be of great importance in predicting rotor system behavior. A computer program that solves the Reynolds equation for the above conditions will be described and sample calculation results presented.

Study of Static Fluid Forces in a Squeeze Film Damper with a Circumferential Groove

1995 ◽  
Vol 209 (4) ◽  
pp. 263-274
Author(s):  
J X Zhang
Keyword(s):  
Fluid Pressure ◽  
Squeeze Film ◽  
Fluid Inertia ◽  
Traditional Use ◽  
Fluid Force ◽  
Squeeze Film Damper ◽  
Fluid Forces ◽  
Supply Pressure ◽  
Static Fluid ◽  
Approximate Expressions

Approximate expressions are obtained for static fluid pressure and force for a centrally grooved squeeze film damper (SFD) resting at an equilibrium position without vibration. The analysis shows that, to some extent, grooved SFDs may share some characteristics with hydrostatic bearings, due to the existence of the lubricant supply pressure. Thus static fluid force and hence oil stiffness may exist in SFDs, in addition to the conventional inertial and damping coefficients for SFDs. This paper is solely focused on the static fluid forces and oil stiffness generated in an SFD with a finite length groove. Flow continuity is used at the centre of the groove, which takes into account the effects of the inlet oil flowrate and oil supply pressure. This use of flow continuity differs substantially from the traditional use of constant pressure in the central groove, and it provides better results. At the interface between the groove and the thin film land, a step bearing model with ignored fluid inertia is employed. It is verified by both the theory and previous experiments that the static fluid force and stiffness are linearly proportional to both the lubricant supply pressure and the eccentricity ratio of the SFD journal.

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