# Equivalent Clearance Model for Solving Thermohydrodynamic Lubrication of Slider Bearings With Steps

Hideki Ogata, Joichi Sugimura

Research output: Contribution to journalArticle

3 Citations (Scopus)

### Abstract

This study focuses on the thermohydrodynamic lubrication (THD) analysis of fluid film bearings with steps on the bearing surface, such as Rayleigh step. In general, the Reynolds equation does not satisfy the continuity of fluid velocity components at steps. This discontinuity results in the difficulty to solve the energy equation for the lubricants by finite differential method (FDM), because the energy equation needs the velocity components explicitly. The authors have solved this issue by introducing the equivalent clearance height and the equivalent gradient of the clearance height at steps. These parameters remove the discontinuity of velocity components, and the Reynolds equations can be solved for any bearing surfaces with step regions by FDM. Moreover, this method results in pseudocontinuous velocity components, which enables the energy equation to be solved as well. This paper describes this method with one-dimensional and equal grids model. The numerical results of pressure and temperature distributions by the proposed method for an infinite width Rayleigh step bearing agree well with the results obtained by solving full Navier-Stokes equations with semi-implicit method for pressure-linked equations revised (SIMPLER) method.

Original language English 034503 Journal of Tribology 139 3 https://doi.org/10.1115/1.4034457 Published - Jan 1 2017

### Fingerprint

Bearings (structural)
clearances
lubrication
chutes
Lubrication
Reynolds equation
Fluids
discontinuity
Pressure distribution
Navier Stokes equations
Lubricants
fluid films
Temperature distribution
lubricants
pressure distribution
continuity
Navier-Stokes equation
energy
temperature distribution
grids

### All Science Journal Classification (ASJC) codes

• Mechanics of Materials
• Mechanical Engineering
• Surfaces and Interfaces
• Surfaces, Coatings and Films

### Cite this

In: Journal of Tribology, Vol. 139, No. 3, 034503, 01.01.2017.

Research output: Contribution to journalArticle

@article{7b00e3baaec54744b9b8222daf07cb40,
title = "Equivalent Clearance Model for Solving Thermohydrodynamic Lubrication of Slider Bearings With Steps",
abstract = "This study focuses on the thermohydrodynamic lubrication (THD) analysis of fluid film bearings with steps on the bearing surface, such as Rayleigh step. In general, the Reynolds equation does not satisfy the continuity of fluid velocity components at steps. This discontinuity results in the difficulty to solve the energy equation for the lubricants by finite differential method (FDM), because the energy equation needs the velocity components explicitly. The authors have solved this issue by introducing the equivalent clearance height and the equivalent gradient of the clearance height at steps. These parameters remove the discontinuity of velocity components, and the Reynolds equations can be solved for any bearing surfaces with step regions by FDM. Moreover, this method results in pseudocontinuous velocity components, which enables the energy equation to be solved as well. This paper describes this method with one-dimensional and equal grids model. The numerical results of pressure and temperature distributions by the proposed method for an infinite width Rayleigh step bearing agree well with the results obtained by solving full Navier-Stokes equations with semi-implicit method for pressure-linked equations revised (SIMPLER) method.",
author = "Hideki Ogata and Joichi Sugimura",
year = "2017",
month = "1",
day = "1",
doi = "10.1115/1.4034457",
language = "English",
volume = "139",
journal = "Journal of Tribology",
issn = "0742-4787",
publisher = "American Society of Mechanical Engineers(ASME)",
number = "3",

}

TY - JOUR

T1 - Equivalent Clearance Model for Solving Thermohydrodynamic Lubrication of Slider Bearings With Steps

AU - Ogata, Hideki

AU - Sugimura, Joichi

PY - 2017/1/1

Y1 - 2017/1/1

N2 - This study focuses on the thermohydrodynamic lubrication (THD) analysis of fluid film bearings with steps on the bearing surface, such as Rayleigh step. In general, the Reynolds equation does not satisfy the continuity of fluid velocity components at steps. This discontinuity results in the difficulty to solve the energy equation for the lubricants by finite differential method (FDM), because the energy equation needs the velocity components explicitly. The authors have solved this issue by introducing the equivalent clearance height and the equivalent gradient of the clearance height at steps. These parameters remove the discontinuity of velocity components, and the Reynolds equations can be solved for any bearing surfaces with step regions by FDM. Moreover, this method results in pseudocontinuous velocity components, which enables the energy equation to be solved as well. This paper describes this method with one-dimensional and equal grids model. The numerical results of pressure and temperature distributions by the proposed method for an infinite width Rayleigh step bearing agree well with the results obtained by solving full Navier-Stokes equations with semi-implicit method for pressure-linked equations revised (SIMPLER) method.

AB - This study focuses on the thermohydrodynamic lubrication (THD) analysis of fluid film bearings with steps on the bearing surface, such as Rayleigh step. In general, the Reynolds equation does not satisfy the continuity of fluid velocity components at steps. This discontinuity results in the difficulty to solve the energy equation for the lubricants by finite differential method (FDM), because the energy equation needs the velocity components explicitly. The authors have solved this issue by introducing the equivalent clearance height and the equivalent gradient of the clearance height at steps. These parameters remove the discontinuity of velocity components, and the Reynolds equations can be solved for any bearing surfaces with step regions by FDM. Moreover, this method results in pseudocontinuous velocity components, which enables the energy equation to be solved as well. This paper describes this method with one-dimensional and equal grids model. The numerical results of pressure and temperature distributions by the proposed method for an infinite width Rayleigh step bearing agree well with the results obtained by solving full Navier-Stokes equations with semi-implicit method for pressure-linked equations revised (SIMPLER) method.

UR - http://www.scopus.com/inward/record.url?scp=85043268484&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85043268484&partnerID=8YFLogxK

U2 - 10.1115/1.4034457

DO - 10.1115/1.4034457

M3 - Article

AN - SCOPUS:85043268484

VL - 139

JO - Journal of Tribology

JF - Journal of Tribology

SN - 0742-4787

IS - 3

M1 - 034503

ER -