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7.1 THE FINITE-ELEMENT MODEL AN D A NALYSIS OF STATIC CONTACTRESISTANCE AND THERMAL PROCESS FOR CONTACT W ITH FILMLi Kui*, Su Xiuping*, Li Zhigang*, Lu Jianguo*, Zhang Guanshen g**

*Hebei U niversity of Technology, Tianjin(300130), China*"Fuzhou University, Fuzhou(054002), ChinaABSTRACT

Contact resistance and thermal process are very important parameters for contact. The film oncontact surface has influence on contact resistance and the thermal process. This paper hasanalyzed the static contact resistance and the thermal process, and then the finite-element modelsare proposed for contact with film. The contact boundary condition is automatically meet incalculating with the finite-element method for contact without film, but it will be changed whenthe contacts are covered with film. We have developed the finite-element program for contactwith film. Our results for resistance of single-spot contact are approximate to the theory value.Finally we have analyzed the effect of the film on thermal process.Keyw ords: Contact Resistance, The rmal Process, Film, Finite-Element Method

I INTRODUCTIONContact resistance and thermal process are tow prime

parameters for contacts and have influence on theperformance of contact. The researchers have devotedthemselves to these models. R. Holm had developed thetheory of constriction resistance for single spot that has beenaccepted widely[']. Later, other models for multi-spots haveappeared. A . Greenw ood had studied the contac t resis tancewith statist ics method['] and the multi-degree constrictionr es is ta nc e h as b ee n d e ~ e l o p e d [ ~ ' ~ - ~ ] .any researchersdeveloped models by using the computer s imula t ion andsta t i s t ics methods, and t ry to expla in the randomvariabili ty for con tact resistance.

Joule hea t tha t i s produced by the current f lowingthrough the contac t makes a r i se of tempera ture . Thecontac t resis tance i s h igher than the resistance o fconductor i t se l f . For th is reason, the tempera ture on thecontac t spots i s h igher than on others . The ca lculat ion oftempera ture r i se i s complex and the ca lcula t ion maydivide into two par ts . one par t i s for s teady-sta tetempera ture , the other i s for t ransient tempera ture . Inmany f i led, such as in contac t welding, the thermalprocess analysis i s necessary. Many researchers , St ruaw R.Robertson, A. Oberg, and others , have stud ied the contac tthermal process wi th

However , there i s the f i lm on the co ntac t surface . T hef i lm has inf luence on the contac t resis tance and thethermal process. The contact boundary condition must bet rea ted when we have ca lcula te the contac t resis tance andthermal process because the contac t boundary condi t ion i schanged by the f i lm. In this paper , we ca lcula ted andanalyzed the contac t resistance and the thermal process bythe f ini te e lement method. The current f ie ld i s analyzedand the contac t resis tance can be ca lcula ted basis on theresults of current f i led. Th e heat source i s ob ta ined by theresul ts o f current f i led when we an alyzed the tempera turer ise and the thermal process .

I1 T H E F I N I T E -E L E M E N T M O D E L O F C O N T A C TRE s sTAN CE FOR CONTAcT W I T H F I L M - ~The film, such as oxide film and sulphide film, is formed

on the contact sur face when the contact is in the atmosphere.As a result, the electric conduction mechanism of contactbecomes complicated. The film has influence on thedistribution of current in the contact and the contact resistance.The analysis and the calculation are of significance in theoryand practice. The film on the contact surface is divided intoconducting film and insulating film. The conducting film haslittle influence on the electrical conductivity of contact spots,but the insulating film must be fritted in order to conductcurrent and the contact become metal contact or quasi-metalcontact. The insulating film may conduct current by tunneleffect if the film is very thin. On the other hand, the shape andthe size and the number and distribution of contact spots haveinfluences on the conductivity of contact, so it is difficult tocalculate the contact resistance in theory. We consider theinfluence of spots on the contact resistance and havedeveloped the finite-element method (FEM).

Fig. 1. The Sketch of Contact Mod elWhen the film is very thin and it can conduct current by

tunnel effect, the contact resistance may be given in theory by( I ) [ ' ] :

where: p is the resistivity of contact(C2.m);

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a is the radius of contact spot(m);(3 is the resistivity of fi lm (0m 2).

The contact model is shown in Fig. 1. In Fig. 10'0'' isthe contact spot and 00' is the radius of contact spot. Theelectric potential, 9 ,s a solution function for current fikdwhen we solve the contact resistance. It can be solved by (2) .

cp = 9,

The boundary condition consists of the first condition andthe second condition in usually. In some case, the secondcondition becomes homogen eous boundary condition, such asAB boundary in Fig. 1. If there isn't any film on co ntact spoi:s,the contact boundary con dition is

(3)

For contact boundary of contact without film, theboundary condition is automatically meet in FEM. Even whenthe film is very thin and the thickness may be ignored, thefilm contact boundary isn't automatically meet. The currentflows through the film, the electric potential on both sides (offilm is difference and the voltage drop is formed. Theboundary condition of contact spots with film is

pan, cp 1 -Where: (p l an d (p 2 is the electric potential on both sides of'

y an d y is the electric conductivity of contacto s the resistivity of film on the spots.

film,material,

If the resistivity of film, CT , s 0, the electric potential cinboth sides of film, (pl an d 02, s equal. For this reason, (3) isa special equation of (4). When we calculate the contactresistance by FEM, the film boundary condition must be dea Itwith variational method. Equation (2) and (4) constitute theFEM model of contact resistance for contact with film.

I11 THE FINITE-ELEMENT MODEL O F T H E R M A LP R Z E X S F O R -C C NT A CT W I T H F IL M

The tempera ture of contac t r i ses by the Joule hea twhi le the current f low through the contac t . However , theJoule hea t increases when the f i lm is formed on thecontac t , and the tempera ture of contac t obviously r i ses.

~

-~

The contac t model i s shown in Fig. 1. The max imumaverage tempera ture r i se formula i s (5) for contac t wi thsymmetry structurer61.

( 5 )where B is 4% ;

KT is the coefficien t of heat radiation(w/m'."C );q, i s in ternal hea t sour ce of conduct (w /m3);qs i s hea t so urce tha t i s formed by contac tA is a rea of conduct (m2);P i s the cross sec t ion per imeter(m);h i s the thermal conduct ivi ty coeff ic ient .

The thermal field is similar to the current field in thecalculation form of FEM. The thermal field may be describedas follows:

[c,y$ V ( h V T )+ q ,

resis tance(w/m*);

( 6 )

Where: The initial condition is = &Tf is the ambient temperature of contact;C, i s the speci f ic hea t coeff ic ient of contac ty i s densi ty of contac t mater ia l (kg/m3).

When there isn't any film on the contact spots, the contact

mater ia l (Ukg C );

boundary is (7). T,=qdT, dT2 (7)- h l - - h 2 - = ( )1 an, dn2

Equation (7) is the boundary condition for contact withoutfilm, it is automatically meet in FEM. If the contact is coveredwith the film, the contact boundary is changed. Its boundarycondition is shown as follows:PI=T2

dT, dT2 1 ( 8 )- - - -A - = - - ( c p -( p )'2 1 2dn, an, owhere: T , and T, are the temperature of both sides of film;

cpl an d c p 2 is electric potential of both sides of film.As the film is very thin, T, is equal to T,, bu t (pl isn't

equal to < p 2 . When the current flow through the film, the

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A. Contact Resistance

Film Resistivity(C2.m')Contact Resistance FEM(mQ> Theory

Joule heat is produced. (p, an d (p2 are known functions as thethermal field is solved. If the film resistivity, 0 ,s 0, (pl isequal to ( p 2 . For this reason, (7) is a special equation o f (8).For the film boundary, the boundary condition, (S), can'tautomatically meet and must be dealt with variational methodin FEM. Equation (6) an d (8 ) constitute the FEM model ofthermal process for contact with film.

0 7x10.' ' 1 ~ 1 0 - ' ~0.039 2.270 3.2270.044 2.273 3.229

V ~ CALCULATION EXAMPLEAccording to our analysis, we know that the contact

boundary is changed by the film. The film boundary isn'tautomatically meet in FEM, so we must deal it withvariational method. We have programmed for contact withfilm by FE M. The contact resistance can be obtained from theelectric potential in the current filed, and the maximumtemperature of contact can be obtained from thermal processin thermal field.

We take a contact for example, the contact material iscopper and the radius of the conduct spot, a, is 0.1". If th econtact spot is single spot and is in the center of the contact,the current flow symmetrically through the contact spot. Asthe contact material is copper, we only calculated one ofcontacts in FEM. The physical parameters of contact are asfollows:

The coeff ic ient of hea t radia t ion, K, , s 10w/m2"C;The radius of co nta ct, r, is 2"Th e radi us of spot, r,, is 0. l m m ;The resistivity, P , s 1.75 X 51 mThe thermal conduct ivi ty coeff ic ient , h , s 40lwim "CThe speci f ic hea t capaci ty , Cp li is 3439205J/m3 "C .

Because the contact spot is very small, we have app lied thelocal refined mesh on FEM , as shown in Fig. 2.

82.57.63-fx

104.0 129.8 160.8 197.89.08 10.7 12.4 14.2

Fig. 2 . The Sketch of mesh formed286.018.3

360.2 437.2 529.1 640.620.3 22.5 24.5 26.2

B. Thermal ProcessFor the thermal filed as shown in Fig. 2, the contact1) ab, cd and od in Fig. 2 are homogeneous second2) bc in Fig. 2 is the third boun dary cond ition;3) There are tw o species for the conduct spot, oa. When

there isn't any film on the contact surface, the boundarycondition is heat insulation condition boundary condition.When there is some film on the contact surface, the boundarycondition is film boundary condition as (8).

boundary is dealt with method below:boundary condition, i. e. heat insulation;

According to above process method of boundary, themodel may be applied to the thermal process for short-time,and may also be applied to the thermal process for long-time.In the model, the influence of film on the contact resistancehas been considered. The thermal process for contact withoutfilm in 50A is listed in Table B. The maximum temperaturerise for contact with film in 50A is listed in Table C.

Tab le B The Thermal Process At The Contac t SDotI Time ( s ) I 5 I 11 1 18.2 I 26.8 I 37.2 I 49.6 I

Temperature("C )Time (s )

Temperatur e( "C)Time (s )Temuerature("C )

0.9864.66.32

-242.516.3-

.6 6 I 2.40 I 3.21 I 4.13 I 5.16 I

1 Time ( s ) 1773.71 933.4 I 1125 I 1355 I 1631 I 1962 ITemperature("C) 127.8 I 28.8 I 29.9 I 30.7 1 31.0 I 31 .1

Note: The current is 50A, and od is 500".

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Film Resistivity(0.m)FE M

nalvsis Result[61Note: The current is 50A, and od is 500.

From Table 3, we know that the temperature rises acutelywhen the contact is covered with film. For this reason, Oncethe contact is covered with film, the contact fault will becaused. The analysis results in Table C are calculated by ( 5 ) .In literature (6), the results are average temperature rise ofcontact in the condition that the quantity of heat, which ISproduced by the film resistance and the constriction resistance,is regarded as uniform effect on wh ole contact. There is somedifference from actuality . When the film resistance increase,the quantity of heat increases obviously. The temperature ofcontact is inhomogeneous, and the average temperature shouldnot correctly represent the temperature of contact. In this case,the calculation error by (5) increase and the results are smaller.The results of FEM are higher than the results of literature (61,and the results of FEM are able to represent the temperature ofcontact.

0 7x10- l x lO- o31.2 292 40332.0 253.3 348

V CONCLUSIONThis paper analyzed the model of FEM for the contact

resistance and the thermal process, and developed the modelfor contact with film. The contact boundary of contact spots ISchanged when the contact is covered with film. The filmboundary is dealt with variation method in FEM. The analys ISof contact resistance and the thermal process have contributedto the study of contact reliability and the contact weldingphenomenon. The temp erature rises acutely when the contact

is covered with film, so the film has great influence on thecontact reliability and the contact welding. To multi-spots,they have influence on each other, the contact resistance andthe thermal process is difficult to calculate in theory. Thisproblem is able to be solved by FEM. We will analyze andcalculate the contact resistance and the thermal process forcontact with film in further.

REFERENCE(1 ) R.Holm. Electric~~ Contact Theory and Application.

Springer-Verlag, 1967.(2) A.Greenwood, et al. Contact of Nominally FlatSurface, Proceeding of the Royal S ociety, A. VoL-295,1966(3) B.J.P.Willamison. The Microworld of the ContactSpot, The 27th Holm Conference on Electrical Contact,1981.(4) Robert D .Malucci. Multispot Model of Contacts based

on Surface Features, The 34th Holm Conference onElectrical Contact, 1988.

( 5 ) Micheal T. Singer. Electrical Resistance of RandomRough Contacting Surfaces Using Fractal Surface Modelingthe C ontact Interface. IEEE Trans. on CH MT, Vo1.-14 No.11991.

(6) Li Kui, Lu Jianguo, Zhang Guansheng, MathematicalAnalysis of Thermal Process of Static Electrical Contacts,High Voltage Apparatus, No.1 1997.(7) S m a n R. Robertson. A Finite Element Analysis of theThermal Behavior of C ontacts, IEEE. T rans. on CH MT Vo1.-5 , N o . l 1981.(8 ) A. Oberg, et al . Computer Simulation of the Electricaland T hermal on Electrical Contacts, The 17Th nternationalConference on Electrical Contacts, Japan, 1994.

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