Static and Dynamic Characteristics for a Pressure-Dam Bearing

2008 ◽  
Vol 130 (5) ◽  
Author(s):  
Bader Al-Jughaiman ◽  
Dara Childs
Keyword(s):  
Frequency Ratio ◽  
Reynolds Equation ◽  
Dynamic Properties ◽  
Added Mass ◽  
Equation Model ◽  
Journal Bearings ◽  
Infinite Length ◽  
Fluid Inertia ◽  
Test Conditions ◽  
Load Conditions

Measured rotordynamic force coefficients (stiffness, damping, and added mass) and static characteristics (eccentricity and attitude angle) of a pressure-dam bearing are presented and compared to predictions from a Reynolds-equation model, using an isothermal and isoviscous laminar analysis. The bearing’s groove dimensions are close to the optimum predictions of Nicholas and Allaire (1980, “Analysis of Step Journal Bearings-Infinite Length and Stability,” ASLE Trans., 22, pp. 197–207) and are consistent with current field applications. Test conditions include four shaft speeds (4000rpm, 6000rpm, 8000rpm, and 10000rpm) and bearing unit loads from 0kPato1034kPa(150psi). Laminar flow was produced for all test conditions. A finite-element algorithm was used to generate solutions to the Reynolds-equation model. Excellent agreement was found between predictions and measurements for the eccentricity ratio and attitude angles. Predictions of stiffness and damping coefficients are in reasonable agreement with measurements. However, experimental results show that the bearing has significant added mass of about 60kg at no-load conditions, versus zero mass for predictions from the Reynolds-equation model and 40kg using Reinhardt and Lund’s (1975, “The Influence of Fluid Inertia on the Dynamic Properties of Journal Bearings,” ASME J. Lubr. Technol., 97, pp. 159–167) extended Reynolds-equation model for a plain journal bearing. The added mass quickly drops to zero as the load increases. Measured results also show a whirl frequency ratio near 0.36 at no-load conditions; however, a zero whirl frequency ratio was obtained at all loaded conditions, indicating an inherently stable bearing from a rotordynamics viewpoint.

Static and Dynamic Characteristics for a Pressure-Dam Bearing

2007 ◽  
Author(s):  
Bader Al-Jughaiman ◽  
Dara Childs
Keyword(s):  
Frequency Ratio ◽  
Reynolds Equation ◽  
Added Mass ◽  
Equation Model ◽  
Radial Clearance ◽  
Static Characteristics ◽  
Test Conditions ◽  
Stiffness And Damping ◽  
Element Algorithm ◽  
Load Conditions

Measured rotordynamic force coefficients (stiffness, damping, and added-mass) and static characteristics (eccentricity and attitude angle) of a pressure-dam bearing are presented and compared to predictions from a Reynolds-equation model, using an isothermal and isoviscous laminar analysis. The bearing’s groove dimensions are close to the optimum predictions of Nicholas and Allaire (1980) and are consistent with current field applications. The bearing has a diameter of 117.1 mm (4.61 in), a length-to-diameter ratio of 0.655 and, a nominal radial clearance of 0.133 mm (5.25 mils). The upper pad of the bearing has a step located at 130° and a 0.620 mm (15.75 mils) deep dam. The bottom pad has a deep, centered relief track over 25% of the pad’s axial length. Test conditions include four shaft speeds (4000, 6000, 8000 and 10000 rpm) and bearing unit loads from 0 to 1034 kPa (150 psi). Laminar flow was produced for all test conditions. A finite-element algorithm was used to generate solutions to the Reynolds equation model. Excellent agreement was found between predictions and measurements for the eccentricity ratio and attitude angles. Predictions of stiffness and damping coefficients are in reasonable agreement with measurements. However, experimental results show that the bearing has significant added mass of about 60 kg at no-load conditions, versus zero mass for predictions from the Reynolds-equation model and 40 kg using Reinhardt and Lund’s extended Reynolds equation model. The added mass drops quickly to zero as the load increases. Measured results also show a whirl frequency ratio near 0.36 at no-load conditions; however, a zero whirl frequency ratio was obtained at all loaded conditions, indicating an inherently stable bearing from a rotordynamics viewpoint.

The Influence of Fluid Inertia on the Dynamic Properties of Journal Bearings

1975 ◽  
Vol 97 (2) ◽  
pp. 159-165 ◽  
Author(s):  
E. Reinhardt ◽  
J. W. Lund
Keyword(s):  
Journal Bearing ◽  
Dynamic Properties ◽  
Journal Bearings ◽  
Graphical Form ◽  
Inertial Forces ◽  
Virtual Mass ◽  
Fluid Inertia ◽  
Eccentricity Ratio ◽  
First Order ◽  
First Order Perturbation

Based on a first-order perturbation solution in a modified Reynolds number an analysis is presented to determine the effect of the fluid film inertial forces on the dynamic properties of a journal bearing. The corrections to the regular amplitude and velocity coefficients are found to be small, but the accompanying acceleration coefficients which may correspond to a virtual mass of several times the mass of the journal itself, could become significant for short rotors. Numerical results are given in graphical form with dimensionless coefficients as functions of the operating eccentricity ratio.

Influence of Groove Size on the Static and Rotordynamic Characteristics of Short, Laminar-Flow Annular Seals

2007 ◽  
Vol 129 (2) ◽  
pp. 398-406 ◽  
Author(s):  
Dara W. Childs ◽  
Matthew Graviss ◽  
Luis E. Rodriguez
Keyword(s):  
Energy Equation ◽  
Groove Depth ◽  
Added Mass ◽  
Equation Model ◽  
Radial Clearance ◽  
Pressure Perturbation ◽  
Test Results ◽  
Rotordynamic Coefficients ◽  
Test Conditions ◽  
Groove Test

Test results are presented for a smooth seal and three centrally grooved seals that are representative of buffered-flow oil seals in centrifugal compressors. The seals are short (L∕D≅0.21), with a diameter of 117mm and a nominal radial clearance of 0.085mm, netting the clearance-to-radius ratio 0.0015. The grooves have groove depth to clearance ratios (Dg∕Cr) of 5, 10, and 15. Test conditions include three shaft speeds from 4000rpm to 10,000rpm, three inlet oil pressures from 24bar to 70bar, and seal eccentricity ratios from 0 (centered) to 0.7. Dynamic results include stiffness, damping, and added-mass coefficients; static results include stator position, attitude angles, and seal leakage. Stiffness, damping, and mass coefficients plus leakage are compared for the seal geometries. Results show that all rotordynamic coefficients consistently decrease with increasing seal groove depths, and seal leakage is largely unchanged. Comparisons are also made between experimental results and predictions from a computer program based on a Reynolds + energy equation model. The model includes the assumption that a groove is large enough to create separate lands within the seal, creating a zero or negligible pressure perturbation within the groove. Test results show that even the deepest groove depth tested is not deep enough to satisfy this assumption.

Dynamic Properties of Multi-Lobe Water Lubricated Bearings With Temporal and Convective Inertia Considerations

2017 ◽  
Author(s):  
Saeid Dousti ◽  
Paul Allaire ◽  
Bradley Nichols ◽  
Jianming Cao ◽  
Timothy Dimond
Keyword(s):  
Stability Analysis ◽  
Dynamic Behavior ◽  
Reynolds Equation ◽  
Dynamic Properties ◽  
Added Mass ◽  
Damping Properties ◽  
Inertia Effects ◽  
The Stability ◽  
Water Pumps ◽  
Stiffness And Damping

In this paper, the extended Reynolds equation proposed by Dousti et al. [1] is applied to predict the dynamic behavior of different fixed geometry bearings used in vertical water pumps. The influence of convective and temporal inertia effects is studied in regular and preloaded multi-lobe bearings. It is shown that the convective inertia is more influential at the presence of preload and higher rotational speeds and alters the stiffness and damping properties of the bearing. The temporal inertia leads to the prediction of considerable lubricant added mass coefficients in the order of journal mass. The stability analysis shows depending upon the geometry of the bearing, the new extended Reynolds equation may predict higher or lower logarithmic decrement.

Theoretical Investigation of Fluid Inertia Effects and Stability of Self-Acting Gas Journal Bearings

1999 ◽  
Vol 121 (4) ◽  
pp. 836-843 ◽  
Author(s):  
G. Belforte ◽  
T. Raparelli ◽  
V. Viktorov
Keyword(s):  
Reynolds Equation ◽  
Equation Of Motion ◽  
Journal Bearings ◽  
Fluid Inertia ◽  
Stability Parameters ◽  
Inertia Effects ◽  
Stability Diagrams ◽  
Intensive Use ◽  
Stability Limits ◽  
Theoretical Results

The journal equation of motion and the complete Reynolds equation of compressible fluid film are numerically solved and a computer program is developed. The formulas are for externally pressurized bearings, but results are shown only for self-acting bearings. For certain cases, the validity of the theoretical results is verified by comparison with the experimental data available from the literature. Through intensive use of the program, journal center trajectories are obtained and effects of fluid inertia are investigated. New stability parameters are presented and stability diagrams are established for bearings with L/D = 0.25, 0.5, 1, 1.5, and 2. The rotor unbalance effects on bearing stability limits are illustrated for several cases.

Modeling of Flexible Tilting Pad Journal Bearings With Radial Oil Injection

2008 ◽  
Author(s):  
Asger M. Haugaard ◽  
Ilmar F. Santos
Keyword(s):  
Finite Element ◽  
Reynolds Equation ◽  
Dynamic Properties ◽  
Journal Bearings ◽  
System Of Equations ◽  
Servo Valve ◽  
Tilting Pad ◽  
Dimensional Finite Element ◽  
Oil Injection ◽  
Tilting Pad Journal Bearings

The static and dynamic properties of tilting-pad journal bearings with controllable radial oil injection are investigated. The tilting pads are modelled as flexible structures and their dynamics are described using a three dimensional finite element framework and linear elasticity. The oil film pressure and flow are considered to follow the modified Reynolds equation, which includes the contribution from controllable radial oil injection. The Reynolds equation is solved using a two dimensional finite element mesh. The rotor is considered to be rigid. The servo-valve flow is governed by a second order ordinary differential equation, where the right hand side is controlled by an electronic input signal. The constitutive flow pressure relationship of the injection nozzles is that of a fully developed laminar velocity profile and the servo-valve is introduced into the system of equations by a volume conservation consideration. The Reynolds equation is linearized with respect to displacements and velocities of the nodal degrees of freedom. When all nodal points satisfy the static equilibrium condition, the system of equations is dynamically perturbed and subsequently condensed to a 2 by 2 system, keeping only the lateral motion of the rotor. As expected, rotor stability is heavily influenced by the control parameters.

Elastohydrodynamics Applied to Active Tilting-Pad Journal Bearings

2010 ◽  
Vol 132 (2) ◽  
Author(s):  
Asger M. Haugaard ◽  
Ilmar F. Santos
Keyword(s):  
Finite Element ◽  
Reynolds Equation ◽  
Dynamic Properties ◽  
Flexible Structures ◽  
Journal Bearings ◽  
System Of Equations ◽  
Tilting Pad ◽  
Dimensional Finite Element ◽  
Oil Injection ◽  
Tilting Pad Journal Bearings

The static and dynamic properties of tilting-pad journal bearings with controllable radial oil injection are investigated theoretically. The tilting pads are modeled as flexible structures and their behavior is described using a three-dimensional finite element framework and linear elasticity. The oil film pressure and flow are considered to follow the modified Reynolds equation, which includes the contribution from controllable radial oil injection. The Reynolds equation is solved using a two-dimensional finite element mesh. The rotor is considered to be rigid in terms of shape and size, but lateral movement is permitted. The servovalve flow is governed by a second order ordinary differential equation, where the right hand side is controlled by an electronic input signal. The constitutive flow-pressure relationship of the injection orifices is that of a fully developed laminar velocity profile and the servovalve is introduced into the system of equations by a mass conservation consideration. The Reynolds equation is linearized with respect to displacements and velocities of the nodal degrees of freedom. When all nodal points satisfy static equilibrium, the system of equations is dynamically perturbed and subsequently condensed to a 2×2 system, keeping only the lateral motion of the rotor. As expected, bearing dynamic coefficients are heavily influenced by the control parameters and pad compliance.

Experimental Rotordynamic Coefficient Results for a Load-on-Pad Flexible-Pivot Tilting-Pad Bearing With Comparisons to Predictions From Bulk-Flow and Reynolds Equation Models

2004 ◽  
Author(s):  
L. E. Rodriguez ◽  
D. W. Childs
Keyword(s):  
Reynolds Equation ◽  
Flow Model ◽  
Dynamic Stiffness ◽  
Added Mass ◽  
Bulk Flow ◽  
Quadratic Functions ◽  
Force Model ◽  
Fluid Inertia ◽  
Frequency Dependency ◽  
Tilting Pad

Experimental dynamic-stiffness-coefficient results are presented for a high-speed, lightly loaded, load-on-pad, flexible-pivot tilting-pad bearing. Results show that the real part of the direct dynamic-stiffness coefficients are quadratic functions of the excitation frequency. This frequency dependency is modeled well by an added-mass coefficient, and the resultant [M], [K], and [C] matrix model is frequency-independent versus a conventional [K] and [C] model that is frequency dependent. The dynamics introduced by the additional pad degrees of freedom (including pad inertia and web moment stiffness) and the effects of fluid inertia in the lubricant film account for part of this frequency dependency. Experimental results are compared to numerical predictions from models based on: (i) the Reynolds equation, and (ii) a Navier-Stokes (NS) equations bulk-flow model that retains the temporal and convective fluid inertia terms. The NS bulk-flow model results correlate better with experimental dynamic stiffness results, including added-mass terms. Both models underestimate the measured added-mass coefficients for the full excitation range; however, they do an adequate job for excitation frequencies up to synchronous frequency. The frequency dependency predicted by using a [K] and [C] model can be removed by adding a mass matrix to the reaction-force model with either a Reynolds equation or a bulk-flow NS model, with a very considerable speed up in calculation of damped eigenvalues for rotor-bearing systems.

A Review of Journal Bearing Thermal Effects on Rotordynamic Response

2020 ◽  
Vol 143 (3) ◽  
Author(s):  
Dongil Shin ◽  
Jongin Yang ◽  
Xiaomeng Tong ◽  
Junho Suh ◽  
Alan Palazzolo
Keyword(s):  
Thermal Effects ◽  
High Performance ◽  
Thermal Instability ◽  
Reynolds Equation ◽  
Dynamic Properties ◽  
Critical Role ◽  
Journal Bearings ◽  
Constant Viscosity ◽  
Bearing Design ◽  
Dynamics Models

Abstract Traditional analysis of journal bearings assumed a constant viscosity which simplified the solutions for static and dynamic characteristics and responses. Today's high-performance machinery requires more accurate models wherein temperature and viscosity distributions in the film must be calculated. Thermal effects in journal bearings have a strong influence on both static and dynamic properties, and consequently play a critical role in determining rotor-bearing system performance. This paper presents an extensive survey of the thermal modeling methods and effects in journal bearings. The subjects include various bearing types, and recent progress in thermal bearing design and thermal instability problems observed in fluid and gas film hydrodynamic bearings. The extent of the survey ranges from conventional Reynolds equation models to more advanced computational fluid dynamics models.

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