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- 1. Biswajit Bera / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 5, September- October 2012, pp.404-411 Adhesional Friction Law and Adhesive Wear Law of Micromechanical Surface Contact Biswajit Bera* *(Department of Mechanical Engineering, National Institute of Technology Durgapur, India)ABSTRACT The paper describes the investigation on Ka 3 power of load P a 2 P 2/ 3 .To avoidadhesional friction law and adhesive wear law of micromechanical surface contact. Adhesion R the violation of the theory, Bowden and Tabortheory of loading force and friction force is simply, mentioned that all asperities should deformincorporated in multiasperity contact to find out plastically and real area of contact is linearly static coefficient of friction which supportsAmontonss law of friction. New adhesive wear proportion to load P a 2 H a 2 P . Thoughlaw is developed from almost linear relationship the theory is well accepted, still there is a questionof dimensionless real area of contact and why real area of contact is linearly proportional todimensionless adhesive wear volume, and it is load in so many tribosystem where plasticcompared with existing Archards adhesive wear deformation does not occur.law. This is investigated in adhesive MEMS surface contact considering adhesion model of elastic solid.Keywords - Real area of contact, Adhesional However, there are two type of adhesion model ofloading force, Adhesional friction force, elastic solid; one is JKR adhesion model [3] whichCoefficient of friction, Adhesive wear law considers adhesion force within contact area of elastics solid sphere and another is DMT adhesion1. Introduction model [4] which considers adhesive force out side of Friction could be defined as the force of contact area of elastic solid sphere. First of all,resistance that occurs when one body moves Chang et al. [5] have developed multiasperitytangentially over another body. In the 15th century adhesion model of metallic rough surface contactda Vinci discovered a law about dry sliding friction, based on DMT adhesion model. Thereafter,which was rediscovered by Amontons about 200 Roychowdhury and Gosh [6] have considered JKRyears later. Friction laws were stated by French adhesion model for study of adhesive rough surfaceengineer Guillaume Amontons [1] in 1699 from the contact but have evaluated external Hertzian load inconclusions of his experimental work which are presence of adhesion, though which could begiven as follows: evaluated directly. However, adhesion component of JKR model is not considered for evaluation of a) The friction force linearly proportional to adhesion of multiasperity rough surface contact. The the normal load between the two bodies in adhesive component of JKR adhesion model is contact. considered for present study of adhesive MEMS b) The friction force is independent of the surface contact. Actually, Johnson et al. [3] has apparent area of contact between the two extended Hertz model considering adhesion of solid bodies. elastic sphere based on energy method. Thereafter, on the basis of same method, Savkoor and Briggs [7]Thereafter, microscopic analysis of friction process has extended JKR adhesion model and developedwas described by Bowden and Tabor [2] in 1931. adhesional friction model of elastic solid sphereThe theory was based on following two statements: under tangential loading. The SB adhesional friction model is considered for finding adhesional friction of a) The friction force is dependent on real area MEMS surface contact. of contact between two bodies. b) The friction force is dependent on shearing On the other hand, due to rapid growth of strength of adhesive bond formed between micro-machine, it has become important to study the two bodies at tip of asperities. wear phenomena in the nano-scale under ultra low loading condition. Archards adhesive wear law [11] The adhesional friction theory of Bowden and Tabor is essentially based on the classical concept ofis appeared to be inconsistent with Hertz theory of adhesion of metallic surface as proposed by Bowdendeformation of contacting elastic asperities, which and Tabor [2]. The fundamental idea is that thepredicts that the contact area should vary as 2/3 welded junctions are formed at the pick of the 404 | P a g e
- 2. Biswajit Bera / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 5, September- October 2012, pp.404-411 asperities due to localized high adhesion and the Ta 4 2 RF 3 R 2 subsequent shearing of the junctions from weaker material causing adhesive wear. Similar idea is G K 0 implemented to find new adhesive wear law considering adhesion component of JKR adhesion 4 2KR 3 R 1.5 1.5 2 (3) model [3]. Thereafter, it is compared with existing GK Archards adhesive wear law. where 1 2 1 1 2 2. Single asperity contact G G1 G2 2.1 Single asperity real area of contact JKR adhesion theory has modified Hertz 2.4 Single asperity adhesive wear volume theory of spherical contact. It predicts a contact radius at light loads greater than the calculated Hertz If wear particle is in the shape of hemispherical and radius. As asperity tip is considered spherical, the is cut off from tip of the asperity, wear volume is adhesion model of single asperity contact could be 2 extended to multiasperity of rough surface contact. Va a 3 3 So, real contact area of single asperity is 2 R F0 3 R 6 RF0 (3 R ) 2 2 R 3 3 K A a F0 3 R 6 RF0 (3 R ) 2 K Substituating F K (R) , we get 1.5 Substituting F K (R) , we get 1.5 0 R a R 2 1.5 1.5 3 R 2 6 R 3.5 1.5 9 2 2 R 4 (4) 2 Va R 3 R 2 6 R 3.5 1.5 9 2 2 R 4 3 3 K K K2 A a R 1.5 1.5 (1) K K K2 3. Multiasperity contact First of all, Greenwood and Williamson 2.2 Single asperity adhesional loading force [8] developed statistical multyasperity contact model of rough surface under very low loading condition According to JKR adhesion model, the expression and it was assumed that asperities are deformed of adhesional loading force for each asperity contact elastically according Hertz theory. Same model is is modified here in adhesive rough surface contact and it is based on following assumptions: Fa F0 3 R 6 RF0 (3 R ) 2 i. The rough surface is isotropic. ii. Asperities are spherical near their summits. KR 0.5 1.5 3R 6KR1.5 1.5 (3R) 2 (2) iii. All asperity summits have the same radius R but their heights vary randomly. where 1 3 1 1 1 2 2 2 iv. Asperities are far apart and there is no K 4 1 E E2 interaction between them. v. Asperities are deform elastically according and E1 , E2 , 1 and 2 are Young’s modulus and to JKR adhesion theory poisson’s ratios of the contacting surfaces vi. There is no bulk deformation. Only, the respectively, asperities deform during contact. Flat plane where surface energy of both surfaces, 1 2 12 2.3 Single asperity adhesional friction force δ Savkoor and Briggs theory has found adhesional Z friction of spherical contact under tangential loading. d As asperity tip is considered spherical, the adhesional friction model of single asperity contact could be extended to multiasperity of rough surface Mean contact. According to the Savkoor and Briggs model, the expression of adhesional friction force for Rough surface each asperity contact is Fig. 1 Rough surfaces contact 405 | P a g e
- 3. Biswajit Bera / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 5, September- October 2012, pp.404-411 Multiasperity contact of adhesive rough surface has R 0.5 shown in Fig.1. According to, GW model, two rough (R) 3(R) K surface contact could be considered equivalently, F * ()d 0.5 2 contact between rough surface and smooth rigid 0 6(R) 2 R 1.5 9 2 (R) 2 surface. Let z and d represents the asperity height K K and separation of the surfaces respectively, measured from the reference plane defined by the mean of the asperity height. δ denotes deformation of asperity by flat surface. Number of asperity 0 R 00.5 3A 0 B0 1 h 2 contact is exp d 2 0.5 1.5 0 6A 0 B0 R 0 9 2 A 0 B 0 2 2 2 2 N c N ( z )dz (5) d where dimensionless surface roughness parameter, where N is total number of asperity and (z ) is the A 0 R and dimensionless surface energy Gaussian asperity height distribution function. parameter, B0 K 3.1 Multiasperity real area of contact 3.3 Multiasperity adhesional friction force n So, from eq (1) and (5), real area of contact for multiasperity contact is So, , from eqn (3) and (5), total adhesional friction force for multiasperity contact is A N A a ( z )dz T N c Ta d 2 KR 2 N 3 R (z)dz 4 3 R 2 6 R 3.5 1.5 9 2 2 R 4 3 1.5 1.5 2 N R 1.5 1.5 d K K K2 (z)dz d G K Dividing both side by apparent area of contact An Dividing both side by AnK 0.5 2 R T 4 * 2(R) 2 3 (R) 1.5 2 2 ()d 1.5 1.5 R G K 0.5 (R) 3 (R) 1.5 1.5 2.5 K K 0 K A* ()d R R 0.5 2 0 6 4 ( R) 3 1.5 9 5 (R) 3 K K h 2 2A 0 B0 R 0 0.5 1.5 3 2 A 0 B0 4 1 2 2 2 exp d 1.5 A1.5 .5 3 2.5 A1.5 B R 0.5 1 1 h 2 0 GK 2 2 0 0 0 0 exp d 0 6 A 0 B0 R 0 9 A 0 B0 R 0 2 4 3 0.5 1.5 5 3 2 2 3.4 Multiasperity adhesive wear volume 3.2 Multiasperity adhesional loading force So, from eqn (4) and (5), adhesive wear volume for So, , from eqn (2) and (5), adhesional loading force multiasperity contact is for multiasperity contact is V N c Va F Nc Fa N Va (z)dz N KR 0.5 1.5 3 R 6 KR 1.5 1.5 (3 R ) 2 (z)dz d d 2 6 R 3.5 1.5 9 2 2 R 4 Dividing both side by AnK 3 R 2 N R 1.5 1.5 (z)dz d 3 K K K2 Dividing both side by A n 406 | P a g e
- 4. Biswajit Bera / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 5, September- October 2012, pp.404-411 ROUGH SMOOT H 0.5 R 1.5 R INT ERMEDIAT E SUPER SMOOT H (R) 3(R) 2 K 0.003 ADHESIONAL LOADING FORCE (F* )V * ()d 3 0 2 R 1.5 R 1.5 2 6(R) 2 9 (R) 2 2 0.002 K K 0.002 0.001 2 A 0 R 0 3A 0 B0 R 0 1 h 2 0.5 1.5 exp d 0.001 3 0 6A 0 B0 R 0 9 A 0 B0 R 0 2 2 1.5 1.5 2 2 2 2 2 0.000 4. Results and Discussion 4 3 2 1 0 -1 Tayebi and Polycarpou [9] have done MEAN SEPARAT ION (h) extensive study on polysilicon MEMS surfaces and four different MEMS surface pairs. Similarly, Fig.3 Adhesional loading force tribological properties of the MEMS surfaces are being considered for present study as input data as Johnson et. al. first mentioned that shown in table 1 [Appendix A].The material deformation of spherical contact would be greater properties of MEMS surface samples are modulus of than the deformation predicted by Hertzian spherical elasticity, K =4/3E = 112 GPa, modulus of rigidity, G contact. It is mentioned that only attractive adhesive = 18.42 GPa hardness, H = 12.5 GPa, and poisions force acts within Hertzian contact area and it ratio, ν1 = ν2 = 0.22 increases deformation of sphere resulting higher contact area. From Fig.2, dimensionless real area of 4.1 Investigation on adhesional friction law contact increases with decrement of dimensionless mean separation exponentially. It is found that ROUGH SMOOT H maximum real areas of contact for the all cases of INT ERMEDIAT E SUPER SMOOT H MEMS surfaces increase as smoothness of MEMS 0.90 surfaces increase. Dimensionless real area of contact 0.80 for super smooth MEMS surface is very high almost REAL AREA OF CONTACT (A * ) 0.70 near to the apparent area of contact due to presence of strong attractive adhesive force. On the other 0.60 hand, real area of contact is very small for the rough 0.50 MEMS surface contact. Fig.3 depicts variation of 0.40 dimensionless adhesional loading force with 0.30 dimensionless mean separation. From the loading 0.20 expression of JKR adhesion model, it is found there 0.10 is two component of force; one is Hertzian deformation force (i.e. external force) and another is 0.00 adhesive force. Fig.3 shows that adhesional loading 4 3 2 1 0 -1 forces are also increases with decrement of MEAN SEPARAT ION (h) dimensionless mean separation exponentially. As smoothness of MEMS surfaces increases, Fig.2 Real area of contact deformation force decreases but adhesive force increases. So, deformation force and adhesive force are inversely proportional according to consideration of roughness as well as smoothness and there should be a reference MEMS surface where both the force should be minimum such a way that total force should be small [10]. This is happening for smooth MEMS surface. Now, adhesional loading force for rough and intermediate MEMS is much more than that of smooth MEMS surface due to mainly Hertzian deformation force. Similarly, adhesional loading force of super smooth MEMS surface is much more than that of smooth MEMS surface due to mainly high adhesive force. 407 | P a g e
- 5. Biswajit Bera / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 5, September- October 2012, pp.404-411 ROUGH SMOOT H ROUGH SMOOT H INT ERMEDIAT E SUPER SMOOT H INT ERMEDIAT E SUPER SMOOT H AREA COEFFICIENT OF FRICTION (T * /A* ) 0.08 0.02AREA COEFFICIENT OF LOAD (F * /A* ) 0.07 0.01 0.06 0.01 0.05 0.01 0.04 0.01 0.03 0.01 0.02 0.00 0.01 0.00 0.00 0.00 4 3 2 1 0 -1 4 3 2 1 0 -1 MEAN SEPARAT ION (h) MEAN SEPARAT ION (h) Fig.4 Area coefficient of load Fig.6 Area coefficient of friction Fig.4 shows area coefficient of load versesdimensionless mean separation. This coefficient is From Fig.5, adhesional friction forceconsidered to understand the relationship in between increases with decrement of dimensionless meanreal area of contact and loading force. Generally, it separation exponentially. It is found that maximumis assumed that real area of contact and load are adhesional friction force for the all MEMS surfaceslinearly proportional as mentioned by Bowden and increases as smoothness of MEMS surface increases.Tabor considering plastic deformation of asperity. Adhesional friction force for super smooth MEMSFor mean separation smaller than 1, area coefficient surface is very high due to presence of strongfor all four cases are comparatively small and are of attractive adhesive force. On the other hand,the slightly descending with same magnitude. adhesional friction force is very small for the roughHowever, as mean separation larger than 2, MEMS surface contact.deviation in the coefficient among the four casesbecomes increasing prominent and it maintain Fig.6 shows area coefficient of frictionalmost different constant value with mean verses dimensionless mean separation and it followsseparation. The separation in between 2 and 1, there the similar nature of curve as shown for areais transition of the coefficient from higher different coefficient of the loading force. Similarly, It showsvalue to lower descending constant value. So, from non linear relationship in between real area ofthe discussion, it is found that it do not support the contact and friction force.linear relationship in between real area of contactand the loading force ROUGH SMOOT H INT ERMEDIAT E SUPER SMOOT H ROUGH SMOOT H COEFFICIENT OF FRICTION (T * /F* ) 0.50 INT ERMEDIAT E SUPERSMOOT H 0.45 ADHESIONAL FRICTION FORCE (T ) 0.0008 * 0.40 0.0007 0.35 0.30 0.0006 0.25 0.0005 0.20 0.0004 0.15 0.10 0.0003 0.05 0.0002 0.00 0.0001 4 3 2 1 0 -1 0.0000 MEAN SEPARAT ION (h) 4 3 2 1 0 -1 MEAN SEPARAT ION (h) Fig.7 Coefficient of friction Fig.5 Adhesional friction force Fig.7 displays variation of coefficient of friction with mean separation. It is found that static coefficient of friction is almost constant except for 408 | P a g e
- 6. Biswajit Bera / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 5, September- October 2012, pp.404-411the super smooth MEMS surface. So, the Amontonslaw of static friction is validated for adhesive ROUGH SMOOT Hmicromechanical surface contact. Only for the INT ERMEDIAT E SUPER SMOOT Hsupersmooth MEMS surface contact, coefficient of 160.00 AREA COEFFICIENT OF WEAR (V * /A* )static friction suddenly drops at close contact though 140.00nature of curve of adhesional loading force andadhesional friction force for supersmooth MEMS 120.00surface is same. 100.00 80.00 4.2 Investigation on adhesive wear law 60.00 ROUGH SMOOT H 40.00 INT ERMEDIAT E SUPER SMOOT H 20.00 100.00 90.00 0.00 ADHESIVE WEAR VOLUME (V ) * 80.00 4 3 2 1 0 -1 70.00 MEAN SEPARAT ION (h) 60.00 50.00 Fig.9 Area coefficient of wear 40.00 * 30.00 So, Area coefficient of wear V V K A * adh 20.00 A 10.00 V K adh A 0.00 4 3 2 1 0 -1 Where real area of surface contact, A P according MEAN SEPARAT ION (h) H to Bowden and Tabor theory Fig.8 Adhesive wear volume P Fig.8 depicts variation of adhesive wear V K adh Hvolume with mean separation. It is found thatmaximum adhesive wear volume for the all cases of Where V= Wear volume, Kadh = adhesiveMEMS surfaces increase as smoothness of MEMS wear coefficient (i.e. area coefficient of wear), P =surfaces increase. So, super smooth MEMS surface normal load, H = soft material hardness, σ = rmsproduces maximum adhesive wear volume whereas roughness of surface.rough MEMS surface produces very low adhesivewear volume. According to new adhesive wear law, adhesive wear coefficient increases with increment Fig.9 shows area coefficient of wear verses of MEMS surface contact. And Kadh = 0.25 for roughdimensionless mean separation. This coefficient is surface, Kadh = 5 for smooth surface, Kadh = 30 forconsidered to understand the relationship in between intermediate surface, and Kadh = 120 for superreal area of contact and wear volume. From the smooth surface.nature of curves, it is found that dimensionlessadhesive wear volume is almost linearly proportional .with dimensionless real area of contact. So area Now, wear rate, v v × no. of pass per revolutioncoefficient of wear is almost constant. × RPS v n p RPS Generally, Pin on Disk tester are commonly used to measure wear rate. If circular cross sectional pin of diameter, d is placed on disk at diameter, D, no. of pass per revolution, np Total area crossed Dd D 4 d 2 / 4 d Cross sec tional area of pin 409 | P a g e
- 7. Biswajit Bera / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 5, September- October 2012, pp.404-411However, in comparison of new adhesive wear law Referenceswith Archards law of adhesive wear, the new law is [1] G Amontons, Histoire de lAcadémiemuch more appropriate from the point view of Royale des Sciences avec les Mémoires devolume concept. In case of well accepted Archards Mathématique et de Physique (1699)law of adhesive wear, sliding distance is on the planeof real area of contact and so, how does [2] F P Bowden and D Tabor, The Friction andmultiplication of both the two parameter produce Lubrication of Solids (Oxford Universityvolume whereas in case of new law of adhesive Press, New York 1950)wear, r.m.s. roughness perpendicular to the plane ofreal area of contact which produces volume removal [3] K L Jhonson, K Kendall, and A D Roberts,in the form of adhesive wear. Surface energy and the contact of elastic solids, Proc. R. Soc. Lond., A 324, 1971,5. Conclusions 301-313 The study is the theoretical investigation onexisting static friction coefficient and adhesive wear [4] B V Derjaguin, V M Muller, and YU Plaw. From the study of micromechanical contact of Toporov, Effect of contact deformation onMEMS surfaces, following conclusions could be the adhesion of particles, J. Coll. and Inter.drawn: Sc., 53, 1975, 314-326 a) When micro-rough surfaces are come in contact due to application of external force, [5] W R Chang, I Etsion, and D B Bogy, spherical tip of the contacting asperities Adhesion model for metallic rough form adhesive bond followed by JKR surfaces, Journal of Tribology, 110, 1988, adhesion theory. 50-56 b) As smoothness of surfaces increase, it [6] S K Roy Chowdhury and P Ghosh, produces much more strong adhesive bond Adhesion and adhesional friction at the at the tip of the contacting asperities. contact between solids, Wear, 174, 1994, 9- 19 c) Real area of contact increases with adhesional loading force nonlinearly which [7] A R Savkoor and G A D Briggs, The effect is generally, considered linearly of tangential force on the contact of elastic proportional as stated by Bowden and solids in adhesion Proc. R. Soc. Lond., A Tabor. 356, 1977, 103-114 d) Similarly, real area of contact and static [8] J A Greenwood, and J B P Williamson, adhesional friction force are also Contact of nominally flat surfaces. Proc. R. nonlinearly proportional. Soc. Lond., A 295, 1966, 300-319 e) Static coefficient of friction is almost [9] N Tayebi and A A Polycarpou, Adhesion constant for micromechanical surface and contact modeling and experiments in contact which is theoretical evidence of microelectromechanical systems including Amontons law of friction. roughness effects, Microsyst. Technol., 12, 2006, 854-869 f) Justified new adhesive wear law is developed where adhesive wear volume is [10] B Bera, Adhesion and adhesional friction of equal to multiplication of real area of micromechanical surface contact. Journal contact and rms roughness. Coefficient of of Engineering and Applied Sciences, 6, adhesive wear increases as smoothness of 2011, 104-108 surface increase. [11] J F Archard, Contact and rubbing of flat g) Finally, though above study is done for surfaces. Journal of Applied Physics, 24, micro-rough surface contact of MEMS but 1953, 981-988 it could be applicable for macroscopic study of tribo-system as interface is always microscopic.AcknowledgementsI would humbly thank to Prof. B Halder, NITDurgapur, India whose inspiration and support havemade the work successful. 410 | P a g e
- 8. Biswajit Bera / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 5, September- October 2012, pp.404-411 APPENDIX A Table.1 Input data Combined Rough Smooth Intermidiate Super Smooth MEMS Surfaces η (m-2) 14.7.1012 11.1. 1012 17.1012 26.1012 R (m) 0.116.10-6 0.45.10-6 1.7.10-6 26.10-6 σ (m) 15.8.10-9 6.8.10-9 1.4.10-9 0.42.10-9 γ (N/m) 0.5 0.5 0.5 0.5 K (N/m2) 112.109 112.109 112.109 112.109 G (N/m2) 18.42.109 18.42.109 18.42.109 18.42.109 A0 27.10-3 34.10-3 41.10-3 53.10-3 B0 2.825.10--4 6.565.10--4 31.887.10--4 74.405.10—4 R0 7.342 66.176 1214.285 5600.000 411 | P a g e

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