A Study of Thermohydrodynamic Squeeze Films

1974 ◽  
Vol 96 (2) ◽  
pp. 198-205 ◽  
Author(s):  
S. M. Rohde ◽  
H. A. Ezzat
Keyword(s):  
Heat Conduction Equation ◽  
Reynolds Equation ◽  
Energy Equation ◽  
Time Dependent ◽  
Fluid Film ◽  
Squeeze Film ◽  
3 Dimensional ◽  
Temperature Distributions ◽  
Film Parameter ◽  
The Mathematical Model

This paper presents an analysis of the thermohydrodynamic performance of squeeze films. The mathematical model consists of a 3-dimensional Reynolds equation, a 3-dimensional time dependent energy equation, and a 3-dimensional time dependent heat conduction equation. The system of equations is solved numerically. Fluid film pressure and temperature distributions and the temperature distribution in the solids are presented. Fluid film velocity profiles as a function of time are also shown. The load-time characteristics for different operative conditions are studied. It is shown that a thermohydrodynamic squeeze-film parameter can give rise to a phenomenon which radically changes the fluid film performance.

Thermohydrodynamic Lubrication Analysis of Slider Bearings With Steps on Bearing Surface

2009 ◽  
Author(s):  
Hideki Ogata
Keyword(s):  
Reynolds Equation ◽  
Energy Equation ◽  
Fluid Velocity ◽  
Differential Method ◽  
Fluid Film ◽  
Bearing Surface ◽  
Fluid Film Bearings ◽  
Temperature Distributions ◽  
Finite Differential Method ◽  
Good Agreement

This study focuses on the thermohydrodynamic lubrication analysis of fluid film bearings with step on the surface such as a Rayleigh step bearing. In general, the Reynolds equation does not satisfy the continuity of the fluid velocity components at steps. This discontinuity results in the difficulty to solve the energy equation for the lubricants, because the energy equation needs the velocity components explicitly. The author has solved this problem by introducing the equivalent clearance height and the equivalent gradient of clearance height at steps. These parameters remove the discontinuity of velocity components and the energy equation as well, so that one can solve these equations on all of the bearing surfaces including the step region by finite differential method (FDM). The numerical results of pressure and temperature distributions by the proposed method for a Rayleigh step bearing were compared with the results obtained by a commercial CFD package. These results showed good agreement with each other. This method is extended to 2D unequal grid problems.

scholarly journals About the Accuracy and the Grid Convergence of the Numerical Solution of the Energy Equation in Fluid Film Lubrication

2018 ◽  
Author(s):  
Silun Zhang ◽  
Mohamed-Amine Hassini ◽  
Mihai Arghir
Keyword(s):  
Numerical Solution ◽  
Reynolds Equation ◽  
Energy Equation ◽  
Computation Time ◽  
Fluid Film ◽  
Hydrodynamic Analysis ◽  
One Dimensional ◽  
Grid Convergence ◽  
Film Lubrication ◽  
Fluid Film Lubrication

The present work is focused on the numerical solution of the complete energy equation used in fluid film lubrication. The work was motivated by the fact the complete energy equation has no analytic solution that could be used for validations. Its accuracy and computation time are related to the employed numerical method and to the grid resolution. The natural discretization method (NDM) applied on different grids is systematically compared with the spectral method (the Lobatto Point Colocation Method or LPCM) with different polynomial degrees. A one dimensional inclined slider is used for the numerical tests and the energy equation is artificially decoupled from Reynolds. This approach enables to focus all the attention on the numerical solution of the energy equation. The results show that the LPCM is one or two orders of magnitudes more efficient than the NDM in terms of computation time. The energy equation is then coupled with Reynolds equation in a thermo-hydrodynamic analysis of the same 1D slider; the numerical results confirm again the efficiency of the LPCM. A thermo-hydrodynamic analysis of a two-lobe journal bearing is then presented as a practical application.

A study of a journal bearing lubricated by couple stress fluids considering thermal and cavitation effects

2002 ◽  
Vol 216 (5) ◽  
pp. 293-305 ◽  
Author(s):  
X-L Wang ◽  
K-Q Zhu ◽  
C-L Gui
Keyword(s):  
Couple Stress ◽  
Heat Conduction Equation ◽  
Reynolds Equation ◽  
Energy Equation ◽  
Theoretical Study ◽  
Journal Bearing ◽  
Fluid Model ◽  
Load Capacity ◽  
Modified Reynolds Equation ◽  
Couple Stress Fluids

A theoretical study of a finite grooved journal bearing lubricated with couple stress fluids is made considering both thermal and cavitation effects. On the basis of the Stokes couple stress fluid model, the modified Reynolds equation and the energy equation are derived and then numerically solved together with the heat conduction equation. The solution to the modified Reynolds equation is determined using the Elrod cavitation algorithm. The effects of couple stress on the performance of a journal bearing are investigated. It is observed that the lubricants with couple stress, compared with Newtonian lubricants, not only yield an obvious increase in load capacity and decrease in coefficient of friction but also produce a slight increase in the temperature of lubricants and bush and a slight decrease in the side leakage flow.

scholarly journals Accuracy and Grid Convergence of the Numerical Solution of the Energy Equation in Fluid Film Lubrication: Application to the 1D Slider

Lubricants ◽  
2018 ◽  
Vol 6 (4) ◽  
pp. 95
Author(s):  
Silun Zhang ◽  
Mohamed-Amine Hassini ◽  
Mihai Arghir
Keyword(s):  
Numerical Solution ◽  
Reynolds Equation ◽  
Energy Equation ◽  
Computation Time ◽  
Fluid Film ◽  
Hydrodynamic Analysis ◽  
One Dimensional ◽  
Grid Convergence ◽  
Film Lubrication ◽  
Fluid Film Lubrication

The present work is focused on the numerical solution of the complete energy equation used in fluid film lubrication. The work was motivated by the fact that the complete energy equation has no analytical solution that can be used for validations. Its accuracy and computation time are related to the employed numerical method and to the grid resolution. The natural discretization method (NDM) applied on different grids is systematically compared with the spectral method (the Lobatto Point Colocation Method or LPCM) with different polynomial degrees. A one dimensional inclined slider is used for the numerical tests, and the energy equation is artificially decoupled from the Reynolds equation. This approach enables us to focus all the attention on the numerical solution of the energy equation. The results show that the LPCM is one or two orders of magnitude more efficient than the NDM in terms of computation time. The energy equation is then coupled with the Reynolds equation in a thermo-hydrodynamic analysis of the same 1D slider; the numerical results confirm again the efficiency of the LPCM. A thermo-hydrodynamic analysis of a two-lobe journal bearing is then presented as a practical application.

Solution for the Pressure and Temperature in an Infinite Slider Bearing of Arbitrary Profile

1967 ◽  
Vol 89 (4) ◽  
pp. 445-452 ◽  
Author(s):  
E. J. Hahn ◽  
C. F. Kettleborough
Keyword(s):  
Energy Equation ◽  
Fluid Film ◽  
Navier Stokes ◽  
Subsequent Paper ◽  
Slider Bearing ◽  
Navier Stokes Equation ◽  
Temperature Distributions ◽  
Elastic Distortion ◽  
Temperature And Pressure ◽  
State Pressure

An iterative method of calculating the steady-state pressure and temperature distributions in the fluid film for infinitely wide slider bearings is presented. The bearing profile is assumed to be quite general, rendering the method particularly applicable to problems involving thermal or elastic distortion. The viscosity of the lubricant is regarded as a function of temperature and pressure; the density as a function of temperature only. The inertia terms are retained in the simplified Navier-Stokes equation and the energy equation includes the compression work term. Heat transfer between the bearing surfaces and the fluid film are accounted for. Several numerical examples are evaluated and compared with existing solutions. The solution presented is believed to be the most complete to date. A subsequent paper will deal with the effect of thermal distortions of similar geometrical arrangements described herein.

Performance characteristics of two-axial groove journal bearing for different groove angles

2018 ◽  
Vol 70 (2) ◽  
pp. 432-443
Author(s):  
K.R. Kadam ◽  
S.S. Banwait
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Heat Conduction ◽  
Pressure Distribution ◽  
Heat Conduction Equation ◽  
Reynolds Equation ◽  
Energy Equation ◽  
Journal Bearing ◽  
Three Dimensional ◽  
Content Type

Purpose Different groove angles are used to study performance characteristics of two-axial groove journal bearing. In this study two grooves are located at ±90º to the load line. The various angles of grooves have been taken as 10° to 40° in the interval of 5°. Different equations such as Reynolds equation, three-dimensional energy equation and heat conduction equation have been solved using finite element method and finite difference method. Pressure distribution in fluid is found by using Reynolds equation. The three-dimensional energy equation is used for temperature distribution in the fluid film and bush. One-dimensional heat conduction equation is used for finding temperature in axial direction for journal. There is a very small effect of groove angle on film thickness, eccentricity ratio and pressure. There is a drastic change in attitude angle and side flow. Result shows that there is maximum power loss at large groove angle. So the smaller groove angle is recommended for two-axial groove journal bearing. Design/methodology/approach The finite element method is used for solving Reynolds equation for pressure distribution in fluid. The finite difference method is adopted for finding temperature distribution in bush, fluid and journal. Findings Pressure distribution in fluid is found out. Temperature distribution in bush, fluid and journal is found out. There is a very small effect of groove angle on film thickness, eccentricity ratio and pressure. Research limitations/implications The groove angle used is from 10 to 40 degree. The power loss is more when angle of groove increases, so smaller groove angle is recommended for this study. Practical implications The location of groove angle predicts the distribution of pressure and temperature in journal bearing. It will show the performance characteristics. ±90° angle we will prefer that will get before manufacturing of bearing. Social implications Due to this study, we will get predict how the pressure and temperature distribute in the journal. It will give the running condition of bearing as to at what speed and load we will get the maximum temperature and pressure in the bearing. Originality/value The finite element method is used for solving the Reynolds equation. Three-dimensional energy equation is solved using the finite difference method. Heat conduction equation is also solved for journal. The C language is used. The code is developed in C language. There are different equations which depend on each other. The temperature is dependent on pressure viscosity of fluid, etc. so C code is preferred.

Effects of a Groove on the Behavior of a Squeeze Film Between a Grooved and a Plain Rotating Annular Disk

1999 ◽  
Vol 121 (4) ◽  
pp. 808-815 ◽  
Author(s):  
M. Mahbubur Razzzaque ◽  
Takahisa Kato
Keyword(s):  
Film Thickness ◽  
Power Dissipation ◽  
Applied Load ◽  
Reynolds Equation ◽  
Fluid Film ◽  
Squeeze Film ◽  
Angular Orientation ◽  
Governing Equations ◽  
Annular Disk

A model simulating the squeezing process of an annular disk rotating against a grooved counterpart has been developed. Grooving effects are incorporated using the narrow groove assumption. Disks are considered impermeable, rigid, perfectly aligned, and smooth. It is assumed that the fluid film is isothermal and obeys Reynolds equation. The governing equations derived from the model are solved numerically. The effects of groove geometry, orientation and applied load on film thickness, transmitted torque, speed, squeeze time, and viscous power dissipation have been calculated and analyzed. It has been found that angular orientation significantly affects the squeezing process. Squeeze time and power dissipation are less for grooves with angular orientation in the range 40–60 deg.

scholarly journals Numerical computation of the damping and stiffness coefficients of the classical and magnetorheological squeeze film damper

2018 ◽  
Vol 157 ◽  
pp. 08001
Author(s):  
Petr Ferfecki ◽  
Jaroslav Zapoměl ◽  
Michal Šofer ◽  
František Pochylý ◽  
Simona Fialová
Keyword(s):  
Mathematical Models ◽  
Reynolds Equation ◽  
Stokes Equations ◽  
Fluid Film ◽  
Squeeze Film ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Squeeze Film Damper ◽  
Stiffness Coefficients ◽  
Thin Fluid Film

Technological solution, frequently used to suppress vibrations in rotating machines, consists in adding damping devices between the rotor and its frame. This is enabled by dampers working on the principle of a squeezing thin classical or magnetorheological fluid film. The Navier-Stokes equations, Reynolds equation, and modified Navier-Stokes equations are used to determine the pressure distribution in the thin fluid film. The damping and stiffness coefficients are computed by the developed procedure presented in this paper. The proposed computational approach is based on the perturbation of the synchronous circular whirling motion. The carried-out computational simulations show that the investigated mathematical models of the squeeze film damper and magnetorheological squeeze film damper allowed computation of the damping and stiffness coefficients. It has been found that the stiffness coefficients computed by the proposed mathematical models may be different.

The Prediction of Film Thickness in a Mechanical face Seal with Circumferential Waviness on both the face and the seat

1982 ◽  
Vol 24 (1) ◽  
pp. 37-43 ◽  
Author(s):  
A. V. Ruddy ◽  
D. Dowson ◽  
C. M. Taylor
Keyword(s):  
Film Thickness ◽  
Reynolds Equation ◽  
Closed Loop ◽  
Lubrication Theory ◽  
Fluid Film ◽  
Squeeze Film ◽  
Two Dimensional ◽  
Face Seal ◽  
The Face ◽  
Mechanical Face Seal

The effect of two-period waviness on both the face and the seat of a mechanical face seal is examined theoretically in this paper. A closed-loop cyclic solution of the two-dimensional Reynolds' equation including squeeze-film effects is described. Results for a 45 mm diameter seal are presented which show that squeeze-film effects play an important role in protecting the fluid-film over parts of the cycle where the entraining effect is small. The analysis can be extended to allow for misalignment of the sealing faces and for the incorporation of mixed-lubrication theory.

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