Contact analysis of rough surfaces under transition conditions in sliding line lubrication

ELSEVI ER

1. Introduction

When

3ented rl\ a function of normal

two surfaceh are slidiq

on each other. the luhricu-

tion regimes of these \urt’xx\ are of particular interest For understanding their hehavior in contact. If the luhricalion regimes can be effectively conlirmed, it would help with the mai.~tenanceof machine putis and to predict the performance of machinery. The Strlheck curve wab tirc;t recognized by Stribeck [ I 1,who observed the variation of \liding friction using the Hersey viscosity.

number

( qN/r).

N is the angular

velocity.

where

q i\ the lubricant

and 1’ is the average

contact pressure. The Stribeck curve divided lubrication into three regimes: thick tilm. thin Mm. and boundary lubricalion. Beerbower [ 21classitied the regimes and modes of lubricalion and wear according IO Ihc seventy of damage ah a function of the normal load. A series of experimental

[3-91

projects were proposed

to study the lubrication

conditions

by IRG

of sliding concen-

trured sleel contacts. It was shown thiu the mode of lubrication. known ;IY rhe transition diagram, can be repre* hx.

t Hh-MbS-h.3 I-21 IO

force and sliding speed. The

transition curve from partial elastohydrodynamic lubrication 10 boundary lubrication depends upon lubricant viscosity 13.41. ac well 2~ upon Hertzian contact pressure 15.6/. An increase In surfaceroughness or a decreasein oxygencontent of the lubricant both result in a considerable reduction in load carrying capacity at the tirst and third primary transitions. while the loadarrying capacity at the second primary tnnsition is not affected 171. There is evidence that differences in load-curyng capacity is caused by using different additives or by using different types of steel 181. All previous work thal led to theconceptionof thetransitiondiagramwas performed with newly machined. virgin metallic surfaces. During the crocsed-cylinder geometry run-in the surfaceconlacfh of concenlrated

steel showed that the transition from the

partial

EHD to the scuffing may take some lime 19 I. Lim and

Ashby

[ lOjIntroduced

theconceptof

wearmechanismmaps

quantities plotted on orthogonal axes were used respectively to represent conta pressureandslidIn! velocity-related parameters. Lubricant effects in the fricrion transilion from boundary fo microelasrohydrodynamic luhrlcation were investigated by using a ball-on-flat Motesin which dimensionless

J.H. HWI~R! Wear219 (I99Xj 205-212

206

ter ( I I 1, The specific film thickness neededfor the transition of heavily loaded friction from boundary to mixed lubrication wns also investigated [ 121. It was found that the running-in

Table 2 Experrmentsl canditlons

process is very sensitive to the initial lubricating conditions. All machining surfaces are rough. so contact between surfaces is restricted 10 discrete spots at the tips of the surface asperities. The phenomenon of contact between two rough surfaces is of fundamental importance in the study of friction,

wear, lubrication, thermal and electrical contact resiwtce I 13-16].The parametersaffecting thecontactchancteristics in thesepapers include the real contact area,theplasticcontact area, friction coefficient, and plasticity index. Many tribological phenomena such as subsurface crack initiation [ 171. scuffing [ IS]. wear [ 191, etc.. are related to plastic deformation. Hirst and Hollander [201 and Francis [ 2 I 1provide experimental and theoretical evidence confirming the usefulness of the plasdcity index in sliding damage and deformation behavior. In like manner. these contact characteristics between two rough surfaces play nn important role in the understanding of transition of lubrication modes. The main purpose of this paper is 10 establish the transition diagram under sliding line contact in continuously operating machines. Using the microcontact model for rough surfaces as a base, the variations of contact behavior from one transition curve to another transition curve were investigared.

2. Experimental equipment and testing conditions The experimenls were conducted on a ring-on-block experimental tester ( see Fig. I 1.Specifications of test specimens

Tablr 3 Phykd

the tert lubricant

propertier of

Dcnsily I 15°C. g/ml

1

txxI

Flab point 03 Kinematic vibcwy

Xl fd

I

WC

h?.I

100°C

x.3 I

Vihcntity index Thermal conduclivdy (\r/m”C Prcwrc-viwobily

I

coefficient (GPu

9x

U.145 1.17

’1

are shown in Table I. The lower block is stationary while the upper disk rotates at a constant speed. The disk drive power used in the experiment consisted of a 5-hp motor driven by a

continuously variable speed controller. The experimental conditions were eleckonically monitored by a digital instrumentation system. The syslem measured the speedofrotation,

oil and specimen temperatures, electrical contact resistance. applied load. friction force, and the specimen displacement. A levered bar connected to the specimen support structure was used lo measure the vertical displacement of the bottom specimen. A wear gauge was vertically positioned at the end of the lever bar and waa used to obtain successive readings on the wear depth of the bottom specimen. Experimental condidons are shown in Table 2.

All the test specimens were completely immersed in an oil cup with a thermal controlling system. By means of u heater. the oil temperature before tesling was maintained at 80°C. The lubricant used was a plain mineral oil: its physical properties are given in Table 3. The machine was brought up to a sliding speedof 0.39 m/s. Each new test was given a runningin of aboul8 min at a load of 45 N and the disk sliding speed of 0.39 m/s. The goal of the running-in process was to flatlen possible sharp edges in the surf;lce profile. The tirst load of IO0 N was lhen applied to the bottom specimen for I min by an air pressure loading system. and then released for 3 min

Dmicnwn

(mm)

Diameter 75 x uidlh 12.4x 12.4x I!4

M;l~crlal\

I3.J

JIS SCM 415. carhurircd. we-harden4

HRC 5X-hl)

JIS SCM 415. carlwired; ctwhardcncd HRC S&hi)

in order lo lower the oil temperature to XOi I.K.

The

sequential loads were imposed step by step folIowine the same procedure until ucut’tingoccurred. The loadin; whcdule

is in Table 4. Measurements of the roughnes+ of the ring surface were done with il portable pmtilomctcr.

The dircctron

of roughness;of the test specimens is parallel to the dircctmn

of motion.

The surfcorder

puter through an A/D

calculalion of contact

wa

converter

connected

to a perwn;tt

for C];U;I prwx4n~

cow and the

p:wtleter~.

3. Resultsand discussion Fig. 2 gives an example of the fnction coefticlent and the electric4 contact rcsi6tance rccndingc for 1~0 operating condirinnv during Wp load process.Mt’wc’mvl of the frlrtlon

Load (

N)

cnefticient and contact recistanceC;IIIhc mhrned to dstw Ihe onset of boundary luhrtc;ltion. Scul’tin~ hch;kr u ;I\ contirmed by the friction ccret’ticient and war wxr\. Bctiw the lOad of600 N. tar the sliding \pt’ed of I.7 ml\ ,md the average roughness value of 0.2 pm. the friction cnefticicnt increases and the cont;lct rekmcs dccrca~c~ rharply. After

the load ofBOO N. the friction coefticlent drcre,l\es yr;ldu;lll~ and the cnnracr resictance maintains under Cl limikd

rqc

(5-7111. These reds indicate that h&c the loal 4 hO0N opposing Sllrtk3 in COtltilCI move pro;rc\sbclv cloror to each other with the i;xrca+! land. A\ the qxlrLltlon hetwecn contacting surface\ decrenw. there iu an increa\c m the l’riction cocfticient and ;I decreae In

cnntact rw.t;uvx

After

bearing the load of 600 N, there k some matq

of the tuo

rubbing surfaces due to the Hearing procca. Thir

C;IUW~

the

tnction ccxtliclcnt to decrease pradually. Boundnty tilmcre;IIC~detinitc Cot~tid rekhnce between rutfaces Ac ;I result. the contxt condmon change\ from ;I mixed lubncation IO a houndar> luhnc,ltion regime. The operating condition % l\

hich ~hc contact load il; X(W)N ic considered a transition

pomt. C’ntlcr thc\t! cnnditionq. with

In/\.md

an ,wra:e

c’ontxt rcwt;uw

:I

sliding speed of 0.79

rouehnea value of

I.I pm.

there is little

and a sharp decline in the friction coefli-

clent iit mitral loadin: +lagr\. This indicates that contacting Mkc\ N crt III boundary luhnci\tmn. The wear and mating prc\cr\\o occur WUlliiUlt3W~l~ illld begin at inilial conlxt. The tinal ~;II,I for each curve reproem the IN load stqejusl hctorc scut dltlonc.

tin; t,ulure. Comparing thexe two operating con-

II I\ WCII

IhA il ION loud i\ able to create hwndary

luhr~c;~twnuntlcr the conditmns ofa low sliding speed and P high a\cra~c roughnes!. vnlue. Factors other Ihnn the contact lo;J. siding ywd.

and rnu;hneqs value should Ao he cnn-

kldcrcd u hen txnnininy the onqef nf suftin$ failure.

01 02 1)3 IU 05

06 07

OX (19 IO II I? 13

I-l IS I6 I7 IX IO

31 !I !?

Fig. 3 shows transition diagrams for line contacts at different initial average roughness values. For the block speci-

men with an initial roughness value of 0.2 km, al combinations of specific load (load per contact lengrh) and sliding speedwhich fall below the curve AI-S-AL the con-

The real conlact area itself is important in understanding

many tribological phenomena, such ns wear, adhesion, friction force, and frictional healing. Using the surface profile, load parameler, surface roughness parameter, and material parameter in the contact model described in Appendix A, the

tact condition is mixed lubrication. The curve AI-S is called the first transition curve. Below the first transition curve. if the specific load increases and crossesthis curve, a transition

real contact area ratio (red contact ilreil per apparent area, AJA,, 1.plastic contact area ratio (plastic contact area perreal contact area, A&A,). and plasticity index just beforethe tran-

from mixed lubrication to boundary lubrication takes place.

sition points can be obtained. Fig. 4a shows the effects of the sliding speed on the real contact area ratio and on the contact area at the transition curves for the initial average roughness value of 0.2 pm, Regardless ofthe tirst and second transifions,

The limiting

critical load for this first transition curve

decreases gradually with increasing sliding speed.The scuff-

ing takes place due to a complete failure of the lubrication above the line A2-S-AX The upper curve AZ-S is called the second transition curve. Between the tirst transitioncurveand the second transition curve, if the specific load increases and it crosses the second curve. a transition from boundary lubrication to scuffing failure takes place. The critical load for this second transition curvedecreases with increasesin thesliding speed,The curve S-A3 is culled the third transition curve. If the specific load is increased at V> V, a direct Innsition from mixed lubrication to scuffing failure takes place. The transition diagrams of specimens with higher rough-

the real contact area ratio and the real contact area decrease and approach a stable value when Ihe sliding speed increases. The stable value is the value at the S point of the third transition. This result suggests that the real contact area of rough surfaces should be changed to prevent theoccurrence ofscuffing failure at high sliding speeds. The effects of frictional heal ( = friction coefficient X contact pressure X sliding speed,fpV) on scuffing have been discussed for a long time [22 I. However, frictional heat on rough surfaces occurs at Ihe film on rhe real contact area. For such a reason, when

ness values are different from that of specimens with the roughness value of K,, = 0.2 pm. From Fig. 3 it is observed that all transition curves drop when the average roughness

E

ot2-

the average roughness value of the block specimen, the

I ;

oto-

smaller thr specific load neededto enter boundary lubrication

E

value of rhe specimen increases. It isconcluded that the larger

or scuffing regime. It is interesting to note that the contact condition had entered boundary lubrication al the sliding speed of 0.79 m/s for R, = 0.6 pm and R,, = I, I km. This indicates thaf the first transition curve in Fig. 3 is not solely related 10low sliding speed. Thedecrease ofthe load-carrying capacity al relatively low speeds is in agreement with obser-

& s

ti Oo6 I E 8 0041 a 002a:

vations made in other film lubrication experiments. Before the inflection point

(point

ow~oE*O

I) the load-carrying capacity of

00

014

for low roughness valuev than for high roughness values.

is independent of the surface roughness value of rhe specimen. The porsible reason ic rh;lr the presenl experiment u\;ed LI running-in process and line conlacl. while the work of Begclinger and de Gee did not usea running-in process before concenlraled coniact tests. There ic a discrepancy between the contacl characteristics of Iwo experiments. The position of the separation point (point S) will influence rhe range of boundary lubrication and the choice of design paramelers in continuously operating machines. Beyond the +liding speed

V,.machine pari failure occurs at a relatively low specific load. It was seen that the smaller the averag roughness value of a specimen the smaller was rhe specilic load ;Ind rhe slower way rhe sliding speed for rhe position of poinr S in Fig. 3.

10

20

30

40

50

60

70

Sltding speed (m/s)

the lubrication film decreaseswith decreasing the sliding speed 141. Fig. 3 shows that inflection point occurs earlier Comparing the second transition curve in Fig. 3 with Ihe work of Begelinger and de Gee I7I is interesting. Their results found thrillthe location of the second trandtion curve

oorl-

P 3

(b)

012

4, s 010 f! I m' 008 H E

006

8 i u u

004 i 002 A-+

OE'O

comparing Fig. 3 with Fig. Ja. it is clear that the critical load and real contact load at the second kan
or mlvsd lubrication.

Under an average roughness value. the &/A,, ratios :md A, can be ordered as (A,IA,,),,>(A,/A,,),>_lr\,/A,,),,, and (A,)Il > (A,), 2 (A,),,,. In short. the above quences of real contact area ratio and contact area can still be yatistied for alI

Average

roughnns vaM(@n)

roughness values and sliding speeds according to Fy. 4a.h. When two rough surfaces are pressed together. the high pressure will give rke to elastic and pMic deformation al the tips of the surface asperities. Therefore, the IoIiil conM areu consists of a mixture of both elastic and plastic cont;rct areas (A, =A, -t A,,). The plastic conMcI are;1ratio ( A,,/A, ) and plastic contact area vs. sliding speed ;It the transition

contact ilrcil from boundary lubrication IO scuffing failure for any \lidinp speed. The variation is relative large under low

curves for the initial average rouphnevs VAIL' of 0.2 p.m are

spied Ihun that under high sliding speed.

shown in Fig. 50. When the sliding speed of block specimens

The pladic contact area ratio and plastic contact area vaiy according IO the mitial average roughness value at three tmnhition points for the sliding speed of 1.57 m/s. The data on whir ,ue shown in Fig. 5b. The plastic contact area ratio increase\ and the plastic contact areadecreases with all three types of trunc;itlon points as the initial average roughness

increases. the plastic contact area ratio incnascs and the pIastic contact ;Lreitdecreases for the tirsl and second transition points. Due to the inverse correlation in the values A,,/& and A,,. it is shown that with increases in eliding speed for two kinds of transition points the reduction mtc of rhc elastic contact tirea is larger than that of the pl;~~tic contact area

of

Furthermore, rhe variation phenomenon aI the second trimsition point is I;argc Ihan that at the tirst transition point. For ti given sliding speed in Fig. 5a. the A,,/A, ratios and A,,canbeordereda~(A,,/A,),>(A,,/A,)~~~nd(A,,),,>(A,,),. Comparing this with (A, )II> (A,), in Fig. 4a. it indicatesthat during this experiment all contact ureas. including the total contact area, the plastic contact area. and the rlastic contact area. increase during the process from boundary lubrication to scuffing failure. However, the rate of increase oftheelastic contact area is larger than that of the plastic contazl area at a given sliding speed. Conversely. the increase in the amount of the elaslic COIIIXI areit is smaller than lhat of the plastic

increases from R,,= 0.2 km IO R,, = I, I km. Comparing A,/ ,4, ;md A,, with A, in Fig. 4b. it is shown that the decrease in the rate of the elastic contact area is larger than thal of the plastic contact area with increases in average roughness villue. Furthermore, the variation effecr is most notable in the uccond transition and is negligible in the third transition. For the contilct chamcteristics from the tirsttransition IO the yccond transition. the A,,/A, ratios and A, can be ordered iIh I.~,,lA,),l,>~Al,IA,),>(A,,IA,),, and (API,,>(A (A,, )l,l. Hence. the increase in the rate of the elastic contact area is larger than that of the plastic contact area from boundary lubrication to scuffing failure for all roughness values. The lower the ;Ivemge roughness value, the smaller thedevi-

rtion of the three transition points. For a high average roughnessvalue of

I,I Frn. the deviation oftheplastic contact area

0 12 (2)

ratio is almost the s;Lme.However, in Fig. 5b. we tind iI

minimum plastic contact 3re:t ratio of 874 at R.,4.2

ptn

and V= I.57 m/s, and in Fig. 5a WC find 3 minimum ratio of 704 for 1111 operating conditions. This shows that the greater part in the contact area is the plastic contact area from the boundary lubrication to the scufling failure. Fig. 6a illustrates the variation of the friction coefficient with the sliding speed at the transition curve for the initial average roughness value of 0.2 pm. Regardless of the first and the second tnnsition points, the friction coefficient decreases with increases in the sliding speed.As described above. continuous mating occurs after the boundary lubrication undercontinuous operating lubricated conditions. It is

0.0

1.0

Sliding speed(m/s)

shown in Fig. 62 that the friction coefficient at the first transition point is higher than that at the second kmsition point for any sliding speed. The difference in the friction coefficients between the two transition points decreasesgmduully as the sliding speed increases. This result because. as the Ming speed increases. the contact loads between the two

o’i2 j”/5zGzGq

transition points become smaller and fewer. The effect of the muting process on rough surfaces is lessened dueto the reduction of contact toads. This conlinuously operating experiment is not consistent with the discrete load experiment resuhs. Fig. 6b shows the effects of initial averageroughnessvalue on the friction coefficient at the three transition points for the sliding speed of I.57 m/s. For each specimen, the friction coefficient at the lirst transition point is higher than that at the second transition point for itll average roughness values. The larger the average roughnessvalue. the larger the friction coefficient 11the third transition point. However, for the first and the second transition points. the difference of the friction

coefficients al avenge roughness valuesof 0.6pm and I. I pm is so small as IO be negli@ble. The operatin@conditions Mow the lirst transition are known us region I (RI) in the transition diagram. und those between the tirst transition und

opruphicul properties of the solids. Greenwood and William-

the second transition are known as region II I RN). The scuff-

son’s work illustrated that Ptiw dominates the contact behavior and the land has little efiect. The experiments of

ing regime are known as region III ( RIM ). Fig. 6a.b illustrate

Hirst and Hollander lZOl showed that U;;,, is :I scuffing

that the friction coefticients of alI roughness values have no

indicator. The plasticity index was moditied by Horng

obvious boundary for ail three regimes. The values of the

to suit more general geometric contact shapes. The general

friction coefficient for the initial roughnessvalues from 0.05 pm to I ,I pm in this and the previous experiment [231can be summarized as:fu CO. I andO. <.fk,, <0.3. It alsocan

plasticity index can he expressedas

I 161

(I)

be concluded from all the friction coelricient recordings that $I >fHII, fi >fHI and &llr >.t;(,, under 4iding lint contilct in

where H is the hardness ofthe sotier contacting mnteriols. rr,

continuously operating machines. Thev res4 are not corktent with wnrk which does not employ the running-in process before concentrated contact

is the xtand;lrd devia1ion of asperity heights, and R,,, is the

experiments, such as the work by Begelinper and de Gee 181.

IIis concluded from the ahove discussion that both the roughness value and the running-in process are important faclorv influencing the friction coefticient in the three repimeb.

mean effective radius of curvature. E’ is usually referred to ;IS the effective elatic modulus and K( e) and Et e) are the complete elliptic inlegrula of the tirst and second kinds. The effectsof the sliding speed and initial roughness value on the general pli\sticity index were presented in Fig. 7. Besides nt the of inflection points. the general plasticity index at trmsi-

Another importan contnc~ parameter i\ the pluaticity

tion curves incresrs with the increase in roughness value

. which ~3% tirst introduced by Grccnwcwl und Williamson I I.1 I. This index combines the material and top

and sliding \pced. For the same roughness value. at the tirst transition point the plasticity index before the intlection point

index, q,;,

tact ;ue;t. and the elastic cont;lct area, increase during the proce\+

from boundary lubrication toward Fcuffing failure.

The increased rate of the elastic contact area is larger than

that of the pladic contact area.The effect of the variation is notable under smaller roughness values and lower sliding speeds. However, the part of plastic deformation in lotal contact area Increased al transition curves as the sliding load or rou(Thne+

value decreased.

If IC clear I~UI not

only the roughness value but also the

runninp-in processis an important factor affecting the friction roeflicient in the three regimes. The values of all friction

rrcordings can be summarized as: fH1J,,,,fi >.fKI, andf,,,,>f,,, under slid-

coefticient

O.O.lS< In;

t,,,

line lubric;rted contact in continuously operating

machme>. In this experiment the greater part of the total

contact

xe;l

plastic deformation at transition

rqxriences

curls\ ahcther the general plasticity in&x is low or high

may be larger than that after the intlection poml. The nmsc of values for the second transition is from 0.79 10 4.19. It indicates that the general plasticity index cannot he consid-

ered us the single parameter in scufting failure. Fig. 7 shows that ql > VI, for all roughnas values i\nd sliding speedsin this experiment. It indicatec that the gencrd plasticity index decreasesgradually from boundary luhricution to scufting failure. Furthermore, the deviation between

(0.7Y-3.7’) I~Accordingly. the value of avenge roughnessis from 0.2 ro I.I pm. After theinflectionofthetnnsitioncurve. rhe general pknticity index decreasesgradually from boundiI9 luhricat ion to scuffing failure ( V’,> lu,,)for all roughness A rltherwiderangeoftheplasticily

value\ and 4idingspeeds.

mdcv show+ il cannot be ;L single indicator for the second tranfirion. increase\ the

The

zenem plasticity index al transition curves

\clth increases in the sliding speed or decreasesin

rou:hne\\ calue.

transitions is reduced when the slidins speed i+ increased. Comparing Fig. 7 and Fig. 5. the greater the general plasliciry index, the more the plastic area ratio. However, the greater part of the total contact area is plilstic deformation whether

Acknowledgements

the general plasticity index is low or high (0.7Y-3.79). The author gralefully acknowledges the National Science Council

4. Conclusions

(8 Taiwan.

ROC.

which supported this research

I 2E-I SO-OO?R. The personal support 0fS.T. Lin. W.C. Zeng and P.Y. Wang is also appreciated.

under franI NSC 86-21

Three transition curvesot’rough surt’acecontuct+havebeen studied in sliding linecontinuous openIionenperimenta.Thc conditions studied in the experiments included

(i) from (ii) from boundary lubrication toward scufting failure. and (iii ) from mixed lubrication toward boundary

lubricrrtion.

mixed lubrication toward scuffing failure. The transition diagram shows ;1similar shqe for the different nrqe roushness values. However, the critinl speck loads aI transition for higher roughness values were located in inferior positions on the rransirion diagram.

Appendix A

The conlacl characteristics of rough surfaces can be catcuLlted with rhe elliptic elastic-plastic microcontact model by Homg

1I h I

The model is given below as

The A,/A,, ratios and A, can he ordered ;Is ( A,/A,, ),, > ( A,/ A,,),s_(A,/A,,),,,and

tA,),,>tA,),r(A,),,,atagivencliding speedfor any roughness value. In addition. the deviation

,I * (II,

r\,ltl)=rlA,,“H,,,P(e)

(:-&&ad:


the values of the tirst transition and second translt ion points in A,/A,, and A, decreases when the sliding speed incre:;ncs.

of

Except for the inflection point on the tirst transition curve,

I

the sequence of A,,/A, and A,, can be rcprevnted 11s(A,,/

tqA,,nR,,,,f,(e) I?Wh-w,(2 I

A,),l,> &IA,),> tA,,IA,),, and (A,,),,> IA,,),> (Al,)III ata given sliding speed for any roughness value. Three kinds of

-.I,(e)M4:)d:

contact area. including the totid contact area. the plastic con-

,I * “8,

(Al)

cffcct of running4n on the load carrying cupachy of thin-lilm lube103 t IOXI I !03? I 0. [IO) S.C. Lim. M.F A\hhy. Wear mcchunism map\, Asia Melall. 3.5 cited c’mcrrntnted contXl\. ASME J. Luhriciltl’m

(19x71 l-18. 1I I 1 Z. Yang. Y.W. Chung, H.S. Cheng. Luhrlcant effcclr III thctnnsuinn from bmutdrty 1’) micn~clastohydr’~dynan~ic luhnuation. Trth’llogy Tmnh. 3Y II9961 Y7CY78.

[I ?I

A.G. Khurrhudov. Y .N. Drordov, K. Kate. Tr;m\ttimul in lubricated hervily load sliding cnntxt ofcunmicr

-f,(e))ldd:)d:

phcnomata

und rbxl. Wear

IX4 II9951 170-116.

[13 1J.A. Greenwcrxl.

where

J.B.P. Willum~~m. Comrct

(

ofnominally ilut hurfxc.

Prnc. R. Sot. Londnn A 195 1966) 1W3lY.

(A31

[141 W.R. Ch;mg.Cnntact. [151 M.R.

f2(e)=

(

d9e)O.S

2K(e,t7 I-e’y5

)

AdheGun ~ndSt~ti~Fr~Ctinn’~fMu~alltc Rtrugh

Surfxe~. PhO therib. Univcr\ny nl Cuhtorniu. Berkclcy. IYX6. Sridhar. M.M. Yovanovich. Elat’lplastic

cuntnct conduct:mce

model for Ismmpic cunfurmmg rnugh surfacer and sompxiu,n

(Ad)

erperimenlb. ASME J. Tribnlogy

with

IIX ( 14061 3-Y.

[ Ihj J.H. Homg. An elliptic elatic-plastic

asperity tmcmcotatct model

for rough surfaces. ASME J. Tribology I?0 t I’)981 X24X.

(A5)

f

1171 N.P. Sub, The drkumnation theory of uelr. Wcx 25 1973)

1IX]

III-

IX F. Hlrano. Y. Yomtlmto. Effect of molecular weight dwhutinn minerrl oil\ ‘1 scufling under mllmg/~lidmp

of

ccmditinn, Mechumcll

Engineers convention on Trihology, Swansea, 11)7X.434

(19 1R.O. Ritchte, On the relationship

hetweendekunmatmn \hcur und the

imtiatton and growth of f’uiguc cmcks m uhrahigh \trenfth \lcel. Fundamentals of Tribology. MIT. 197%

[ZO] W. Hirst. A.E.

Hnllunder, Surface timsh and d;unqe in 4tdmg. Proc.

(

R. Snc. London 337 1974) 379494.

1?I 1Ii A.

Fmnci\. Application

of sphcricrl indentation mech:mlcs to

reversible md irrevcnihle contact hetwecn rough surkus.

Wcnr 15

II9771 Xl-?6Y,

[221 A. Dyson,

1975, Scufting--r

review. Pan I and Pdfl 2. Trlhol. Int..

Vol. x. pp. 77-87, I 17-12.

Il.311.H. Homg.Swliehc)fIribnlqsal hehwr

nndwprmtionbetween

+tnfucr+ ttt mitittl houndnry luhrtcatum. War. ?I6

I1998) X-14.

Jeng-Haur Horng gradunted in Nova1 Architecture and Marine Engineering in 1981 at the National Cheng-Kung University. and received his PhD degree in mechanical engineering at the same university. He is head of the laboratory of Thermal Engineering, und assaciate professor at the National Huwei Institute of Technology. His research interests are mainly in the area of dry and boundary lubricated friction and wear. especially the effect of surface roughness on Tribology, contact temperature, contact mechanics and induarial research.