Numerical Study Of Coated Electrical Contacts

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1 Excerpt from the Proceedings of the COMSOL Conference 21 Pris Numericl Study Of Coted Electricl Contcts Per Lindholm Mchine Design KTH Brinellvägen 83 SE-144 Stockholm Abstrct: Electricl contcts consists of prts where the surfces re in contct nd where the ctul physicl contct occur just in few contct sperity points scttered over the whole pprent contct re. Through these contct spots between the two mting bodies the mechnicl lod nd the electric current is trnsmitted. Often soft coting is used to enlrge the rel contct re. Modeling the mechnicl stress on the contcting mteril includes nonliner effects of the electric conduction nd het genertion s well s the ctul mechnicl contct of the sperities. COMSOL Multiphysics hs been used to model these thermo electromechnicl phenomen when two surfce sperities re in contct. Keywords: Electricl contcts, 1. Introduction The contct mechnics of electricl contcts hs been well investigted by mny reserchers during the lst decdes [1,2,3]. The physicl spects on the phenomen involved in the trnsfer of electricity over contct interfce includes dvnced knowledge in mechnics, mterils nd physics. Nonliner effects s the contct itself nd mteril properties tht chnges with the mount of current nd temperture in the contct mkes it difficult to investigte nd simulte. Surge rresters re protective devices on the grid which consists of semi conductive zinc oxide (ZnO) blocks stpled together in stck nd pretension vi glss fiber loops [4,5]. They re coted with luminum coting to improve the current cpbility nd give good contct between the blocks. Figure 1 show such block combintion in contct indicting the contct spots occurring when two rough surfces re in contct [6,7]. Previous work [8] hs shown the increse in temperture due to the joule heting effect for different mteril combintions. This work dds the structurl mechnics to the solution nd exmines the mteril combintion relevnt in the surge rrester cse. Figure 1. Schemtic view of the contct spot formtion when two rough surfces re in contct. This pper presents numericl study of n sperity in contct with the influence of coting thickness to the mount of trnsferred current in the contct. 2. Theory In sttionry electricl contct the contct members re connected by pretension mechnicl lod to physiclly connect the members together. The mechnicl lod F is crried by the sperities in contct. The size of the mechnicl contct A cn be described by the reltionship between the hrdness H nd the lod. F A (1) H However the ctul size of the contct spot the - spot tht trnsfers the current is just frction of the mechnicl loded spot. The size depends minly on the oxide lyer nd other impurities which covers the metllic contct surfce. Holm [1] hs shown tht the constriction resistnce R s with the sme metl resistivity on both members cn be clculted s: R s 2 (2)

2 The multiphysics problem consists of solving combintion of structurl mechnic problem, het trnsfer nd the electric current field. 2 Figure 2. Schemtic figure of the coted contct sperity with oxide lyer nd the current pths indicted. In relity the surfce sperities come into contct nd contct definition between the surfces would be needed in solving the complete problem. However this hs shown to be very sensitive nd hrd to solve when the joule heting prt is dded. Therefore simplifiction hs been done where the Hertzin contct pressure distribution is used s mechnicl lod. Previous work by the uthor [8,9] hs used similr pproch in completely different ppliction. At the contct interfce between sphericl indenter nd n opposite surfce the pressure distribution cn be clculted ccording to the Hertz eqution from [7]: 2 r p( r) pmx 1 (3) 2 for ll r<, is the contct rdius of the Hertzin contct. The temperture dependence, T, of the electric conductivity cn be described by the following eqution: 1 1 T T ref Substrte Coting Oxide lyer (4) 5. Numericl model The Comsol 4. model is defined s Joule Heting nd Therml Expnsion multiphysics model. The specil cse for xisymmetry is used nd the conditions for sttionry conditions is clculted. A therml liner elstic mteril model is used. Prmeteriztion: The Comsol cpbility of prmeteriztion hs been used where ll the prmeters re defined in the globl prmeter definition. Tble 1. Prmeters used in the model (setup vlues). Nme Expression Description B 5[µm] Model width H 1[µm] Model height Rc 14[µm] Contct rdius ct 4[µm] Coting thickness 4[µm] -spot dimeter I 4[A] Current Am pi*b^2 Model cross section J I/Am Current density p 2[MP] Mximum Hertzin pressure mt 1[µm] Element size Tble 2. Vrible used in the model. Nme Expression Description pn p*sqrt(1-r^2/rc^2) Contct pressure distribution Geometry: The geometry is defined from the prmeters into single prt. The prt is divided in n -spot prt, size, where the current nd het is trnsferred nd lod crrying prt, size Rc, where the lod is defined. A coting thickness ct defines the thickness of the coting mteril. Figure 3 shows the geometry with the used geometricl prmeters. where is the resistivity t the reference temperture T ref nd is the resistivity temperture coefficient.

3 Rc ct Mesh: The mesh is defined s mpped mesh with fixed element size close to the -spot nd the lod re of the prmeter mt µm. Qudrtic elements re used. H Mteril properties used in the clcultions for ech combintion is shown in tble 2. The substrte hs similr mteril ZnO which is semiconductor with nonliner resistivity depending on the voltge cross the specimen [4,5]. Figure 3. Geometry of the Comsol model Electricl boundry conditions: On the verticl right outer boundry nd on the top surfce from the -spot rdius to the outer end electricl insultion is defined, tht is no electricl current is pssed over the surfce. n J The top surfce over the distnce on the -spot is grounded nd on the bottom surfce norml current density is pplied s the electricl lod on the model. Het trnsfer boundry condition: The outer boundries sme s for the electricl cse is thermlly insulted tht is the het flux over the surfce is zero. n k T The temperture on the top nd bottom boundries re set to 293K.. B Mechnicl boundry condition: The bottom boundry s well s the right verticl boundry hve roller constrints tht mens the motion in the direction norml to the surfce is constrined but it is free to move in the tngentil direction of the surfce. Tble 3. Properties of the mteril dt used in the model collected from [2] nd [5]. Property Substrte Coting Young s modulus [GP] Poisson s rtio [-] Density [kg/m 3 ] Coefficient of therml expnsion [1/K] 6.6e-6 2.3e-5 Reltive permittivity [-] 1 1 Therml conductivity [W/(mK] Het cpcity t constnt pressure [(J/(kgK)) ] Reference resistivity [ m] Resistivity temperture coefficient [1/K] Reference temperture [K] e e-8 1e-9 4.6e Meltingpoint [ o C] 66 Hrdness [N/mm 2 ] 2

6. Experimentl results The results consist of study of the prmeters in the model.

Figure 4 shows the stress deformtion under lod from sphericl indent t no current.

When the current is incresed the temperture lso increses s resistive heting in the constriction -spot.

contct. Figure 6. Temperture [ o C] in the model t J n =4A. Stremlines show the energy flux. Deformtions re scled 1 times. Figure 4.

b 8 7 6 5 4 3 =2µm 2 =4µm 1 =1µm 5 1 15 2 Current [A] Figure 7.

4 6. Experimentl results The results consist of study of the prmeters in the model. First study of the ppliction of the lod nd then incresing the current over the sperity from the nominl prmeter dt set up. Figure 4 shows the stress deformtion under lod from sphericl indent t no current. Figure 5 then shows the Tresc-sher stress t incresing current pssing through the -spot constriction. When the current is incresed the temperture lso increses s resistive heting in the constriction -spot. Figure 6,7 nd 8 show the temperture development up to the melting temperture of the coting nd in figure 7 the voltge drop over the contct. Figure 6. Temperture [ o C] in the model t J n =4A. Stremlines show the energy flux. Deformtions re scled 1 times. Figure 4. Model under pressure lod nd I=A. Mximum sher stress [MP]. Deformtion scle 1. b =2µm 2 =4µm 1 =1µm Current [A] Figure 7. Mximum temperture in the model for different -spot sizes s function of current pssing through the contct. Temperture [ o C] c d Figure 5. Model under pressure lod nd the current through the spot is incresed in J n =A, b J n =1A, c J n =3A nd in d J n =4A. Current density stremlines is lso indicted in the figures. Voltge drop [mv] 7 =2µm 6 =4µm 5 =1µm Current [A] Figure 8. Voltge drop over the contct -spot

5 From the initil stte defined in tble 1 the coting thickness is vried from 2-12µm. Figure 9 show the mximum temperture development in the model due to chnge in coting thickness t the sme pplied current density. In figure 9 the mximum sher stress (Tresc stress) is shown on the boundry between the coting nd the substrte for different coting thicknesses. Temperture [ o C] Coting thickness[µm] Figure 9. Mximum temperture in the model for different coting thicknesses. Tresc stress [MP] ct=2µm ct=6µm ct=12µm Rdius [µm] Figure 9. Tresc sher stress in the interfce of substrte nd coting for different coting thicknesses. investigted. Problems with defining pirs nd ese to hve flexible model investigting different prmeters pointed towrds the chosen solution. Another wy to investigte the effect of joule heting in the sperity is to used the whole geometry s shown in figure 2 nd use the contct resistnt functionlity t suitble boundries defining the -spot nd the resistive oxide lyer. However the pretension lod from the outer clmping force is then hrd to ccomplish. In this simultion tempertures spred out rpidly in the coting due to the much lower conductivity of the coting in reltion to the substrte. The sher stress mxim shifts upwrd towrds the surfce due to therml expnsion of the complete structure. Coting thickness reduces mximum temperture nd evens out sher stresses in the interfce to the substrte. Future work would be to investigte the effect of elstoplstic mteril model 8. Conclusion The work show possible wy to simulte the combined deformtion nd resistive heting problem in n electricl contct. It gives illustrtive nd esy wy of investigting the effects of coting thickness, -spot size, contct lod nd size. 7. Discussion Modeling n electricl contct combines severl physics into the sme simultion. Comsol hs shown to hve the cpbility of combining these res. In this work severl modeling pproches were tested. A contct model ws nlyzed but the solver hd problems finding solution when the combined multiphysics ws simulted lso segregted multiphysics contct solution ws

6 9. References 1. R. Holm, Electricl Contcts - Theory nd Applictions, 4th Ed., Springer-Verlg, Berlin P.G.Slde, Electricl Contcts - Principles nd Applictions, Mrcel Dekker, New York M.Brunovic, V. Konchits, N.Myshkin, Electricl Contcts - Fundmentls, Appliction nd Technology, CRC Press Tylor Frncis Group, Mobedjin M. Jonnerfelt B., Stenström L., Design nd testing of polymer-housed surge rresters, GCC CIGRÉ 9th Symposium, Abu Dbi, Hddd A., Wrne D.F., Advnces in High Voltge Engineering, The Institution of Electricl Engineers, London, UK, T.R. Thoms, Rough Surfces, 2nd Ed. Imperil College Press, London 7. Johnsson K.L., Contct Mechnics, Cmbridge University Press, Å. Öberg, K.E. Olsson, O.Sksvik, Computer simultion of the electricl nd therml behviour of electricl contcts, Proc 17th Int. Conf. on Electricl Contcts, 1994, pp Lindolm P., Björklund S., Svhn F., Method nd surfce roughness spects for the design of DLC cotings, 26 Wer 261 (1), pp Lindholm P., Svhn F., Study of thickness dependence of sputtered crbon coting for low friction vlve lifters, 26, Wer 261 (3-4), pp Acknowledgements This work ws supported by the Swedish Foundtion for Strtegic Reserch

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