Braunovic - Electrical Contacts - Fundamentals, Applications and Technology [Missing Index] (CRC, 2007)

q 2006byTaylor&FrancisGroup, LLCq 2006by Taylor&FrancisGroup, LLCPrefaceThe multidisciplinary study of the electrical contact in modern engineering is signicant, but oftenneglected. The scientist and engineers who have spent their professional lives studying andapplying electrical contacts know that these components are critical to the successful operation ofall products that use electricity. In our civilization, all electricity transmission and distribution, mostcontrol, and most information exchange depends upon the passage of electricity through anelectrical contact at least once. The failure of an electrical contact has resulted in severeconsequences, e.g., an energy collapse of a megapolis, a failure of the telephone system, and eventhecrashofanairplane.Ragnar Holm, the prominent researcher, renowned engineer, and inventor, developed the validityof electrical contacts as its own technical discipline with his book Electric Contacts (1958). The50 years following its publication have given a rm conrmation of the accuracy of his predictionsandconclusions. Sincethat time, however, therehasbeenahugeincreaseintheapplicationofelectricalcontacts.Forexample,theeraoftheinformationhighwayandthedevelopmentoftheintegrated circuit have created new challenges in the use of electrical contacts. The use of electricalcontacts onthe microscopic scale presents numerous problems never consideredbypreviousgenerationsof researchersandengineers. ThefutureMEMS/NEMStechnologyisanother areawherethetheoryandpracticeoftheelectricalcontactisofcriticalimportance.The purpose of the authors has been to combine the progress in research and development in theareas of mechanical engineeringandtribology, whichHolmpostulatedtobekeysegments inelectrical contacts, with the new data on electrical current transfer, especially at themicro/nanoscale.This bookcomplements therecent volumeElectrical Contacts: Principles andApplications(publishedbyMarcelDekker,1999).Ittakesapracticalapplicationsapproachtothesubjectandpresents valuable design information for practicing mechanical and electrical engineers. In fact, theinformationcontainedherewillserveasanexcellentsourceofinformationnotonlyforanyonedeveloping equipment that uses electricity, but for postgraduate students who are concerned aboutthepassageofcurrentfromoneconductortoanother.The authors of this book have many years of research and practical experience. One unusual andinterestingaspect of the books development is that it comes throughthe cooperationof thedifferent approaches to the subject from the West and the East. They have succeeded in making thebulkof researchandengineeringdata equallyclear for all the segments of the internationalaudience.PaulG.SladeIthaca,NewYorkq 2006byTaylor&FrancisGroup, LLCThe AuthorsDr. Milenko Braunovicreceived his Dipl. Ing degree in technical physicsfrom the University of Belgrade, Yugoslavia, in 1962 and the M.Met. andPh.D. degrees inphysical metallurgyfromtheUniversityof Shefeld,Englandin1967and1969, respectively. From1971until 1997, hewasworking at Hydro-Quebec Research Institute (IREQ) as a senior member ofthe scienticstaff. He retired from IREQ in 1997 and established his ownscientic consulting company, MB Interface. From 1997 until 2000 he wasconsulting for the Canadian Electricity Association as a technologyadvisor. He is presently R&D manager with A.G.S. Taron Technologies inBoucherville,QC,Canada.During the last 30 years, Dr. Braunovic has been responsible for the development andmanagementofa broadrangeofresearch projects forHydro-Quebecandthe CanadianElectricalAssociation in the areas of electrical power contacts, connector design and evaluation, acceleratedtestmethodologies,andtribologyofpowerconnections.HehasalsoinitiatedandsupervisedtheR&D activities in the eld of shape-memory alloy applications in power systems. Dr. Braunovicisthe author of more than 100 papers and technical reports, including contributions to encyclopaediasandbooks, inhis particular areas of scienticinterests. Inaddition, hefrequentlylectures atseminars world wide and has presented a large number of papers at various internationalconferences.For his contributions to the science and practice of electrical contacts, Dr. Braunovic received theRagnar Holm Scientic Achievement Award in 1994, and for his long-term leadership and serviceto the HolmConference on Electrical Contacts he received, in 1999, the Ralph ArmingtonRecognitionAward. He is alsoa recipient of the 1994IEEECPMTBest Paper Award. Hesuccessfully chaired the Fifteenth International Conference on Electrical Contacts held in Montrealin1990, andwasatechnical programchairmanof theEighteenthInternational ConferenceonElectrical Contacts held in Chicago in 1996. He is a senior member of the Institute of Electronicsand Electrical Engineers (IEEE), the American Society for Metals (ASM), the Materials ResearchSociety (MRS), the Planetary Society, the American Society for Testing of Materials (ASTM), andTheMinerals,Metals&MaterialsSociety(TMS).Dr.ValeryKonchitswasbornonJanuary3,1949inthecityofGomel,Belarus.He graduated from Gomel State University in 1972. He receivedhis Ph.D. degree in tribology from the Kalinin Polytechnic Institute, Russiain1981.In 1972, he joined the Metal-Polymer Research Institute of the NationalAcademy of Sciences of Belarus in Gomel. In 1993, he became the head ofthe laboratory in the Tribology Department. Since 2001, Dr. Konchits hasbeenDeputyDirectoroftheMetal-PolymerResearchInstitute.The scientic interests of Dr. Konchits lie mainly in electricalcontacts frictionandwear, contact phenomenaat their interfaces, andelectrophysical diagnosticmethodsoffriction. Heistheauthorofmorethan 80 papers and holds 10 patents. He is also the co-author of a monograph in Russian, Tribologyofelectricalcontacts(authors:KonchitsV.V.,MeshkovV.V.,MyshkinN.K.,1986,Minsk).q 2006byTaylor&FrancisGroup, LLCProf. Nikolai Myshkin was born on May 12, 1948 in the city of Ivanovo,Russia. He graduated from the Power Engineering Institute in 1971 with adegreeinelectromechanics.HasreceivedhisPh.D.fromtheInstituteforProblems in Mechanics of the Russian Academy of Sciences in 1977. Thesame year, he joined the Metal-Polymer Research Institute in Gomel wheresince1990hehasbeenHeadoftheTribologyDepartment. Hehasalsobeenthedirector of MPRI since2002. Heearnedhis Dr.Sc. degreeintribology in 1985 and became a full professor of materials science in 1991.He was elected as a correspondent member of the Belarus NationalAcademyofSciencesin2004.He received the USSR National Award for Young Scientists in 1983, theAwardforBest ResearchgivenbytheBelarusNational AcademyofSciencesin1993, andtheAwardoftheRussianGovernmentinScienceandTechnologyin2004.The scientic interests of Prof. Myshkin lie mainly in the characterization at micro and nanoscalesurfaces, the contact mechanics of solids, wear monitoring, electric phenomena in friction,tribotestingequipment,andaerospaceengineering.Hehasauthoredorco-authoredmorethan180papersand60patents.Heisaco-authoroftheTribology Handbook (Russian edition 1979, English translation 1982), monographs Physics,Chemistry and Mechanics of Boundary Lubrication (1979), Tribology of Electric Contacts (1986),AcousticandElectricMethods inTribology(Russianedition1987, Englishtranslation1990),StructureandWearResistanceofSurfaceLayers(1991), TextbookinMaterialsScience(1989),Magnetic Fluids in Machinery (1993), the English textbook Introduction to Tribology (1997), andTribology:PrinciplesandApplications(2002).Prof. Myshkin is chairman of the Belarus Tribology Society and vice-president of theInternational Tribology Council. He is also assistant editor-in-chief of the Journal of Friction andWear,andamemberofeditorialboardsofTribologyInternational,TribologyLetters,IndustrialLubrication and Tribology, and the International Journal of Applied Mechanics and Engineering.q 2006by Taylor&FrancisGroup, LLCAcknowledgmentsIn the preparation of the book, the authors have used a large number of published materials, either inthe formof papers in referenced journals, or fromthe websites of different companies andorganizations.Inbothcases,properpermissionsforusingthesematerialshavebeenobtained.Inmanyinstances, theauthorsobtainedtherequiredinformationdirectlyfromtheauthorsof thepapersorfromthecompanyauthorities.The authors are indebted to Dr. Paul Slade for writing the preface of the book. Special thanks gotoDr.DanielGagnonofHydro-QuebecResearchInstitute(IREQ)inVarennes,QC,Canadaforprovidingessentialreferencematerialandfruitfuldiscussionsconcerningcertaintopicsofpowerconnections.Theauthors aregrateful toDr. Mark. I. Petrokovets for fruitful discussionandhis helpinpreparation of Chapters 2, 3 and 5. We also thank Dr. Denis Tkachuk for his valuable assistance inpreparationofthemanuscript.Acknowledgementismadetothemanyindividualsandcompanyauthoritiesforpermissiontouse the original material and, in particular, to modify the original gures to maintain the uniformityof graphic presentationthroughout the book. The followingis a list of these individuals andcompanyauthorities.Prof. George M. Pharr, Department of Materials Science and Engineering, University ofTennessee, Knoxville, USAfor providingthe papers onnanoindenationtesting methods andinstrumentationandallowingmodicationofsomeoftheguresappearinginthesepapers.Prof.DorisKuhlmann-Wilsdorf,DepartmentofMaterials ScienceandEngineering, Universityof Virginia, Charlottesville, USAfor permissiontouse the informationonber-brushes anddislocationnatureoftheprocessesoccurringduringfriction.Dr. Roland Timsit of Timron Scientic Consulting, Inc., Toronto, Canada for permission to usetherelevantmaterialfromhispapersandpublications.Dr.RobertMalucciofMolex,Inc.,Lisle,IL,USA,forpermissiontousetherelevantmaterialfrom his papers and publications and modify some of the gures from his original publications citedinthisbook.Dr. Bill Abbott of Batelle, USA for helpful suggestions and discussions regarding the problemsofcorrosioninelectricalandelectronicconnections.Dr.SophieNoel,LaboratoiredeGenieElectrique,Supelec,GifsurYvette,Franceforhelpfuldiscussionsconcerningthelubricationofelectrical contactsandpermissiontousesomeofdatafromthepublicationscitedinthisbook..Dr. Magne Runde of the Norwegian University of Science and Technology, Norway, for helpfuldiscussionsconcerningtheproblemofelectromigrationinelectricalcontacts.Prof. ZoranDjuricandMilosFrantlovicoftheCenterforMicroelectronicsTechnologiesandSingle Crystals, MTM, University of Belgrade, Serbia and Montenegro for providing theinformationonthewirelesstemperaturemonitoringsystem.Dr. Bella Chudnovsky of Square D, USA, for helpful discussions concerning the whiskerformation in electrical contacts and for permission to use the information on the On-Line WirelessTemperatureMonitoringSystemforLV,MVelectricalequipmentfondon thecompanywebsite(http://www.squared.com).Prof.L.K.J.VandammeoftheDepartmentofElectricalEngineering,EindhovenUniversityofTechnology, The Netherlands for providing and allowing the use of reference materials concerningthenoiseinelectricalconnections.Mr. Larry Smith of USi, Armonk, NY, USA, for permitting the use of the images anddescriptions of the Power-donut unit found on the company web site (http://www.usi-power.com).q 2006byTaylor&FrancisGroup, LLCDr. Young-kook (Ryan)Yoo, Director ofGlobalSalesandMarketing ofPSIA Corp.Sungnam462-120, Korea, for permissiontousedescriptionsof different surfaceanalytical equipment aspostedonthecompanywebsite(http://www.psiainc.com.).Dr.G.PalumboofIntegranTechnologies,Inc.,Toronto,Canadaforprovidingtheinformationonthegrainsizeeffectsinnanocrystallinematerials(http://www.integran.com).Mr. J. Renowden of Transpower New Zealand, for providing the information concerning the eldapplicationsofthemicroohmeterOhmstikonpowerlines(http://www.transpower.co.nz).Mr. J. LeboldofBoldstarinfrared, Canadaforpermissiontousetheinfraredimagesfromthecompanywebsite(http://www.boldstarinfrared.com).R.N. Wurzbach of Maintenance Reliability Group (MRG), York, PA, USA for permission to usedescription of the web-based cost benet analysis method for predictive maintenance(http://www.mrgcorp.com).ndb Technologie, Inc., Quebec, Canada for permission to use the information about themicroohmetersfoundontheirwebsite(http://www.ndb.qc.ca).In addition, the authors would like to acknowledge the courtesy of the following companies forallowing the use of the information found on their respective websites: Omega Madge Tech., Inc.,(http://www.omega.com), FLIRSystems (http://www.irthermography.com), Mikron Infrared,Inc.(http://www.irimaging.com),ElectrophysicsCorp.(http://www.electrophysics.com),InfraredSolution, Inc. (http://www.infraredsolutions.com), ElwoodCorp. (http://www.elwoodcorp.com),SensolinkCorp.,(http://www.sensorlink.com).Lastly,itisapleasuretoacknowledgeandexpressourgratitudetoMrs.K.Braunovicforhergeneroushospitalityshowntotheauthorsduringthepreparationofthebookmanuscript.q 2006by Taylor&FrancisGroup, LLCIntroductionThis book provides detailed analytical models, state-of-the-art techniques, methodologies and toolsusedtoassessandmaintainthereliabilityofabroadclassofmovingandpermanent electricalcontacts in many technological devices, such as automotive and aerospace components, high- andlow-power contact joints, slidingandbreakingcontacts, electronicandcontrol apparatus, andelectromechanical systems. It providesacomprehensiveoutlineof thetribological behavior ofelectrical contacts that is rarely discussed in the existing literature; these are problems ofconsiderableinterestforresearchersandengineers.Focusing on the main mechanical and electrical problems in connections with the eldapplicationsandtherelationshipbetweenstructureandproperties, thisvolumeprovidesawell-balancedtreatment of themechanicsandthematerialsscienceofelectrical contacts, whilenotneglectingtheimportanceoftheirdesign,development,andmanufacturing.Thebookprovidesacomplete introductionto electric conductionacross a contacting interfaceas a function of surfacetopography, load, and physical-mechanical properties of materials, and the interrelation ofelectrical performance with friction and wear; it takes into account material properties and lubricanteffects. Consideration is given to the deleterious effects of different degradation mechanisms, suchas stress relaxation/creep, fretting, differential thermal expansion, and the formation ofintermetallics, as well as their impacts on operating costs, safety, network reliability, powerquality. Various palliative measures toimprove the reliabilityandserviceabilityof electricalcontactatmacro-,micro-,andnano-levelsarealsodiscussed.This bookdiminishes alargegapbetweenengineeringpracticewidelyutilizingempiricallyfoundmethods for designingandoptimizingthecontact characteristics andtheoryrelatingtotribological and electromechanical characteristics of the contacts. The main trends in the practicalsolutions of the tribological problems in electrical contacts are discussed in terms of contact design,research and development of contact materials, coatings and lubricants and the examples ofpracticalapplicationsinvariouseldsaregiventhroughoutthebook.Covering a wide range of references, tables of contact materials, coatings and lubricationproperties, as well as various testing procedures used to evaluate these properties, the book will beanindispensablepracticaltoolforprofessional,research,designanddevelopmentengineers.Thebook (or parts of it) can be used not only as a reference, but also as a textbook for advanced graduatestudents and undergraduates, as it develops the subject from its foundations and contains problemsandsolutionsforeachchapter.q 2006byTaylor&FrancisGroup, LLCTable of ContentsPartIFundamentalsofElectricalContacts ................................................................................................1MilenkoBraunovic,ValeryV.Konchits,andNikolaiK.MyshkinChapter1IntroductiontoElectricalContacts ..........................................................................31.1 Introduction..............................................................................................................................31.2 SummaryofBasicFeatures......................................................................................................6Chapter2ContactMechanics ....................................................................................................92.1 SurfaceofSolids ......................................................................................................................92.2 SurfaceTopography ..............................................................................................................112.3 ModernTechniquesofMeasuringSurfaceParameters........................................................172.4 ContactofSmoothSurfaces..................................................................................................212.4.1 PlasticandElastoplasticContacts............................................................................ 232.5 ContactbetweenRoughSurfaces ..........................................................................................272.5.1 GreenwoodWilliamsonModel ................................................................................ 272.5.2 MultilevelModel ...................................................................................................... 292.5.3 TransitionfromElastictoPlasticContact ................................................................ 33Chapter3Tribology ................................................................................................................353.1 Friction....................................................................................................................................353.1.1 LawsofFriction ........................................................................................................ 353.1.2 RealContactArea .................................................................................................... 383.1.3 InterfacialBonds(AdhesionComponentofFriction) .............................................. 383.1.4 DeformationatFriction............................................................................................ 413.1.5 FrictionasaFunctionofOperatingConditions ...................................................... 423.1.6 ThePreliminaryDisplacement .................................................................................. 443.1.7 Stick-SlipMotion ...................................................................................................... 463.2 Wear........................................................................................................................................473.2.1 StagesofWear .......................................................................................................... 483.2.2 SimpleModelofWear .............................................................................................. 483.2.3 BasicMechanismsofWear...................................................................................... 503.2.4 AbrasiveWear .......................................................................................................... 523.2.5 AdhesiveWear .......................................................................................................... 563.2.6 ProwFormation........................................................................................................ 573.2.7 FatigueWear.............................................................................................................. 573.2.8 CorrosiveWear.......................................................................................................... 593.2.9 FrettingWear............................................................................................................ 593.2.10 Delamination.............................................................................................................. 623.2.11 Erosion...................................................................................................................... 643.2.12 CombinedWearModes............................................................................................ 643.3 Lubrication..............................................................................................................................653.4 CurrentTrendsinTribology ..................................................................................................67q 2006byTaylor&FrancisGroup, LLCChapter4ContactMaterials ....................................................................................................714.1 MetallicContactMaterials....................................................................................................714.1.1 PropertiesofContactMaterials................................................................................ 714.1.1.1 Copper........................................................................................................714.1.1.2 Aluminum..................................................................................................754.1.1.3 Silver..........................................................................................................764.1.1.4 Platinum......................................................................................................784.1.1.5 Palladium....................................................................................................784.1.1.6 Gold ............................................................................................................794.1.1.7 Rhodium......................................................................................................794.1.1.8 Tungsten......................................................................................................794.1.1.9 Nickel ..........................................................................................................804.1.2 MetalsandAlloysforHeavy-andMedium-DutyContacts .................................... 804.1.3 MetalsandAlloysforLight-DutyContacts ............................................................ 834.1.4 MaterialsforLiquid-MetalContacts ........................................................................ 854.1.5 SpringContactMaterials.......................................................................................... 874.1.6 Shape-MemoryAlloysandTheirApplicationsinElectricalContacts.................... 884.2 CoatingsforElectricalContacts ............................................................................................894.2.1 BasicRequirements.................................................................................................. 894.2.2 SurfaceEngineeringTechnologies............................................................................ 914.2.2.1 SurfaceSegregation....................................................................................924.2.2.2 IonImplantation ........................................................................................944.2.2.3 Electroplating..............................................................................................944.2.2.4 ElectrolessPlating ......................................................................................974.2.2.5 Cladding......................................................................................................974.2.2.6 ChemicalDeposition ..................................................................................994.2.2.7 PlatingbySwabbing..................................................................................994.2.2.8 PhysicalVaporDepositionTechnology ....................................................994.2.2.9 Electro-SparkDeposition(ESD) ..............................................................1004.2.2.10 IntermediateSublayers ............................................................................1014.2.2.11 MultilayeredContacts ..............................................................................1014.2.3 CoatingMaterials .................................................................................................... 1024.2.3.1 CoatingsforPowerConnectors(CopperandAluminumJoints)............1024.2.3.2 CoatingsforElectronic/ElectricalApplications ......................................1044.3 CompositeContactMaterials..............................................................................................1114.3.1 CompositeMaterialsforContactsofCommutatingApparatuses.......................... 1114.3.2 Self-LubricatingCompositesforSlidingContacts................................................ 1184.4 NanostructuredMaterials ....................................................................................................1254.4.1 BulkPropertiesNanomaterials ............................................................................ 1274.4.2 MechanicalProperties ............................................................................................ 1274.4.3 ElectricalProperties ................................................................................................ 1314.4.4 MagneticProperties................................................................................................ 1364.4.4.1 GiantMagnetoresistance(GMR) ............................................................1364.4.4.2 BallisticMagnetoresistance(BMR) ........................................................1384.4.5 Nanotubes ................................................................................................................ 1404.4.6 ThermalStability.................................................................................................... 1424.4.7 CharacterizationTechniquesforNanostructuredMaterials.................................. 1434.4.7.1 Nanoindentation........................................................................................1434.4.7.2 ScanningProbeMicroscopes ..................................................................144q 2006by Taylor&FrancisGroup, LLCChapter5CurrentandHeatTransferacrosstheContactInterface ......................................1495.1 ContactResistance................................................................................................................1495.1.1 CircularandNoncirculara-Spots............................................................................ 1495.1.2 EffectofSignalFrequency...................................................................................... 1545.1.3 SizeEffects,Nanocontacts ...................................................................................... 1575.1.4 EffectofSurfaceFilms............................................................................................ 1605.1.5 EffectofContactGeometry .................................................................................... 1665.1.6 ConductivityofRoughContact .............................................................................. 1725.2 InterfacialHeating................................................................................................................1805.2.1 PrinciplesofHeatConductionTheory .................................................................. 1815.2.2 SimpleProblemsofHeatConductionTheory........................................................ 1835.2.3 ContactSpotsHeatedbyElectricalCurrent .......................................................... 1885.2.3.1 Film-FreeMetalContact ..........................................................................1885.2.3.2 HeatingofContactSpotsHavingSurfaceFilms....................................1905.2.3.3 FieldIntensityintheContactClearancewithTunnel-ConductiveFilms........................................................................1945.2.4 FormulationofHeatProblemwithFriction.......................................................... 1955.2.5 FlashTemperatureofElectricalContact ................................................................ 1985.2.6 ThermalInstabilityofFrictionContact .................................................................. 2005.2.6.1 ThermoelasticInstability..........................................................................2015.2.6.2 InstabilityCausedbyTemperature-DependentCoefcientofFriction ..............................................................................2025.2.6.2 InstabilityRelatedtoFrictionModeVariation........................................202Chapter6ReliabilityIssuesinElectricalContacts ..............................................................2056.1 SignicanceofElectricalContactsReliability....................................................................2056.2 ElectricalContactRequirements..........................................................................................2066.3 FactorsAffectingReliability ................................................................................................2066.4 ConnectionDegradationMechanisms..................................................................................2086.4.1 ContactArea ............................................................................................................ 2096.4.2 Oxidation ................................................................................................................ 2116.4.3 Corrosion.................................................................................................................. 2126.4.4 Fretting.................................................................................................................... 2146.4.4.1 MechanismsofFretting............................................................................2176.4.4.2 FactorsAffectingFretting ........................................................................2196.4.4.3 FrettinginElectricalContacts..................................................................2196.4.4.4 ContactLoad ............................................................................................2216.4.4.5 FrequencyofMotion................................................................................2236.4.4.6 SlipAmplitude..........................................................................................2246.4.4.7 RelativeHumidity ....................................................................................2246.4.4.8 Temperature..............................................................................................2266.4.4.9 EffectofCurrent ......................................................................................2266.4.4.10 SurfaceFinish..........................................................................................2286.4.4.11 Hardness....................................................................................................2296.4.4.12 MetalOxide ..............................................................................................2306.4.4.13 CoefcientofFriction ..............................................................................2306.4.4.14 ElectrochemicalFactor............................................................................2306.4.5 IntermetallicCompounds ........................................................................................ 230q 2006byTaylor&FrancisGroup, LLC6.4.5.1 EffectofElectricalCurrent ......................................................................2326.4.6 Electromigration ...................................................................................................... 2376.4.7 StressRelaxationandCreep.................................................................................... 2406.4.7.1 NatureoftheEffectofElectricCurrent ..................................................2416.4.7.2 EffectofElectricCurrentonStressRelaxation ......................................2426.4.8 ThermalExpansion.................................................................................................. 2476.5 ImpactofConnectionDegradation......................................................................................2486.5.1 PrognosticModelforContactRemainingLife ...................................................... 2506.5.2 EconomicalConsequencesofContactDeterioration............................................ 2566.5.3 PowerQuality.......................................................................................................... 258PartIIApplicationsofElectricalContacts ..............................................................................................261MilenkoBraunovic,ValeryV.Konchits,andNikolaiK.MyshkinChapter7PowerConnections ................................................................................................2637.1 TypesofPowerConnectors ................................................................................................2637.2 DesignFeaturesandDegradationMechanisms..................................................................2637.2.1 BoltedConnectors .................................................................................................. 2637.2.1.1 FrettinginBoltedConnectors ..................................................................2697.2.1.2 FrettinginAluminumConnections..........................................................2717.2.1.3 Intermetallics ............................................................................................2727.2.1.4 CreepandStressRelaxation ....................................................................2757.2.2 Bus-StabContacts.................................................................................................... 2767.2.3 CompressionConnectors........................................................................................ 2797.2.3.1 DegradationMechanismsinCompressionConnectors ..........................2817.2.3.2 Corrosion ..................................................................................................2827.2.3.3 FrettinginCompressionConnectors........................................................2837.2.4 MechanicalConnectors .......................................................................................... 2847.2.4.1 Binding-HeadScrewConnectors ............................................................2857.2.4.2 InsulationPiercingConnectors ................................................................2897.2.4.3 WedgeConnectors....................................................................................2897.2.5 WeldedConnectors.................................................................................................. 2907.3 MitigatingMeasures............................................................................................................2927.3.1 ContactAreaConnectorDesign............................................................................ 2927.3.2 ContactPressure ...................................................................................................... 2947.3.3 SurfacePreparation.................................................................................................. 2967.3.4 MechanicalContactDevices.................................................................................. 2977.3.4.1 Retightening..............................................................................................3007.3.4.2 BimetallicInserts......................................................................................3017.3.4.3 TransitionWashers..................................................................................3017.3.4.4 MultilamContactElements......................................................................3027.3.4.5 Shape-MemoryAlloyMechanicalDevices ............................................3027.3.4.6 Self-RepairingJoints ................................................................................3037.3.5 Lubrication:ContactAidCompounds .................................................................... 3047.4 InstallationProcedures ........................................................................................................306q 2006by Taylor&FrancisGroup, LLCChapter8ElectronicConnections..........................................................................................3098.1 TypesofElectronicConnections ........................................................................................3098.2 MaterialsforElectronicConnections ..................................................................................3098.2.1 SolderMaterials...................................................................................................... 3108.2.2 Lead-FreeSolders.................................................................................................... 3128.2.2.1 Tin............................................................................................................3128.2.2.2 TinSilver ................................................................................................3128.2.2.3 TinSilverBismuth..................................................................................3138.2.2.4 TinSilverCopper....................................................................................3138.2.2.5 TinSilverCopperAntimony................................................................3148.2.2.6 TinSilverAntimony..............................................................................3148.2.2.7 TinBismuth............................................................................................3148.2.2.8 TinCopper ..............................................................................................3158.2.2.9 TinIndium..............................................................................................3158.2.2.10 TinIndiumSilver....................................................................................3168.2.2.11 TinZinc....................................................................................................3168.2.2.12 TinZincSilver ........................................................................................3168.2.2.13 TinZincSilverAluminumGallium....................................................3178.3 DegradationMechanismsinElectronicConnections..........................................................3178.3.1 Porosity .................................................................................................................... 3198.3.2 Corrosion/Contamination ........................................................................................ 3228.3.2.1 PoreCorrosion..........................................................................................3228.3.2.2 CreepCorrosion........................................................................................3238.3.2.3 Tarnishing................................................................................................3248.3.3 Fretting.................................................................................................................... 3278.3.4 FrictionalPolymerization ........................................................................................ 3348.3.5 IntermetallicCompounds ........................................................................................ 3368.3.6 CreepandStressRelaxation.................................................................................... 3488.3.7 Electromigration ...................................................................................................... 3538.3.8 Whiskers .................................................................................................................. 3578.4 MitigatingMeasures............................................................................................................3618.4.1 EffectofCoating .................................................................................................... 3618.4.1.1 GoldCoatings..........................................................................................3618.4.1.2 PalladiumandPalladiumAlloys..............................................................3628.4.1.3 TinCoatings ............................................................................................3648.4.1.4 NickelandNickel-BaseAlloys................................................................3648.4.2 EffectofLubrication.............................................................................................. 364Chapter9SlidingContacts....................................................................................................3699.1 TribologyofElectricalContacts ..........................................................................................3699.1.1 InterrelationofFrictionandElectricalProcesses.................................................. 3709.1.2 RoleofBoundaryFilms .......................................................................................... 3719.1.3 MainMeansofImprovingReliabilityofSlidingContacts.................................... 3719.1.4 TribophysicalAspectsintheDevelopmentofSlidingContacts............................ 3739.2 DryMetalContacts ..............................................................................................................3769.2.1 Low-CurrentContacts ............................................................................................ 3769.2.1.1 EffectsofLowCurrentandElectricalFieldonFriction ........................3779.2.1.2 EffectofInterfacialShear ........................................................................378q 2006byTaylor&FrancisGroup, LLC9.2.1.3 Adhesion,Transfer,WearDebrisFormation,andSurfaceTransformation............................................................................3809.2.2 High-CurrentContacts............................................................................................ 3869.2.2.1 EffectsofElectricalCurrentonTribologicalBehavior ..........................3869.2.2.2 InuenceofElectricFields ......................................................................3909.2.2.3 EffectofVelocity....................................................................................3929.2.2.4 EffectofMaterialCombinationofContactingMembers........................3939.2.2.5 ElectroplasticEffectinSlidingContact..................................................3949.2.2.6 FrictionandCurrentTransferinMetalFiberBrushContacts ................3969.2.3 StabilityoftheContactResistance.ElectricalNoise............................................ 4009.2.3.1 ContactNoiseinClosedConnections......................................................4009.2.3.2 ElectricalNoiseinSlidingContacts ........................................................4029.3 LubricatedMetalContacts ..................................................................................................4149.3.1 Introduction.LubricationFactors............................................................................ 4149.3.2 ElectricalPropertiesofLubricatingBoundaryLayers.......................................... 4159.3.3 ConductivityofLubricatedContacts ...................................................................... 4199.3.3.1 EffectofLubricantonConductivityneartheContactSpots ..................4199.3.3.2 EffectofLubricantonConductivityofContactSpots............................4209.3.3.3 ExperimentalStudiesofElectricConductivityofLubricatedContacts ............................................................................4279.3.3.4 ContactResistancebetweenVerySmoothLubricatedSurfaces ............4309.3.3.5 TemperatureDependenciesofContactConductivity..............................4319.3.4 LubricationFactorsinSlidingContacts ................................................................ 4339.3.4.1 EffectofLubricantOrigin........................................................................4349.3.4.2 LubricantDurability................................................................................4359.3.4.3 TribochemicalAspectsofLubrication....................................................4389.3.4.4 EffectofVelocityinLight-CurrentContacts ..........................................4419.3.4.5 EffectsofLubricantContactProperties..................................................4429.3.4.6 CurrentPassageandFrictioninHigh-CurrentLubricatedContacts..................................................................................4449.3.5 LubricantsforElectricalContacts .......................................................................... 4499.3.5.1 LubricantsforSlidingElectricSwitchContacts ....................................4509.3.5.2 LubricantsforSlidingContactsofSensors ............................................4519.3.5.3 SelectionofContactLubricants..............................................................4549.4 CompositeContacts..............................................................................................................4549.4.1 EffectofIntermediateLayersonElectricalCharacteristics.................................. 4559.4.1.1 StructureandElectricalPropertiesofIntermediateFilms ......................4569.4.1.2 MechanismofCurrentPassagethroughtheContactwithIntermediateFilms....................................................................................4609.4.1.3 InuenceofPolarityonConductivityinCompositeMetalContact ........................................................................4679.4.2 TheLubricatingEffectofElectricalCurrent ...................................................... 4719.4.2.1 EffectofCurrentonFrictionCharacteristics..........................................4719.4.2.2 MechanismoftheLubricatingActionoftheElectricCurrent............4739.4.2.3 EffectofBrushMaterialonFrictionBehaviorwithElectricCurrent ........................................................................................4779.4.3 ElectricalWear ........................................................................................................ 4799.4.3.1 WearofCurrentlessContacts ..................................................................4799.4.3.2 EffectofCurrentonWear........................................................................4809.4.3.3 FactorsLeadingtoElectricalWearintheAbsenceofSparking ................................................................................483q 2006by Taylor&FrancisGroup, LLC9.4.3.4 InuenceoftheElectricFieldintheClearance ......................................4899.4.3.5 WearwithSparkingandArcing ..............................................................4919.4.3.6 SomeWaystoReduceElectricalWear..................................................493PartIIIDiagnosticandMonitoringTechnologies....................................................................................495MilenkoBraunovic,ValeryV.Konchits,andNikolaiK.MyshkinChapter10ElectricalMethodsinTribology..........................................................................49710.1 SurfaceCharacterization ....................................................................................................49710.2 DiagnosisofContactAreaandFrictionRegimes ............................................................50310.2.1 FormationofContactArea.................................................................................. 50310.2.2 ControlofSlidingContactwiththePresenceofOxideFilms .......................... 50810.2.3 ExperimentalStudyofMetallicContactSpotsFormation ................................ 50910.3 EvaluationofTribologicalPerformanceofMaterialsandLubricants..............................51110.3.1 EvaluationofLoad-BearingCapacityandLubricityofSurfaceFilms ............ 51110.3.2 EstimationofLubricantInterlayerShearStrengthunderImperfectLubrication.......................................................................................................... 51510.3.3 EvaluationofThermalStabilityofMaterialsandLubricantsbyElectricalMethods.......................................................................................... 51710.3.4 ControlofSurfaceCoatingsandFilms .............................................................. 51910.3.5 NovelSystemsforMeasuringandAnalysisofContactCharacteristics............ 52110.3.5.1 MethodofTriboscopy ....................................................................523Chapter11MonitoringTechnologies ......................................................................................52911.1 ThermalMeasurements ......................................................................................................53011.1.1 InfraredThermography........................................................................................ 53211.1.2 BasicFeaturesofInfraredThermography .......................................................... 53211.1.3 TypesofInfraredThermalSystems.................................................................... 53411.1.4 SMETemperatureIndicators .............................................................................. 53811.1.5 TemperatureStickers(Labels) ............................................................................ 54011.1.6 RemoteTemperatureSensors.............................................................................. 54111.2 ResistanceMeasurements..................................................................................................54211.3 MonitoringContactLoad(Pressure)..................................................................................54511.4 UltrasonicMeasurements ..................................................................................................54611.5 WirelessMonitoring..........................................................................................................54811.6 CostBenetsofMonitoringandDiagnosticTechniques..................................................552Appendix 1:Methods ofDescriptionof RoughSurface ........................................................555Appendix 2:Shape-Memory Materials....................................................................................565Appendix 3:ElectricalContactTables ....................................................................................585References....................................................................................................................................599q 2006byTaylor&FrancisGroup, LLC1Introduction to ElectricalContacts1.1INTRODUCTIONAnelectricalcontactisdenedastheinterfacebetweenthecurrent-carryingmembersofelectri-cal/electronicdevicesthat assurethecontinuityof electriccircuit, andtheunit containingtheinterface. Thecurrent-carryingmembers incontact, oftenmadeof solids, arecalledcontactmembersor contact parts. Thecontact membersconnectedtothepositiveandnegativecircuitclampsarecalledtheanodeandcathode,respectively.Electrical contacts provideelectrical connectionandoftenperformother functions. Theprimarypurposeof anelectrical connectionistoallowtheuninterruptedpassageof electricalcurrent acrossthecontact interface. It isclear that thiscanonlybeachievedif agoodmetal-to-metalcontactisestablished.Theprocessesoccurringinthecontactzonearecomplexandnotfully explained within the limits of present knowledge. Although the nature of these processes maydiffer, theyareallgovernedbythesamefundamentalphenomena, themostimportantbeingthedegradationof thecontactinginterfaceandtheassociatedchangesincontact resistance, load,temperature,andotherparametersofamultipointcontact.Electrical contactscanbeclassiedaccordingtotheirnature, surfacegeometry, kinematics,designandtechnologyfeatures, current load, application, andbyothersmeans.13Ingeneral,electrical contactscanbedividedintotwobasiccategories: stationaryandmoving. Figure1.1representsthemost general classicationofelectrical contactsaccordingtocontact kinematics,functionality,anddesignfeatures.Instationarycontacts, contact membersareconnectedrigidlyorelasticallytothestationaryunit of a device to provide the permanent joint. Stationary contacts are divided into nonseparable orall-metal(welded,soldered,andglued),andclamped(bolted,screwed,andwrapped).Nonsepar-able(permanent)jointshaveahighmechanicalstrengthandprovidethestableelectricalcontactwith a low transition resistance. A nonseparable joint is often formed within one contact member.For example, in commutating devices, only materials with a complex composition and arc-resistantworkinglayersareusedasthecontact members. Theyaremadebycontact welding, soldering,coating,deposition,electrosparkalloying,andmechanicalmethodsofjoining.Clamped contacts are made by mechanically joining conductors directly with bolts or screws orusingintermediateparts,specically,clamps.Thesecontactsmaybeassembledordisassembledwithoutdamagingthejointintegrity. Thesimplestcaseofaclampedcontact isthejointoftwomassive conductors with at contact surfaces, such as busbars. A more complex joint congurationis a contact comprising several conductors, such as joints of a multistrand wire and clamp that areusedforjoiningwireconductorsintransmissionlines.Thenatureof clampedandall-metal contactsisdifferent. Thisisbecauseintheall-metalcontacts there is no physical interface between conductors, whereas in clamped contacts the inter-faceis controlledbythecontact pressureandtheabilityof thematerial toundergoplastic3q 2006byTaylor&FrancisGroup, LLCdeformation. The lowerthe specicresistance and hardness of a material,the higher its corrosionresistanceand, consequently, thelowerthecontacttransitionresistance. Forthisreason, contactsurfaces are usually covered with soft, corrosion-resistant materials such as tin, silver, cadmium, orsimilar materials. Different surface cleaning techniques are often used to improve thejointconnectability.Inmovingcontacts, at least onecontact member isrigidlyor elasticallyconnectedtothemovingunit of adevice. Dependingontheir operatingconditions, thesecontacts aredividedintotwocategories: commutatingandsliding. Commutatingcontactsintermittentlycontrol theelectric circuit. They fall into two categories: separable (various plug connectors, circuit breakers)and breaking. The latter are used for a periodical closing and opening of an electrical circuit, such asindifferent switches, contactors, relays, andsimilardevices. Becauseofdifferencesinbreakingpower, current, and voltage, there is a great variety of breaking contacts. The breaking contacts canbeclassiedaslight-,medium-andheavy-duty:Light-duty contacts carry very lowcurrents, operate at voltages up to 250 V, and display noappreciable arc-related electrical wear. The successful operation of these devices dependsmainly on maintaining relatively low and stable contact resistance and also on the selec-tion of the contact materials. The factors that must be taken into account are tendency tooxidize (tarnish); presence of dirt, dust or other contaminants on the contact surface; andcontact design (form, size, contact pressure, and nish). Light-duty contacts are intendedforuseininstrumentcontrols,generalautomation,radioanddatacommunication,andtelecommunication systems.Medium-dutycontactscarryappreciablyhighercurrents(see5Aabove)andoperateatvoltages up to 1000 V. For this group, electrical wear is of prime importance. The factorsgoverningcontact material selectiontomeet theverysevereoperatingconditionsincludetendencytowelding, material transfer, anderosion(pitting). Applicationsofmedium-dutycontactsarecontrol devicesfor industrial, domestic, anddistributionnetwork applications.Electric contactsStationary MovingSliding CommutatingBinding Brush Slider Trolley Separable Relay BreakingSolderedweldedbondedCurrent-carryingbussesCurrentpickoffs ofelectricaland weldingmachines Rheostats,potentio-meterscodesendersCurrentpickoffs ofcranes andtransportPlugconnectorsand circuitbreakersOperate under conditions of friction and wearFIGURE 1.1Classicationofelectricalcontacts.Electrical Contacts: Fundamentals, Applications and Technology 4q 2006by Taylor&FrancisGroup, LLCHeavy-duty contacts carry very high currents (tens of kA) and operate at very high voltages(hundreds of kV). The most common types of these connectors are contactors, starters, andcircuit breakers.In sliding contacts, the contacting parts of the conductors slide over each other without separ-ation. Current passage through the contact zone is accompanied by physical phenomena (electrical,electromechanical, and thermal) that produce changes in the state (characteristics) of surface layersof the contacting members that differ when operating without current (see Figure 1.2). The severityof theprocessesoccurringat contact interfacedependsonthemagnitudeandcharacter of thecurrent passingthroughthecontact, theappliedvoltage, operatingconditions, andcontactmaterials.4,5Thephysical processes occurringinthecontact zoneof slidingcontacts canbeclassiedasfollows:Slidingcontactswithaheavyelectricalcontactloadarecontactswherebycurrentsorvoltagesarecommutated, inducingmechanical, thermal orelectrical effectsincludingsparkingandarcing.Theseeffectsthusproducechangesinthestate(properties)ofthecontact members. The necessary condition of such an operating regime is that the voltageacross disclosed contacts exceeds the minimal electric arc voltage for the materials used;Sliding contacts with a moderate electrical contact load are contacts where mechanical,thermal or electrical effects, excluding sparking and arcing, change the state of the matedsurfaces.Thevoltageacrossopenedcontactsisbetweenthesofteningvoltageandtheminimalelectricarcvoltageforthematerialused;Slidingcontactswithalowelectrical contact loadarecontactswherenoadditionalphysical phenomenaandchanges areinducedinthestateof thematedsurfaces. Inthiscasethevoltageacrossopencontactsislessthanthesofteningvoltage.Themost important andwidelyusedtypesofslidingcontactsincludecontactsofelectricalmachines, current pick-offs of transport andliftingmachines, andof radio-electronicdevices,andcontrol andautomaticsystems. Asarule, slidingcontactsfor electrical andtransportationmachinesareintendedtocommutatecurrentsof amoderateandhighintensitywhilethoseforradio-electronic devices and control and automatic systems are usually low-current level contacts.Physical effectsThermal Electrical ElectromechanicalElectroplastic effect Sparking and arcingSoftening/melting ofsurface layersElectrodynamicrepulsionFrittingElectrotransportEffect of electricalfield on oxidationFIGURE 1.2Possibleeffectsonthepassageofelectricalcurrentthroughtheinterface.Introduction to Electrical Contacts 5q 2006byTaylor&FrancisGroup, LLCForelectricalmachines,therearetwotypesofslidingelectricalcontacts:brush-collectorandbrush-collector ring, inwhichthebrusheswithdifferent polaritiesslideover onefrictiontrack(brush-collector) or different rings(brush-collector ring).1,6Collectorsarecommonlymadeofelectrolyticcopperorcopperwithsmalladditionsofcadmium,silver,magnesium,zirconium,ortellurium.Collectorringsaremadeofcopperalloyswithzinc,lead,andaluminumand,insomecases (very high peripheral velocities), of ferrous metals and their alloys. Brush materials are basedmainlyonmulticomponentcompositesofgraphite,soot,copper,andcokepowders.7Slidingcontactsareveryimportant componentsinmanydevicesusedinautomatic, teleme-chanical, and communication equipment, such as different potentiometers serving aselectromechanical sensors.8,9Their design is wide ranging and, despite their low material consump-tion,theyareexpensivepartsofmachinesanddevicesduetoanextensiveuseof noble metalsintheir production. Fromamechanical viewpoint, theoperatingconditionsof low-current slidingcontacts are quite favorable because sliding velocities are low and loads on the contact members arelight;thus,asarule,thesedevicesareprotectedagainstharmfulenvironmentfactors.1.2SUMMARY OF BASIC FEATURESIt has been established that real surfaces are not at but comprise many asperities.1Therefore, whencontact is made between two metals, surface asperities of the contacting members will penetrate thenatural oxideandother surfacecontaminant lms, establishinglocalizedmetalliccontactsand,thus, conducting paths. As the force increases, the number and the area of these small metalmetalcontact spotswill increaseasaresult oftherupturingoftheoxidelmandextrusionofmetalthroughtheruptures.These spots, termed a-spots, are small cold welds providing the only conducting paths for thetransferofelectrical current. Adirect consequenceofthisisaporouscontact whereinltratingoxygen and other corrosive gases can enter to react with the exposed metal and reduce the metalliccontact areas. Thiswill eventuallyleadtodisappearanceof theelectrical contact, althoughthemechanical contact between the oxidized surfaces may still be preserved. The real contact area Ar isonlyafractionoftheapparentcontactareaAa,asillustratedinFigure1.3.Rm2aConductor resistanceApparent (nominal) contact areaReal contact areaLoad-bearing areaQuasi-metallic contact areaConducting contact area (a-spots)Constriction resistanceDiameter of a-spotRcRmRcaFFIGURE 1.3Schematicofcurrentconstrictionandrealcontactarea.Electrical Contacts: Fundamentals, Applications and Technology 6q 2006by Taylor&FrancisGroup, LLCThe relationship between the applied normal load Fc, hardness of the metal, H, and the apparentcontactarea,Aa,isgivenbythefollowingexpression:FcZxHAa: (1.1)Thehardness, H, inthisexpressionrepresentsameasureof theabilityof ametal toresistdeformation due to point loading; x is the pressure factor and depends on the amount of deformationof the asperities and is equal to 1 in most practical contact systems. On the other hand, Holm1hasshownthathardnessisrelatedtotheyieldstress(sy)bythefollowingexpression:H Z3sy: (1.2)Theresults,showninTable1.1,expresstherealcontactareaasapercentageoftheapparentcontactarea, Aa, atvariousnormalloads. Itshouldbenoted, however, thattherealcontactareacalculated in this manner includes the load-bearing area which is covered with the oxide lm and isnot, therefore, a dependable path for transfer of electrical current. Therefore, the conducting contactareawillbeonlyasmallfractionofthecalculatedrealcontactarea, generallyconsideredtobemuchsmallerthan1%.It should be pointed out that the electrical interface of an a-spot is far different from the singlecircular contact spot. Current passingacrossacontact interfaceisconstrictedtoowthrougha-spots. Hence, theelectrical resistanceofthecontact duetothisconstrictedowofcurrent iscalled constriction resistance and is related to the basic properties of metals such as hardnessandelectricalresistivity. Holm1hasshownthattheconstrictionresistanceforasinglea-spotcanbeexpressedasRsZr1Cr2=4a; (1.3)where r1 and r2 are resistivities of the contacting metals, and a is the radius of the metal-to-metalcontactarea.Ifthetwocontactingmetalsarethesame,thentheconstrictionresistancebecomesRsZr=2a: (1.4)Because the metals are not clean, the passage of electric current may be affected by thin oxide,sulphide, andother inorganiclmsusuallypresent onmetal surfaces. Consequently, thetotalcontact resistanceof ajoint is asumof theconstrictionresistance(Rs) andtheresistanceTABLE 1.1Effect of Normal Load on Real Area of Contact for Clean SurfacesReal Contact Area/Apparent Contact Area (Ar/Aa) (%)Alloya/Applied Load 10 N 100 N 1000 NAl(H-19) 0.01 0.1 1.0Al(H-0) 0.05 0.5 5.0AlC0.75%MgC0.15% Fe(H-19) 0.01 0.1 1.0AlC0.75%MgC0.15% Fe(H-0) 0.02 0.2 2.0Cu(H-0) 0.008 0.08 0.8a(H-0),fullyannealed; (H-19),fullyhardened.Introduction to Electrical Contacts 7q 2006byTaylor&FrancisGroup, LLCofthelm(Rf)RcZRsCRfRfZs=pa2;(1.5)where s is the resistance per area of the lm. Both tunnelling and fritting are considered operativemechanisms for the current transfer across the lm. In most practical applications, the contributionoftheselmstothetotalcontactresistanceisofminorimportancebecausethecontactspotsareusuallycreatedbythemechanicalruptureofsurfacelms.Thecontact resistanceis themost important anduniversal characteristicof all electricalcontactsandisalwaystakenintoaccountasanintegralpartoftheoverallcircuitresistanceofadevice.Therefore,althoughitissignicantlysmallerascomparedwiththeoverallcircuitresist-ance, the changes in the contact resistance can cause signicant malfunctions of the device. This isbecausethecontact resistancecanvarysignicantlywiththechangesinthereal contact area,contact pressurevariations, resistivelmnonuniformity, andotherfactors. Thisresultsinlargevoltageincreases, thusmakingtheneadjustment or goodoperationof devices difcult. Forinstance, theinstabilityandhighvaluesof contact resistanceareespeciallynoticeableinbulkDC potentiometers, whose resistive members are relatively thick and have a highspecicresistance.Therearemanyparametersthat canbeusedtoassesstheoperatingefciencyof electricalcontacts.Amongtheseparameters,perhapsthemostimportantareelectric(thetransitionvoltagedrop,commutationnoise,erosionresistance),tribological(thewearresistanceandfrictioncoef-cient) andchemical (corrosionresistance). Inthefollowingchapters, detailedanalyses of thefactorsaffectingthepropertiesandperformanceofelectricalcontactswillbegiven.Electrical Contacts: Fundamentals, Applications and Technology 8q 2006by Taylor&FrancisGroup, LLC2Contact Mechanics2.1SURFACE OF SOLIDSThefeaturesofasolidsurfaceasaphysicalobjectaregovernedbyitsspatialarrangementasaboundarybetweentwophases.10Theatomsandmoleculesbelongingtothesurfacehavefewerneighbors than those in the bulk. This simple fact has far-reaching consequences for geometry andphysics of a surface: the interactions between its atoms and their neighbors vary, distorting the forceeldthat penetratestothedepthofseveral interatomicdistances. Giventhisfact, theexcessofenergytosurfaceenergyappears;consequently,thesurfaceinteractswiththeenvironment.Thisprocessistermedadsorption.Therearephysicalandchemicaltypesofadsorption.PhysicaladsorptionischaracterizedbythevanderWaalsinteractionsbetweentheadsorbateand the solid surface. As a rule, its energy of the interaction is below 20 kJ/mol. The polymolecularlmsadsorbedonthesurfaceareremovedrelativelyeasily.The chemical adsorption energy is quite high (80400 kJ/mol), usually producing a monolayeronthesurfacethatishardtoremove,eventhroughtheuseofelevatedtemperatures.Inaddition,chemical reactionsbetweenthe surfaceandthe activeelements, such asoxidationin the environ-ment, shouldberemembered. Unlikethecaseforchemisoption, thesereactionsresult inabulkphaseonthesurface.Theenvironment exerts verydifferent effects onasolidsurface.10Inthe1920s, A. Joffedemonstratedthathalidecrystals,e.g.,NaCl,thatarebrittleindryair,becomeductileinamoistatmosphere and show an increase in strength. Joffe ascribed this effect to a water lm on the solidsurface, assuming that the water heals surface microcracks. This circumstance holds signicance intribological behavior of materialsfor whichJoffeseffect takesplace. For example, aluminumoxide is sensitive to water vapor, and high-strength steel exposed in pure hydrogen is sensitive to asmall concentration of oxygen. An attack of some active environmental species on the solid surfaceof metalsor nonmetals maychangethemechanical behavior of surfacelayersbecauseof thewedging, orRebinder, effect (Figure2.1). Thisphenomenonwasrst observedbyP. Rebinder.Asarule, thespeciesareof organicorigin(fattyoxides, alcohols, soaps, etc.) andarepresentinlubricants.The adsorbed lm may have the opposite effect, producing surfacehardening. This hardeningoccurs in, for example, oxides on certain metals (the Roscoe effect). Hence, the surface adsorptivityproducesaneboundarylayerwithastructureandbehaviordifferingfromthoseofthesurfacelayer ofthe solid.Figure2.2 shows schematically thatthe structureofthe boundary layer is quiteintricate. The appearance of each sublayer depends upon the conditions of fabrication of a part. Thelayersmaymutuallypenetrateoneanotherthroughthesystemofmicrocracks.Theboundarylayermaybeinadiversityofphysicalstates, rangingfromnearlygaseoustosolidcrystalline. Boththe basic parameters (temperatureandpressure) andthe patternofinteractions withthesolidphasedetermineits state. Themechanical behavior of boundarylayers demonstrates a wide spectrum of properties ranging from viscous and viscoelastic behaviortoperfectelasticity.9q 2006byTaylor&FrancisGroup, LLCWhentwosolidsapproacheachother, onlytheir molecular eldsinteract andgeneratetheattracting force responsible for their bonding or adhesion. This latter state implies the appearance ofmolecularbondsbetween thematedsurfaces.Thethermodynamicworkofadhesion,ga, betweentwobodies(1and2)isequal totheworkofreversibleadhesivedetachment; thisisfrequentlydeterminedbytheDupreequation:gaZg1Cg2Kg12;where g1 and g2 are the surface energies of surfaces 1 and 2 before contact (their free energies) andg12istheinterfaceenergy.2.2SURFACE TOPOGRAPHYWhen investigating the real contact, it should be remembered that machine-part surfaces deviate tovarious extents fromdesignshapes that are usuallydesignedtobe geometricallydue toFPFFIGURE2.1Effect of wedgingout producedbypolar moleculesinsurfacecracks. P, loadinducedbyadsorbedlayer;F,forcesofwedgingout.MetalTransition layerBoundary absorbed layerMetal oxidesAdsorbed gasAdsorbed moisturePolar molecules (Lubricant)FIGURE 2.2Structureofsurfacelayerofmetallicpart.Electrical Contacts: Fundamentals, Applications and Technology 10q 2006by Taylor&FrancisGroup, LLCmanufacturingor other considerations.11,12Areal surfaceis not ideal becauseof asperitiesappearingduringmachiningandsubsequent use. Theextent of deviationparticularlydependsuponthestructureof contactingmaterials. Thesolidsurfaceexperiencestheeffectsof variousfactorsthatcanbeclassiedintomanufacturing,operational,andstructural.The height (amplitude) dimensions of asperities range extensively from decimal fractions of ananometer toseveral millimeters. Thespacingparametersof theasperitiesarestill wider andsometimesextendthelengthofthepart itself. Thelowerlimitsoftheserangesrelatenaturallyto the dimensions of atoms and molecules; the upper limits depend on the conditions of machiningand the structure of the materials in question. There are apparently no physically imposed limits ofexistence of the asperities within these height and spacing ranges. Nevertheless, the investigation ofroughsurfacesandthedevelopmentofsuitablemeasuringequipmentindicatethatitismethodo-logically reasonable to divide the asperities into four dimensional levels: errors in form, waviness,roughness,andsubroughness(Figure2.3).Errorsinformaredenedasshapedeviationsof areal surfaceor prolefromthesimplegeometry having a great spacing (SZ15,000 mm) and relatively small height (DZ150 mm). Asa rule, D/S%0.001. The errors in form are usually single, irregularly spaced surface departures. Forcylindrical parts, they can be oval facets in the cross-section and taper, and barrel-shaped cambersinthelongitudinal section; lackofrectilinearityandatnesscharacterizeshapedeviationsofaatsurface.Errorsinformresultfromfaultymachining,lackoftoolprecision,wearoftools,andelasticdeformations inthesystemof lathe-tool-workpieceproducedbyfactors suchas thevariablecuttingforce.Sometimesshapedeviations aredeterminedquantitativelybytheparameter; Dbeingthegreatestdistancebetweenthereal surfacepointsandthesurfaceenvelopingthelatteralongthenormal (Figure 2.3). The enveloping surface is dened as the nominally shaped surface contactingwiththerealsurfaceandlyingoutsidethematerialofthepart,sothatanydeviationofthepointmostdistantfromtherealsurfacewithinaspeciedareashouldhavetheminimummagnitude.Roughness is usually excluded when errors in form are analyzed. In reality, these errors and theroughnessspeciedforthesamesurfaceareinterrelated;therefore,atoleranceontheformerroralsoimposesrestrictionsontheroughness. For example, it isacceptedthat theroughness, Rz,shouldbeatleast1.52timeslessthanthehighestshapedeviations.When studying a contact between real surfaces, it should be borne in mind that errors in formtendtoredistributethepressurewithintheapparent contact area; asaconsequence, thestressconcentrationoccursintherelevantcontactareas,andrubbingsurfacesundergounevenwear.Wavinessisacombinationofnquasiperiodicasperitieswitharelativelylargespacingalongtheportionexceedingthespeciedsamplinglength,l,formeasuringthesurfaceroughness.Thewaviness covers the followingdimensional area: the spacingof asperities is 0.810 mmsswRw3Rmax421FIGURE 2.3Components of surface prole. (1) error in form, D; (2) waviness; (3) roughness; (4) subrough-ness;Sw,Rw,wavinessspacingandheight;S,Rmax,roughnessspacingandheight.Contact Mechanics 11q 2006byTaylor&FrancisGroup, LLC(bigger parts may have a larger upper limit, up to 200300 mm); the height is 0.01500 mm. Somecountries (Germany, Switzerland, and the United States, for example) have standards for waviness.Thereisnostrict distinctionbetweenwavinessandroughness. Conventionally, forthecon-venienceof measurement andclassication, either thewavinessspacing(thelower spacingofwaviness shouldexceedtheassessment lengthusedfor roughness measurement) or theratiobetweenthespacingandthewavinessheight(assumed,asarule,tobeover40)servesassuchaseparatingboundary.Vibrations(forcedorself-excited)inthelathe-tool-workpiecesystemarethemaincauseofwavinessthat mayalsoresult fromfrictionandwear. Thecluster structureof thereal contactbetweensolidsismostlyduetowaviness, makingthelatter animportant subject instudiesofenergytransferacrossthecontactzone.Roughness constitutes a surface microrelief, and it is dened as a population of asperities with arelativelysmallsampling;itismeasuredusingtheassessmentlength,l,showninFigure2.4.Usually, roughness is produced by tracks of machining tools (a cutter, a mill, an abrasive cutter,etc.), and the quality of roughness depends on the kinematical design, the method of machining, themechanical properties of a material, and vibrations in the lathe-tool-workpiece system. The originalroughness of working surfaces undergoes signicant modication during frictionand wear, and itreaches theso-calledequilibriumroughnessthat is apparentlyreproducedunder normalfrictionconditions.Subroughnesspresentsthene(nanometerscale)structureofarealsurface,anditiscloselyrelatedtotheso-calledphysical relief.It involves theaccidental andimperfect locationofcrystallographicplanes, chaoticallydistributedgrains, andislet-typelmsincludingoxidesandadsorbedones. Forsomepartiallycrystallinepolymers,thesubroughnesscanbeconnectedwithalternating crystalline and amorphous regions of dozens of nanometers in size. Its study can provideanewinsightintothetheoryof friction,wear,andlubrication.Hence,therealsurfacehasasetoftopographicelementsthatcanbedividedintotwogroupsandfourlevelsofshapedeviations:macrogeometry(errorsinformandwaviness)andmicrogeo-metry (roughness and subroughness). They possess different scales and patterns of distribution, andtheyplaydifferentrolesintheprocessesof frictionandwear.Conditionally,theregionsofexist-ence of each can be represented by some subsets in the coordinate system with the axes being theheight of asperities, H, and the mean distance, S, between them (Figure 2.5). Even when the surfacehastheasperitiesofthesamelevel,itsdescriptionpresentsanontrivialproblem.Thedescriptioncanbefacilitatedif itsobjectivesareclearlyunderstood. At present, four approachesexist intribologytodescribingrealsurfaces:deterministic,parametric,probabilistic,andfractal.Thedeterministicapproachpresentsasurfacedescriptionassomeperiodic, continuous, orpiecemealcontinuousfunction. ItiseducativetocomparethesketchmadebyCoulombin1821(Figure 2.6a) with that borrowed froma contemporary monograph by Johnson in 1987(Figure2.6b).13Althoughsuchimagingofthesurfacemayseeminglybena ve, itallowsoneofFIGURE 2.4Roughsurfaceprole.Electrical Contacts: Fundamentals, Applications and Technology 12q 2006by Taylor&FrancisGroup, LLCthefundamental features of roughsurfacestheir discrete(patchy) patterntobereected,whereasstochasticbehaviorasanotherfeatureisignored.Theparametricmethodisbaseduponthedescriptionofasurfaceusingaset ofsomepar-ametersthat aredetermined, asarule, byanalyzingsurfaces intwoor threedimensions. Theroughnessparametersarecalculatedinrespecttosomereferenceline(surface)thatisplottedinadenitemanner.Themeanline(surface)isusuallyusedasthereferenceline.The surface prole is generally characterized by a set of parameters. There is a variety of suchsets; the parameters include height (amplitude), sampling, and those of a hybrid type. A discussionfollowsofthebasicparametersusedinengineeringpracticeandresearch.The arithmetic average roughness, Ra, is dened as an arithmetic mean of the departures of theroughnessprolefromthemeanlineoveronesamplinglength,l:RaZ1ll0}z(x)}dx; (2.1)wherez(x)istheproleequationwhichisfrequentlysetinagraphicortabularform.Inthelastcase,RaiscalculatedbytheformulaRaZ1nXniZ1zi(2.2)Height (m)103102101100101102103104105Spacing (m)101100101102103104105106SubroughnessRoughnessWavinessErrors in formFIGURE 2.5Relationbetweentypicaldimensionsofbasictopographicelementsofrealsurface.(a)(b)FIGURE 2.6Fragmentofsketchby(a)Coulomband(b)Johnson.Contact Mechanics 13q 2006byTaylor&FrancisGroup, LLCUsually, Ra is averaged over several consecutive sampling lengths from 2 to 20 in accordancewiththenationalstandard.Theparameterisidenticaltoarithmeticaverage(AA)andcenter-lineaverage(CLA).The root-mean-square (RMS) roughness, Rq, is dened as the RMS deviation of the prole fromthemeanlineoversamplinglength:RqZ1ll0z2(x) 1=2(2.3)orRqZ1nXniZ1z2i !1=2:The parameters Ra and Rq differ insignicantly in magnitudes. For the same surface, Ra is lessthanRqby630%.Thus,aregularsine-shapedprolewithasingleharmonics,theratioRq/Raisequalto p/23/2z1.11;fortheGaussianprole,RqZ1.25Ra.The10-pointheight(orzoneroughness), Rz, isseparationoftheaverageofthevehighestpeaks and the ve lowest valleys within a single sampling length (peak [valley] is dened as localmaximum[minimum]above[below]prolemeanline):RzZX5iZ1}zip} CX5iZ1}ziv} !.5; (2.4)where zip is the height of the ith highest prole peak, ziv is the depth of the ith deepest prole valley.Thesamenotation,Rz,isoftenusedfortheaveragepeak-to-valleyheight,whichisfoundbyaveragingoverveconsecutivesamplinglengthsofseparationofthehighestandlowestpeakineachsamplinglength(Figure2.7).Themaximumpeak-to-valleyheight, Rmax,isthelargestsinglepeak-to-valleyheightinveadjoining sampling lengths. The parameter is a sensitive indicator of high peaks or deep scratchesbuthasalargescatterduetorandomsampling.Thestandardsspecifysomespacingparameters.Spacing alongthemeanline,Sm,isthemean spacingbetweenprolepeaksatthemeanline,measured over the assessment length. Here, a prole peak is the highest point of the prole betweenanupwardsanddownwardscrossingofthemeanline.ZP1P2P3P4P5RmaxxV5 V4V3 V2V1L1L2L3L4L5FIGURE 2.7ConsecutivebasiclengthsL1KL5makinguptheratinglength,L.Electrical Contacts: Fundamentals, Applications and Technology 14q 2006by Taylor&FrancisGroup, LLCSpacing of peaks, S, is the mean spacing of adjacent local peaks, measured over the assessmentlength. Alocal peak is the highest part of the prole measured between two adjacent minima, and it isonly included if the distance between the peak and its preceding minima is at least 1% of the peak-to-valleyoftheprole. NormallyspeciedinaRussianstandard, theseparametersalsoexistinhybrid form.Bearing ratio, tp, is the length of bearing surface (expressed as a percentage of the assessmentlength, L) at a given height, p, below or above the reference line (Figure 2.8). A plot of bearing ratioagainst surfaceheight isnamedthebearingratiocurve(orAbbottFirestonecurve). Thecurveallows one to estimate the contact area of mating surfaces and to assess the expected rate of wear.Theinitialportionofthecurveisconvenientlyapproximatedbytheexponentialfunction:h Zb3v; (2.5)where3Za/Rmax, aisthedistancebetweenthehighestlineofproleandthe speciedlevelp.band n are the parameters of the parabolic approximation of initial part of bearing ratio curve. Theydependonthetypeofmachining.The probabilistic approach to describing the rough surface geometry is based on the theories ofprobabilityandrandomprocesses. Asarule, itismorelaborconsuming, yettheeffortispartlycompensatedbymorecompleteinformationaboutthesurfacetopography.Thisapproachallowstreatingtwo-dimensionalorthree-dimensionalsurfacesassomestatisticalsampleofproleordi-nates(orpeaksofasperities)orassomerealizationofarandomprocess.Intherst case, theset ofheights(theordinates) oftheprolez(x)istreatedasarandomvariablethatisdescribedinthetheoryofprobabilityby thecumulativeprobabilityfunction F(z).The function is the probability that random variable z(x), the prole height z, for example, takes avaluelessthanorequaltoz:F(z) ZPz(x)%z:ThefunctionF(z)istheintegraloftheprobabilitydensityfunctionf(x),i.e.,F(z) ZzKNf (z)dz: (2.6)Theprobabilitydensityf(z)inthissituationisthefractionoftheseproleordinatesthatarelocated within the interval (z, zCdz). In other words, f(z)dz is the probability of nding an ordinate inthat range. It is simplest to determine the function f(z) by plotting a relevant histogramfollowed by itsapproximation. Most often these histograms are successfully approximated with the Gaussian curve:f (z) Z1s2p_ exp K(zKa)22s2 !; (2.7)ZL0 50Bearing ratio, tp100%FIGURE 2.8Schematicofbearingcurveconstruction.Contact Mechanics 15q 2006byTaylor&FrancisGroup, LLCwhere s is the standard deviation of the prole ordinates (identical to the roughness parameter, Rq,described above), which characterizes the scattering of the randomvariable, while a is its expectation(mean value of prole ordinates). If the ordinates are normalized by s and they are measured fromthemean line of prole, then aZ0 and the Gaussian (normal) probability density is written as:f (z) Z1s2p_ exp Kz22 !: (2.8)WhentheordinatesofroughsurfacesdistributeaccordingtotheGaussianlaw,theyarecalledGaussian or normal surfaces. A comparative simplicity of their description has provoked numeroustheories of contact interactions between them. Yet, it should be remembered that in engineering, thesurfacesarefrequentlyquitedifferent fromnormal surfaces. Hence, theconclusionsbasedonthe Gaussian models should be treated in a highly critical way, as some rough approximation of thereal situation.The probabilistic approach is generalized by the concept based on the theory of random elds(processes), whichtreatsaproleasarandomeld. ThismethodwasdevelopedprimarilyforGaussian (isotropic and anisotropic) surfaces. Its advantages become remarkable when analyzing athree-dimensionalsurface.This paper will not discuss the mathematical renements of the method, which can be consultedinpublications.Belowaregiventhemainresultsofapplicablesignicance.Theprobabilitydensityofsummitheightsisdescribedbythefollowingequation:p(x+1 ) Z3_2px+13(2aK3)a2 !1=2exp(KC1x+21 ) C32p_2a(x+21K1)&!1 Cerf x+132(2aK3) 1=2 !exp K12x+21 C2pa3(aK1) !1=2!1 Cerf x+1a2(aK1)(2aK3) 1=2 !exp Kax+212(aK1) !'; (2.9)wherex+1Zx1=m1=20isthedimensionlessheight ofsummit; aZm0m4/m22isthebandwidthpar-ameter; C1Za/(2aK3). This equationis termedNayaks distribution. Nayakwastherst toproposeitexactlyinthisformfordescribingroughsurfaces.14Thedistributionpdependsonthespectralmomentsonlyinsomedimensionlesscombinationathat can be determined fromthe surface prologram. The bandwidth parameter ais associated withthe width of the surface spectral density. The larger the parameter a, the broader the spectrum, i.e., thebandofwavelengthsmakingupthegivensurfaceiswider. Anarrowband(a/1.5)indicatesapproximate equal length of all the waves.The bandwidth parameter varies from 1.5 to innity; the distribution of Nayak degenerates intotheknownRayleighandGaussiandistributionsattheselimitvaluesofthebandwidthparameter:pR(x+) Z0; x+!0;23_2p_hx+2K1 Cexp(Kx+2)iexp(Kx+2); x+O0;8>>>>>:pG(x+) Z12p_ exp K12x+20@1A:(2.10)Electrical Contacts: Fundamentals, Applications and Technology 16q 2006by Taylor&FrancisGroup, LLCItisobviousthatthetransitionfromtheGausstotheRayleighdistribution(withdecreasingtheparametera)increasestheprobabilityoftheexistenceofhighersummits.The fractal approach to describing rough surfaces has attracted tribologists because the rough-ness parameters of a real surface proved to be substantially dependent on the resolution of availablemeasuringinstrumentsbecauseof themultiscalecharacter of roughnessanditsnonstationaryfeatures. Thesequalitiesof roughsurfaceshavestimulatedthesearchfor amethodof surfacecharacterizationthat couldprovidethestructural informationonroughness. Parameterswouldbe invariant for all scale levels. By not very rigorous denition, the fractal is a structure comprisingthecomponents resemblingthewholeinsomesense. Roughsurfaces frequentlysatisfythisdenition. If theaccuracyof measurementsis increasedsuccessivelybyregisteringner andner surfacedetails, thefractal roughness appears thesameat anyscaleof magnication(Figure2.9). Hence, thefractal dimensionsrepresentinfact theonlyparameterfullydescribingthe rough surface. This fact, considered as the basic advantage of the fractal approach, has been thecauseofitscriticism. Itishardtoimaginethatsuchintricateobjectslikeroughsurfacescanbedescribedwithasinglenumber.Combinedmethodsareusuallyemployedinpractical research: adeterministicdescriptioninvolves probabilistic components, or a fractal description uses spectral roughness characteristics.MoredetailanalysisofroughnessdescriptionispresentedinAppendix1.2.3MODERN TECHNIQUES OF MEASURING SURFACE PARAMETERSAt present there are many methods of studying surface topography.11,15The stylus methods remainthe most popular; the results have been the foundation of modern standards. Optical methods usingelectromagneticradiationhavebecomepopular. Thereareelectricalandthermal methodsusingvariouselectrical phenomenaandheat transfer throughtheroughcontact. Figure2.10showscapabilitiesofvariousmethodsformeasuringthesurfaceparameters.Ananalysisof moderntendenciesshowsthat theinterestsof scienceandtechnologyhaveshiftedtowardsobtainingdataaboutverysmoothsurfaces,i.e.,themicro-andnano-scalerough-ness and reconstruction of three-dimensional images of real surfaces. Still, as in the past, the stylusmethodsretaintheirfoothold(Figure2.11).In these methods a ne stylus slides over the surface, replicating its relief. Displacements of thestylus in the vertical direction are converted into electrical signals that are recorded as prologramsand/ordigitizedforPCprocessing.Theheightofasperities issmaller, asarule,than theirhorizontal dimensions.Therefore,it isbetter to record a prole trace with vertical magnication greater than that in a horizontal direction(Figure 2.12a). Figure 2.12 shows that the impression on the surface prole strongly depends on theratio between the scales of magnication and that the real roughness is inclined more steeply thanP1 Original profileP2 Enlarged view of profile P1P3 Enlarged viewof profile P2FIGURE 2.9Fractalrepresentationofrealsurfaceroughness.Contact Mechanics 17q 2006byTaylor&FrancisGroup, LLCPickupGear boxTransducerSurfaceAmplifierData loggerStylusDatumFIGURE 2.11Schematicofstylusprolometer.Spacing(m)105104103102101100101102103Height (m)105104103102101100101Stylus profilometryOptical profilometrySEM-based methodsLarge scanAFMSmall scanAFM STMMolecularcontactPrecision contactMicro contactAtomic-molecularroughnessPhysical relief MicroroughnessWavinessFIGURE 2.10Diagram of the height and spacing parameters and the ranges of vertical-lateral resolution fordifferentmethodsofroughnessmeasurement.Electrical Contacts: Fundamentals, Applications and Technology 18q 2006by Taylor&FrancisGroup, LLCthe prole trace shows it to be. The optical methods are most popular because of their high verticalresolution(!0.1 nm). Thelaws of light diffusionreectedbysurfaceasperities allowonetodetermineanumberofessentialcharacteristicsofroughsurfaces,suchasthestandarddeviationandtheradiusofcorrelation. Effortsareknownofusingellipsometryformeasuringroughnessparameters.10Electronmicroscopyis asignicant methodof scienticallystudyingof roughsurfaces.Actually there is a large group of noncontact methods based on transmission and scanning electronmicroscopy(diffusion,elastic,orsecondaryelectrons)andtechniques(processingstereocouples,installingauxiliarydetectors,etc.).Studiesof verysmoothsubroughsurfaceshavebeenadditionallystimulatedafter scanningtunnel microscopy(STM)was pioneered and rst made public in 1982. Physically,STM is basedon the tunneling of electrons between two closely spaced electrodes. The principle of operation of atunnel microscope(Figure2.13)impliesthat thedisplacement ofthemetallicneedlexedinathree-coordinatepiezodriveoverthetarget surfaceinducesatunnel current ImintheclearancebetweenthemundertheeffectofvoltageU:ITZUexp(KAF1=2d);whereFisthepotential barrierintheclearancedbetweentheneedleandthesurface; Aistheproportionalitycoefcient (AZ1 whenFis measuredin electron-voltsandthe clearance, d, is inAngstroms). When the voltage in the clearance is maintained constantly (as it is usually practiced),theclearanceisvariedbythefeedbacksystemcontrollingthedisplacementoftheneedlebythepiezodrivetomaintainthemagnitudeof thetunnel current. Thesurfaceproleisobtainedbytracingthestylustravel (providingthat thepotential barrier alongthepathremainsconstant).Yet, studieshaveshownthat thevibrating-electrodemethodallowsthesurfaceswithavariableworkfunctiontobestudied.(a)(b)(c)X5000X5000X1000X5000X5000X100E F G HY YXXAY YBCX XDFIGURE 2.12The prole real surface with different vertical and horizontal magnication. (a) vertical ampli-cation exceeds horizontal amplication 50 times; (b) same surface when magnication ratio is 5:1; (c) surfacewith identical vertical and horizontal magnication. (Adapted from Hutchings, I. M., Tribology: Friction andWearofEngi