scholarly journals Numerical Investigation of Pressure Profile in Hydrodynamic Lubrication Thrust Bearing

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Farooq Ahmad Najar ◽  
G. A. Harmain
Keyword(s):  
Reynolds Equation ◽  
Hydrodynamic Lubrication ◽  
Pressure Profile ◽  
Grid Refinement ◽  
Average Value ◽  
Lubricant Oil ◽  
Pressure Profiles ◽  
Tilting Pad ◽  
Minimum Film Thickness ◽  
Grid Independence

Reynolds equation is solved using finite difference method (FDM) on the surface of the tilting pad to find the pressure distribution in the lubricant oil film. Different pressure profiles with grid independence are described. The present work evaluates pressure at various locations after performing a thorough grid refinement. In recent similar works, this aspect has not been addressed. However, present study shows that it can have significant effect on the pressure profile. Results of a sector shaped pad are presented and it is shown that the maximum average value of pressure is 12% (approximately) greater than the previous results. Grid independence occurs after 24 × 24 grids. A parameter “ψ” has been proposed to provide convenient indicator of obtaining grid independent results. ψ=|(Prefinedgrid-PRefrence-grid)/Prefinedgrid|, ψ≤ε, where “ε” can be fixed to a convenient value and a constant minimum film thickness value of 75 μm is used in present study. This important parameter is highlighted in the present work; the location of the peak pressure zone in terms of (r,θ) coordinates is getting shifted by changing the grid size which will help the designer and experimentalist to conveniently determine the position of pressure measurement probe.

Pressure Boundary Layer in a Transient or Steady Gas Film and Mass Interaction

1970 ◽  
Vol 37 (4) ◽  
pp. 945-953 ◽  
Author(s):  
F. C. Hsing ◽  
H. S. Cheng
Keyword(s):  
Boundary Layer ◽  
Steady State ◽  
High Speed ◽  
Numerical Scheme ◽  
Reynolds Equation ◽  
Equations Of Motion ◽  
Pressure Profile ◽  
Tilting Pad ◽  
Static Solutions ◽  
Gas Bearing

This paper presents a numerical scheme capable of yielding accurate pressure profile for the transient and steady hydrodynamic gas film generated by high-speed relative motion of two nonparallel surfaces. The numerical difficulties associated with high compressibility numbers for the gas film Reynolds equation were overcome by employing a set of systematically generated irregular grid spacings based on a coordinate transformation. By coupling the fluid-film solution with the equations of motion of a tilting pad, the dynamics of the mass film interaction were treated. Results are presented for both steady-state and dynamical solutions. Static solutions for a 120-deg partial-arc gas bearing have been used for comparison.

Three-Dimensional Hydrodynamic Lubrication Analysis of Cylinder Liner-Piston Ring

2013 ◽  
Vol 871 ◽  
pp. 27-31
Author(s):  
Shi Feng Zhang ◽  
Shu Hua Cao ◽  
Jiu Jun Xu
Keyword(s):  
Piston Ring ◽  
Reynolds Equation ◽  
Variable Viscosity ◽  
Hydrodynamic Lubrication ◽  
Three Dimensional ◽  
Cylinder Liner ◽  
Asperity Contact ◽  
Crank Angle ◽  
Minimum Film Thickness ◽  
Friction Analysis

This paper constructs a three-dimensional transient hydrodynamic lubrication model for cylinder liner-piston ring based on the three-dimensional transient average Reynolds equation and asperity contact model. A computer program was written with FORTRAN to calculate hydrodynamic lubrication, in which the surface roughness, the variable viscosity effect and the deformation of the circumferential direction of the cylinder liner are taken into account. The film pressure distribution in different crank angle during the stroke, minimum film thickness and friction are computed and analyzed with this program. This three-dimensional transient hydrodynamic lubrication model provides a design basis for the friction analysis of cylinder liner-piston ring.

Analysis of Tilting Pad Journal Bearings With Heat Transfer Effects

1988 ◽  
Vol 110 (1) ◽  
pp. 128-133 ◽  
Author(s):  
J. D. Knight ◽  
L. E. Barrett
Keyword(s):  
Heat Transfer ◽  
Reynolds Equation ◽  
Pressure Profile ◽  
Journal Bearings ◽  
Solution Technique ◽  
Inlet Temperature ◽  
Tilting Pad ◽  
Turbine Bearing ◽  
Tilting Pad Journal Bearings ◽  
Sample Case

An approximate solution technique for tilting pad journal bearings is presented. The method makes use of approximations to the axial pressure profile and the temperature profiles and includes heat transfer between the film and its boundaries. A second order profile is assumed to represent the temperature distribution across the film. The classical Reynolds equation is applied, using the viscosity based on the cross-film average of temperature. The transfer of heat in the pads is modeled as purely radial conduction, and the journal surface temperature is given by a circumferential average of the film temperatures. Results of calculations are presented for a sample case representative of an industrial compressor or turbine bearing and are compared to isothermal results. The dynamic characteristics in this case are found to vary by 10 to 35 percent for a change in lubricant inlet temperature of 28°C. Temperature distributions in the lubricant and on the surfaces of the pads are given.

Inertia Effect in Hydrodynamic Lubrication With Film Rupture

1987 ◽  
Vol 109 (1) ◽  
pp. 86-90 ◽  
Author(s):  
H. I. You ◽  
S. S. Lu
Keyword(s):  
Reynolds Number ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Hydrodynamic Lubrication ◽  
Inertia Effect ◽  
Fluid Inertia ◽  
Film Rupture ◽  
Minimum Film Thickness ◽  
Rupture Model ◽  
Modified Reynolds Equation

The modified Reynolds equation in conjunction with the modified Coyne-Elrod rupture model is used to investigate the inertia effect on the pressure distribution in converging-diverging bearings. The modified Reynolds equation is solved analytically for infinitely long bearings, including the cylinder-plane bearing and the journal bearing. The results showed that the fluid inertia tends to stretch the fluid film and to move the film rupture point farther downstream. The effects are profound even at a moderate value of the reduced Reynolds number, Re* ≈ 0.13 based on the minimum film thickness.

Temporal and Convective Inertia Effects in Plain Journal Bearings With Eccentricity, Velocity and Acceleration

2012 ◽  
Vol 134 (3) ◽  
Author(s):  
Saeid Dousti ◽  
Jianming Cao ◽  
Amir Younan ◽  
Paul Allaire ◽  
Tim Dimond
Keyword(s):  
Reynolds Number ◽  
Turbulent Flows ◽  
Reynolds Equation ◽  
Stokes Equations ◽  
Hydrodynamic Lubrication ◽  
Operating Conditions ◽  
Inertia Effects ◽  
Pressure Profiles ◽  
Impulsive Loads ◽  
Developed Pressure

This paper extends the theory originally developed by Tichy (Tichy and Bou-Said, 1991, Hydrodynamic Lubrication and Bearing Behavior With Impulsive Loads,” STLE Tribol. Trans. 34, pp. 505–512) for impulsive loads to high reduced Reynolds number lubrication. The incompressible continuity equation and Navier-Stokes equations, including inertia terms, are simplified using an averaged velocity approach to obtain an extended form of short bearing Reynolds equation which applies to both laminar and turbulent flows. A full kinematic analysis of the short journal bearing is developed. Pressure profiles and linearized stiffness, damping and mass coefficients are calculated for different operating conditions. A time transient solution is developed. The change in the rotor displacements when subjected to unbalance forces is explored. Several comparisons between conventional Reynolds equation solutions and the extended Reynolds number form with temporal inertia effects are presented and discussed. In the specific cases considered in this paper, the primary conclusion is that the turbulence effects are significantly more important than inertia effects.

scholarly journals Numerical analysis and experimental research on load carrying capacity of water-lubricated tilting-pad thrust bearings

2018 ◽  
Vol 19 (2) ◽  
pp. 201 ◽  
Author(s):  
Xiuli Zhang ◽  
Gengyuan Gao ◽  
Zhongwei Yin ◽  
Yanzhen Wang ◽  
Chao Gao
Keyword(s):  
Film Thickness ◽  
Thrust Bearing ◽  
Hydrodynamic Lubrication ◽  
Optimization Method ◽  
Load Carrying Capacity ◽  
Thrust Bearings ◽  
Lubrication Regime ◽  
Tilting Pad ◽  
Load Carrying ◽  
Minimum Film Thickness

Water-lubricated bearings are expected to be widely used because of convenience, green, safe and energy saving. The purpose of this study is to investigate the load carrying property of water-lubricated tilting-pad thrust bearings. A large amount of numerical analyses are undertaken based on computational fluid dynamics and the optimization method of pivot location and the calculation method of minimum film thickness are summarized. A thrust bearing is designed according to the numerical results and is tested by experiments. The experimental results validate the numerical method and the minimum film thickness to surface roughness ratio corresponding to the change of bearing lubrication regime from mixed lubrication to hydrodynamic lubrication is obtained.

Numerical and Experimental Research of the Slurry Film in Chemical Mechanical Polishing (CMP)

2010 ◽  
Vol 102-104 ◽  
pp. 669-674
Author(s):  
Fei Yan Lou ◽  
Qian Fa Deng ◽  
Ju Long Yuan
Keyword(s):  
Film Thickness ◽  
Chemical Mechanical Polishing ◽  
Applied Load ◽  
Reynolds Equation ◽  
Rotation Speed ◽  
Hydrodynamic Lubrication ◽  
Three Dimensional ◽  
Mechanical Polishing ◽  
Film Pressure ◽  
Minimum Film Thickness

A three-dimensional hydrodynamic lubrication model for chemical-mechanical polishing is presented based on the Reynolds equation and Reynolds boundary condition. By solving the Reynolds equation, the slurry film pressure distribution has been obtained. The effects of minimum film thickness and the wafer tile angle on the film pressure are analyzed, and the influence of the polishing applied load and rotation speed on slurry film thickness and tilt angle are discussed. At last, by experiment, it is found that the simulation results are similar to experiment results which film thickness is increasing with the increasing of rotation speed, decreasing of the applied load. It is proved that the simulation is reliable.

Influence of new surface micro-structures on the performance behaviours of fluid film tilting pad thrust bearings

2021 ◽  
pp. 095440622110309
Author(s):  
JC Atwal ◽  
RK Pandey
Keyword(s):  
Mass Conservation ◽  
Performance Parameters ◽  
Algebraic Equations ◽  
The Finite Element Method ◽  
Thrust Bearings ◽  
Lubrication Equation ◽  
Tilting Pad ◽  
Minimum Film Thickness ◽  
Newton Raphson ◽  
Micro Structures

Performance parameters such as power loss, minimum film thickness, and maximum oil temperature of the sector-shaped tilting pad thrust bearings employing the new micro-structural geometries on pad surfaces have been investigated. The lubrication equation incorporating the mass-conservation issue is discretized using the finite element method and the solution of resulting algebraic equations is obtained employing a Newton-Schur method. The pad equilibrium in the analysis is established using the Newton-Raphson and Braydon methods. The influence of attributes of micro-structures such as depth, circumferential and radial positioning extents have been explored on the performance behaviours. It is found that with the new micro-structured pad surfaces, the performance parameters significantly improved in comparison to conventional plain and conventional rectangular pocketed pads.

scholarly journals Propagation of radiosonde pressure sensor errors to ozonesonde measurements

2014 ◽  
Vol 7 (1) ◽  
pp. 65-79 ◽  
Author(s):  
R. M. Stauffer ◽  
G. A. Morris ◽  
A. M. Thompson ◽  
E. Joseph ◽  
G. J. R. Coetzee ◽  
...  
Keyword(s):  
Pressure Sensor ◽  
Atmospheric Pressure ◽  
Pressure Profile ◽  
Mixing Ratio ◽  
Concentration Cell ◽  
Pressure Profiles ◽  
Dependent Variables ◽  
Sensor Errors ◽  
Subsequent Addition ◽  
Total Column

Abstract. Several previous studies highlight pressure (or equivalently, pressure altitude) discrepancies between the radiosonde pressure sensor and that derived from a GPS flown with the radiosonde. The offsets vary during the ascent both in absolute and percent pressure differences. To investigate this problem further, a total of 731 radiosonde/ozonesonde launches from the Southern Hemisphere subtropics to northern mid-latitudes are considered, with launches between 2005 and 2013 from both longer term and campaign-based intensive stations. Five series of radiosondes from two manufacturers (International Met Systems: iMet, iMet-P, iMet-S, and Vaisala: RS80-15N and RS92-SGP) are analyzed to determine the magnitude of the pressure offset. Additionally, electrochemical concentration cell (ECC) ozonesondes from three manufacturers (Science Pump Corporation; SPC and ENSCI/Droplet Measurement Technologies; DMT) are analyzed to quantify the effects these offsets have on the calculation of ECC ozone (O3) mixing ratio profiles (O3MR) from the ozonesonde-measured partial pressure. Approximately half of all offsets are > ±0.6 hPa in the free troposphere, with nearly a third > ±1.0 hPa at 26 km, where the 1.0 hPa error represents ~ 5% of the total atmospheric pressure. Pressure offsets have negligible effects on O3MR below 20 km (96% of launches lie within ±5% O3MR error at 20 km). Ozone mixing ratio errors above 10 hPa (~ 30 km), can approach greater than ±10% (> 25% of launches that reach 30 km exceed this threshold). These errors cause disagreement between the integrated ozonesonde-only column O3 from the GPS and radiosonde pressure profile by an average of +6.5 DU. Comparisons of total column O3 between the GPS and radiosonde pressure profiles yield average differences of +1.1 DU when the O3 is integrated to burst with addition of the McPeters and Labow (2012) above-burst O3 column climatology. Total column differences are reduced to an average of −0.5 DU when the O3 profile is integrated to 10 hPa with subsequent addition of the O3 climatology above 10 hPa. The RS92 radiosondes are superior in performance compared to other radiosondes, with average 26 km errors of −0.12 hPa or +0.61% O3MR error. iMet-P radiosondes had average 26 km errors of −1.95 hPa or +8.75 % O3MR error. Based on our analysis, we suggest that ozonesondes always be coupled with a GPS-enabled radiosonde and that pressure-dependent variables, such as O3MR, be recalculated/reprocessed using the GPS-measured altitude, especially when 26 km pressure offsets exceed ±1.0 hPa/±5%.

Dynamic Analysis of Tilting-Pad Journal Bearing—Influence of Pad Deformations

1994 ◽  
Vol 116 (3) ◽  
pp. 621-627 ◽  
Author(s):  
H. Desbordes ◽  
M. Fillon ◽  
C. Chan Hew Wai ◽  
J. Frene
Keyword(s):  
Film Thickness ◽  
Pressure Field ◽  
Journal Bearing ◽  
Maximum Pressure ◽  
Tilting Pad ◽  
Minimum Film Thickness ◽  
Dimensional Finite Element ◽  
The One ◽  
Tilting Pad Journal Bearing ◽  
Tilting Pad Journal Bearings

A theoretical nonlinear analysis of tilting-pad journal bearings is presented for small and large unbalance loads under isothermal conditions. The radial displacements of internal pad surface due to pressure field are determined by a two-dimensional finite element method in order to define the actual film thickness. The influence of pad deformations on the journal orbit, on the minimum film thickness and on the maximum pressure is studied. The effects of pad displacements are to decrease the minimum film thickness and to increase the maximum pressure. The orbit amplitude is also increased by 20 percent for the large unbalance load compared to the one obtained for rigid pad.

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