On-the-Theory-of-Lubrication-and-Its-Application-t

doi:10.1098/rstl.1886.0005,157-2341771886Phil.Trans.R.Soc.Lond. OsborneReynolds DeterminationoftheViscosityofOliveOilExperimentalBeauchampTower'sExperiments,IncludinganOntheTheoryofLubricationandItsApplicationtoMr.  References:Emailalertingservicehereright-handcornerofthearticleorclickReceivefreeemailalertswhennewarticlescitethisarticle-signupintheboxatthetop:Phil.Trans.R.Soc.Lond.TosubscribetoThisjournalis©1886TheRoyalSocietyTheRoyalSocietyiscollaboratingwithJSTORtodigitize,preserve,andextendaccesstoPhilosophicalTransactionsoftheRoyalSocietyofLondon.®[157]IV.OntheTheOt'YofLubricationanditsApplicationtoMr.BEAUCHAMPTOWER'SExperiments,includinganExperimentalDeterminationoftheViscosityofOliveOil.ByP'rofessorOSBOH-NEREYNOLDS,LL.D.,F.R.S.ReceivedDecember29,1885,-ReadFebruary11,1886.[PLATE8.JCONTENTS.SECTIONI.-INTRODUCTORY.ARTICLE.Discordanceotexperimentalresults.•,.....,.....,.,.,.,..............•..,1Mr.TOWER'Sdiscoveryoftheseparatingfilmofoil,&c.......................,...2Thaideaofahydrodynamicaltheoryoflubrication....••.....,..,...,......•..3TheequationoflubricationmentionedbeforeSectionA,Montreal,andsubsequentlyintegrated.....................•..............••....................••4,Thecomparisonofthetheoreticalresultsw:ithexperimentalshowsatemperatureeffect5Determinationofthevariationofviscosityofoliveoilbringsthetheoryintocompleteaccordancewithexperiments,andshowshowvariouscircumstancesaffecttheresults...•..••.'.....,.'.....••.•..........................•...........•6Thedifferenceintheradiiofbrassandjournal,andthepointofnearestapproaehofbrasstojournal,andexplanationofincrease,Cl.heatingonfirstreversal.'.........'7Thelimitsofcompletelubrication,incompletelubrication,andnecking............7AThegeneralarrangementofthepaper..........................................8SECTIONn.-THEPROPERTIESOFLUBRICANTS.Definitionofviscosity...........................,............................'.9Thecharacterofviscosity.............'......•.........•..................,...10Thetwoviflcosities...•............,.................•,.........'............•11Expe~imentaldetermination'ofthevalueofftforoliveoil,&c.,f).gs:2and3,Table1.12Thecomparativevaluesforftfordifferentfluidsapddifferentunits.•.....•........13SEC'l'IONIlL-GENERAl!VIEWOFTHEACTIONOFLUBRICATION.Thecaseoftwonearlyparallelsurfacesseparatedbyaviscousfluid........•......14ThecltSeofrevolvingcylindricalsurface....,.................................15Theeffectoflimitedsupplyoflubricatingmaterial...................;.,...•....16Therelationbetweenresistance,load,andspeedforlimitedlubrication~.'.........17Theconditionsofequilibriumwithcylindricalsurfaces...•................,.....17.ATheweal'andheatingofbearings......,...,.....,...'....................18158PROFESSORO.REYNOLDSONTHE'fHEORYO:FLUBRICATIONSECTIONIV.-THIlEQUATIONSOFHYDRODYNAMICSASApPLIEDTOLUBRICATION.,\RTICLE.Thecompleteequationsforinteriorofviscousfluidsimplified....................19Theboundaryconditions.........•.....................................•.•..20Thefirstintegrationoftheresultingequations-equationsoflubrication...........•21Theconditionsunderwhichfurtherintegrationhasbeenundertaken.............•22SECTIONV.-ApPLICATION'1'0CASESINWHICHTHEEQUATIONSARECOMPLETELYINTEGRABLE.Parallelplanesurfacesapproachingeachother,thesurfaceshavingellipticalboundaries23Planesurfacesofunlimitedlength.....•.................•...•..•,.........•..24SECTIONVr.-THEINTEGRA'fIONOFTHEEQUATIONSFORCYLINDRICALSURFACES.Generaladaptationoftheequations.................................•.•.....•25Themethodofapproximateintegration.•........,............................•215Integrationoftheequations............................'..................•.•27SECTIONVII.-SOLUTIONOFTHEEQUATIONSFORCYLINDRICAl,SURFACES.cand~ismallcomparedwithunity.•.........•.......................•..••28Furtherapproximationtothesolutionoftheequationsforparticularvaluesofc,Plate8,figs.1,2,and3..........................................•.••..29~='5thelimittothismethodofintegrating.•.•.......,.......•.......•...•....29ASECTIONVIII.--,-'1'REEFFECTSOFHEATANDELAS'l'ICn'y.JLandaareonlytobeinferredfromexperiments.•...............•.•............30Theeffectoftheloadandthevelocitytoa,ltera...............•..•......•••....31Theeffectofspeedonthetemperature.............•....••...•...•...........•32Theformu!ffifortemperatureandfriction,andinterpretationofconstants,•...,....33Themaximumloadatanyspeed...•..•.••••..'................•........•...•..33ASECTIONIX.-ApPLICA'fIONOFTHEEQUATroNSTOMR.TOWER'SEXPERIMENTS.ReferencestoMr.TOWER'Sreports,TablesI.,IX.,andXII.......................34TheeffectofneckingthejOUl'nal.....................•........................35FirstapproximationtothedifferenceintheradiiofthejournalandbrassNo.1....36'1'heriseintemperatureofthefilm,owingtofriotion.........................•..37Theaotualtemperatureofthefilm...........