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ExperimenteⅡｅＧｒｉｉｎｄｅｗｅｒｄｅｎｄａ【iirangefijhTtOdassGummircibM、galsdcnwiskcscnFIicsscuuwcsensiihnlichanzusehenistmnddeswege、OimCegensatzzurfestcnRcibung･nichtnotwendiger-weisemitAbriebvcrbumdenistNachdi⑥serTheoriesin(ldieReiblIngslGTiMtedcsCummisdcAvalBrcn BcriibTungsf1iicheproPoTtioTlal・ＤｉｅwahreBcriihrtungslliichci5t(lⅡrchoPIastiscI1cDcfornMLtion〔lcrUnebenheitenaufderGummiobeＴＩｌａｃＩｌｅｂｅｓｔｉｍｍｔｐｍｉｔｄｃｍＥrgcbniH．（kus筒GlommiAmoH1tons，GesetznichtfoIgt、DieGesetzederGummireibungwe｢ｄｅｎａｕｓ⑥iIuIachcJuModeⅡenabgcIeitctundexperimentellzufriedeTlstellendbestiitigt， AbriebentstehtdurChmechaniScllesVersagendesGummisuIuterdenvondenUncbenllcitcn

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ＭｏｄｅｒｎｗｏｒｋｎｏｎｔｈｅｍｅchanismofslidingfrictionandfrictionalweaTofsolidshas

broughttolighttheimportantroleplayedintheseproccsscsbythemicrotopography oftherubbingsurfaceswhoseroughnessmakesthetruearcaofcontactsmallandpro‐ duceshighpressureswheretheasperitiesmeet､Undertheinflucnceoftheselocalstresscs， irreversiblejunctionsareformedbetweentherubbingmcmbers,andtIlefrictional workdoneinslidingistheenergynecessaTytobreakthcsejunctions､Tllus,friction

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olsolidsisaconcomitantolabTasion,alM1tllcf｢ictio】1allorceisproportionaltotllctrucarUiLofco1Utact・

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Inspiteoftllisdiflerencebetweenrubbl9rilndsolidlriction,thelineofattackwhich hasprovedsosuccessfulintbetheoryo⑬11i(llrictioncanwithadvantagebebrought tobearonrubbeTfriction・Attentionmu馬ＬＩＵ【)ｗｃｖｅｒＤｂｃｐａｉｄｔｏｔｈｅｆａｃｔｔｈａｔｒｕｂber

鰯erallycxpcricncesfrictionandwearllnlhrcoluditionsdifferentfromthosecomm・nlI1substanccssucl1asmctalsandfibrcs．]《ⅡI〕berhardlyい'erslidesonotherTubber‐

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WorkoIuthい'clocitydcl〕⑥】】(IcnccofrubbcrlTicliu】1901mrrcfcrredtohasbcuJ1carric〔loutatvelociticsnotexcccdingabＯｕｔｌｃｍ/SCC・WithI1ighcrvelocities，slidingat

constaJlttangentialforccbccomesunstable，Ｉ〕｢[･HlIIuMLblybecauscofthetempeTatuTcriscdllctodissipationoIfTictionalcnergy・ItIlIlPIlID19comcsncccssaTytoreversctllc

tecll】】i(luea1】dmcasuTcfrictionalforcesatl)｢'0瓢9riI)cdvclocitics・ExperimcntslMwcbcc】１carricdoutwhicllalIowcdtlUcfTictionKlllL．、I)cr6LturcTisctobcmeasuTedattｌｌｃ

ｓａｍｃｔｉｍｃ５・Tllcsli(lcrwasatllcrmocouplegiviI1KH1gcomctTiccontactareaofabout

lmm曾wllichwasprcsscdagainstarotatingrII1’1)c『(lisc・Figs.＋(a)ａｎｄ(b)givethcrcsuItsobtail1c〔ｌｏｎａ】11ｍfilledandacarbonbl81clK-IilIc(lcoml〕oundof､naturalrubbcr，

ItwiIlbcsccllthattllcinitialincrcascoftllcco(91(icic】ILoffrictio】1witl1incrcnsi】ngvcloc‐

ityisnotmaintaincdatI1igllcrspeedsbutgivcHwitytoagraLdualdecrcase・Tllcloa〔ldcl〕cndcnccoftI1ecocfficicntoffrictionmadcい'i〔lclutintIlescgrapluswillbctrcatcdindctailinlatcrscctions・

ＴＩ】eco11sidcrablctcml〕craturcTiscisal〕proxim6Ltclyl〕roI〕ortioI1altot】uesquarcroot

orthcvclocity・ThisdcI〕cndcncehasbccnl)rcdic(c〔lulcorcticaIlybyJAI2Gl§l《`forvcry

lliglwclocitybutal〕pcaTstobcvalidforawidcrr61U1gctllangivenbyJAEGElt`st1)cory､ＩｔｃｉＬｌ１ｂｃｓｌｕｏｗｎｔｌｌａｔｔ１ｌｃｏbscm'cddccrcascI〕Itllccocfficicntoffrictiomat】ligbcr

vcIociticsagrccs(lu8lIitativclywithtllctllc()Ｔｙ《'｢1.111〕1)crfrictioD1exp｢csscdbyc(1,.(2)ｉＩａⅡowiLl1cci田mHM1《PfortllcsimultaH1coll5化l1lll(､r8lturcrisc・Thccomparisｏｍｃａｎｂｃ

ｏＩ〕ｌｙ《llIKlIitdlIivcbせじ&Luscitisncccssarytocxlr6I1)()l8Ltcfromrc5ultsobtai】lcdatvcloc‐itic3bClowlcm/scctovclociticsrcaching-l《〕ＩｌｃｌＩ１/sじc､Assumingtllatthetcmpcraturc

riＳｃ()bcystIlcTUlation

Jノーハノｉｉ （４）

'

DUI

Ｉ９Ｂ０ ９１‐

９１‐Ｉ

suggc筋(c〔11〕Ｖｔｌ１ｃｃｘｌ，crinlcI1talc､.i〔lence,iIIl(Ｉ別11)s1illltingcqn.(4)ineqn．(2)，ｔ]〕ｅ￣

IrictioIl6Llforcci息givc】11)ｙｕ(11】.(5)：

γノー鷹"－'f(7,,ＭＶ可'`'8ヂ (5)

whcrc7bisroomlcml)crilturcintllcabsolutc蔦c6Ilc・Ｔｌlcshapcolthecurvcpredicted

l)yc〔IHI.(5)issllownillFig.」(c),whicbhasbcc11cillclllKltcdwiththefolIowil1gnumeTicalvalues:Ｅ〃＝２０，()o(〕cal/molc,Ｔｏ＝３０()｡Ｋ,ｒ＝５(l〔1Kｃｍ~lscclandl'０＝エol3cmscc-1・ＴＩＤｉｓｃｕｍ･ercproduccstllcsalientfeaturcsｏｌｌｌＩｃ⑪l〕erimentalcurves,ａｎｄitappcaTs

tIlHlttllcdecrcascofthccoefficicntoffTictioIUwi(Ilincrcasingvelocitycan1argelybe

attributcdtothcfrictiomaltcmperaturcri5c．

Nｉ

111．ＬＯＡ】）、ＥＩＣ】2Ｎ、】:ＮＣ)§ＯＦｌＲＵＢＢＩ§I（】了[《ｌＣＴｌ(〕ＮＯＮＳＭＯＯＴＨＳＵＲＦＡＣＥＳ

Ｔｌｌｃｖｉｕｗｓｏｌｌｔｌｌｃ】1aturcofrubbcrfrictionI〕lItlorwardintbeprccedingsectionimply

tIMlttl】clTictiol1allorccisI)rol)ortionaltotIlctrucarc&lofcontacM，andthusconform

witIlllDU1IIcoryoIsolidfrictio】Ibricflyr□．iいⅦ(lintllclNTItoDucTIoN,Ｔｈefrictional

lorccノ『脂dlccordinglygivcnbyc(111(6)

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2.0 ＩＯＣ

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ＵｌｏＵｍ湯」ＯＬ一五Ｌｏ」ＵＵＬｏ』｜□亡◎」ごＵ－ＬＬ

■⑥~

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Fig.４.FrictionaltempcTatqDTerisc・ｆＩノ組ndcccflicientso(frictionﾉ41〕lottcdng81illstsli《lingvcIocity(a),onanunIilIedvulcanizateofnatluralrubber;(b),onanatuuTalTml〕bcrtyrctTcadcompoIundfiⅡedwith45p・P.h・ＭＰＣblack,TheaveTagenormalloads(glaregiveninbrackcts.(c),thcorcticalvelocitydependenceoftbcfrictionalforce,calculatedfromeqn.(5)Ｃ｢apIIs(a)ａｎｄ(b)l｢ｏｍ｢c『､５．

庇らた”）Ic6sP.“７

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1１

anditwillbcassumedthatvelocityａｎｄｔｃｌⅡl)crKuturceIfcctsmvolveonlytheforce

factoT9D､Intheabsenceofayieldpressurc,itisnotadmissibletoputApropoTtional totllcIIormalload,ａｓｉｓｄｏｎｃｉｎｔｈｅｔｈｅｏｒｙｏｆｓｏｌｉｄｆｒｉctionwberesllapeandsizeof

thcsurfaccaspcriticsareimmateriaLAnａｓsumptionhastbereforetobemadeabout

tl1caspe｢itiesonrubbersurfaceswhicbisc(ｍ《lucivetotreatmentbytheoryormodel

cxpcrimentwitI1outbcingtoofar-Ietchcd､FroIuIbothpointsofviewitisadvantageous toiLl)proximatethcTubbersurfacctoana｢｢;l)'()IiLlcntical,closclyspaccdhemispheres

ofr51dius'7．ThismodelismeanttoapplynIllytoconventionalIymouldedsamples･ Itisfurtherassumedthattheelasticbellavi()llroftllcrubbercan,forthestrainsoc-

curring]1ercJbcdescribedbyasingleelasticc《DIlHt：111tEwllicbwiUbedefinedpresently，

ItfollowsfromdimensionalconsiderationstllmIIIlctruearcaofcontactwithanideally

snIm熟、thplaneundcrthcnominalpressure′mustobeyarclationoftheform

、ｲｰｸﾞ:ど`bIWE)p'‘ （７）

、

、

－０や８△｜■廿廿Ⅱ０１巳８１■０１０６■□０９口ｑ箔０１０Ｂ・ＤＣ・・１０－・己■ＢＪｑ

．■●７－‐

’○伯ロロⅥ□Ⅱ山一叩ⅡⅢ印叩肌止ⅢⅢ０仇ｌ川ⅡいⅢ小１００４１’ｗ・旧０忠’■・Ｐ』ＤｈｕＪＪ研Ⅱ

wherethec'sandβ'sareconstants､Aplottじdagainst(》/E)shouldyieldauniversal

curveforrubbersofdifferentstiffness,ＴＩｌｅｃ()efficientoffrictionderivedfromeqns．

(6)ａｎｄ(7)is：

浜＝ｗＥどclJwE)p'0-1 （８）

：…！！

andnolongercontail1stllcradiｕｓγoftIlcaspcritics，

Modelexperimentsontbecompressiｏｎｏｆｌａ｢gehcmisphcres7haveshownthatthc

rcsultslitquitcaccumte】ｙｔｈｃｅ(luation〆

孝ｌ＝ｃ⑪n筋t､/Ｗ３ (９）

Tllissimplerelatio11agrecswiththcthcorcticalexpressionderivedbyHERTz8from

classicalelasticitytl1coryforsphericalcontacts,ｅ(1,.(r(〕）

（＃､$!、

』-(誌,)ｼ,（1．１wIlcnthePoisson

l2〔1,.(Iu)willbc

Thccocfficient

ratiol1astllevalue＆a1,1Ｊ｢()l1riiLtcforrubl〕cr・Listhenormalload・uscdtodcIinctbceffMiwIllodIlIuＳＥ・

offrictionresultingfrolII,’''''3.(H)ａｎｄ(9)isthcn：

/8＝（ＷｌＩ)(/'ﾉﾉ!)-Ｖ, (皿） ｑ

whercnumericalconstantsllavebeｅｎａｌ〕H[)｢|)(ＤＩｌｉＩ１ｔｈｃ「actor9D、ThcasperitiesonTubbersurfacesare，１１(DwIwcr,notisolatedanddonotdeformin-

dcpcndentlyfromcachothcrbutwillj【)篇tい'筒tlIeVbarrcloutduringcompression、

Tlliswillcausedcl〕Klrtu｢ｃｆｒｏｍｃ(1,.（11),I)Ｍ１Ｉｌ)illHmorcI〕ronouncedastl】eloadin-

crcas(Ｄｓａ】1〔ｌｔｂｃａｓｌ)criticsHLrcsqucczcdjlll(）i1部)lidｌ〕l〔)ckprcsenti】ｌｇａｃｏＩ１ｔａｃｔａｒｃａ

(ICPじ､〔IingonlyIittlcoD1tbeloa〔ＬＴｈｉｓｓｃ(Iuじ11c(､()lい'cntsllasbccI1followcdbymcamsofasccondmodclcxl〕c｢imcntinwI1icI1as(Io18llmP5巴ｔＤｆ２５smallllemisphercswascom-

pressedunder･varinbleload・Fig.５showstIlL:cIDntKlctarcasunder3differentpressuresna化〃"“３，.ﾀﾞｴｧ ニリーー００．

蝋L■割｡■I.

vｏＬ１（Ⅱ057/58） Ａ･ＳＣＨＡＬＬＡＭＡＣＨ 302

､●■ ０

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■０６

⑨⑦③④④

⑨①④⑥①

③③③、⑨

⑨●●⑨⑭

④②．⑮④⑱

ｒ１１１

鋤勧③懲趨

②懲鯵⑲鰯

船側船側鮒⑨鐘鰯④愚

ａｂ．ｃ

Fig.５.ContactaTeaofmodelrubbeTsKDrlaccunder3dillercntl〕rcssonTcs:(a).色.Ⅱ４ｋｇ/cm2;(b),７．７５kg/ｃｍ２;(c),６６．．ｋｇ/cmg・Rcducedo85x．

■◆■

の●■』

anddemonstratesllowtheasperitiesatfirstdeformwithoutmutllalintcrlerenccias

isseenfromthecircuIaTshapeoftheircontactareas,butatl1igl)erloadscloscupfinally

intoablunteds〔luarepatternwithlittlespaceleftintheinteTstices・TI1caTcasof

contactunderthcvariousloadshavebeenmeasurcd｣usingonlythcimUerOhcmispheres

astbeouterhemispheresaresubjecttoendeffects､Tl1eareasodctermincd,whcndivid‐

edbythenormalloadandmultip1iodwit11thceffectivcmodulusEofthcmodcl， E

shouldaccordingtoeqn(8)representauniversalcuWeoIthcproduct(ﾃﾉ`)when plottedagainst(，/E).ThiscurveisshowninthelogaritllmicplotofFi9.6.Atvalues

ofけ/E)lowerthano､ｴ,thecuTvehasbeencontinuedasstraightlineofslopc-J/３

wellestablishedbytl1cmodelexperimentswithlaTgesingle】lcmisphcTes,Ｔｌ】ispTessuTc

regionmaybecalIedHertzianregionincontrasttothesaturationrangeathigher

pressures・

TheexpeTiTnentalpointsmarkedinFig.６havebeenobtainedonplateglasstracks，

■ ▲、Ⅱ

け▽■0

９■Ｐ６Ｌ■０●■■‐ＯＧ■■■■■■０５０９８６９．０５６６

ロケ■

－１．０ エ

ミレ｡

｡ □､

０．５

０．０

－ＯＳ

~~a｡‐１．５‐I。‐0.5０，．９，｡÷ＣＬＳＦｉｇ．６．LoaddependcnccofthecoefficientofrubbcrlrictiononpIategIass、Ｆｌ８１１１ｉｎｃ：tlhcorcticalcuTvedeterminedｂｙｍｅａｎｓｏＩｅｑｎ.（】Ⅱ）andthcmodclexperimcntofl7i9.5.ＡｔｏＤ.《l)'namicfrjctionato､oo2I6cm/sec､Ｅ,staticlTictionVa]uesIorAtoDITomrcL7・foTEIromrcf､０．

ルル”"“s力.“７

GＶＺ

「。 二盲亘ご弓ご盲。夢、＝､～路 ～△

▲△

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VOL.’（1957/58） ＩＴＲＩＣＴＩＯＮＡＮＤＡｌＩＩいＨＩｌＩＮＯＩｒｌＲＵＢＢＥＲ 393

wllichmaybeconsideredideallysmｏｏｔ１ｌｃ()n1IDarcdwiththeTubber，andshowthe

cxtcntolagrcemcntwiththesimplctheorylin【!(ｌｏｕｔａｂｏｖｃ・Themeasurementscarried

outwithcompoundsAtoDwercdetermin8Lti(DIlH(〕Itl)ccocfficientOfdynamicfriction，

theonlyarbitraryconstantusedinfittiIlgI11じｐＤｉ】ItstothGcurvcbeingtllcforce

constantP.ＴａｂｌｅｌｇｉｖｅｓｄｅｔａｉｌｓｏｆＥａｎｄ帆．

16

OO

ＴＡＭＩ」１１

ノハハＲｍＯＵｚ ｏ，Ａｇ/rUjJ2 a00IPo8fルイ『、、

９仏

Ｉ１１

luu1rillc〔ｌｎａｔｌｕｍＩｒｌｕｂｌ〕cx・

unfillc〔lnatQu｢a1rubbcr

lD11lille(１１１atluralrubber

UUatumIrlII〕l)ｃｒＩｉⅡc〔Ｉ

ｗｉｔｌ１うＣｌ〕.Ｐ｣】、１－いFblacIに

１１．８Ｈ

１8.3 』().０

，，，Ｉ

ＡＢＣｌ

｛Ｊ望０戸

◎ｌＰ１

ｑ■℃

Ｐ９９の』Ⅱ

lｌ Ｍ

ｉｌ

･１１．０ ＩＣ･４７ ｣彌鰄、

ThevaluesforcompoundEarecoefficientsoIstaticfrictionreplottedfromacurve

givcnbyTIIrRIoN,､Inthiscase,themoduluswasnotknownandhadtobeadjusted togivcbestfit・Ｔｂｃｐｒｃｓｓｕｒｅｓｃｍｐｌｏｙｅｄｉｌｌｔ]lcdyl1amicfrictionexperimentswcre

notlargccB1oughtobringmutualintcrfcrcncc(〕ｌｔllcaspcritiesintoplayandcovGr

onlytl1cHcrtzianrange・Thctheoryisobcy('1111(’１℃untillowvaluesof(ｶﾉE)arcreachcdwhcrctllccoefliciel】toffrictio1waTicslcsHwiⅡ11M)TmaIloadtha】1cxpccted・ＴＩｌｌＲＩｏＮ,s

staticfrictionvaluesreachwellintothesatur;LIi〔)nrangeandagreewiththetheoretical

cu｢vc,I-IiglIcrprcssuresllavebcencmp10yc〔11)ｙｌ北ＮＮＹ１ｏ,ｗ１】oinvcstigatedthcfrictionoIanumberofcompouJldsonpolishedstcc11111〕ricatcdwitholiveoiLHisrcsultsare

giveninFi9.7ａｎｄｓｈｏｗｔｈａｔａｔｌａｒｇｅｎｏ｢ｍall[DHL(1sUlccoeffici(mtoffrictionisnca｢ly invcrsclyproportionaltothepressurG`inagTじじmcntwitllFig､６．．

DENNYfittedhisresultstothecmpiTicalc(１１１.(T2)tIIctypcofwhichhadfirstl〕eGn

suggestcdbyTlllRIoND：

鰊】"』｣－，＋[swAi,）（』贄）

！

⑪。心００

ｌｌＢＰｄ■■Ⅱ▽６．ローマＰ■■０‐０』可

面剋

◇勺ｐ●■０ｄＢ口・ＯＣ０Ｐｊｐ・一

ｐＰＩ

ｐ･。

ＩＩｌｊ

ＩｏＰ４ Ｉｏ－。 ｌｏ－ｚ ＩＯ－Ｉ Ｉｏ ｐ/gb

Fig・７．CoclIicientsof〔lvnamicfrictiononpolis1Ic《IHLcuIIlobricatedwitholiveoi]･ＦｕＵｃｕｒｖｅｃａｌ－び

cll1atedfromcqn･(【｡)･FiguresmaTl[edagainstc〔)10,1〕oⅡ､〔lsarcBSllardncsSes・VelocitVo・ｏＹｃｍ/sec・FrOmTeflD．￣

庇e/β搾りＩＣＢＳ力.￥ｴｱ

｡■

…:蝋鶏＆

｡

▲ＨＹＣＡｐ９ｏ▲ＳＩＬＩＣｏＮＥＢＯ

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ｏＨＹＣＡＲ６ｏ①ＮＡＴＵｎＡＬ６ｏ

＋ＮＥＯＰＲＥＮＥ９ｏ⑨ＮＡＴｕｎＡＬ４ｏ

●ＲＥＣＬＡＩＭ８０▽ＣＥＬＡＴＩＮＥＥ

▼ＧＥＬＡＴＩＮＥＤ

八 ｜●

０△■ｐＦ０ｉ０■０日■■■■■Ⅱ０ⅡⅡⅡ９９６ⅡＰ＋‐・●０００■１００

VOL､１（1957/58） 八．ＳＣＨＡＴエＡＭＡＣＩＩ394 ~チョ

レ‐

whereAisamaterialconstant(nottheareaofcontact1)andEo,thccompressionmodulus・

Accordingtoeqn.(ｴ2)thecoefficientoffrictionbecomescoI1stantatlowpressurcs、

Aseriousdeparturefromthetheoryontheloaddepcndenceofrubbcrlrictionas

representedbythefullcurveinFig､OoccursthereforeoI1Iyatlowloads,Itissuggestcd

thatthisdiscrepanCyarisesfromthefactthatrubberasperities,ｅｖｅｎｉ（ｔｈｅｙcanbe

approximatedtohemispheres，arenotidenticalbutstatisticallydistributedinsize・

TheinHuenceofthisinhomogeneitywiUbemostpronouncedatlownormalloadswI1en

onlytIlelargeraspeTitiesareincontactWiththetrackbecausconincrcasingtheload thetrueareaofcontactincreasesatagreaterratethanwitIlidenticalasperities・A

quantitativeestimateofthiseffectcanbeobtainedbyassumingthatｔｈｅｒａｄｉｉｏｆｔｌ】e

asperitieshaveadistributionfunction/(i')｡'becomingzeroforamaximumradius

γ,,!“・Atlowpressure,whereonlythelargestasperitiesareinvolved,ｔhedistribution

functioncanbereplacedbyitstangent,ｓａｙ

丑一・＝

一過】

/(r)`l′＝conSt.(７，Mｍ－γ)〔lｒ ('3）

Assuming,fUrthermore,thevalidityofHERTz,sequationsbothforaTeaofcontactand

compressionofhemispheres,thecalculationhastheresultthat ’0

ｓｏ

/JloWWEノーCOnSt,け/万)-V， (】4） １１

０’１００

８１■●

ＡＲｃＩＩＡＲＤ］lhascarriedoutasimnarcalculation，makingtheassumptionthatthe

asperitiesareidenticalhemispheresevenlydistributedondiffCrentlevels・Thecoeffi-

cientoffrictionisinthiscaseproportionaltop-nA.Itwillbeseenthereforethatany

inbomogeneityoftherubbersuTfacetendstoreducethepressuredependenceofthc

coefficientoffriction・Ｉｔｓｈｏｕｌｄａｌｓｏｂｅｂｏｒｎｅｉｎｍｉｎｄｔｈａｔmacroscopicallyimperlcct

contactbetweenrubberandtrack,whichmayeasilyoccuTundcrlowloads,willaffect

thefrictionalbehaviourinasimilarway・Thisproblemwillbediscusscdinmo｢edetail

whendealingwithfrictiononroughsurfaces・

RATNERANDSoKoLsKAvAﾕ２havesuggestedthefollowingscmi-empiricalrelation betweenthecoefficientofstaticrubberfrictionandJlormalloadL：

ijl l:Ｉ

一宇

･１１ ６１

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TheinitialincreaseoftheimpedanｃｅｏｆｔｈｅｆｒｅｓｈｓａｍｐＬｉｓｄｕｅｔｏｄｅｆｏｒmationof

therubberasperitieswhichaTeshearedduringsliding・Thefrequency-dependeJIceoftheimpedanceafterabrasionindicatesthatthecurrentthroughthesamplehasalarge capacitivecomponent・TheinteTpretationofthisresultisthatstructurebreakdown

inthesurfacelayerhasgonesofarthatthefiUerpartic1esarealmostcomp】etelyisolatedfromeachother・Thelayerhas,forpracticalpurposes,becomeadielectric・Thatthis

effectisreaUyduetochanｇｅｓｉｎｔｈｅｓｕｒｆａｃｅａｎｄｎｏｔｉｎｔｈｅｂｕｌｋｏｌｔｈｅｓａｍｐｌｃｃａｎｂｅ ｓｈｏｗｎｉｎｔｈｅｆｏｌｌｏｗｉｎｇｗａｙ･

Ｉｆ,insteadofapp1yinganalternatingvoltage，adirectvoltageisconnectedacross thesample，thedirectcurrentvoltagedropisconcentratedinthesurfaceskinand， thelayerbeingthin，shouldproduceahighelectricfieldstrength･This,ｉｎｉｔｓｔｕｍ， shouldgiveTisetoelectrostaticattractionbetweGnsampleandtTack，incrcasethe normalloadandthereforealsothefrictionalforce･Thisexpectationhasbeenborne

outｂｙｅｘｐｅｎｍｅｎｔａｓｃａｎｂｅｓｅｅｎｉｎＦｉｇ・ェ３Ｍoderatevoltagcssufficetoincreaｓｅｔｈｅ●

frictionalforceconsiderably，thusgivingindependentproofo（the・cxistenccofan

inhomogeneouslayeｒｏｎｔｏｐｏｆｔｈｅｓａｍｐｌｅ・ＴｈｅｔｉｍｅｅｆｆｃｃｔｓｓｌｌｏｗｎｉｎＦｉｇ・ェ３arediscussedintheoriginalpublication，

AnestimateforthethicknessofthelayeTcanbeobtaincdfromtheincreaseinfTic-

"β/βγ…BSP￥'７

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。‐■ＯＵ１０ｐ，Ｉ？‐ｐＤｑ０ニロロ■●曰０９０－．８，－‐｜■■Ⅱ８●・ｈＢ６－，Ⅲ■１１守叶一Ｂ－Ｂ０ＩＬＩ・００’１◇山！。Ｉ－０９℃

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VOL.Ｉ（Ⅱ057/58） ＦＲＩＣＴＩＯＮＡＮ】）AIjIいＳＩＯＮＯＦＲＵＢＢＥＲ 4ｍ

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７０７５８０８５９０９５１００１０５１１０１１５１２０１２Ｓ１３０

(`識､,、MinuLeS△０９．K３．Ｔｈｃｅｆｆｅｃｔｏｆｄ.c，potentialsonthe（rictiUDnnlforceofanabraded･caTbonblack-loaded sampIe・Abscissa,ｓＩｉｄｉｎｇｔｉｍｅ，FTomrcflo．

tionalforceundertheinfluenceoftheappliedd.c､potentiaIdifferenceifanassumption ismadeonthedielectricconstaｎｔｏｆｔｈｅｌａｙｅｒ､Thecalculationhasshownthatthe

ordcrofmagnitudcofthelayerislo－２ｃｍ．

ＶＬＩＮＴＲＩＮＳＩＣＡＩ９ＲＡＳＩＯＮ

Ｔｏｊｕｄｇｅｆromtheprecedingsection,nodistinctionneedbemadebetweenfilled

andunfiIlcdrubbersifapictureoftheab｢a5ioD]mechanismisdeducedfromourscratch-

ingexpcrimcnts､Thcqualitativediffercnccinsurfaccdamageonfilledandunfilled compoundsobservedduringthatinvestigationcanbeatt｢ibutedtothefactthatit

wascarricdoutwithsampleswhicllhadundCrgonenoprc-stressingeflects・

御earingtllcscconsiderationsinmmd,atheoryofabmsionl3haSbeenbuiltupon[IleresultsillustratedbyFig8・IthasbeenassumedthattearsacrosｓｔｈｅｐａｔｈｏｆｔｒackasperitiesaTethefiTstand,attlucsKlluI(Bｔｉｍｅ,「ate-determiningstageintI1eabra-sionproccss,ｔｂｅｄｃｔａｃｈｍｅｍｔｏｆｔｈｅａｂｍ(l(P(１１)Klrticleduringsubsequentpassesofthe abrasiveoverthetearbeinggovernｃｄｂｙＫＬｍｃｃｈａｎｉｓｍｓｉｍｉｌａｒｔｏｔｈａｔｄｉscussedin

conncctionwitllFig・ｒｒ・ＴｈｅｖｏｌｕｍeoIlIlcabradedpaTticlehasbeentakentobe

proportionaltotI1ecubeofthelengtholtIlcoTigimaltears・Inspectionofthephoto‐graphsinFig,sindicatesthattheseteKmmrcofｔｈｅｓａｍｅｏＴｄｅｒｏｆｍａｇｎｉｔｕｄｅａｓｔｌ１ｅ ｗｉｄｔｈｏｆｔｈｅｔｒａｃｅ,Ithasthereforebecna雛umcdthatlengtlloftearanddiametｅｒｏｆｔｂｅarcaofcontactareproportionaltoe8Ldl()Ｉｈｅｒｓｏｔｈａｔｉｔｏｎｌｙｒｅｍａｉｎｓｔｏｄｅｔermine thcarcaofcontactundcrvariousconditiuIls・ModelcxperimentsinwhichanumberofcompoundslMwebeenindentedbyalargL9爵l〕IICrchavesbownthatthediameteｒｏｆｃｏｎｔａｃｔｎｆｏＩｌｏｗｓｔｏａｇｏｏｄａｐｐｒｏｘｉｍａｔｉｏｌ１ｌｈｃｃｌｌｂｃｒｏｏｔｌａｗ

Ｄ■０口。し

０白・ＢＣｑＰ▲■■■■０ⅡⅡｑ・Ｉ・‐●６↑■０■００

,fＰ７ Ｑ｡

、＝cuu腺Ｌクリ、 (Ⅱ6）

whicI111asalsobcenlbundvalidforthccoIIIID1℃＆sionofrubbcrspheTes,Itfollowsfrom ルル施川“５ｶ.“７

２４０Ｖ 。、 ／￣

声－－ヶ 2ｑＯＶ

･叩「

■■■■■■■■■■■■■■

￣

■■■■■■■■■■■■■

一一顔､。「

－－Ｊ

k９

Ｏ

Ｚ

Ｏ

Ｓ

ａＯ ５１０１５２０２５３０３５４０４ｓ

朝v}￣

120Ｖ ｏｎ ア

こ＝￣ ‘ 屯一炉－￣

￣

１割↑０５ ０

０Ｚ ａ

｜ Ｉ ’ VOL､１（1957/58） 4oｚ Ａ･ＳＣＨＡＩＴ－ＡＭＡＣＨ

eqn.(ｴ6)anddimensionalconsiderationsthattheabrasivewcarIl'pcrunitarcaof

sampleshouldbegivenbyeqn.(r7)：

W-colust.γ(，/E） (】7）

whereγistheradiusofcurvatureatthetipoftlIeabrasivcgrain,Accordingtoc(ln`(I7)，

rubberabrasionshouldincreaselineaT1ywithincreasingnoTmaIload，

WhenattemptingtoverifyexperimeiitallyatheoreticaIloaddepcndenceofTubbeT

abrasion,caremustbetakentoavoidcontaminationofthetrackbyimpuritiesissuing

fromtheTubber,Asinthecaseoffrictionexpenmentsprcviouslyreferredto,thiscan

beachievedbyacetone-extractionofthesamples・ＴｈｅerraticnatureoftI1eresults

obtainedotherwiseisiUustratedbyFig.ｒ4.Twotyretreadsamplesofnaturalrubber

oneofwhichhadbeenextractedjwererepeatedlyabradedeachonitsowntrackof

6ocmlengthUnderaloaｄｏｆ２.r４ｋｇ,themteofabrasionoftheextTactedｓａｍｐｌｅｒｅ‐

mainedreasonablyconstantbuttherateofthenot-extractedsampledecreasedsteadily

tovelylowva1ues・ThetrackbecameprogressivelydaTkerintheprocess・Underthehigherloadof8・Ｉ４ｋｇＯｔｈｅｒａｔｅｏｆａｂｒａｓｉｏｎｏｆｔｈｅｅxtractedsampledecTeasedsIiglltlybuttheabrasionofthenot-extractedsamplei"〃Ｂａｓｅ‘considerably,whilstagradllal

■否

口印萩

Ｐ⑤ロ十

、

（●■■ワニ■日日ⅡⅡⅡⅡⅡⅡⅡⅡⅡⅡⅡⅡⅡⅡⅡⅡⅡⅡⅡⅡⅡｕＢＢＵ・クユヮニタⅡ。■■ⅡⅡⅡⅡ■ⅡⅡ００口■日日日日口０■Ⅱ０口■曰■ⅡⅡⅡ、’二仏□・△■■■■■■■Ⅱ■■■■Ⅱ■■００■■■■■■■■■■■■Ｕ００Ｄ

Ｏ

ｏ

ａ

Ｏ

Ｅ。」奇Ｅ」Ｅ・扇Ｅｐく

1０ ２０Ｒｕnｓ ３０

［ⅡⅡⅡⅡ［ⅡⅢⅡⅡⅡⅡⅡ［ⅡⅡⅡⅡⅢⅢⅢ［１－－－－－」５

Ｏ

Ｏ

ａ

Ｏ

１

１

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5０

－１■Ⅱ口巳１■０Ｐ。

０．０

５１０ＲｕｎＳ１５

Ｆｉｇ．】４.VariationsintherateofabrasionoIanot-extractedandancxtTnctcdnatu｢aIrubben,ＩＤＩ￣canizatefilledwith5op・Ｐ.ｈ・MpCblackwhenusingrcPcatedlytIBcsamcsiliconcarbidct｢ack(Icngtlu160cm)．

尺どん”〃“s少･“７

■、

￣￣~宅ヨ

－－－へＩｏｏｄ■２．１４ｋｇ

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￣

巳

。

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Ｉｏｏｄｐ８､1４

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ｄｆｒｏｍｈｅｒｅ

１１－

巳ＣＯ

vｏＬ１（ｴ957/58） ＦＲＩＣＴＩＯＮＡＮＤＡＩＢｌ(ＡＳＩＯＮＯＦＲＵＢＢＥＲ ４o３

●『’ｄ□Ⅱ

clcaringofthistrackwasobserved・InthM8Ltt⑥I･casetl】esampleappearedtofuI1ctionlikearubbereraser・Ingeneral，ｉｔｈａｓｂｃｃ】１１(〕uI1dthatcontaminationofthctrack

becomesprogressivelymoreseriouswith〔lccru81singrateofabrasion・ItalsotcndstobemoretroublesomewithsyntheficthanwithnKltumlrubbcr・

ThercsultsgiveninFig､r5l1avebeenobtdlinu〔lwithflatextractedandvacuum-dried

samplcsonfreshabrasive(GaTnetpaperwitlMLmcallgrainsizeofo､ｴ3ｍｍ).Further-

more,thedirectionofabrasionwasreve｢slxl81ncrc8lcllTunof64cminordertoprevent theformationofso-calledabrasionpatterjlswhicharethesubjectofthefollowing section・AbrasiontakingplaceunderthcseconditioJ1swiUbeca11ed‘`intrinsic，,abra-

sionFig・エ５ｓｈｏｗｓｔｈａｔｔｈｅproportionaliIyofintrinsicabrasionandnormalloadgivenbyeqn.(r7)isconfirmedbyexperimc1It．

00

llj il1 Od

＋■8

lｉ ｌｌｉ ｌｌｌ

伊

1１

(;蝉,､、

■●‐■９。。▲■▲■ｒ０ⅡⅡ■０日日●’０■。。■０。

■已巴

■U

Fig.Ⅱ5.IntrinsicabrasioTlplottedagainstnoTmalI1rc錨lIrc,Compounds:Ａ,KryIene(･･Coldrubber,,）fiⅡｅｄｗｉｔｌｕ５ｏｐ.ｐ､ｈ・ＨＡＦｂＩａｃｋ；ＢｔｏＤ・natuTHuITllbI】ｃＴＩｉｌｌｅｄｗｉｔｈ：Ｂ，５ｏｐ・P.ｈ・ＨＡＦｂｌａｃｋ；Ｃ０７５ｐ.p､h･fincthc｢maIblack；、，Ｉ３ｏｐ・ｐｈ・PKltljluHon`sactivatcdCaCO3・Velocity,ｏ､６６ｃｍ/sec，Ｆromrcf.nｺ．

Ｉ Eqn.(［7)predictsalsothatabrasionshouldbcproportionaltotheradiusofcurvatureof

tllcgrainbutindcpendentofitssize､Ｔｗｏdistinctpossibilitiesarisehere・ＩｎｔｈｅｃａｓｅｏｆＲりん形"“s力.乎'７

／

／

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〃

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０ １

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VOL］（ｴ957/58） 4０４ Ａ･ＳＣＨＡＬＬＡＭＡＣＨ 》碑（’

「１１

polyhedralgrainsofdifferentgradethereisnoaﾚｱjoγjreasonw]lytI1eslla｢pnessofthe cornersshouldbeaffectedbytheiTsizesothatabrasiomshouldbcindependentofthe

coarsenessoftheabrasiveThisconclusionhasbeentestedbycarryingoutabrasion experimentsongaTnetpapersofdiffeTentgTades；ｔＨｅｒｅｓｕｌｔｉｓｇｉｖｅｎｉｎＴａｂｌｅｌＬ ●●

~￣ﾜｰ

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八m】RASION】ＮＪＯ－３Ｃｍ３/ｍ,cｍ:ＯＮCAR】VETFAP正ＲＯＦＤＩＩ;【『HRENTCOARSl2肘皿S局.（IFT(】ｍｒｃ(.1ｺ.）

GmilU8ir6DjDl0DU ０．６Ｊ 、.『］ ⑪ぶり

NDrojllUIpPFssMrB』jbg化DDI００．３３ I･鞠０．５３ﾙ89⑰.Ｊ]ﾙUf●■

NaturaIrllbberwith

５ｏｐ.ｐ｣､、HAFbIackNatuuTalrubbcrwiｔＩＵ７５ｐ.ｐ､ｈ・

fincthermaIbUnck

Kry1enewith5olp､Ｐ.}u、ＨＡＦｂｌａｃｋ

１．６０６．００1．７６６．８２】.８J８．９７

浬○ＯＩＯ,Ｃｓ空.９７Ｊ３．ＯＳ３．＄３Ｊ３．７０

Ｊ.､1３５．，６１．８３7.5◎空.RＩｕＯＩｏ

Ｐ・ユ・ユ

TablelIshowsthatwhilstabrasionisnotstrictlyindepcndentofthccoarscncssof

theabrasive,ａｎａｌｍｏstfivefoldincreaseingrainsizeleadsintheworstcasetonomore

than７０％increaseinabrasion

lncontrasttopolyhedralgrains,wearonabrasivesu｢faccswhichcanbeapproxim-

atedtoclose-packedspheresshouldbeproportionaｌｔｏｔｈｅｇ｢ainsizc・Sucllabrasivcs

arenotavailablebutToadsurfacesmayfallintothiscategory、AfewexpeTiments

havebeenmadconconcreteroadsofdiffercntrougImessandithasbccnfound】３tllat

inthisspecificinstanceabrasiononacoarsetrackwasalmostfouTtimcshighcrthan

⑪nasmoothertrack・A1thoughitwasnotpossibletomakeaquantitativccomparison

betweenthetworoughnesses,ｔｈｅｒｅｓｕｌｔｃｏｎｆｉｒｍｓｔｈａｔｔｈｅｌａｗｓｏｌabrasiondepcndin

partonthenaturｅｏｆｔｈｅｔｒａｃｋ，

Thetestsofthetheoryofintrinsicabrasiondiscussedsofarconcerno】11ytheinflucncc

ofextemalparametersontherateofabrasion・Animportanttcstofanytheorymust

bewhetheritallowstheTelativeintrinsicabrasionTesistancesofamytwocompounds

tobepredictedfromtheiTphysicalproperties・IntbisrespectonIybroadly〔Iualitative

relationshavebeenascertameduｐｔｏｎｏｗ．Ｉthasbeenpointcdoutinscctionlvthat

theoriginalteaTsassumedtobethedominantfactorinabrasionresistanceareducto

tensilefailuTe,Abrasionshouldthereforeincreasewithdecreasingtensilestrength，

Accordingtoeqn.（r7),abrasionshouldalsoincreasewithdecrcasingstifiness・Itis

interestingtonoteinthiscontextthatinempiricalattempts2otocoTrclateab｢asion

withphysicalpropertiesithasbeenfoundpossibletoestablishcouTclationequations

ofthetype

◆

け0

晶沙０ｌＩＩＩＩＩＩＩｌＩＩｌ仏ｒ０ＩⅡⅡＩ８０ＩＩＩＩＩ－Ｎ切ｉＩ０ＩＩＩｌＩＩＩＩＩＩｌ脇６

●￣

■己■

●●

芦靜

’ Ⅱ′＝αｏ＋ｎｌｘＳ】loTcluardnesS＋、鴬ｘｔｃｎ&i】cHtrcngtlu

where、｡，n1anda2areconstants・Statisticalｗｏｒｋｏｆｔｈｉｓｋｉｎｄｄｏｃｓｌ１ｏｔ，ofcoursc，

involveaphysicalpictuTeoftheabrasionproccss・

庇β/ｅｒＢ０Ｉ“ｓＰ・ヂJ７

‐・Ｉ’１１‐‐Ｉ‐ｉ－１‐－‐‐‐↑

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’１

InassessingTelativcabrasionvalucsfr()mtcnsilcstTcngthandstiffness,ｔｗｏ(Iuali‐ ficationsmustbetakenintoconsideration.Ｔ11(D9itiffncssopcratinginabrasionistbat ofthchiglllyprcstressedtop1ayerwhicl1isl()wcrlhKlntl1atoftl1ebulkmaterial､Second‐

lylbccauseofthesmallscalcoftbeelemcllmry6LI)ruLsio】Iproccsstl1elocalratcsofclong-ationarcvcryhigh・IfforcxamplethcconmcIKlrcaL1〕ctweenabrasivegrainandrubberisaboutl/Ioommindiameter,aslidingvclocil)'()１１ｃｍ/sccwillgivearateofcxtcnsion‐

to-l)｢cakofaboutl()｡,()()()％/SCC・Atsuchratc5,tcnsilcstrengthmayapprcciablydilleTlromthatdctcrmincdbyconventionalmctho(１日.ＧＩ(1:ENsMITH21hasrecentIystudiedthcwLriatiomoftcnsilcstrengthwithratcolelongationofrubbercompounds

andllasloundtl1attl】ctcnsilestrengthofunfilledGR-Sincrcasespronounccdlywithincrcasingratcofelongation,Thiscompoundoffersthereforeanopportunitytoinves‐

liliWW,１１;:１１::ｉＩｉｌＷｌＷｉ臘鰯謡::{!:1噸91.MjWi鶉篭iWWi謡ImcasurcmcntsandGI(EI§NsMITH,ｓｄａｔａａｒｃｇｉｖｃｎｉｎＦｉｇ・エ6.Ｉｎｔｈｅエ,０００－fO1drangeof

vclociticscovered,tensilestrengthasfuncti〔》l】ofmte伽andintrinsicabrasionresistance

(asscssedhereasthereciprocalofabradedwciglltforagiventracklengtb)asfunctio11

ofveIocityobeythcsamepowerlawwithintbclimitsofcxperimentale｢ro｢・Tbisresult

appcarstobcconfirmatoryevidencefortlＵｃｃｌ()HCconncctionbetweentcnsilestrength andintrinsicabl･asion．

１１

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ｑ円鳴川Ⅳ仙川悩侶ⅢⅢ叩６１旧川叱ｉｌ０ＮＷ川旧・秘○ｋ川肛Ⅲ川Ⅷ川Ⅲ租刈曰旧、ⅡⅡⅢⅢＪⅢ小Ⅷｎ１ｌＩｈｊⅢⅡ剖咀■■Ⅲ泗旧用Ⅵ９１・仙測１Ⅱ四月Ｒ川咀叩刊６０口Ⅱ別呵？Ｊ１心も０９８６０冊Ｊ冊凹冊ＩＩＩ１Ｕａ囚刎

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Fig・エ７exhibitsclcarlytwooftherelevantcharactcristicsofabrasionPatterns・TheirintensityincreaseswithincreasingcoarsenessofthetTack・anditalsoincTeases

withdecTeasingstiffnessofthecompound・Ａｔｈｉｒｄ,andpossiblVthemostimportantpTopcrtyofabTasionpatternsisthatｔｈｅｙincreascthcrateofab｢asion､Thishasbeen

slDownbythefollowingexperiment・Ｔｗｏｓａｍｐｌｅｓｏｌｔｂｃｓａｍｅｃｏｍｌ)oundwereabradedonthesametrackbutonlvonewasallowedtodevelopapattcrn・Ontheothersample，formationofpatternwaspTeventedbyperiodicallvchangingthcdirectionofabrasion ◆

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ratesofabrasioninthetwoseriesofmeasurcmcntsareshowninFig､r8aslunction

oftbclcngtlloftheabrasivepath・Asseenfromcurvc(a),thcrateofabrasionatcon‐

stantdirectionincreasesforaconsiderabletinlcbcforebecomingconstantandtlle

patteTnbaslullydevcloped・Inintrinsicabrasion,cuTvc(b),onlylittlechangeoccursin

theinitialstagcsoftheexpeTimcnLandtbefinalvalueoftherateofabrasionｉｓｌｏｗｅｒ

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Thcexplanationoftheadditionalwearcausudbyabrasionpatternsemergesfrom am緬mimationofthcirprofiles・Cr・sssectionstllr･ughtwodifferentabrasionpattemsarcrcI)Toducc〔linFig，１０ａｎｄｓｂｏｗ,ｆｉｒｓｔｏfall,tllatthcphenomenonasitoccuTson

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ｓｅｅｎｉｎｂｏｔｈｐ｢ofilespointagainstthedirectionoIabrasion,Whenmovingovertrackor road,tIleyarcbentbackward,thusexposingtllcirundersidctoabrasionandprotecting fromabmsionpartofthesurfaceintheirrcar・This･givesrisetothepeculiar``under-cuttingD,effects・TheteethwearprogressivelytIliImcruntilthecrestsarebodilytornofflcavingbluntedges,ｓｏｍｅｏｆｗｈｉｃｈａｒｅｓｃｃｎｉｎＦｉｇ・l9Inthemeantime,theridgescontinuctogrowoutoftheunderlyingbulkmuLtcrialandtllepatternistoaceTtain

degreeself-perpetuating,Whenkeepingapatterl1lM1dcrobservationduringanabrasion experiment，itisfOundthatitmaintainsitsgclluralconfigurationforshorttiｍｅｓｂｕｔ ｍｏｖｅｓａｓａｗｈｏｌｅａｃｒｏｓｓｔｈｅｓｕrfaceinthediructionofabrasion18.Ｔｈｅreasonisthat

theattackoftlueabrasiveontherubberhas,Klsitwcre,aforwardcomponent・BecauseofthegTeatdifferenceinscaIebetwecnthesizeoftheparticlescomingoff

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oftbetotalabrasivewear・ThiscontributiontoabrasionwiIlｂｃｒｃｆｅｒｒｃｄｔｏａｓ``patternabrasion,,…

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cleaTlyshownbytherelativeabrasionfiguresobtainedfoTthetwosamｐｌｅｓｓｈｏｗｎｉｎ Ｆｉｇエ７.TheintTinsicabrasionsofthesecompoundsareverynearlyequalbutonceapattemhasdevelopedonthem,theabrasionofthesoftercompoundishigherthantbe abrasionofthehardeTcompound,ａｓｓｈｏｗｎｉｎＴａｂｌｅｌｌＬ

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WithequallydevelopedpatteTns，therelativeratesoIpattemab｢asionmaybe expectedtodependonthemechanicalstrengthoftheTubbcr・CompaTisonwithexperi‐mentallydeterminedstrengthdatashouldinpTincipalbeeasieTheTethaninthecase

ofintrinsicabrasionsincethelaTgerscaleofthephenomenonrcducestheratesofstTain byseveralordersofmagnitude・Anexampleofsimilar-sizedpattemsgivingdifferentrelativeratesofpatternabrasionisprovidedbycarbonbIack-fiUedcompoundsof natura1rubberandGR-S・Abrasionpattemsproducedonthesecompoundswhemslidingoverdifferentroadsurfacingsareshowni、Fig.２０.Thissctofphotograpbsindicatescertamdifferenccsintheappearanceoftheabradedsurfaceswhichmaybedueto differentmechanismsoffailureoperatingonthetwocompounds． ＲどんrGD8姥sかｷﾞｴﾌ

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ofcyclesnecessarytoachievethiswastakentobeameasureofresistancetotearprop-

agation、Ｔｈｅｓａｍｐｌｅｓｗｅｒｅ１ｍｍｔｈｉｃｋａｎｄ２５４ｃｍｗｉｄｅ,ｔｂｃｗｅｉｇｈｔｗａｓ４１４ｇａｎｄ

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propagationofnaturalrubberundertheconditionsofthiscxperimentappearstobe

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inTableV,butitwillbeseenthattheobserveddiffeTenceinpattemabrasiononnatural

rubberandGR-Scompoundsagreesqualitativelywiththedifferencesinmecllanical

strengtbthougbttogoveTnpatter】labTasion､SimilaTresultshavebcenobtail1edwitll

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AsimpletheoryofabTasionpattemｓｈａｓｂｅｅｎｄｅｖｅlopcdinclosccom】cctionwith

thetheoryofintrinsicabrasionl3、Theprofilesofabrasio】】pattcrnssllowninFig､I9

makeitclearthatthephenomenonmustbeginwithpartoftheabradedTubbcrsurfacc

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thisinitialstepisfacilitatedbylipsofthetypeseeninFi9.8(b)whicIla｢ethrownup

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teaTsandlipswillbelargerthantheaverage,Astheabrasivcl1assesoverthelipsand

stTetchesthemouttheywillcoveroneormoretearsinthcirrearandprotectthem

fromfurtherdamagebeforetluelipsretract・ThusalinearpeTiodicstructuTeisinitiated

which，however,doesnotyetconstituteanabrasionpattcmbccauseofthelackof

lateralalignmenLWhenabradedrubbeTsurlacesarecxaminedduTingcarlystages

ofpatterndevelopment，suchincipientformationsaTeindcedobservedassllownin

Fig､２r(a).ThesefragmentaryabrasionpatteTnsmustbccxpcctedtomig｢atcacross

thesurfaceinthesamewayascompletepatteTnsbutthcrateofmigrationissubject

torandomeffectsandoccasionallytworidgesegmentscomcabreastandlincupwith

respecttoeachother､Thedevelopmentofthcpatterniｓｔｌｌｃｒｅforearelativclyslow

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produceanabrasionpatternunderthesccollI1itions・TI1ispointisillustratedbyFi9.22．Atypicaltyrctreadcompoundo[naturalrllbl)crwasabradedunderotberwiscidentical

clrcumstancesongarnctandemerypaper・Abrasiononthegarnetbeingrapid，ｏｎｌｙvestigcsofanabTasionl〕atternaTeformed，whereasapronouncedpattemdcvelopsontllcblunteremcrypal)cr・SimilareffectshKlvebeenobscrvcdwhencomparingrubbersurfmccsabradcdonfrcshandrepcatedlyuscdspccimcnsofthcsameabrasivc，This

isals()ｏｎｅofthercasonswhyabrasionpattcmsIormwithgreatcreasconroadsurfac-

綴uIIillll側:Yb鶏継(,既|h;;::１W;認『鯨蝋…[hmtwh…ridgcsbccomccomparablcinsizcwiｔｈｔｈｅ[limImsionsoftheabrasivCgrain，thesllape

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１ １１ ofthegrainsbecomesimportant、IntIIecaseoffilledrubbcrstlIcrcisatendencyfor

theabrasiveparticlestoploughthroughtberidgesandpToduccscoTingmaTks・Tl1is

effectisshownbythephotographsinFig､z3whicharetwopicturcsofthesameabraded

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incidenceoftheiuumination､Ｉｎｃａｓｅ(a),tllelightwasparaIleltothedirectionof

abrasionandshowsupawclldefinedifnotveryintensepattern;i】1case(b),wl1crethc

liglltwasatTightanglestothedirectionofabrasion，onlyscoril1gmarksarcsecn，

Becauseofthelackofcontinuityintheridges,ｓｕｃｈａｐａｔｔｃｒｎｍａｙｂｅｃａｌｌｅｄａ``pseudo-

abTasionpatteTn'0.IngeneraLnoscoringma｢kscanbediscovcrcdonToad-aI〕Tadedrubbersurfaces・

Inthcprevious1ypublishedtheoryofab｢asionpattcms13itbasbecnassumedtllat

theiTspacingdependsonlyoｎｔｈｅｓｉｚｅｏｆｔｈｅｌｉｐｓｆｒｏｍｗｈｉｃｈｔｂｅyoTiginate・Tllislip

beingsolelydeterminedbytbelengthoftbeteaT,ｉｔｈａｓｂｅｅｍｄｅｄｌｌｃｅｄｔｈａｔｔｂｅｓＩ〕acing

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byexperimentsonacommercialabrasive(gametpaper)andhasbcenfoundtorcprc‐ senttheexpe｢imentalfindingsTemarkablywell､Fig､エフshows,however,thatc〔ln.(18）

willnotadequatelVdescribepatternsproducedonroadsurfaccs・

Thedifferenceinthespacingsofthｅｐａｔｔｅｒｎｏｎｔｈｃｔｗｏｃｏｍｌ)oundsoldilIcrent

stiffnessshowninthisfiguTeislargeTthanpredictedbyc〔1,.(r8)accordingtowlIich

thespacingshouldbeproportionaltotheinversecuberootoftbcmodulus,ＴＩＩcratio ofmoduliofthese2mbbersis1.85,givingatheoreticalratioofspacingsequaltoonly

l:Ⅱ.225.ThedifferenceinstiffnessoftheabradedsuTfaccswillactuallybecvcnsmaller

than工.８５becauseofpTe-stressingeffects，

ItissuggestedthatonroadsurfacesorgeneTallyonabrasivcswitllgrainsoflarge

radiusofcurvaturetheasperitiesinsteadofcuttingth｢oughtheridgcsglideoveTthem

andelongatethembyfriction・ThespacingisthendeteTminedbytheequilibriumof

fTictionalandelasticTestoTingfoTcesJtisshowninthenextsectionthatthefrictional

forceF/ofasphericalgrainwiththediametermisgivenbythec〔luation(20）パノーｃｏｎｓＬ７`【2(ｶﾉE)ﾘ。

庇e/〃β加“ｓＰ.“７

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1！ VOL.Ｉ（1057/58） ＦＲＩｃＴＩＯＮＡＮｌ〕AnIい葡I()Ｎ（)lfItIJllIBl§I《

+1３

Assuming，furthermorc，Hooke･ｓｌａｗｔｏｈｏｌ〔ｌ「urthelocalelongation，thcretractivelo｢ccJFrmustbcgivcl1byarclatiｏｎｏｆｔｂｃ「〔Drm

ノア「＝ｃ《DnHt.ｓ『Ｕノゴ

ｗｈｃｒｃＮｉｓｔｈｃｓｌ)acinga11〔い，ｔ１ｌｃｄｉａｍｃｔｃＴｏｌｔｌｌｃａｒｃａｏｌｃｏ､tact、Substitutinglor《Ｉ｢romc(111.(r6)andc(IllatingI7an〔１１｢,rcsulIsilItllcfollowingexpressionfo｢tllespacing：

.-…:鋤(;)り゛，`,ｌｗＩ)ＣＴＯ(（sthcdiameteroftheclose-packc(ＩＳＩ)I】cricalabrasivegrains・Ｔｈｉｓｅ(luationgivcsastronger〔lcpendenceofthcspKlcingsonbothmodulusandpressurethanc(1m.(r8),butinpracticeitisdiflicultto(1ｒｉｕｗａｓｂａ｢pdivi〔linglinebetweenthetwo91i鱒Qs.;lsissccnfromtheexperimentalrIDHlI1IHgiveninTabIeVI．

ＴＡＩｌＬｌｉＶｌ

ＳＦＡＣｌＮＣＳＯＦＡＥＲＡＳＩＯＮＰＡ１・ＴＩｉｌＲＮ筍ｐＲＯＤＵＣＥＤＯＮＴＡＲＭＡＣ・

ＮＡＴＵＲＡＬＲＵＢＢｍＲＶＵＬＣＡＮＩＺＡＴＩ鶴ＵｒＩＬＬＩ§ＤＷＵＴＩｌＣＡＩＲＥＯＮＢＬＡＣＫ

51nciｸ０９イリDIDｸリ

妬ハル「“"化J８１

ざゴルPJh.〃・ＩＦJJWルアｍＪＭＦＤ８１

ｆ５ｐＰ.A､〃`IＦ ⅡＩ

Pressure,ｏ,６６ｋｇ/cｍ= lnrcs田ure･望.６８ｋｇ/cｍ２ｒＰ

〔D・当Oo

ID腋１７⑪

1.Ｈ⑪

Ⅱ､６８

雪.２Ｚ

0.Ⅱ５５ ０.男Ｉ之

u､３７

Inthistable,「pistlleratiooftbespaciIlｇ３８１ｔｔｌｌｃｔｗｏｐ｢essures・ItstheoTeticalvalue

is,accordingtoeqn.(r8),(2.68/0.66)Ｉﾉ,＝1.5()5,6uldKlccordingtoeqn.(Ⅱ9),(2.68/0.66)ｿ, ＝2.18,ＴｌｌｃｒａｔｉｏｏｆｔｈｃｓｐａｃｉｎｇｓｏｎｔｈｃｔｗI〕ｃ()mpoundsis妬Assuming，ａｓａｇｕｉｄｅ，thatthcmtioofthemoduliisI.85,'cis,altcTc(111．（I8)，（1.85)'/3＝L225andafter cqn.(r，),1.351V,＝２．６０４．Itappearsthercforc[romthclimitedexperimentaIevide､Ｃｅ

洲鯉ＩＩＷＡ麓麗鰹瞬::１W&鑑|恕:!:;fp……､'m・ＩｔｓＩ}ouI(IlinallybcmcntionedthatabrasionpattcrnscanhaveconsideTablediag-

U1osticvaIuewhendctcrminingthemodcofwcnrtakingplaceu】1derconditionsnotacccssiblcto〔lircctobservation,Thisappli(ＰｓｌＤ&lTticularlytotyreswheretl]erelativemotionbctwccntyrcandtｒａｃｋｃａｎｂｃｄｅ〔111(?,'(１［｢omabrasionpattcms23．

Ｖ111．ＦＪＲＩＣＴＩＯＮＯ鷲！((》Ｕ〔;ｌｌＳＵＲＩＴＡＣＩＺＳ

ＡｂＴａｓｉｏｎｏｆｒｕｂｂｅＴａｓenvisagcdinthel)I･［'c(DlIil1gsectionsisaconsequenceoflocal lrictionalstressessctupbytheaspcritiesoftlIL9Lmckanddoesnot』incontTasttosolidIriction,reactonthcfrictionalforces・Friction(DnrougllsurfacescantluerefoTebetreatedbymctllodssimilartotl1oseemployed（orlrictiononsmoothsurfaces，without

regardbeingpaidtoanymechanicalfailuTecI1瓢liI1giH1thewakeofthetrackasperities・NocaIculationisnecessarytoseethattllcclDcfficicntoffrｉｃｔｉｏｎｉｓｌｏｗｅｒｏｎａｒｏｕｇｈ

ｔｈａｎｏｎａｓｍoothsurfaccbecauseofthesmallcrareaofcontact・ＴｈｉｓｉｓｓｈｏｗｎｂｙｔｈｅfollowingdataobtaincdwithanextractGdsamplcofanaturalrubberty｢ｅｔＴｅａｄｃｏｍ－ Ｉ)oundongIassgroundwithsiIiconcarbidcofdifferentgrade・ルノPrFJI“ｓｐ・ィJ７

､pO

Ill

illlll

ロ

'１ １１

' 4Ⅱ４ VOL､１（1057/58） 八．ＳＣＨＡＴⅡＡＭＡＣＩＩ

９ｓ〒

５▲

TABLEV11

COEFFlClENToFFHUCTUOlvONCRoUNDcLAsS.（lFromrcI・訓）

Diameterofsilicon

carbidegrainomm CocHicientulfTiction

PIatcglass

望・７９

ｏ・ｏｃ７

Ｌ３６

０．ｏィZ

Ｌｌ８

ｏ･Ｌｌ【

】．ニロ

Theessentialdifferencebetweenrubberfrictiononsmoothandroughsurfaceslies，

however,intheirloaddependence・Ｔｈｅ・reasonforthisdivcrgenceistbatoIuarough

trackboththetmeandtheapparentareaofcontactdependontheload,Aquantitative

estimateoftheeffectcanbederivedfromthemodelemployedinthethcOryofintrinsic

abrasion・Thetipsofthetrackasperitiesareagaintakentobesphericalandlargecom‐

paTedwiththerubberasperities､Grossdeformationoftherubberbytluctrackasperities isassumedtoobeyHertz,sequationsforsl〕hericalcontacts,andtbetrucareaofcontact

contributedbyeachTubberasperitytobeproportionalto(ﾉｹﾉﾉE)ﾂ｡，whercWistllc localpressure・Thecalculationhastheresultthatthefrictionalforccproduccdbyatrackasperityis

０１

毬Ｒ毬Ｒ

(=o） Fノーヮ(ｶﾉE)・ﾉ.‘１V・洲．▲■■■■、■■■■、■■■■■■■■■■■■■■■■凸Ｐ９‐Ⅱ●しけ■６日■、▽．■Ｖ６■■ＰＤＢＢ■■■■■・０●０凸０ｌｂ■■ＥＤＦ■ｑ０．６『ＯＳ。●０■■ロロ、Ⅱリーーーム■Ⅱワ９００９■１■口０００■曰Ⅱ‐０●０００－‐０６‐１－もＢＧＢＴ０００

’。‐０９５０９０■■■■０，■■■■■■７６００■■■■■■０００Ⅱ９０■■■■６■■凸■■■■■ｌＵＧ■０Ｆ０．０‐’００００１．７０↓▲■■■■１０１０‐ＩＩ９ｈ０ｉ９Ｉ０■■■ＤｌｌＢＵ■５ｃ●□■０？ｑ・ＩＤし’・Ｂ９０

Ｄ６‐‐‐‐０■。‐ⅢＨ０●Ⅲｐ６Ｌｗ－０い６７．０Ｐ’０。‐ⅢＩⅡＰｕ刮○』Ｈ１‐帆０‐‐’。‐－‐Ｏｕｒ‐片‐００口■。‐０－１－０９Ｉ。‐’９０宮９８□。．‐‐

可,．●可,．●

and

似一c…農('｜`'γ･('/歴１－V． い）の己の己

１ １。

whereristheTadiusofcurvatureanddthesizeofthetTackasperities・Therclation

(21)wasfirstproposedinaslightlydifferentformbyLINcoLN2`、Eqn.(２０)hasbeenconfirmedexpeTimentallyl3withanumberofcompoundsat

pressuresuptoabout２．５ｋｇ/cm2・Fig.２４givesthecoefficientoflrictionofthreedifferentcompoundsonsiliconcarbidepaperatpressuresupｔｏｎｅａＴｌｙｌｏｋｇ/cmaAt higherpressure,eqn.(2ｒ)fails,theCbefficientoffTictiondecrea5ingmorerapidlywith increasingpressurethanpredicted・Thereasonforthisdiscrel〕ancyisinallpTobability

●の

O■｡

｢.』：詞１

譜

ｌｉ

；Ｉ‐１

、▲－ｏｚＯＯ－ＺＯ４０．６０．巳１.Ｌ

Iｏｇｏｏｐ ●

Fig・全4.LogaTithmsofcoefficientsoffrictiononsiliconcaTbidcpal〕cr･gra(ＩｃＩ８ｏ,PlottedagainstlogaTithmofnoTmalpTeSSure.(a),unfilledvuIcanizateofnatural｢ubbcr;(b),vlllcanizateolnatuTal rubbcTfiuedwitln5op.p｣】・ＨＡＦｂｌａｃｋ；(c),vulcanizateofGR-S（】《｢沖､c)ｌｉⅡc〔ｌｗｉｔｈ５ｏｐ.p｣u・ＨＡＦｂｌａｃｋ､Velocity,ｏｏｏ２Ｉ２ｃｍ/sec、

庇どん”"“s，､イz７

＝⑤

･Ｑ２

･０．１ (□）

｜::Ｌ マーローロ

､一T-g皇----1b）Ｌ０．１￣へ゜

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ロ

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-０４－０２００．２ＯＬＡ０．６０８－１．０

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VOL.’（Iﾘ57/58） lPl(ＩＣＴＩＯＮＡＮｌ〕AlII(AHIＩＤＮ（)Ｉｆｌｔ【TlBI2ElR+1５

ａｂ

Ｆｉｇ．」５．Fricti〔)､;ＫＩＩ()】.c山I1IriIlg月tart（〕（ｍ《〕ljoDll，ＴＩⅢ．【ⅡIuI》Ii仰lqIdP(〕ＩｒｔＩｌｃｃｎｖｃｌｕＩ)ｃｉ叶６Ｌｍｃａ釦lrcofthetHungcntiaIlorcc、ＮｏｒｍＫｌＩＩ〕｢c錨lurc，ｕ,二SIWじIio笘川`'１．IIIll川(lvluIcmnizatcoIniutⅡralrIIIDber；(b),umtⅡralTlIl〕bcr【ilIc(lwjthうｏｐ.p｣9．卜いITljlKl〔:1L

fm1mm9、

cd

Fig､33(cい･ulcallimtcoIGR-月(I<rylcnc)fiIlc`lwiLlI5UI'.[)｣１．１いFbIacI`;(｡昨u鳥(c).blltsampIcloa《I“IwitlI」.｣３ｋ円/c、笘lor5miu1utcsIDcforetIMP⑥xlDcrim(Buut・Track：garnetpal)どr，grain5izeo・ﾕ９１ｍｍ．

牌turatioIIcffectsimilartothat(lemonstr`llcdinFig､５forthecaseoff]atcontacts．Ｌ＿ａ(lditioIltomutualintcrferencebetweelll･uIDburaspcritics,saturatiollcanhcrcbe

produccdbytherubberfillingthegapsbetwccntllctrackasperities（DENNY1o)． ItisHlttimesobservedthattheforｃｅｎｃｃｃｓｓａｒｖｔｏｓｔａｒｔａｓａｍｐｌｅｏｎａｒｏughtrack

isgreKlturtbant]ｌｅｆｏ｢ｃｃｏｆ(lynamicfriction瓢lIficicI1ttokeepitinmotion・Thispheno-menonof1`startil】gfriction'・hasbeeninveHtigKLtedinanumberofexperiments・Thetimcdcpendenceofthetangentialforcｅｗ【lsrCco｢dedduringtbcstartingperiod，tlledeflectionofthe(lvnamometerlMwingbeencuI1vcrtcdintotheout-of-balancecurrent

ofa2oo()scc-lalternatingcurrentbridge・RCI〕resentativeTesultsarethcoscillogramsinFi9.25,whichshowtheenvelol〕ｅｏｆｔ]1u〕lIt-ol-balancecurrentasｆｕｎｃｔｉｏｎｏｆｔｉｍｅ

(fromlefttorigbt).WiththeunfillednHltIlriLlx･ubbcrvulcanizatc(a),thcforcerises monotonouslyuntilｔｈｅｓａｍｐｌｅｂｅｇｉｎｓｌＩＤＩｌ１Ｉｗｃａｌ１dthcforcebecomcsconstant,but

whentllccompoundisfilledwiｔｈ５ｏｐＩ)｣1.11ＡITI〕Mck(b)thefrictiomLlforccl〕assest】]TougllKLsligbtmaximllmattllcstart、111iHcllcctismorepronouncedwiththeblack-lillcdGR-Scompound(c).Thetmnsitioll〔romrcsttomotionishereKlccompanicdbyavibmtionwhichtakessomｅｔｉｍｅｔｏ《ｌｉｃｏｕｔ・TheexccssofstartinglrictionoverdynamiclrictioniK)crIjascswiththCtin1ljlhＣｓａｍｐｌｃｈａｓｂｅｅｎｉｎｃｏｎｔａｃｔｗｉｔｈｔｈｅ Ｅβに”ＤｌｐＥｓＰ・fJ7

守0

＝

lｌｌ ４ｍ Ａ･ＳＣＨＡＴ－１－ＡＭＡＣＨ VOL.】（r957/58）､ざい

、￣

」

track.Ｉtcanalsobeincreasedbykeepingthesampleunderahigbloadbeforesta｢ting theexperiment，asshownbytheoscillogTamFig25(｡)．TableVIIIgivestypical numericalresults．

） ，、

ＴＡＢＬＥＶＩＩＩ

ＥｘＣＥＳＳＯＦＳＴＡＲＴＩ１ｗＧＦＲＩｃＴｌＯＮＯｖＥＲＤＹＮＡＭＪｃＦＲＪＣＴＯＯＮｏＮＧＡＲＮＥＴＰＡＰＥＲ･ＧＲＡｌＮｓＩＺＥｏ,臼OmmNoTmalpressure，１．２８ｋｇ/cｍ２

ら￣一君

!｡

MUf

fub6Fr

”0/dlJcT

Ｍ21.rIUbbfr D

JoPp.&.HHjG TA6sdwF,ロルァ

ウol81iPOUIFIdf”loUwl

Ｋ〃比ＤＵＢＤ５ｏＰＰ.A､〃JＩＦ

7”sdUDjJごﾛα昨「３８"iDwoM” ２.二ＪＡＨﾉ｢0，８２

COD"PoIlDwノ

ロ〃

Excess`％ ５７．８ ◎ ７．Ⅱ Ⅱ５．５ 3３．３ １１４

‐‐－０

iJWl NoticingtheabsenceoftheeffectinuJufillednaturalrubbe｢,tlleconclusiondrawn

fromtheseresultsisthatstartingfTictiononroughsurfacesisduetoplasticdeformation

ofthesamplebythetrackasperities,pToducingpermanentset、Atthcbeginningofmovement,workmustbedoneindeformingtheTubberwhichhassaggcddowninto

theintersticesbctwcentrackasperities・Inpractice,stal･tingfrictionwiUbedifficult

todistinguishfromstaticIriction,anditispossiblethatthefinitecoefficientofstatic

frictionatinfinitemormalloadfoundbyRATNERANDSoKoLsI<AＹＡ１２ｉｓａｍｅｃｈanical

hindTanceeffectsimilarincharactertostartingfrictionItisinterestingtonotein

thiscontextthatinarecentpublication2qRAＴＮＥＲＡＮＤＬｊｗＲＥＮＴ,Evhaveindel〕en-

dentlydemonstratedthedifferencebetweenstartingfrictionandstaticfriction

Theoccurrenceofstartingfrictionindicatesthepossibilityofanegativcvclocity coefficientofrubberfrictionandcantherefoTeundercertainconditionsinducciL

stabilitiesduringsUding・Stick-slipphenomenaare,ｉｎfact,oftenencolmteredinfriction

expe｢imentswithfilledGR-Scompounds,Startingfrictionmayalsohaveimportant

conscquenceswhenrubberissubjectedtointcrmittentsliding,as,forcxamplc,oIltbe

circumferenceoftyres．

□０泗１４●０Ｆ０５

蝿

■△

。△Ⅱ■□、、菫■■■日◆■■■■■■■ｂ■■■■■■■■Ⅱ■■■■■Ｐ●０町‐ｊ、●７●■■■■■■■凸■■■０■□０●００．■’０００▲Ｕ■■且■１０。

－艀ｑ臼ｑ臼

の￣

１Ｘ･ＣＯＮＣＬＵＳＩＯＮＳ

ＴｈｅｗｏｒｋＴｅｐｏｒｔｅｄｉｎｔｈispaperisafirstattempttoelucidatcsomeolthcmostim-

portantfactoTsgoveTningfrictionandabTasionphenomena,VeryideaIizedmodclshad

tobechoseninoTdertoTeducethedifficultiesinberentinthesubjecttomanagcable

proportions,andatbestonlysemi-quantitativeagrecmentbetweeI1theoryandexl〕cri-mentcanbeexpected・Withintheselimits,theassumptionthatlocaIstressconcentra-

tionsproducedbyfrictionaltractionarethecauseofabrasiomhasbeenjustifiedby

theavailableevidence，abTasionthusemergingasapurelymecbanicalproccss，In

comingtothisconclusiontheoriginoffrictionalforceshasbeencomplctclydivorccd

fromabTasionbuttheexistenceofstartingfrictiｏｎ，discussedａｔｔｈｃｅｎｄｏｆｔｈｃＩａｓｔ

ｓｅｃｔｉｏｎ,tbrowsdoubtonthegeneralvalidityofthishypothcsis・Ifmcchanicalcntanglc-

mentcanplayasignificantroleinrubberfriction，effectssimilartothosHeproduced

whenscratchingrubberwithaneedlemaybeofgreateTimportancethanhasbeen

assumedinthepresenttreatmentoftI1esubject・Itshouldalsobementioncdthatno

theoryis,ａｓyet，availableforthemechanismofstaticfriction・

丘e/ergｵlcesp.ｲｪﾌ

▽ ｂＬ

◆■－

。Ⅱ０１－０６００Ⅱ８ＦⅡｄｐ９ｌ‐ｆ０１０ｈ■０■｜■７９０９冊ｒ０ⅡｕｍＪ咄■■皿旧Ⅲ□Ｂ旬日ｒＤＩ・日７０■■価０砒和・０

VOL.’（Ⅱ957/58） ＦＲＩＣＴＩＯＳｌＡＮＤＡＢＲＡＳＩ()ＮＯＦＲＵＢＢＥＲ ４１７

ItIIasbeendemonstratedthattherclKLtivewearresistanceofanytwo

compoundsisnotaconstantbutcandependpronouncedlyontheconditionsof

testing・Ｔｈｉｓvariabilityisduetothelormationofabrasionpatternswhichdevelopondifferentcompoundswithdifferentintensityandwhosecontributiontothetotal

abrasivcloss〔lcpendsonthemechanicalstrengtlIofthecompound,Abrasionpatterns

arethoughttoinHuencerelativeratesoftyreweaTlmderdifferentconditionsofservice聖

butnospccificreferencehasbeenmadeinthispaI〕crtotyres,forthefollowingreason・

Tyrcwcaroccursｗｈｅｎthereisrelativemolionintheareaofcontactbetweenthe

circumfcrcnｃｅｏｆｔｈｃｔｙｒｅａｎｄｔｈｅｒｏａｄａｎｄｉｓｔｌｌｃreforeintimatelyconnectedwiththe

mccIMmicsofsIippingwheels・Ｔｌｌｉｓｉｓａｔｏｐｉｃｏｆｓｏｍｅｃｏｍｐｌｅｘｉtyinvolvingthelarge‐

scaIcelasticpropcrtiesofthewheel,differencesinwhichmayovershadowdifferences

if11鯛､､cabrasionTesistanceofthctyretread・Thcsameconsiderationsapplytoab｢asionmachincswbicharcdesignedtoimitateconditionsencounteredbytyresandemp1oy

smallrotatingsamplesundergoingvariousformsofsljpInspiteofitsintricacy,thG

problemisamcnabIctotheoreticalwork81n(181I〕rcliminaryresulthasbeengivenin

ａｎ(xurlicrl〕ublication22・Ｉｔｉｓｈｏｐｅｄｔｏｐｒｃ３(911t6lII1oreadvancedapproachtoitinthenearluture．

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