Tribology in Industry. Friction and Wear Processes Thermodynamic Approach

Transcription

1 Vol. 36, No. 4 (2014) Tribology in Industry RESEARCH Friction and Wear Processes Therodynaic Approach M. Banjac a, A. Vencl a, S. Otović a a University of Belgrade Faculty of Mechanical Engineering, Kraljice Marije 16, Belgrade, Serbia. Keywords: Friction Wear Energy dissipation Entropy generation Non equilibriu therodynai Corresponding author: M. Banjac University of Belgrade Faculty of Mechanical Engineering, Kraljice Marije 16, Belgrade, Serbia E ail: banjac@as.bg.ac.rs A B S T R A C T Tribology, as the scientific and professional discipline within the echanical engineering, studies phenoena and processes on the interacting surfaces, in direct and indirect contact and in relative otion. It includes the study and application of the principles of friction, wear and lubrication, as well as phenoena connected with these processes. Given that a process involving friction is always accopanied by transforation of energy, ore precisely an energy dissipation process which generates entropy, the concept of therodynaic entropy production analysis represents one of appropriate tools for studying and analysing the behaviour of coplex friction and wear processes. This paper presents a review of published works in which the therodynaic approach was used in analysing the friction and wear processes in tribosystes Published by Faculty of Engineering 1. INTRODUCTION Analysis of the literature ay bring us to conclude that ost of the published papers that investigate the processes of friction and wear are using a heuristic approach, which thus becae not the exception, but the rule for studying these processes [1]. At the sae tie, although they represent different anifestations of the sae physical processes, due to historical separation of their research, odels developed for desibing the friction and wear have ostly reained without clear correlation and defined utual dependence of their anifestations [2,3]. Consequently, it can be said that, regardless of the large nuber of proposed odels that desibe these processes in available literature, their applicability is still considerably restricted and does not have the desired level of generality. On the other hand, although there is no doubt that friction and wear essentially represent typical energy processes, therodynaic analyses of these processes are very rarely present in the literature on tribology. During these processes occurs the conversion of echanical work or kinetic energy into other types of work, energy and heat, like the work of friction, the work for plastic deforation, the work for wear, i.e. conversion of works into internal (theral), cheical, potential and other fors of energy. The aount of heat resulting fro dissipation of the work of friction force is around 80 to 90% of that work [21]. Therefore, it can be said that the analysis of these processes can not be considered coplete, unless 341

2 perfored also fro the aspect of the law of conservation of energy, i.e. fro the aspect of the First law of therodynai. Besides their energy related character, these processes occur with a proinent dissipation of energy, as well as in the teperature and cheical non equilibriu, often with the occurrence of cheical reactions. That is why these processes ust unavoidably be also classified in the group of irreversible therodynaic processes. Hence, it is clear that in order to obtain a coplete picture of these processes, their analysis should be ade through the Second law of therodynai, i.e. through the balance of entropy (property of state that desibes the degree of irreversibility of all physical processes). Due to all above entioned, this paper presents an attept to desibe the friction and wear processes through a typical therodynaic approach. Because of their nature and the need to include in the desiption processes of exchange of aterial between the contact surfaces, that is the loss of aterial in the for of wear products, a tribological syste that includes the two contacting bodies with their contact surfaces, was treated as an open therodynaic syste. That is why it is desibed through three basic laws defined for open therodynaic systes: the law of conservation of ass (continuity equation) and the First and Second law of therodynai. Unlike the approach used so far [4 8], defining these balances based on the Prigogine theory of irreversible processes and the Gibbs Entropy Forula [9,10], which cobines the First and Second law of therodynai, this paper uses the fors of these three laws which are used in the conventional technical therodynai. This was done priarily because of identified shortcoings of the Prigogine theory of irreversible processes in defining balances. Naely, the balances defined in this way either do not recognize energy and entropy effects of the exchange of aterial between contact surfaces or include the in a too coplicated way. 2. MODEL 2.1 The physical odel Wear has been defined as the progressive loss of substance fro the operating surface of a body occurring as a result of relative otion at the surface, while friction has been defined as the resisting force tangential to the coon boundary between two bodies when, under the action of an external force, one body oves or tends to ove relative to the surface of the other [22]. This definition of friction refers ostly to the external friction and do not specifically include the internal friction (viscosity). External friction, and wear occurring in this case, will be the subject of this analysis. Thus, a considered physical odel is ade up of two solid bodies in direct or indirect contact which are in relative otion against each other. Each body, viewed fro a therodynaic point of view, is a therodynaically open syste (subsyste), where the boundaries of each of the subsystes include the outer contours of the corresponding body and pass through their contact surface. Exchange of aterial between these bodies through this contact surface is exactly the reason that these systes have to be treated as open (Fig. 1). Zone of tribological effects I Fn Sliding direction Control boundary of body I Ff = μ Fn Control boundary of body II Fig. 1. Physical odel of the tribological syste and the areas of echanical action (F f friction force; F n noral force; μ coefficient of friction). 2.2 The therodynaical odel Therodynai is based on two fundaental laws; the first law iplies conservation of energy and the second iplies that, for any process to take place, the change in entropy has to be zero or positive. Entropy therefore can only be eated, never destroyed. The first law is independent of the type of the process [21]. With the previously defined conditions, the ass balance of the subsyste which akes the body I (Fig. 2a), i.e. overall change in ass of the first body can be defined by the equation: d in =d( I ) cv +d out, (1) 342

3 where: d( I ) cv is change of ass of the body I (body into control volue) in a differentially sall oent of tie dt, d in is the ass of aterial of the body II, which is to be transferred to the body I in a differentially sall oent of tie dt, d out is the ass of aterial of the body I which is separated by wear fro the body I in a differentially sall oent of tie, and cv is the control volue. specific internal energy of supplied and specific internal energy of reoved aterial. d in d( I) cv d out (a) The second ain balance equation for the control volue of the body I represents the balance of energy or the First law of therodynai. For the so defined control volue (Fig. 2b) this balance in differential for, i.e. for a differentially sall oent of tie dt, is as follows: d(u) cv Σ μ dn + Σ de u in d in δq Σ δw (b) u out d out δ Q+ δ W + u d =d( U) j=1 j in in cv μ dn μ d n + d E + uoutd p n r k k l l i k=1 l =1 i=1 reactants products out, (2) where: δq is the eleentary quantity of heat transferred to the body I in a differentially sall oent of tie, δw j is the different type of eleentary work done on the body I (work for overcoing adhesion forces, work for eating plastic deforation, etc.), d(u) cv is the differential change of internal (theral) energy of the body I (body into control volue), u in is the specific internal (theral) energy of the ass d in, u out is the specific internal (theral) energy of the ass d out, μ k dn k and μ l dn l are the eleentary cheical work or eleentary energy of cheical reaction of the k th and l th coponent, μ k and μ l are the cheical potentials of cheical reaction of the k th and l th coponent, dn k and dn l are the oles of substance k and l with the cheical potential μ k and μ l transported fro the syste to its surroundings, de i is the change of other fors of its internal energy, e.g. electrocheical, photocheical, etc. Opposite to the aforeentioned approach based on Prigogine theory of irreversible processes and Gibbsons relation, two new ters u in d in and u out d out, appear in the equation (2), and represent the energy transferred into the control volue of body I with ass transfer d in and out of the control volue of body I by wear d out, respectively. The u in and u out denote ds gen s in d in qda T d(s) cv s out d out Fig. 2. Scheatic view of the balance of ass, energy and entropy of a tribological syste. Finally, the third ain balance equation for the control volue of the body I is the balance of entropy equation or the Second law of therodynai (Fig. 2c). This law in differential for, i.e. for a differentially sall oent of tie dt is: qda d S + + s d =d( S) + s d, (3) gen in in cv out out T where: ds gen is the entropy generation that occurs in the control volue of the body I caused by irreversible processes within the control volue (processes of dissipation of echanical work, cheical reactions, nonequilibriu processes of heat and ass transfer, etc.); qda T is an ineent of entropy originating (c) fro the transfer of heat to the body I (where q is the specific heat flow, da is the eleentary surface of the control surface and T is the teperature of that eleentary surface), d(s) cv is the differential change of entropy of the body I and s in and s out are the specific entropy of ass d in and d out, respectively. 343

4 3. CAUSES OF ENTROPY GENERATION Unfortunately, balances written in this way are too general and have no practical use regardless of their universality. Just because of that, all attepts in defining the odels of tribological systes with laws of therodynai, defined in this and siilar way, had a very liited success [5,6,11 14]. In addition, all attepts of theoretical elaboration of particular ters ade so far, because of the extree coplexity of the derived equations and the accopanying inability of their solution, did not lead to the desired result. For this reason, in order to ake balance equations ore applicable for practical use, the existing phenoenological (epirical) relationships that define specific processes which occur during wear and friction were used for defining the particular ters which exist in the. These processes are connected by the sae causes of irreversibility. Since Klaecki [5] and then also Bryant [8] proposed their classification, soe of the atheatical relations already proposed by these authors will be used. As identified causes of irreversibility the authors specify: the dissipation of work for overcoing the adhesion forces, the dissipation of work for abrasion (plastic deforation) process, the dissipation of work for fracture (eating acks and fissures), the processes of change in state of aterial, cheical reactions, heat conduction and diffusion processes. Each of these causes of entropy inease will be explained in detail. 3.1 Dissipation of echanical work used for overcoing the adhesion forces Dissipation of echanical work used for overcoing the forces of adhesion is the work that is being spent for overcoing the electroagnetic interolecular forces of attraction of solids at sall distances. These sall distances occur between the contact surfaces of the tribological syste eleents in the process of friction and wear. During these processes work dissipates and turns into other fors of energy, first heat and then into the internal (theral) energy. Since this work is defined as the product of the interface surface energy γ (the surface tension of fluids in the case of fluids) and the newly eated surface area da s, its energy value can be defined as: δ W = γda. (4) ad Using the general expression that correlates the transferred aount of heat δq, the change of entropy substance ds and its teperature T δ d S = Q T, (5) under the assuption of coplete dissipation of echanical work into heat when astering the adhesion forces, entropy change caused by this irreversible process can be written as: S δwad γ d Sgen, ad = = das, (6) where T is the local teperature of the body I. It is iportant to note that under the influence of these types of electroagnetic interolecular forces the adhesive wear of aterials occurs. This type of wear is anifested by the transfer of aterial between the two contact surfaces, as well as by eation of wear products. The parts of energy and the parts of entropy, exchanged in that way between the control volues are covered by the appropriate ters in equations (2) and (3) i.e. u in d in and u out d out and s in d in and s out d out, respectively. Therefore, the ters s in d in and s out d out do not belong to the part of generated entropy, but to the part of entropy exchanged along with the exchange of substances. 3.2 Dissipation of echanical work used for abrasion (plastic deforation) process The process of abrasion, which is happening during the utual oveent of contact surfaces, as a result of penetration of asperities of harder aterial into the surface layers of softer aterial is accopanied by ploughing and/or cutting (plastic deforation) of both contact surfaces. Thus, the work used for abrasion of the surface could be defined as the product of the work for abrasion reduced to unit volue (work per volue) w pl and eleentary change of the body volue dv: δ W = w dv. (7) ab Extensive studies on the relationship between abrasion, i.e. plastic deforation of the surface, ab 344

5 and dissipation of energy were conducted by Fouvry at all. [15 17]. They found that there is a linear function between the volue of the worn aterial and dissipation of the energy used during this process. They have presented this linear relationship by defining the appropriate coefficients for a large nuber of tested aterials. One of the analysed cases, with a well defined linear dependence, is shown in Fig. 3. where U is internal energy of ack growth. Based on the foregoing and in accordance with the equation (5), the generation of entropy caused by this irreversible process can be deterined as: δ W ( G 2 γ) d Sgen, = = da, (11) where T is the local teperature of the acked aterial at the ack tip. 3.4 Dissipation of energy used for phase transition process Fig. 3. Linear relationship between the dissipated energy during the process of fretting wear and worn aterial volue [4]. Generation of entropy caused by irreversible process of abrasion in accordance with equation (5) can be deterined as: δwgen, ab wab d Sgen, ab = = dv, (8) where T is the local teperature of the body. 3.3 Dissipation of echanical work used for eating acks and fissures Work that is used for eating of acks or fissures on the surface, as well as for the processes associated with the surface fatigue wear, i.e. pitting and to soe extent erosive wear, is defined by the epirical expression: δ W =( G 2 γ)da, (9) where G is the energy release rate during the process of eating acks, reduced to a unit ack area, γ is the surface energy, and A is the area of acks surface. So, the energy release rate is defined as: U G =, (10) A The energy required for a phase transition, i.e. that is consued during the process of elting and subsequent reystallization of the etal surface can be deterined as the product of the specific energy or latent heat absorbed or lost during the phase change fro a liquid to a solid state r sol and ass of olten etal liq : d Ephase = rsold liq. (12) According to equation (5) and in the case of coplete dissipation of that energy, generation of entropy caused by this irreversible process can be deterined as [8]: desol rsol d Sgen, phase = = d phase phase liq, (13) where T phase is the local teperature of the aterial in the place of phase change. 3.5 Change of entropy caused by the cheical reactions Due to its special significance, the energy of cheical reactions, associated with corrosive and oxidative wear, was singled out fro other energy influences in the equation of energy balance (2) and presented by the following expression: he p n k k l l k =1 l =1 reactants products d E = μ dn μ dn. (14) Appropriate change in entropy caused by different cheical reactions, in accordance with the expression (5) can be defined as: d S = ch p n μkdnk μldnl k=1 l=1 Tch, k Tch, l, (15) 345

6 where T ch,k and T ch,l are the local teperature at the place of cheical reaction for reactants and for products. 3.6 Change of entropy caused by the heat conduction process The process of conduction of the heat throughout the body, released during friction δq occurs in the teperature ibalance between the teperature at the boundary surface T s and the teperature inside the body T b. Because of that teperature ibalance, this process inevitably causes an inease of entropy, which can be defined as [9]: 1 1 d Sgen, Q = δq. (16) Ts Tb In considering the aount of released heat δq, it should be noticed that it is only a part of the total dissipation of echanical energy. As entioned, a part of that energy is spent on the overcoing the adhesion, abrasive wear, foration of acks and fissures, etc. The deterination of allocation of echanical energy and the share of its conversion into heat have studied by Chen and Li [18,19] and Elale et al. [20]. Figure 4 shows the distribution of generated heat during sliding, for different loads, as a function of distance fro the contact surface. structure of the body I or into the body II should be also taken into account. 4. CONCLUSION Although the therodynaic approach offers the possibility of a systeatic analysis of behaviour of tribological systes, it is not yet sufficiently developed to have the practical use. For that approach to reach practical use, it should be iproved and copleted by the corresponding constitutive equations, which will connect the ain physical processes with their energetic and entropic effects. Their eation will certainly require additional, dedicated experiental studies of individual processes. However, despite its shortcoings, this approach based on using ain laws of physi: ass balance, energy balance and entropy balance, to reach a universal tribological odel, still reains very proising, due to its ethodical feature. Acknowledgeent The authors are grateful to the Ministry of Education, Science and Technological Developent of the Republic of Serbia, which has financially supported this paper through the projects TR 33018, TR 33047, TR and TR Fig. 4. Share of heat in the total dissipated energy depending on the distance fro contact surface [4]. 3.7 Generation of entropy due to diffusion processes Although the assued physical odel does not anticipate a third body (lubricating fluid), in the case that it exists, generation of entropy caused by the process of diffusion of that fluid into REFERENCES [1] K.C. Ludea: The state of odelling in friction and wear and a proposal for iproving that state, Journal of Korean Society of Tribologist and Lubrication Engineers, Vol. 11, No. 5, pp , [2] I.V. Kragelskii: Friction and Wear, Butterworth and Co., Bath, [3] E. Rabinowicz: Friction and Wear of Materials, John Wiley and Sons, New York, [4] H.A. Abdel Aal: Therodynaic odeling of wear, in: Q.J. Wang, Y. W. Chung (Eds.): Encyclopedia of Tribology, Springer, New York, 2013, pp [5] M. Airi, M.M. Khonsari: On the therodynai of friction and wear A review, Entropy, Vol. 12, No. 5, pp , [6] B.E. Klaecki: Wear An entropy production odel, Wear, Vol. 58, No. 2, pp ,

7 [7] B.E. Klaecki: A therodynaic odel of friction, Wear, Vol. 63, No. 1, pp , [8] M.D. Bryant, M.M. Khonsari, F.F. Ling: On the therodynai of degradation, Proceedings of the Royal Society A, Vol. 464, No. 2096, pp , [9] M.D. Bryant: Entropy and dissipative processes of friction and wear, FME Transactions, Vol. 37, No. 2, pp , [10] I. Prigogine: Etude Therodynaique des Processus Irreversibles, Desoer, Liege, [11] D. Kondepudi, I. Prigogine: Modern Therodynai fro Heat Engines to Dissipative Structures, John Wiley & Sons, Inc., New York, [12] OECD Research Group on Wear of Engineering Materials: Glossary of Ters and Definitions in the Field of Friction, Wear and Lubrication: Tribology, Organisation for Econoic Cooperation and Developent, Paris, [13] B.E. Klaecki: An entropy based odel of plastic deforation energy dissipation in sliding, Wear, Vol. 96, No. 3, pp , [14] A. Zitrowicz: A therodynaical odel of contact, friction and wear: I governing equations, Wear, Vol. 114, No. 2, pp , [15] A. Zitrowicz: A therodynaical odel of contact, friction and wear: II constitutive equations for aterials and linearized theories, Wear, Vol. 114, No. 2, pp , [16] A. Zitrowicz: A therodynaical odel of contact, friction and wear: III Constitutive equations for friction, wear and frictional heat, Wear, Vol. 114, No. 2, pp , [17] S. Fouvry, P. Kapsa, H. Zahouani, L. Vincent: Wear analysis in fretting of hard coatings through a dissipated energy concept, Wear, Vol , pp , [18] S. Fouvry, T. Liskiewicz, Ph. Kapsa, S. Hannel, E. Sauger: An energy desiption of wear echaniss and its applications to oscillating sliding contacts, Wear, Vol. 255, No. 1 6, pp , [19] S. Fouvry, C. Paulin, T. Liskiewicz: Application of an energy wear approach to quantify fretting contact durability: Introduction of a wear energy capacity concept, Tribology International, Vol. 40, No , pp , [20] Q. Chen, D.Y. Li: A coputational study of frictional heating and energy conversion during sliding processes, Wear, Vol. 259,No. 7 12, pp , [21] Q. Chen, D.Y. Li: Coputer siulation of solidparticle erosion of coposite aterials, Wear, Vol. 255, No. 1 6, pp , [22] K. Elale, D.Y. Li, M.J. Anderson, S. Chiovelli: Modeling abrasive wear of hoogeneous and heterogeneous aterials, in: G.E. Totten, D.K. Wills, D.G. Feldann (Eds.): Hydraulic Failure Analysis: Fluids, Coponents, and Syste Effects, ASTM, West Conshohocken, 2001, pp