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.

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.

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.

Rotordynamic Coefficients Measurements Versus Predictions for a High Speed Flexure-Pivot Tilting-Pad Bearing (Load-Between-Pad Configuration)

2005 ◽  
Author(s):  
Adnan Al-Ghasem ◽  
Dara Childs
Keyword(s):  
Dynamic Stiffness ◽  
Added Mass ◽  
Bulk Flow ◽  
Navier Stokes ◽  
Radial Clearance ◽  
Stiffness Coefficients ◽  
Tilting Pad ◽  
Model Predictions ◽  
Frequency Independent ◽  
Stiffness And Damping

Experimental dynamic force coefficients are presented for a flexure-pivot-tilting-pad (FPTP), bearing in load-between-pad (LBP) configuration for a range of rotor speeds and bearing unit loadings. The bearing has the following design parameters: 4 pads with pad arc angle 72° and 50% pivot offset, pad axial length 0.0762 m (3 in), pad radial clearance 0.254 mm (0.010 in), bearing radial clearance 0.1905 mm (0.0075 in), preload 0.25 and shaft nominal diameter of 116.84 mm (4.600 in). Measured dynamic coefficients have been compared with theoretical predictions using an isothermal analysis for a bulk-flow Navier-Stokes model. Predictions from two models — the Reynolds equation and a bulk-flow Navier-Stokes (NS) equation model are compared with experimental, complex dynamic stiffness coefficients (direct and cross-coupled) and show the following results: (i) The real part of the direct dynamic-stiffness coefficients is strongly frequency dependent because of pad inertia, support flexibility, and the effect of fluid inertia. This frequency dependency can be accurately modeled for by adding a direct added mass term to the conventional stiffness/damping matrix model. (ii) Both models underpredict the identified added-mass coefficient (∼32 kg), but the bulk-flow NS equations predictions are modestly closer. (iii) The imaginary part of the direct dynamic-stiffness coefficient (leading to direct damping) is a largely linear function of excitation frequency, leading to a constant (frequency independent) direct damping model. (iv) The real part of the cross-coupled dynamic-stiffness coefficients shows larger destabilizing forces than predicted by either model. The direct stiffness and damping coefficients increase with load, while increasing and decreasing with rotor speed, respectively. As expected, a small whirl frequency ratio (WFR) was found of about 0.15, and it decreases with increasing load and increases with increasing speed. The two model predictions for WFR are comparable and both underpredict the measured WFR values. Rotors supported by either conventional tilting PAD bearings or FPTP bearings are customarily modeled by frequency-dependent stiffness and damping matrices, necessitating an iterative calculation for rotordynamic stability. The present results show that adding a constant mass matrix to the FPTP bearing model produces an accurate frequency-independent model that eliminates the need for iterative rotordynamic stability calculations.

Static and Dynamic Performance of Pressure Dam Bearings With Dam Steps That Are (I) Square and (II) Filleted

2008 ◽  
Author(s):  
Dara Childs ◽  
Andrew Schaible ◽  
Bader Al Jughaiman
Keyword(s):  
Dynamic Performance ◽  
Operating Conditions ◽  
The Other ◽  
Step Test ◽  
Radial Clearance ◽  
Static Characteristics ◽  
Stiffness Coefficients ◽  
Test Conditions ◽  
Minimum Film Thickness ◽  
Direct Stiffness

Measured rotordynamic force coefficients (stiffness, damping, and added-mass) and static characteristics (eccentricity and attitude angle) are presented for two nearly identical pressure-dam bearings. One bearing has a square step at the dam; the other has a filleted step. Because of reduced manufacturing costs, the filleted-step design is used widely. The bearings’ groove dimensions are close to the optimum predictions of Nicholas and Allaire [2] and are consistent with current field applications. The bearings have 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 bottom pad has a deep, centered relief track over 25% of the pad’s axial length. The upper pad for both bearings has a step located at 130° from the horizontal and a 0.620 mm (15.75 mils) deep dam. The dam on the upper pad of one bearing has a square step; the other bearing has a filleted step. 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 within the bearing lands. For the same operating conditions, the filleted step bearing operates at a lower eccentricity ratio (has a larger minimum film thickness). The filleted step design has higher direct stiffness coefficients. Both cross-coupled stiffness coefficients are positive (favorable for stability) for both designs but the filleted design produces higher values. In regard to direct damping, the filleted-step design has higher damping in the load direction and comparable values in the unloaded direction. Hence, for the same operating conditions, a filleted step design should produce reduced amplitudes at or near a critical speed. With respect to stability as defined by WFR, the filleted design is consistently better (lower value) than the square step design, resulting in an elevated onset speed of instability for the filleted-step design.

Numerical Simulation of Eddy Air-Curtain Dust Controlled Flow Field in Hard Rock Mechanized Driving Face

2012 ◽  
Vol 214 ◽  
pp. 440-444
Author(s):  
Wei Min Cheng ◽  
Wen Nie ◽  
Gang Zhou ◽  
Jun Lei Yang ◽  
Wen Zhou Du ◽  
...  
Keyword(s):  
Flow Field ◽  
Hard Rock ◽  
Equation Model ◽  
Polymer Materials ◽  
Radial Clearance ◽  
Air Curtain ◽  
Controlled Flow ◽  
Full Face ◽  
Local Dust ◽  
The Mathematical Model

The author established the mathematical model of single-phase flow of gas based on the k-ε two-equation model and numerically simulated the eddy air-curtain dust controlled flow field in hard rock mechanized driving face with the help of FLUENT software.The result showed that, after all the pressure ventilation blown out by the radial clearance of mural cylinder, a full-face eddy air-curtain flow field is formed at the roadway section, forming the air-curtain dust controlled flow field that presses the tunneling place equally in front of the driver of roadheader. After the application of the development of new light polymer materials radial cylinder eddy air-curtain dust controlled system was adopted in hard rock mechanized driving face of north conveyor main roadway, reducing the local dust concentration effectively.

A Calculation Method to Investigate the Effects of Geometric Parameters and Operational Conditions on the Static Characteristics of Aerostatic Spherical Bearings

2018 ◽  
Vol 141 (2) ◽  
Author(s):  
Hailong Cui ◽  
Huan Xia ◽  
Dajiang Lei ◽  
Xinjiang Zhang ◽  
Zhengyi Jiang
Keyword(s):  
Experimental Data ◽  
Calculation Method ◽  
Reynolds Equation ◽  
Geometric Parameters ◽  
Static Characteristics ◽  
Optimal Parameters ◽  
Film Pressure ◽  
Operational Conditions ◽  
Pressure Distributions ◽  
Calculation Results

In this paper, a calculation method based on matlab partial differential equations (PDE) tool is proposed to investigate the static characteristics of aerostatic spherical bearings. The Reynolds equation of aerostatic spherical bearings is transformed into a standard elliptic equation. The effects of geometric parameters and operational conditions on the film pressure, bearing film force, and stiffness are studied. The axial and radial eccentricities result in different film pressure distributions; the bearing film force and stiffness are significantly influenced by geometric parameters and operational conditions. The relative optimal parameters are confirmed based on the calculation results. A comparison between the numerical and experimental results is also presented. The highest relative error between the numerical results and the experimental data is 11.3%; the calculation results show good agreements with the experimental data, thus verifying the accuracy of the calculation method used in this paper.

Numerical study on the dynamic characteristics of water-lubricated rubber bearing under asperity contact

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Guo Xiang ◽  
Yijia Wang ◽  
Cheng Wang ◽  
Zhongliang Lv
Keyword(s):  
Elastic Modulus ◽  
Contact Stiffness ◽  
Water Film ◽  
Radial Clearance ◽  
Asperity Contact ◽  
Stiffness Coefficient ◽  
Content Type ◽  
Damping Coefficients ◽  
Rubber Bearing ◽  
Stiffness And Damping

Purpose In this study, the dynamic characteristics of the water-lubricated rubber bearing considering asperity contact are numerically studied, including water-film stiffness and damping coefficients and plastic-elastic contact stiffness coefficient. Design/methodology/approach The Kogut-Etsion elastic-plastic contact model is applied to calculate the contact stiffness coefficient at the bearing-bush interface and the perturbed method is used to calculate the stiffness and damping coefficients of water-film. In addition, the rubber deformation is determined by the finite element method (FEM) during the simulation. Parametric studies are conducted to assess the effects of the radial clearance, rubber thickness and elastic modulus on the dynamic characteristic of water-lubricated rubber bearing. Findings Numerical results indicate that stiffness and damping coefficients of water film and the contact stiffness of asperity are increased with the decreasing of the radial clearance and the dynamic coefficients are less sensitive to the rubber thickness compared with the elastic modulus of rubber. Furthermore, due to the existed groove, a sudden change of the water film direct stiffness and damping coefficients is observed when the eccentricity ratio ranges from 0.6 to 1.0. Originality/value It is expected this study can provide more information to establish a dynamic equation of water-lubricated rubber bearings exposed to mixed lubrication conditions.

scholarly journals Development of a new test rig for the analysis of hydrodynamic bearings for rotors of microGT

2019 ◽  
Vol 113 ◽  
pp. 03002
Author(s):  
Carlo Alberto Niccolini Marmont Du Haut Champ ◽  
Fabrizio Stefani ◽  
Paolo Silvestri
Keyword(s):  
Experimental Data ◽  
Finite Element ◽  
Gas Turbines ◽  
Dynamic Interaction ◽  
Journal Bearings ◽  
Radial Clearance ◽  
Test Rig ◽  
Small Clearance ◽  
Stiffness And Damping ◽  
Good Agreement

The aim of the present work is to design a test rig suited to investigate the dynamic interaction between rotor and hydrodynamic journal bearings in micro gas turbines (microGT), i.e. with reference to small bearings (diameter in the order of ten millimeters). Particularly, the device is capable of measuring the journal location. Therefore, the journal motion due to rotor vibrations can be displayed, in order to assess performance as well as stiffness and damping of the bearings. The new test rig is based on Bently Nevada Rotor Kit (RK), but substantial modifications are carried out. Indeed, the relative radial clearance of the original RK bearings is about 2/100, while it is in the order of 1/1000 in industrial bearings. Therefore, the same RK bearings are employed in the new test rig, but a new shaft has been designed in order to reduce the original clearance. The new shaft enables us to study the bearing behaviour for different clearances, as it is equipped with interchangeable journals. The experimental data yielded by the new test rig are compared with numerical results. These are obtained by means of a suitable finite element (FEM) code developed by our research group. It allows the Thermo Elasto-HydroDynamic (TEHD) analysis of the bearing in static and dynamic conditions. In the present paper, bearing static performances are analysed in order to assess the reliability of the journal location predictions by comparing numerical and experimental results. Such comparisons are presented for both large and small clearance bearings of original and modified RK, respectively. Good agreement is found only for the modified RK equipped with small clearance bearings (relative radial clearance equal to 8/1000). Nevertheless, rotor alignment is quite difficult with small clearance bearings and a completely new test rig is designed for future experiments.

Segmentation Effects on Brush Seal Leakage and Rotordynamic Coefficients

2015 ◽  
Author(s):  
Alexander O. Pugachev ◽  
Manuel Gaszner ◽  
Christos Georgakis ◽  
Paul Cooper
Keyword(s):  
Electrical Discharge ◽  
Electrical Discharge Machining ◽  
Labyrinth Seal ◽  
Performance Characteristics ◽  
Radial Clearance ◽  
Single Plane ◽  
Rotordynamic Coefficients ◽  
Damping Coefficients ◽  
Brush Seal ◽  
Stiffness And Damping

This paper studies the effect of brush seal segmentation on the seal performance characteristics. A brush-labyrinth sealing configuration arranged of one brush seal downstream and two labyrinth fins upstream is studied experimentally and theoretically. The studied brush seal is of welded design installed with zero cold radial clearance. The brush seal front and back rings as well as the bristle pack are segmented radially in a single plane using the electrical discharge machining technique. The segmentation procedure results in loss of bristles at the site of the cuts altering the leakage flow structure in the seal and its performance characteristics. Two test rigs are used to obtain leakage, as well as rotordynamic stiffness and damping coefficients of the seal at different pressure ratios. The CFD-based model is used to predict the seal performance and to study in detail local changes in the flow field due to the segmentation. A back-to-back comparison of the performance of non-segmented and segmented brush seals, as well as baseline labyrinth seal is provided. The obtained results demonstrate that the segmentation in general negatively affects the performance of the studied brush-labyrinth sealing configuration. However, the segmented brush seal shows increased direct damping coefficients.

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