On boundary conditions in lubrication with one dimensional analytical solutions

Shuangbiao Liu

doi:10.1016/j.triboint.2011.11.021

On boundary conditions in lubrication with one dimensional analytical solutions

Shuangbiao Liu^*

^*Corresponding author for this work

Mechanical Engineering

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

This work summarizes different boundary conditions for the Reynolds' equation, classifies them using mathematical terms, and demonstrates their effects. Various analytical solutions for 2D journal bearings are presented and the rupture location depends linearly on the eccentricity ratio. With a given eccentricity and inlet position, the inlet pressure is uniquely related to the flow rate inside the bearing if the bearing is not starved nor choked. Furthermore, a general analytical solution of a dimpled step bearing is derived and it demonstrates the invalidity of the Reynolds condition for discontinuous geometry. Cavitation appears in intermediate groove depth of this step bearing.

Original language	English (US)
Pages (from-to)	182-190
Number of pages	9
Journal	Tribology International
Volume	48
DOIs	https://doi.org/10.1016/j.triboint.2011.11.021
State	Published - Apr 2012

Keywords

Analytical
Boundary conditions
Cavitation
Lubrication

ASJC Scopus subject areas

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

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10.1016/j.triboint.2011.11.021

Cite this

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title = "On boundary conditions in lubrication with one dimensional analytical solutions",

abstract = "This work summarizes different boundary conditions for the Reynolds' equation, classifies them using mathematical terms, and demonstrates their effects. Various analytical solutions for 2D journal bearings are presented and the rupture location depends linearly on the eccentricity ratio. With a given eccentricity and inlet position, the inlet pressure is uniquely related to the flow rate inside the bearing if the bearing is not starved nor choked. Furthermore, a general analytical solution of a dimpled step bearing is derived and it demonstrates the invalidity of the Reynolds condition for discontinuous geometry. Cavitation appears in intermediate groove depth of this step bearing.",

keywords = "Analytical, Boundary conditions, Cavitation, Lubrication",

author = "Shuangbiao Liu",

note = "Funding Information: This work was supported in part by the National Institute of Standards and Technology (NIST) , Advance Technology Program (ATP) grant # 70NANB7H7007 , and Dr. Jean-Louis Staudenmann was the ATP program manager. The author thanks Dr. Diann Hua and Mr. Cletus Kinsey for valuable discussions. ",

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doi = "10.1016/j.triboint.2011.11.021",

language = "English (US)",

volume = "48",

pages = "182--190",

journal = "Tribology International",

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T1 - On boundary conditions in lubrication with one dimensional analytical solutions

AU - Liu, Shuangbiao

N1 - Funding Information: This work was supported in part by the National Institute of Standards and Technology (NIST) , Advance Technology Program (ATP) grant # 70NANB7H7007 , and Dr. Jean-Louis Staudenmann was the ATP program manager. The author thanks Dr. Diann Hua and Mr. Cletus Kinsey for valuable discussions.

PY - 2012/4

Y1 - 2012/4

N2 - This work summarizes different boundary conditions for the Reynolds' equation, classifies them using mathematical terms, and demonstrates their effects. Various analytical solutions for 2D journal bearings are presented and the rupture location depends linearly on the eccentricity ratio. With a given eccentricity and inlet position, the inlet pressure is uniquely related to the flow rate inside the bearing if the bearing is not starved nor choked. Furthermore, a general analytical solution of a dimpled step bearing is derived and it demonstrates the invalidity of the Reynolds condition for discontinuous geometry. Cavitation appears in intermediate groove depth of this step bearing.

AB - This work summarizes different boundary conditions for the Reynolds' equation, classifies them using mathematical terms, and demonstrates their effects. Various analytical solutions for 2D journal bearings are presented and the rupture location depends linearly on the eccentricity ratio. With a given eccentricity and inlet position, the inlet pressure is uniquely related to the flow rate inside the bearing if the bearing is not starved nor choked. Furthermore, a general analytical solution of a dimpled step bearing is derived and it demonstrates the invalidity of the Reynolds condition for discontinuous geometry. Cavitation appears in intermediate groove depth of this step bearing.

KW - Analytical

KW - Boundary conditions

KW - Cavitation

KW - Lubrication

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DO - 10.1016/j.triboint.2011.11.021

M3 - Article

AN - SCOPUS:84857356896

SN - 0301-679X

VL - 48

SP - 182

EP - 190

JO - Tribology International

JF - Tribology International

ER -

On boundary conditions in lubrication with one dimensional analytical solutions

Abstract

Keywords

ASJC Scopus subject areas

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