Adhesive Wear Theory of Micromechanical Surface Contact

Transcription

1 International Journal Of Computational Engineering esearch ijceronline.com Vol. Issue. hesive Wear Theory of Micromechanical Surface Contact iswajit era Department of Mechanical Engineering National Institute of Technology Durgapur, Inia bstract: Microscopically, when two surfaces come in contact, strong ahesive bon is forme at the tip of the asperities an consequently, ahesive wear particle is forme by shearing the interface cause by sliing. On the basis of J ahesion theory, imensionless real area of contact an wear volume are compute numerically for multiasperity contact an It is foun, their ratio is almost constant for ifferent pair of MEMS surfaces. From which ahesive wear law is erive an accoringly, ahesive wear volume is the multiplication of real area of contact an rms roughness sigma. eywor: J ahesion theory, eal area of contact, hesive wear volume, Coefficient of ahesive wear 1. Introuction Wear is a complex process of material removal from the interface of mating surfaces uner sliing motion. ccoring to ahesive wear theory, when two smooth an clean rough surfaces come in contact, col wele junctions are forme at the pick of the asperities through plastic eformation an the subsequent shearing of the junctions from softer material causes ahesive wear particle. Existing almost all laws of ahesive wear are base on experimental finings an empirical in nature. olm [1] assume that ahesive wear was an atomic transfer process occurring at the real area of contact forme by plastic eformation of the contacting asperities. olm propose an equation for ahesive wear, as P V Z where P, an Z are loa, harness an number of atoms remove per atomic encounter respectively. Similarly, rchar [] quantifie ahesive wear for rough surface contact base on single asperity contact as ahesive wear, P V L where L is sliing istance an is wear coefficient which shoul be evaluate experimentally. Still, now, rchar s ahesive wear law is well accepte but it oes not quantify the ahesive wear volume theoretically. In this stuy, effort has pai to quantify ahesive wear volume theoretically. It is consiere that asperities woul eform elastically an they col wel ue to intermolecular ahesion at the contact zone of asperity. Strong ahesive bon is forme accoring to J ahesion theory [] i.e. ahesive force woul act within ertzian contact zone of eforme asperities. This iea is implemente to fin ahesive wear volume an real area of contact for multiasperity contact of rough surfaces such as ahesive MEMS surface contact. Thereafter, from the interrelation of both the parameters, new ahesive wear law has evelope an finally, the new ahesive law is compare an interrelate with existing rchar's ahesive wear law.. Theoretical Formulation.1 Single asperity contact.1.1 Single asperity real area of contact J theory has moifie ertz theory of spherical contact. It preicts a contact raius at light loas greater than the calculate ertz raius. s asperity tip is consiere spherical, the ahesion moel of single asperity contact coul be extene to multiasperity of rough surface contact. So, real contact area of sinle asperity is F F a Substituting F, we get a π δ π δ.5 π γ Single asperity ahesive wear volume If wear particle is in the shape of hemispherical an is cut off from tip of the asperity through shearing of col wele junction, wear volume, 7 Issn 5-5 Online March 1

2 hesive Wear Theory of Micromechanical Surface Contact Va a F F Substituating F, we get.5 Va --. Multiasperity contact First of all, Greenwoo an Williamson [] evelope statistical multiasperity contact moel of rough surface uner very low loaing conition an it was assume that asperities are eforme elastically accoring ertz theory. Same moel is moifie here in ahesive rough surface contact an it is base on following assumptions: a. The rough surface is isotropic. b. sperities are spherical near their summits. c. ll asperity summits have the same raius but their heights vary ranomly followe by Gaussian istribution.. sperities are far apart an there is no interaction between them. e. sperities are eforme elastically an ahesive bone accoring to J ahesion theory f. There is no bulk eformation. Only, the asperities eform uring contact. Multiasperity contact of ahesive rough surface has shown in Fig.1 ccoring to, GW moel, two rough surface contact coul be consiere equivalently, contact between rough surface an smooth rigi surface. Let z an represents the asperity height an separation of the surfaces respectively, measure from the reference plane efine by the mean of the asperity height. δ enotes eformation of asperity by flat surface. Number of asperity contact is N N z z -- c where N is total number of asperity an z is the Gaussian asperity height istribution function...1 Multiasperity real area of contact So, from eq n 1 an, total real area of contact for multiasperity contact is N zz a 7 Issn 5-5 Online March 1

3 hesive Wear Theory of Micromechanical Surface Contact 75 Issn 5-5 Online March 1 zz N Diviing both sie by apparent area of contact n h exp 1.. Multiasperity ahesive wear volume So,, from eq n an ahesive wear volume for multiasperity contact is N c V a V zz V N a.5 zz N Diviing both sie by n.5 V.5 h exp 1. esults an Discussion Tayebi an Polycarpou [5] have one extensive stuy on polysilicon MEMS surfaces an four ifferent MEMS surface pairs. ere, surface roughness, surface energy, an material parameters of the clean an smooth MEMS surfaces are being consiere for present stuy as input ata as given in Table.1.The material properties of MEMS surface samples are moulus of elasticity, = / E = 11 GPa, moulus of rigiity, G = 18. GPa harness, = GPa, an poisions ratio, ν 1 = ν =. Johnson et.al. first mentione that eformation of spherical contact woul be greater than the eformation preicte by ertzian spherical contact. It is mentione that only attractive ahesive force acts within ertzian contact area an it increases eformation of sphere resulting higher contact area. From Fig., imensionless real area of contact increases with ecrement of imensionless mean separation exponentially. It is foun that maximum real areas of contact for the all cases of MEMS surfaces increase as smoothness of MEMS surfaces increase. Dimensionless real area of contact for super smooth MEMS surface is very high almost near to the apparent area of contact ue to presence of strong attractive ahesive force. On the other han, real area of contact is very small for the rough MEMS surface contact.

4 E COEFFICIENT OF WE V / EL E OF CONTCT DESIVE WE VOLUME V hesive Wear Theory of Micromechanical Surface Contact OUG INTEMEDITE SMOOT SUPE SMOOT OUG INTEMEDITE SMOOT SUPE SMOOT MEN SEPTION h MEN SEPTION h Fig. eal area of contact Fig. hesive wear volume OUG INTEMEDITE SMOOT SUPE SMOOT. 1-1 MEN SEPTION h Fig. rea coefficient of wear Fig. epicts variation of ahesive wear volume with mean separation. It is foun that maximum ahesive wear volume for the all cases of MEMS surfaces increase as smoothness of MEMS surfaces increase. So, super smooth MEMS surface prouces maximum ahesive wear volume whereas rough MEMS surface prouces very low ahesive wear volume. Fig. shows area coefficient of wear verses imensionless mean separation. This coefficient is consiere to unerstan the relationship in between real area of contact an wear volume. From the nature of curves, it is foun that imensionless ahesive wear volume is almost linearly proportional with imensionless real area of contact. So, area coefficient of wear is almost constant. So, rea coefficient of wear V V ah or, V a Consiering yieling of asperity of asperity tip ue to loaing force, real area of surface contact, P 7 Issn 5-5 Online March 1

5 hesive Wear Theory of Micromechanical Surface Contact So, V ah P where V= Wear volume, ah = ahesive wear coefficient i.e. area coefficient of wear, P = loaing force i.e. Contact force, = soft material harness, σ = rms roughness of surface ccoring to new ahesive wear law, ahesive wear coefficient increases with increment of MEMS surface contact. n ah =.5 for rough surface, ah = 5 for smooth surface, ah = for intermeiate surface, an ah = 1 for super smooth surface. Now, wear rate, v. v no. of pass per revolution PS v n PS p Generally, Pin on Disk tester are commonly use to measure wear rate. If circular cross sectional pin of iameter, is place on isk at iameter, D, no. of pass per revolution, n p Total area Cross sec tional crosse area of D / pin D In comparison of new ahesive wear law with rchar's law of ahesive wear, the new law is much more appropriate from the point view of volume concept. In case of well accepte rchar's law of ahesive wear, sliing istance is on the plane of real area of contact an so, how oes multiplication of both the two parameter prouce volume whereas in case of new law of ahesive wear, r.m.s. roughness perpenicular to the plane of real area of contact which prouces volume removal in the form of ahesive wear. Now, let us see the interrelation in between new ahesive wear law an existing rchar s ahesive wear law. rchar s ahesive wear law was evelope from single asperity contact irectly as follows; 1 Elementary wear volume of hemispherical shape of wear particle, Va a a.a =1/ rea of contact of asperity sliing istance of asperity Now, for multiasperity contact of rough surface, we have wear volume; V= ah.eal area of contact pparent sliing istance ah. L P ah L First, rchar have evelope interrelation of wear volume with real area of contact an apparent sliing istance but wear volume coul not be calculate theoretically because coefficient of ahesive wear have to be quantifie experimentally. Experimentally, it is foun that coefficient of ahesive wear is of the orer of 1 - to 1 -. ctually, for unit meter sliing istance, ah. L is real sliing istance of truncate asperities only which is of the orer of 1 - to 1 - m. In comparison with new ahesive wear law, real sliing istance is the parameter of rms surface roughness σ which is also of the orer of 1 - to 1 - m. So, new ahesive wear law is an alternative law of ahesive wear by which wear volume coul be calculate theoretically.. Conclusion Finally, alternative ahesive wear theory coul be evelope accoring to Minlin s concept of stick-slip mechanism as follows. Microscopically, when two rough surfaces come in contact, spherical tip of asperity woul eform elastically an it will stick an col wel at the contact zone ue to interatomic ahesive force uner loaing conition. Subsequent impening sliing prouces maximum frictional traction at the junction of asperity contact. fter maximum limit, it woul slip raialy inwar at the circular contact zone of asperity an corresponingly, real area of contact of asperity ecreases proucing ultimate gross slip / sliing. During slipping, if shearing strength at asperity junction is much more than bulk shear strength of one of the surface, fragment of material woul be remove from the softer surface. s a result one ahesive wear particle woul be forme. 77 Issn 5-5 Online March 1

6 hesive Wear Theory of Micromechanical Surface Contact t the en of one pass of sliing, volume of ahesive wear woul be proportional to eal area of contact rms roughness. It woul be of the orer of nm to μm. So, hesive wear rate is linearly proportional to real area of contact = Loa / arness, rms roughness an no. of pass per unit time. eferences [1] olm, Electric contact, Gerbers, Stockholm, Sween, [] J F rchar, Contact an rubbing of flat surfaces. Journal of pplie Physics,, 15, [] L Jhonson, enall, an D oberts, Surface energy an the contact of elastic solis, Proc.. Soc. Lon.,, 171, 1-1 [] J Greenwoo, an J P Williamson, Contact of nominally flat surfaces. Proc.. Soc. Lon., 5, 1, -1 [5] N Tayebi an Polycarpou, hesion an contact moeling an experiments in microelectromechanical systemsincluing roughness effects, Microsyst. Technol., 1,, 85-8 Combine MEMS Surfaces Table.1 Input ata ough Smooth Intermiiate Super Smooth sperity ensity η m - sperity raius m Staanar eviation of asperity height σ m Surface energy γ N/m Moulus of elasticity N/m Moulus of rigiity G N/m oughness parameter Surface energy parameter sperity raius parameter Issn 5-5 Online March 1