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.

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.

Design Optimization of Gas Foil Thrust Bearings for Maximum Load Capacity

2015 ◽  
Author(s):  
Tae Ho Kim ◽  
Tae Won Lee
Keyword(s):  
Experimental Data ◽  
Film Thickness ◽  
Load Capacity ◽  
Maximum Load ◽  
Drag Torque ◽  
Rotor Speed ◽  
Design Guideline ◽  
Film Pressure ◽  
Thrust Bearings ◽  
Minimum Film Thickness

Improvement of the load capacity of gas foil thrust bearings (GFTBs) is important to broadening their application in oil-free microturbomachinery (<250 kW) with high power density. Although GFTBs have the significant advantage of low friction without the use of lubrication systems compared to oil film thrust bearings, their inherently low load capacity has limited their application. The aim of the present study was to develop a design guideline for increasing the load capacity of GFTBs. The Reynolds equation for an isothermal isoviscous ideal gas was used to calculate the gas film pressure. To predict the ultimate load capacity of the GFTB, the pressure was averaged in the radial direction of the gas flow field used to deflect the foil structure. The load capacity, film pressure profile, and film thickness profile were predicted for a GFTB with an outer radius of 55 mm, inner radius of 30 mm, and eight foils each of arc length 45°. The predictions showed that the load capacity of the GFTB increased with increasing rotor speed and decreasing minimum film thickness, and was always lower than the analytically determined limit value for infinite rotor speed (obtained by simple algebraic equations). A parametric study in which the ramp extent (or inclined angle) was increased from 5° to 40°, and the ramp height from 0 to 0.320 mm, revealed that the GFTB had an optimal ramp extent of ∼22.5° and ramp height of ∼0.030 mm for maximum load capacity. Interestingly, the optimal values were also valid for a rigid-surface bearing. The predicted load capacities for a ramp extent of ∼22.5° and increasing ramp height from 0.030 to 0.320 mm were compared with experimental data obtained from a previous work. The predictions for a ramp height of 0.155 mm were in good agreement with the experimental data for all three test GFTBs with outer radii of 45, 50, and 55 mm, respectively. In addition, this paper shows that the predicted drag torque increases linearly with increasing rotor speed and decreasing minimum film thickness, and nonlinearly with decreasing ramp height. The drag torque significantly increased only for ramp heights below the optimal value. The predictions imply that the optimal ramp height improves the load capacity of the GFTB with little change in the drag torque.

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.

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.

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%.

Design Optimization of Gas Foil Thrust Bearings for Maximum Load Capacity1

2017 ◽  
Vol 139 (3) ◽  
Author(s):  
Tae Ho Kim ◽  
Moonsung Park ◽  
Tae Won Lee
Keyword(s):  
Film Thickness ◽  
Load Capacity ◽  
Maximum Load ◽  
Ideal Gas ◽  
Outer Radius ◽  
Test Results ◽  
Rotor Speed ◽  
Design Guideline ◽  
Film Pressure ◽  
Thrust Bearings

The aim of the present study is to develop a design guideline to improve the load capacity of gas foil thrust bearings (GFTBs). The Reynolds equation for an isothermal isoviscous ideal gas calculates the gas film pressure. The film pressure averaged in the radial direction determines the ultimate load capacity. The load capacity, film pressure profile, and film thickness profile are predicted for a GFTB with an outer radius of 55 mm, inner radius of 30 mm, and eight foils each of arc length 45 deg. The predictions show that the load capacity of the GFTB increases with increasing rotor speed and decreasing minimum film thickness. A parametric study, in which the ramp extent (or inclined angle) is increased from 5 deg to 40 deg, and the ramp height from 0 to 320 μm, reveals that GFTBs have an optimal ramp extent of ∼22.5 deg and ramp height of 30 μm for maximum load capacity. A series of maximum load capacity measurements are conducted on four test GFTBs with ramp heights of 50, 150, 250, and 350 μm at the speeds of 12, 15, and 18 krpm. To estimate the maximum load capacity, the applied load is increased until the drag torque rises suddenly with a sharp peak. The test results show that the maximum load capacity generally increases for decreasing ramp height and for increasing rotor speed. The GFTB with a ramp height of 50 μm shows the largest maximum load capacity of 510 N, for example. Test results are in good agreement with model predictions.

The Influence of Injection Pockets on the Performance of Tilting-Pad Thrust Bearings: Part II — Comparison Between Theory and Experiment

2006 ◽  
Author(s):  
Niels Heinrichson ◽  
Axel Fuerst ◽  
Ilmar Ferreira Santos
Keyword(s):  
Film Thickness ◽  
Thrust Bearing ◽  
Three Dimensional ◽  
Leading Edge ◽  
Operating Conditions ◽  
Oil Film ◽  
Thrust Bearings ◽  
Tilting Pad ◽  
High Pressure Injection ◽  
Theoretical Pressure

This is Part II of a two-part series of papers describing the effects of high pressure injection pockets on the operating conditions of tilting-pad thrust bearings. Measurements of the distribution of pressure and oil film thickness are presented for tilting-pad thrust bearing pads of approximately 100 cm2 surface area. Two pads are measured in a laboratory test-rig at loads of approximately 0.5, 1.5 and 4.0 MPa and velocities of up to 33 m/s. One pad has a plain surface. The other pad has a conical injection pocket at the pivot point and a leading edge taper. The measurements are compared to theoretical values obtained using a three dimensional thermoelasto-hydrodynamic (TEHD) numerical model. At low and intermediate loads the theoretical pressure distribution corresponds well to the measured values for both pads although the influence of the pocket is slightly underestimated. At high loads large discrepancies exist for the pad with an injection pocket. It is argued that this is likely to be due to the unevenness of the collar surface. The measured and theoretical values of oil film thickness compare well at low loads. At high loads discrepancies grow to up to 25 %. It is argued that this is due to the accuracy of the measurements.

Thermal Distortion of Spiral-Grooved Gas-Lubricated Thrust Bearings

1971 ◽  
Vol 93 (1) ◽  
pp. 102-111 ◽  
Author(s):  
C. Wachmann ◽  
S. B. Malanoski ◽  
J. H. Vohr
Keyword(s):  
Thrust Bearing ◽  
Load Capacity ◽  
Heat Removal ◽  
Maximum Load ◽  
Thermal Distortion ◽  
Thrust Bearings ◽  
Self Heating ◽  
Worked Example ◽  
Performance Curves

Self-heating during operation causes a bearing to undergo thermal distortion. A method is presented to determine the consequent effects on the load capacity of a spiral-grooved air-lubricated thrust bearing designed for maximum load capacity. The effect of mode of heat removal is discussed. Appropriate performance curves and a worked example are given.

Effects of Grooving in a Circular Step Thrust Bearing

2005 ◽  
Author(s):  
M. Mahbubur Razzaque ◽  
M. Zakir Hossain
Keyword(s):  
Pressure Distribution ◽  
Thrust Bearing ◽  
Load Capacity ◽  
Maximum Load ◽  
Outer Radius ◽  
Hydrodynamic Load ◽  
Bearing Surface ◽  
Lubricant Flow ◽  
Inner Radius ◽  
Minimum Film Thickness

Assuming narrow grooves and considering inertia effect, an equation for the pressure distribution in a grooved circular step thrust bearing has been derived. A parametric study has been performed to investigate the effects of step and groove geometry on pressure distribution, load capacity and lubricant flow rate. Three arrangements of the bearing surface have been studied and it has been found that the maximum load capacity is obtained by putting grooves only on the step. Inertia significantly affects the load capacity. To get increased load capacity with increase of inertia, the step inner radius should be larger than 0.45 times of the outer radius. For the most enhancement of hydrodynamic load, the groove inclination angle should be 135° with the direction of rotation and the depth should be twice the minimum film thickness.

Load Capacity Tests on Tapered-Land and Pivoted-Shoe Thrust Bearings for Large Steam-Turbine Application

1959 ◽  
Vol 81 (2) ◽  
pp. 208-213
Author(s):  
R. E. Brandon ◽  
H. C. Bahr
Keyword(s):  
Bearing Capacity ◽  
Steam Turbine ◽  
Thrust Bearing ◽  
Load Capacity ◽  
Maximum Load ◽  
Full Scale ◽  
Thermal Distortion ◽  
Test Installation ◽  
Land Type ◽  
Thrust Bearings

Results of full-scale maximum load capacity tests on large, 3600-rpm, pivoted-shoe and tapered-land thrust bearings are reported. The results show 700 psi capacity for the pivoted-shoe bearing and 1085 psi for the tapered-land type. Additional evidence of thermal distortion and its effect on thrust-bearing capacity are discussed. A brief description of a new thrust-bearing test installation also is included.

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