Hydrodynamic Analysis of Hydrostatic Bearings With Runner Misalignment and Pad Damage

2013 ◽  
Author(s):  
Timothy Dimond ◽  
David Barnes
Keyword(s):  
Film Thickness ◽  
Analytical Solutions ◽  
Thrust Bearing ◽  
Load Capacity ◽  
Element Solution ◽  
Flow Loop ◽  
Hydrodynamic Analysis ◽  
Hydrostatic Bearing ◽  
Hydrostatic Bearings ◽  
Minimum Film Thickness

Hydrostatic bearings are used in applications where surface speeds are low, or viscosities are insufficient to develop significant load capacity due to shear flow. They are also used in jacking applications for initial liftoff of rotors under low or no rotation conditions, especially for heavy rotors where significant babbitt damage would otherwise occur. Traditional hydrostatic bearing analyses assume isothermal lubricating flows. Analytical solutions also assume that the pressure in the pocket of the hydrostatic bearing is constant. This assumption is only approximately correct for low and zero operating speeds. Analytical solutions also assume that the runner and pad surfaces are parallel. The analytical solutions are not capable of capturing damage or misalignment effects. This paper describes a hydrodynamic analysis of a hydrostatic thrust bearing. The solution is based on a finite element solution to the generalized Reynolds equation. The finite element solution is applied in both the pocket and pad regions of the hydrostatic bearings. The analysis includes a flow loop balance that considers the effects of pressure losses in the lubricant supply piping, allowing for modeling of saturation effects in bearing load capacity. The flow loop balance for the lubrication supply is coupled with the bearing solution. This allows for pad loads to vary as a function of circumferential position in thrust bearings. The analysis was applied to the operation of a hydrostatic thrust bearing system for the HUSIR radio telescope at the Massachusetts Institute of Technology. Simplified models of pad damage and runner misalignment were considered in the analysis. The minimum film thickness and pressure profile was calculated. Runner misalignment reduced minimum film thickness by up to 80% when compared to a parallel runner under identical loading conditions. Runner damage equivalent to twice the nominal film thickness reduced the minimum film thickness by approximately 10%.

An Accurate Solution of the Gas Lubricated, Flat Sector Thrust Bearing

1977 ◽  
Vol 99 (1) ◽  
pp. 82-88 ◽  
Author(s):  
I. Etsion ◽  
D. P. Fleming
Keyword(s):  
Film Thickness ◽  
Thrust Bearing ◽  
Load Capacity ◽  
Thickness Distribution ◽  
Maximum Load ◽  
Accurate Solution ◽  
Operating Conditions ◽  
Thrust Bearings ◽  
Practical Design ◽  
Minimum Film Thickness

A flat sector shaped pad geometry for gas lubricated thrust bearings is analyzed considering both pitch and roll angles of the pad and the true film thickness distribution. Maximum load capacity is achieved when the pad is tilted so as to create a uniform minimum film thickness along the pad trailing edge. Performance characteristics for various geometries and operating conditions of gas thrust bearings are presented in the form of design curves. A comparison is made with the rectangular slider approximation. It is found that this approximation is unsafe for practical design, since it always overestimates load capacity.

Determination of the Discharge Coefficient of a Thin-Walled Orifice Used in Hydrostatic Bearings

2005 ◽  
Vol 127 (3) ◽  
pp. 679-684 ◽  
Author(s):  
S. Charles ◽  
O. Bonneau ◽  
J. Fre^ne
Keyword(s):  
Discharge Coefficient ◽  
Ad Hoc ◽  
Thrust Bearing ◽  
Accurate Estimation ◽  
Hydrostatic Bearing ◽  
Hydrostatic Bearings ◽  
Flow Through ◽  
Thin Walled ◽  
Experimental Bench

The characteristics of hydrostatic bearings can be influenced by the compensating device they use, for example, a thin-walled orifice (diaphragm). The flow through the orifice is given by a law where an ad hoc discharge coefficient appears, and, in order to guarantee the characteristics of the hydrostatic bearing, this coefficient must be calibrated. The aim of this work is to provide an accurate estimation of the discharge coefficient under specific conditions. Therefore an experimental bench was designed and a numerical model was carried out. The results obtained then by the experimental and theoretical approach were compared with the values given by the literature. Finally, the influence of the discharge coefficient on the behavior of a thrust bearing is examined.

Static Characteristics of Gas Foil Thrust Bearing Based on Gas Rarefaction Model

2015 ◽  
Author(s):  
Jiajia Yan ◽  
Guanghui Zhang ◽  
Zhansheng Liu ◽  
Fan Yang
Keyword(s):  
Film Thickness ◽  
Optimization Design ◽  
Reynolds Equation ◽  
Thrust Bearing ◽  
Rarefied Gas ◽  
Load Capacity ◽  
Structural Parameters ◽  
Lubricating Film ◽  
Lift Off ◽  
Foil Thrust Bearing

A modified Reynolds equation for bump type gas foil thrust bearing was established with consideration of the gas rarefaction coefficient. Under rarefied gas lubrication, the Knudsen number which was affected by the film thickness and pressure was introduced to the Reynolds equation. The coupled modified Reynolds and lubricating film thickness equations were solved using Newton-Raphson Iterative Method and Finite Difference Method. By calculating the load capacity for increasing rotor speeds, the lift-off speed under certain static load was obtained. Parametric studies for a series of structural parameters and assembled clearances were carried out for bearing optimization design. The results indicate that with gas rarefaction effect, the axial load capacity would be decreased, and the lift-off speed would be improved. The rarefied gas has a more remarkable impact under a lower rotating speed and a smaller foil compliance coefficient. When the assembled clearance of the thrust bearing rotor system lies in a small value, the lift-off speed increases dramatically as the assembled clearance decreases further. Therefore, the axial clearance should be controlled carefully in assembling the foil thrust bearing. It’s worth noting that the linear uniform bump foil stiffness model is not exact for large foil compliance ∼0.5, especially for lift-off speed analysis, due to ignoring the interaction between bumps and bending stiffness of the foil.

Theoretical Study on Static Performance of Double-Bump Foil Bearings

2021 ◽  
Author(s):  
Fangcheng Xu ◽  
Jianhua Chu ◽  
Wenlin Luan ◽  
Guang Zhao
Keyword(s):  
Finite Element ◽  
Film Thickness ◽  
Thrust Bearing ◽  
Load Capacity ◽  
Static Characteristics ◽  
Thrust Bearings ◽  
Foil Bearings ◽  
Foil Bearing ◽  
Static Performance ◽  
Initial Clearance

Abstract In this paper, single-bump foil models with different thickness and double-bump foil models with different initial clearances are established. The structural stiffness and equivalent viscous damping of double-bump foil and single-bump foil are analyzed by finite element simulation. The results show that the double-layer bump foil has variable stiffness and the displacement of the upper bump is greater than the initial gap when the two-layer bumps contact. A model for obtaining static characteristics of aerodynamic compliant foil thrust bearing is established on the basis of the stiffness characteristics of the double-bump foil. This paper solves gas Reynolds equation, the gas film thickness equation and the foil stiffness characteristic equation via the finite element method and the finite difference method. The static characteristics of the thrust bearings including the bearing pressure distribution, the gas film thickness and the friction power consumption have been obtained. The static characteristics of two kinds of foils have been compared and analyzed, and the effect of initial clearance on the static performance of double-bump foil bearings is studied. The results show that the double-bump foil structure can effectively improve the load capacity of thrust bearing. In addition, the static performance of double-bump foil thrust bearings is between the performance of the single-bump foil bearing and the double-bump foil bearing whose foil’s clearance is zero. The smaller the initial clearance is, the easier it will be to form a stable double-bump foil supporting structure.

Film Thickness and Friction Investigations in a Fluid Film Thrust Bearing Employing A New Conceived Micro-Texture on Pads

2020 ◽  
Vol 143 (6) ◽  
Author(s):  
J. C. Atwal ◽  
R. K. Pandey
Keyword(s):  
Film Thickness ◽  
Thrust Bearing ◽  
Mass Conservation ◽  
Fluid Film ◽  
Element Formulation ◽  
Algebraic Equations ◽  
Pocket Depth ◽  
Lubricating Film ◽  
Minimum Film Thickness ◽  
Radial Length

Abstract This paper presents the performance behaviors (coefficient of friction, minimum film thickness, and pressure distributions) of a fluid film thrust bearing using a newly conceived micro-texture on pads. In the numerical investigation, the Reynolds equation has been discretized using the finite element formulation followed by the solution of algebraic equations employing the Fischer-Burmeister-Newton-Schur (FBNS) algorithm, which satisfies the mass-conservation phenomenon arising due to the commencement of cavitation in the lubricating film. The effects of parameters (micro-texture/pocket depth, circumferential/radial length of micro-texture and pocket, etc.) of new texture on the performance behaviors of the thrust bearing have been explored and presented herein for the range of input data. It has been found that the minimum film thickness has increased up to 48%, and the friction coefficient reduced up to 24% in comparison to conventional plain pad case.

Simulation on Multi-Oil-Cavity and Multi-Oil-Pad Hydrostatic Bearings

2013 ◽  
Vol 274 ◽  
pp. 274-277 ◽  
Author(s):  
Xiao Qiu Xu ◽  
Jun Peng Shao ◽  
Xiao Dong Yang ◽  
Yan Qin Zhang ◽  
Xiao Dong Yu ◽  
...  
Keyword(s):  
Hydraulic System ◽  
Thrust Bearing ◽  
Three Dimensional ◽  
Structure Design ◽  
Analysis Software ◽  
Hydrostatic Bearing ◽  
Hydrostatic Bearings ◽  
Simulation Results ◽  
Three Dimensional Models ◽  
Volume Method

Taking multi-oil-cavity and multi-oil-pad hydrostatic bearings as studied projects, firstly make brief instructions for structure characteristics and working principal of hydraulic system; Then, build three-dimensional models of multi-oil-cavity and multi-oil-pad hydrostatic bearings respectively. Adopting finite volume method, oil film mesh is generated by universal finite analysis software CFD; then, carry on numerical simulations for pressure distribution and temperature distribution of the two studied hydrostatic thrust bearing under various viscosity, and make comparative analysis for difference between the two studied hydrostatic thrust bearing. Based on the analysis of numerical simulation results, the conclusions whether oil-return groove is set for hydrostatic bearing could be received. Simulation results reveal truly the influence of setting oil-return groove or not on hydrostatic thrust bearing, and improve structure design for hydrostatic thrust bearing.

Investigations in Hydrostatic Planar Bearings Compensated by Tapered-Spool Restrictors II: Load Capacity and Static Stiffness

2015 ◽  
Vol 32 (1) ◽  
pp. 71-82
Author(s):  
Y. Kang ◽  
H.-C. Cheng ◽  
C.-W. Lee ◽  
S.-Y. Hu
Keyword(s):  
Film Thickness ◽  
Load Capacity ◽  
Effective Area ◽  
Design Parameters ◽  
Static Characteristics ◽  
Static Stiffness ◽  
Single Action ◽  
Hydrostatic Bearing ◽  
Closed Type ◽  
Maximum Stiffness

ABSTRACTThis study including two parts investigates the influence of design parameters of tapered-spool restrictors and hydrostatic planar bearing on static characteristics of load capacity and static stiffness. The former part provides guides for the design of single-action and double-action tapered-spool restrictors. This part provides design guides for planar hydrostatic bearing and for matching up with tapered-spool restrictor. The equations of flow continuity are utilized to determine the film thickness for open-type planar bearing and worktable displacement for closed-type planar bearing with respect to the recess pressure, respectively. The load capacity can be obtained by multiplying recess pressure by effective area of bearing pad. Furthermore, the static stiffness can be obtained by differentiating the recess pressure with respect to film thickness or worktable displacement. The finding results give that the usage range of recess pressure, and the availability ranges of design parameters of restrictor and bearing parameters. Which are found for getting the maximum stiffness.

Analysis of Starved Thrust Bearings Including Temperature Effects

1987 ◽  
Vol 109 (3) ◽  
pp. 395-401 ◽  
Author(s):  
A. Artiles ◽  
H. Heshmat
Keyword(s):  
Film Thickness ◽  
Thrust Bearing ◽  
Load Capacity ◽  
Operating Conditions ◽  
Geometrical Parameters ◽  
Two Dimensional ◽  
Thrust Bearings ◽  
Direct Iteration ◽  
Finite Thrust ◽  
Raphson Iteration

A method of analysis is described treating starvation in finite thrust bearing pads. A variable-size finite difference mesh is used to represent the two-dimensional temperature and pressure fields. A combination of Newton-Raphson iteration, direct iteration, and column matrix methods are used to solve for the start-of-film and minimum film thickness as well as the coupled two-dimensional energy and Reynolds equations. A parametric study describes the performance characteristics of the tapered land thrust bearing (flowrates, extent of fluid film, temperature rises, load capacity and torque) for different minimum film thicknesses and levels of starvation. This study considered variations in the geometrical parameters such as pad aspect ratio (L/R2=1/3, 1/2, 2/3) and extent of the pad (β=27, 42, and 57 deg) with an optimum taper ratio (β1/β=0.8). It is found that the effects of starvation are fairly small near the flooded condition but accelerate rapidly below the 50 percent starvation level. The start of the film (θ1) depends mostly on the level of starvation, and is essentially independent of the geometrical parameters, operating conditions or film thickness.

Numerical Investigation on the Mixed Lubrication Performance of Water-Lubricated Coupled Journal and Thrust Bearings

2019 ◽  
Author(s):  
Yanfeng Han ◽  
Guo Xiang ◽  
Jiaxu Wang
Keyword(s):  
Friction Coefficient ◽  
Film Thickness ◽  
Thrust Bearing ◽  
Journal Bearing ◽  
Load Capacity ◽  
Hydrodynamic Pressure ◽  
Mixed Lubrication ◽  
Eccentricity Ratio ◽  
Thrust Bearings ◽  
Lubrication Performance

Abstract The mixed lubrication performance of water-lubricated coupled journal and thrust bearing (simplified as coupled bearing) is investigated by a developed numerical model. To ensure the continuity of hydrodynamic pressure and flow at the common boundary between the journal and thrust bearing, the conformal transformation is introduced to unify the solution domain of the Reynolds equation. In the presented study, the coupled effects between the journal and thrust bearing are discussed. The effects of the thrust bearing geometric film thickness on the mixed lubrication performance, including the load capacity, contact load and friction coefficient, of the journal bearing are investigated. And the effects of the journal bearing eccentricity ratio on the mixed lubrication performance of the thrust bearing are also investigated. The simulated results indicate the mutual effects between the journal and thrust bearing cannot be ignored in the coupled bearing system. The increasing thrust bearing geometric film thickness generates a decrease in load capacity of journal bearing. There exists an optimal eccentricity ratio of journal bearing that yields the minimum friction coefficient of the thrust bearing.

Load Influence on Hydrostatic Oil Film Journal Bearing Stiffness Characteristics

2020 ◽  
Author(s):  
Leonid Moroz ◽  
Leonid Romanenko ◽  
Roman Kochurov ◽  
Evgen Kashtanov
Keyword(s):  
Hydrodynamic Lubrication ◽  
Load Capacity ◽  
Dynamic Stiffness ◽  
Fluid Pressure ◽  
Performance Characteristics ◽  
Published Data ◽  
Geometrical Parameters ◽  
Hydrostatic Bearing ◽  
Hydrostatic Bearings ◽  
Stiffness Characteristics

Abstract Hydrostatic bearings are widely used in industry, including aerospace and energy sectors. Hydrodynamic lubrication mechanism has been well studied analytically and experimentally and various types of bearings were developed to provide increasing operating speed, load capacity, stability and efficiency for modern rotating machines. Hydrostatically lubricated bearings have principal difference (in comparison with hydrodynamic bearings) and their characteristics have been an area of continued research. The goal of this work is to develop a robust algorithm, which can predict hydrodynamical characteristics and dynamic stiffness and damping coefficients of hybrid and hydrostatic bearings with increased accuracy and which can be used for engineering/design purposes. The developed approach is based on Reynold’s equations, where the unknown parameters are the rotor position and fluid pressure in recess pockets. Finite difference method in combination with the successive over-relaxation algorithm is used for a numerical solution of Reynold’s equations. Newton’s method is applied to solve the generated system of equations. Applying the developed approach, the effect of load influence on the hydrodynamical and the dynamic stiffness characteristics has been studied. Several hydrostatic bearing designs which are based on the published data were considered to compare the results calculated applying the approach with the experimental and theoretical data given in the literature. Performed study shows when journal eccentricity can’t be neglected while simulating hydrostatic bearing characteristics. Simulations also allow for analysis of how different design/geometrical parameters and initial conditions (supply pressure) influence bearing performance characteristics. The developed approach can be utilized as a practical tool which allows for the prediction of performance characteristics of hydrostatic bearing with increased accuracy.

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