Approximate analytical solution to Reynolds equation for finite length journal bearings

Autores
Vignolo, Gustavo Gabriel; Barilá, Daniel O.; Quinzani, Lidia Maria
Año de publicación
2011
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The understanding of the behavior of hydrodynamic bearings requires the analysis of the fluid film between two solid surfaces in relative motion. The differential equation that governs the movement of this fluid, called the Reynolds equation, arises from the integration over the film thickness of the continuity equation, previously combined with the NavierStokes equation. An order of magnitude analysis, which is based on the relative value of the dimensions of the bearing, produces two dimensionless numbers that govern the behavior of the system: the square of the aspect ratio, length over diameter (L/D)2, and the eccentricity ratio (η). An analytical solution of the Reynolds equation can only be obtained for particular situations as, for example, the isothermal flow of Newtonian fluids and values of L/D→0 or L/D→∞. For other conditions, the equation must be solved numerically. The present work proposes an analytical approximate solution of the Reynolds equation for isothermal finite length journal bearings by means of the regular perturbation method. (L/D)2 is used as the perturbation parameter. The novelty of the method lays in the treatment of the Ocvirk number as an expansible parameter. The zero-order solution of the Reynolds equation (obtained for L/D→0), which matches the Ocvirk solution, may be used to describe the behavior of finite length journal bearings, up to L/D∼1/81/4, and relatively small eccentricities. The first-order solution obtained with the proposed method gives an analytical tool that extends the description of pressure and shear-stress fields up to L/D∼1/2 and η∼1/2 (or combinations of larger eccentricities with smaller aspect ratios, or vice versa). Moreover, the friction force and load-carrying capacity are accurately described by the proposed method up to L/D∼1 and η very near to 1.
Fil: Vignolo, Gustavo Gabriel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Planta Piloto de Ingeniería Química. Universidad Nacional del Sur. Planta Piloto de Ingeniería Química; Argentina
Fil: Barilá, Daniel O.. Universidad Nacional de la Patagonia; Argentina
Fil: Quinzani, Lidia Maria. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Planta Piloto de Ingeniería Química. Universidad Nacional del Sur. Planta Piloto de Ingeniería Química; Argentina
Materia
Hydrodynamic Lubrication
Journal Bearings
Regular Perturbation
Reynolds Equation
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/56209
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/56209
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Approximate analytical solution to Reynolds equation for finite length journal bearingsVignolo, Gustavo GabrielBarilá, Daniel O.Quinzani, Lidia MariaHydrodynamic LubricationJournal BearingsRegular PerturbationReynolds Equationhttps://purl.org/becyt/ford/2.4https://purl.org/becyt/ford/2The understanding of the behavior of hydrodynamic bearings requires the analysis of the fluid film between two solid surfaces in relative motion. The differential equation that governs the movement of this fluid, called the Reynolds equation, arises from the integration over the film thickness of the continuity equation, previously combined with the NavierStokes equation. An order of magnitude analysis, which is based on the relative value of the dimensions of the bearing, produces two dimensionless numbers that govern the behavior of the system: the square of the aspect ratio, length over diameter (L/D)2, and the eccentricity ratio (η). An analytical solution of the Reynolds equation can only be obtained for particular situations as, for example, the isothermal flow of Newtonian fluids and values of L/D→0 or L/D→∞. For other conditions, the equation must be solved numerically. The present work proposes an analytical approximate solution of the Reynolds equation for isothermal finite length journal bearings by means of the regular perturbation method. (L/D)2 is used as the perturbation parameter. The novelty of the method lays in the treatment of the Ocvirk number as an expansible parameter. The zero-order solution of the Reynolds equation (obtained for L/D→0), which matches the Ocvirk solution, may be used to describe the behavior of finite length journal bearings, up to L/D∼1/81/4, and relatively small eccentricities. The first-order solution obtained with the proposed method gives an analytical tool that extends the description of pressure and shear-stress fields up to L/D∼1/2 and η∼1/2 (or combinations of larger eccentricities with smaller aspect ratios, or vice versa). Moreover, the friction force and load-carrying capacity are accurately described by the proposed method up to L/D∼1 and η very near to 1.Fil: Vignolo, Gustavo Gabriel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Planta Piloto de Ingeniería Química. Universidad Nacional del Sur. Planta Piloto de Ingeniería Química; ArgentinaFil: Barilá, Daniel O.. Universidad Nacional de la Patagonia; ArgentinaFil: Quinzani, Lidia Maria. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Planta Piloto de Ingeniería Química. Universidad Nacional del Sur. Planta Piloto de Ingeniería Química; ArgentinaElsevier2011-09info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/56209Vignolo, Gustavo Gabriel; Barilá, Daniel O.; Quinzani, Lidia Maria; Approximate analytical solution to Reynolds equation for finite length journal bearings; Elsevier; Tribology International; 44; 10; 9-2011; 1089-10990301-679XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.triboint.2011.03.020info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0301679X11000752info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:52:19Zoai:ri.conicet.gov.ar:11336/56209instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-03 09:52:19.702CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Approximate analytical solution to Reynolds equation for finite length journal bearings
title Approximate analytical solution to Reynolds equation for finite length journal bearings
spellingShingle Approximate analytical solution to Reynolds equation for finite length journal bearings
Vignolo, Gustavo Gabriel
Hydrodynamic Lubrication
Journal Bearings
Regular Perturbation
Reynolds Equation
title_short Approximate analytical solution to Reynolds equation for finite length journal bearings
title_full Approximate analytical solution to Reynolds equation for finite length journal bearings
title_fullStr Approximate analytical solution to Reynolds equation for finite length journal bearings
title_full_unstemmed Approximate analytical solution to Reynolds equation for finite length journal bearings
title_sort Approximate analytical solution to Reynolds equation for finite length journal bearings
dc.creator.none.fl_str_mv Vignolo, Gustavo Gabriel
Barilá, Daniel O.
Quinzani, Lidia Maria
author Vignolo, Gustavo Gabriel
author_facet Vignolo, Gustavo Gabriel
Barilá, Daniel O.
Quinzani, Lidia Maria
author_role author
author2 Barilá, Daniel O.
Quinzani, Lidia Maria
author2_role author
author
dc.subject.none.fl_str_mv Hydrodynamic Lubrication
Journal Bearings
Regular Perturbation
Reynolds Equation
topic Hydrodynamic Lubrication
Journal Bearings
Regular Perturbation
Reynolds Equation
purl_subject.fl_str_mv https://purl.org/becyt/ford/2.4
https://purl.org/becyt/ford/2
dc.description.none.fl_txt_mv The understanding of the behavior of hydrodynamic bearings requires the analysis of the fluid film between two solid surfaces in relative motion. The differential equation that governs the movement of this fluid, called the Reynolds equation, arises from the integration over the film thickness of the continuity equation, previously combined with the NavierStokes equation. An order of magnitude analysis, which is based on the relative value of the dimensions of the bearing, produces two dimensionless numbers that govern the behavior of the system: the square of the aspect ratio, length over diameter (L/D)2, and the eccentricity ratio (η). An analytical solution of the Reynolds equation can only be obtained for particular situations as, for example, the isothermal flow of Newtonian fluids and values of L/D→0 or L/D→∞. For other conditions, the equation must be solved numerically. The present work proposes an analytical approximate solution of the Reynolds equation for isothermal finite length journal bearings by means of the regular perturbation method. (L/D)2 is used as the perturbation parameter. The novelty of the method lays in the treatment of the Ocvirk number as an expansible parameter. The zero-order solution of the Reynolds equation (obtained for L/D→0), which matches the Ocvirk solution, may be used to describe the behavior of finite length journal bearings, up to L/D∼1/81/4, and relatively small eccentricities. The first-order solution obtained with the proposed method gives an analytical tool that extends the description of pressure and shear-stress fields up to L/D∼1/2 and η∼1/2 (or combinations of larger eccentricities with smaller aspect ratios, or vice versa). Moreover, the friction force and load-carrying capacity are accurately described by the proposed method up to L/D∼1 and η very near to 1.
Fil: Vignolo, Gustavo Gabriel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Planta Piloto de Ingeniería Química. Universidad Nacional del Sur. Planta Piloto de Ingeniería Química; Argentina
Fil: Barilá, Daniel O.. Universidad Nacional de la Patagonia; Argentina
Fil: Quinzani, Lidia Maria. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Planta Piloto de Ingeniería Química. Universidad Nacional del Sur. Planta Piloto de Ingeniería Química; Argentina
description The understanding of the behavior of hydrodynamic bearings requires the analysis of the fluid film between two solid surfaces in relative motion. The differential equation that governs the movement of this fluid, called the Reynolds equation, arises from the integration over the film thickness of the continuity equation, previously combined with the NavierStokes equation. An order of magnitude analysis, which is based on the relative value of the dimensions of the bearing, produces two dimensionless numbers that govern the behavior of the system: the square of the aspect ratio, length over diameter (L/D)2, and the eccentricity ratio (η). An analytical solution of the Reynolds equation can only be obtained for particular situations as, for example, the isothermal flow of Newtonian fluids and values of L/D→0 or L/D→∞. For other conditions, the equation must be solved numerically. The present work proposes an analytical approximate solution of the Reynolds equation for isothermal finite length journal bearings by means of the regular perturbation method. (L/D)2 is used as the perturbation parameter. The novelty of the method lays in the treatment of the Ocvirk number as an expansible parameter. The zero-order solution of the Reynolds equation (obtained for L/D→0), which matches the Ocvirk solution, may be used to describe the behavior of finite length journal bearings, up to L/D∼1/81/4, and relatively small eccentricities. The first-order solution obtained with the proposed method gives an analytical tool that extends the description of pressure and shear-stress fields up to L/D∼1/2 and η∼1/2 (or combinations of larger eccentricities with smaller aspect ratios, or vice versa). Moreover, the friction force and load-carrying capacity are accurately described by the proposed method up to L/D∼1 and η very near to 1.
publishDate 2011
dc.date.none.fl_str_mv 2011-09
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/56209
Vignolo, Gustavo Gabriel; Barilá, Daniel O.; Quinzani, Lidia Maria; Approximate analytical solution to Reynolds equation for finite length journal bearings; Elsevier; Tribology International; 44; 10; 9-2011; 1089-1099
0301-679X
CONICET Digital
CONICET
url http://hdl.handle.net/11336/56209
identifier_str_mv Vignolo, Gustavo Gabriel; Barilá, Daniel O.; Quinzani, Lidia Maria; Approximate analytical solution to Reynolds equation for finite length journal bearings; Elsevier; Tribology International; 44; 10; 9-2011; 1089-1099
0301-679X
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1016/j.triboint.2011.03.020
info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0301679X11000752
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.13397

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