Tribologie + Schmierungstechnik 63. Jahrgang 3/ 2016 5 Aus Wissenschaft und Forschung 1 Introduction The main principle of the lubricant is the separation of surfaces from direct contact and replacement of outer (great) friction of solids to the inner (small) friction in a layer of liquid lubricant. The friction of solids without lubrication ends in the formation of a new surface layer (the third body) which can also be viewed as separation layer. Is it possible to consider this self-organized layer as a solid lubricant? What are the limits (minimum) properties of this self-organized solid lubricant? 2 Triboergodynamics method This paper in its basis is a logical completion of axiomatic analysis of sliding friction (rolling) within the framework of triboergodynamics, a scientific trend suggested by the author [1-3]. The general evolution regularities of states and properties of tribosystem in the frame of triboergodynamics are analysed. Triboergodynamics is based on our modern knowledge of friction: 1. friction is a phenomenon of resistance to relative motion between two bodies, originating at their surfaces contact area; 2. friction is the process of transformation and dissipation of energy of external movement into other kinds of energy; 3. friction is the process of elasto-plastic deformation localized in thin surface layers of rubbing materials. Methodology of triboergodynamics [1-3] is based on the analysis method to plastic deformation of ergodynamics of deformed solids [4-6]. Ergodynamics is a synthesis to the problem of deformation most general laws of thermodynamics for non-reversible processes, molecular kinetics and dislocation theory in their mutual, dialectical tie on the basis of a most general law of nature - the law of energy conservation at its transformations. Within the framework of triboergodynamics the model of elastic-plastic deformation of contact volumes is examined as a generalized mechanism of transformation and dissipation energy and determines essence of resistance to surfaces displacement. Friction is regarded as a global (energetical) phenomenon of relative movement transformation. It strongly obeys equation of energy balance and from thermodynamic point of view it is a competition of two simultaneous, interconnected and opposite tendencies of accumulating * Prof. Dr. of Technical Science Sergey Vasiliy Fedorov Kaliningrad State Technical University 236022 Kaliningrad, Russia Selforganized nano-quantum solid lubricant S. V. Fedorov* Eingereicht: 22. 2. 2015 Nach Begutachtung angenommen: 15. 4. 2015 Es wurden die Gesetzmäßigkeiten der vollständigen Evolution des Tribosystems (Reibungskontakts) betrachtet. Es wurde gezeigt, dass die ideale Evolution des Tribosystems im Zustand der idealen Elastizität des verformten Kontakts endet. Dieser Zustand des Kontakts wird durch Bildung der dissipativen Nanoquantumstruktur gewährleistet. Das Kernstück dieser Struktur bildet ein mechanisches (Nano) Quantum. So eine vollkommene (ideale) Nano-Quantumstruktur sollte man als einen selbstorganisierten harten Schmierstoff betrachten Schlüsselwörter Evolution des Tribosystems, Energiebilanz, Selbstorganisation, Nano-Struktur, mechanisches Quantum, harter Schmierstoff The regularities of most full evolution for the tribosystem (friction contact) have been examined. It shows that the ideal evolution of tribosystem is completed with the state of ideal elasticity of deformable contact. This state of contact is provided by the formation of nano-quantum, dissipative structure. The basis of this structure represents the mechanical (nano) quantum. The perfect nano-quantum structure of contact friction should be regarded as selforganized solid lubricant. Keywords Tribosystem’s evolution, Energy balance, Selforganisation, Nanostructure, Mechanical quantum, Solid lubricant Kurzfassung Abstract T+S_3_16 05.04.16 09: 01 Seite 5 6 Tribologie + Schmierungstechnik 63. Jahrgang 3/ 2016 latent (potential) energy ∆U e of various kinds of defects and damages of contact volumes structures and releasing (dissipation) energy Q due to various relaxation processes. According to the energy balance scheme (Figure 1) for plastic deformation and fracture [4] presented below, equations for friction work W f , frictional force F and friction coefficient µ (without lubrication) are: (1) (2) (3) (4) (5) (6) where ∆U e = V f ∆u e ; Q = V f q; U· e = V f u· e ; u· e = du e / dt: V f - is the deformable (friction) volume; µ - friction coefficient; µ adapt - adaptive friction coefficient; µ T(dis) and µ Q → (dis) - static and dynamical components of dissipative friction coefficient; ∆U T - thermal component of internal energy; N - normal load; l - distance of friction. The latent energy density ∆u e is an integral parameter of tribostate and damageability (failure (∆u * e )). Thus, viewed thermodynamically, the work done by friction forces W f (the friction power W· ), the friction force F and the friction coefficient µ may be classified conventionally into two specific components with different kinetic behavior [4-6]. The first component is associated with microscopic mechanisms of adaptive type and relates to the change of latent (potential) energy (∆u e1 ,∆u e2 ) of various elementary defects and damages that are generated and accumulate in the deformable volumes of materials friction pair (Figure 2). This energy is a unique and integral characteristic of the submicroand microstructural transformations that occur in plastically strained materials [4-6]. This energy is a measure of strain hardening and damageability of materials. The second component is associated with microscopic mechanisms of dissipative type and relates to dynamic recovery processes in which latent energy is released and heat effect of friction (q 1 , q 2 ) take place. This energy originates in the motion and destruction of various elementary defects of opposite signs, the egress of these defects to the surface, the healing of reversible submicroscopic discontinuities, etc. The ratios of the components ∆u e1 and ∆u e2 as well as q 1 , q 2 of the balance vary over a wide range, depending on the physical, chemical, and structural properties of the materials that comprise the friction couple and the friction process conditions. Thus, the thermodynamic analysis of friction (plastic deformation and fracture) has led to generalized (twoterm) relations (1)-(6) for the force F and coefficient of friction µ, which agrees with current concepts of the nature of friction. Relationships (1)-(6) which generalize the mechanism of energy dissipation at friction allow to classify the tri- Aus Wissenschaft und Forschung = + D = Q U W e f , 2 1 2 1 2 1 Q Q U U U U T T e e r r + + D + D + D + D = 2 1 2 1 2 1 Q Q U U U U Q U W T T e e e f & r & r & & & & & & & + + + + + = + = , l Q Q l U U l Q l U F e e e l 2 1 2 1 + + D + D = + D = , = + + + = v Q Q v U U F e e v 2 1 2 1 & & & & = + = v v F v , molecular mechanical F F + = = + + D + D = Nl Q Q Nl U U e e l 2 1 2 1 m ( ) ( ) dis Q dis T adapt dis adapt r m m m m m + + = + = , = + + + = Nv Q Q Nv U U e e v 2 1 2 1 & & & & m adhesion n deformatio m m + = , (6) where ; ; ; ; is the deformable (friction) volume; friction coefficient; adaptive friction coefficient; and static and dynamical components of dissipative friction coefficient; thermal component of internal energy; normal load; distance of friction. The latent energy density is an integral parameter of tribostate and damageability (failure ( )). Figure 1. Scheme of the energy balance for the plastic deformation of a solid body [1-4] Thus, viewed thermodynamically, the work done by friction forces (the friction power ), the friction force and the friction coefficient may be classified conventionally into two specific components with different kinetic behavior [1-3]. The first component is associated with microscopic mechanisms of adaptive type and relates to the change of latent (potential) energy ( ) of various elementary defects and damages that are generated and accumulate in the deformable volumes of materials friction pair (Figure 2). This energy is a unique and integral characteristic of the submicroand microstructural transformations that occur in plastically strained materials [4-6]. This energy is a measure of strain hardening and damageability of materials. The second component is associated with microscopic mechanisms of dissipative type and relates to dynamic recovery processes in which latent energy is released and heat effect of friction ( ) take place. This energy originates in the motion and destruction of various elementary defects of opposite signs, the egress of these defects to the surface, the healing of reversible submicroscopic discontinuities, etc. The ratios of the components and as well as of the balance vary over a wide range, depending on the physical, chemical, and structural properties of the materials that comprise the friction couple and the friction process conditions. Figure 2. Schematic view of elementary friction’s contact [1-3] Thus, the thermodynamic analysis of friction (plastic deformation and fracture) has led to generalized (twoterm) relations (1)-(6) for the force and coefficient of friction , which agrees with current concepts of the nature of friction. Relationships (1)-(6) which generalize the mechanism of energy dissipation at friction allow to classify the tribosystem states. According to ergodynamics of deformed solids (relationships and ) and equations (1)-(6), all exhibitions of friction and wear may be reduced conventionally at least to two basically different states: the first state defines all types of damage and wear, the second — the so-called "wearless" condition. The state of damage and wear is characterized by the components of energy balance (1)-(6), which are responsible for accumulation of internal energy in deformed volumes , i.e. the process is irreversible. The "wearless" state is characterized by the components responsible for dynamic dissipation (reversibility) of strain energy into elastic and structural dissipated energy of friction contact . In its turn, the first state may be classified depending on the relation between potential and kinetic components of internal energy. It is subdivided conventionally into mechanical damage and wear (due to so-called structure activation) and thermal damage and wear (due to thermal activation). For instance, let the thermal component of internal energy be equal to Work of defor Change of heat exchange in the initial state , (5) , (6) where ; ; ; ; is the deformable (friction) volume; friction coefficient; adaptive friction coefficient; and static and dynamical components of dissipative friction coefficient; thermal component of internal energy; normal load; distance of friction. The latent energy density is an integral parameter of tribostate and damageability (failure ( )). Figure 1. Scheme of the energy balance for the plastic deformation of a solid body [1-4] Thus, viewed thermodynamically, the work done by friction forces (the friction power ), the friction force and the friction coefficient may be classified conventionally into two specific components with different kinetic behavior [1-3]. The first component is associated with microscopic mechanisms of adaptive type and relates to the change of latent (potential) energy ( ) of various elementary defects and damages that are generated and accumulate in the deformable volumes of materials friction pair (Figure 2). This energy is a unique and integral characteristic of the submicroand microstructural transformations that occur in plastically strained materials [4-6]. This energy is a measure of strain hardening and damageability of materials. The second component is associated with microscopic mechanisms of dissipative type and relates to dynamic recovery processes in which latent energy is released and heat effect of friction ( ) take place. This energy originates in the motion and destruction of various elementary defects of opposite signs, the egress of these defects to the surface, the healing of reversible submicroscopic discontinuities, etc. The ratios of the components and as well as of the balance vary over a wide range, depending on the physical, chemical, and structural properties of the materials that comprise the friction couple and the friction process conditions. Figure 2. Schematic view of elementary friction’s contact [1-3] Thus, the thermodynamic analysis of friction (plastic deformation and fracture) has led to generalized (twoterm) relations (1)-(6) for the force and coefficient of friction , which agrees with current concepts of the nature of friction. Relationships (1)-(6) which generalize the mechanism of energy dissipation at friction allow to classify the tribosystem states. According to ergodynamics of deformed solids (relationships and ) and equations (1)-(6), all exhibitions of friction and wear may be reduced conventionally at least to two basically different states: the first state defines all types of damage and wear, the second — the so-called "wearless" condition. The state of damage and wear is characterized by the components of energy balance (1)-(6), which are responsible for accumulation of internal energy in deformed volumes , i.e. the process is irreversible. The "wearless" state is characterized by the components responsible for dynamic dissipation (reversibility) of strain energy into elastic and structural dissipated energy of friction contact . In its turn, the first state may be classified depending on the relation between potential and kinetic components of internal energy. It is subdivided conventionally into mechanical damage and wear (due to so-called structure activation) and thermal damage and wear (due to thermal activation). For instance, let the thermal component of internal energy be equal to Work of deformation q u e + D = w p Change in latent energy e u D Thermal effect of deformation q Change in thermal energy T u D Change In internal energy T u D + D = D e u u Energy of heat exchange q r Internal energy in the initial state ( ) 0 u Internal energy ( ) u 0 u u D + = Figure 1: Scheme of the energy balance for the plastic deformation of a solid body [1-4] , (5) , (6) where ; ; ; ; is the deformable (friction) volume; friction coefficient; adaptive friction coefficient; and static and dynamical components of dissipative friction coefficient; thermal component of internal energy; normal load; distance of friction. The latent energy density is an integral parameter of tribostate and damageability (failure ( )). Figure 1. Scheme of the energy balance for the plastic deformation of a solid body [1-4] Thus, viewed thermodynamically, the work done by friction forces (the friction power ), the friction force and the friction coefficient may be classified conventionally into two specific components with different kinetic behavior [1-3]. The first component is associated with microscopic mechanisms of adaptive type and relates to the change of latent (potential) energy ( ) of various elementary defects and damages that are generated and accumulate in the deformable volumes of materials friction pair (Figure 2). This energy is a unique and integral characteristic of the submicroand microstructural transformations that occur in plastically strained materials [4-6]. This energy is a measure of strain hardening and damageability of materials. The second component is associated with microscopic mechanisms of dissipative type and relates to dynamic recovery processes in which latent energy is released and heat effect of friction ( ) take place. This energy originates in the motion and destruction of various elementary defects of opposite signs, the egress of these defects to the surface, the healing of reversible submicroscopic discontinuities, etc. The ratios of the components and as well as of the balance vary over a wide range, depending on the physical, chemical, and structural properties of the materials that comprise the friction couple and the friction process conditions. Figure 2. Schematic view of elementary friction’s contact [1-3] Thus, the thermodynamic analysis of friction (plastic deformation and fracture) has led to generalized (twoterm) relations (1)-(6) for the force and coefficient of friction , which agrees with current concepts of the nature of friction. Relationships (1)-(6) which generalize the mechanism of energy dissipation at friction allow to classify the tribosystem states. According to ergodynamics of deformed solids (relationships and ) and equations (1)-(6), all exhibitions of friction and wear may be reduced conventionally at least to two basically different states: the first state defines all types of damage and wear, the second — the so-called "wearless" condition. The state of damage and wear is characterized by the components of energy balance (1)-(6), which are responsible for accumulation of internal energy in deformed volumes , i.e. the process is irreversible. The "wearless" state is characterized by the components responsible for dynamic dissipation (reversibility) of strain energy into elastic and structural dissipated energy of friction contact . In its turn, the first state may be classified depending on the relation between potential and kinetic components of internal energy. It is subdivided conventionally into mechanical damage and wear (due to so-called structure activation) and thermal damage and wear (due to thermal activation). For instance, let the thermal component of internal energy be equal to Work of defor Change of heat exchange in the initial state Figure 2: Schematic view of elementary friction’s contact [1-3] T+S_3_16 05.04.16 09: 01 Seite 6 Tribologie + Schmierungstechnik 63. Jahrgang 3/ 2016 bosystem states. According to ergodynamics of deformed solids (relationships ∆u = ∆u e + ∆u T and q = ∆u T + q → ) and equations (1)-(6), all exhibitions of friction and wear may be reduced conventionally at least to two basically different states: the first state defines all types of damage and wear, the second - the so-called „wear fee“ condition. The state of damage and wear is characterized by the components of energy balance (1)-(6), which are responsible for accumulation of internal energy in deformed volumes ∆u = ∆u e1 + ∆u e2 + ∆u T1 + ∆u T2 , i. e. the process is irreversible. The „wear free“ state is characterized by the components responsible for dynamic dissipation (reversibility) of strain energy into elastic and structural dissipated energy of friction contact q → = q →1 + q →2 . In its turn, the first state may be classified depending on the relation between potential ∆u e and kinetic ∆u T components of internal energy. It is subdivided conventionally into mechanical damage and wear (due to so-called structure activation) and thermal damage and wear (due to thermal activation). For instance, let the thermal component of internal energy ∆u T be equal to zero (∆u T = 0) and the internal energy variation at damage and wear be defined only by variation of the potential ∆u e (∆u = ∆u e ) component. Then, the mechanical damage and wear with brittle fracture of surfaces take place. On the contrary, if we have ∆u e = 0 (∆u = ∆u T ), then the thermal damage and wear with ductile fracture of surfaces take place. All the intermediate values of the components are associated with quasi-brittle or quasi-ductile fracture of solids. In the most general case, the energy balance at dry friction (1) should be written as (7) In the special case, where the friction is localized into volume of the „third body“ equation (7) develops into (8) According to thermodynamic theory of strength [4], the damageability parameter and the fracture criterion are defined in terms of the internal energy density u accumulated within the strained element of a solid body. A solid body is assumed to suffer fracture if the internal energy density has reached a critical value u * in at least a single macro-volume that is responsible for fracture. 3 Energy interpretation of Leonardo da Vinci (Amonton’s) friction coefficient According to thermodynamic theory of strength [4], the structure parameter should be related to the portion of the accumulated plastic deformation that is responsible for strain hardening. This portion is uniquely and integrally defined by the density of the potential component of internal energy (that is, the latent energy density ∆u e ) of various defects and damages that accumulate in a plastically strained material. With this in mind, if we neglect the heat effect Q of friction, one will infer from the thermodynamic analysis of friction equations (1)-(6) that the Amonton (Leonardo da Vinci) friction coefficient is (9) Consequently, the coefficient of friction has a very deep physical sense. On the one hand, it is the parameter which generally characterizes the resistance of relative displacement (movement) of surfaces, for it reflects the portion of energy, which «is done by friction away» as accumulated latent energy ∆U e , by relation to parameter of external forces work µ * Nl (energy of external relative movement). On the other hand, it is the generalized characteristic of damage, for it is defined of the latent energy density ∆u e as integral characteristic of the structure defectiveness measure, because this energy is the generalized parameter of damage. Here too, coefficient of friction generally reflects the structural order (disorder) of deforming contact volume, since the parameter ∆U e = ∆u e V f is defined as the energy of defects and damages of different types, that are accumulated into contact volumes V f solids. Therefore, the coefficient of friction is a true and generalized parameter of tribosystem state. From this conclusion we can say that the analysis of the evolution of the states of a tribosystem is primarily an analysis of the latent deformation energy accumulated within the contact friction volumes. 4 Energy regularities of rubbing surfaces evolution An analysis of modern experimental data using equations (1)-(9) has shown that the experimental friction curves of type µ = µ(N,v) are the generalized friction curves that reflect the evolution (the change in the friction coefficient) of tribosystem. We propose an energetic interpretation of the experimental friction curves µ = µ(N,v) (Figure 3). According to our concept [1-3], the ascending portion of the friction coefficient curve µ is mainly controlled by processes associated with the accumulation of latent energy ∆U e in various structural defects and damages. Here the increase in µ is due to the increasing density of latent (potential) energy ∆u e and the increasing adaptive friction volume V f . The descending portion of the friction curve is mainly controlled by processes associated with the release and dissipation of energy Q = ∆U T + Q → . Here the decrease in µ is due to the decrease in latent energy density within the friction volume V f or (which is virtu- 7 Aus Wissenschaft und Forschung zero ( ) and the internal energy variation at damage and wear be defined only by variation of the potential component. Then, the mechanical damage and wear with brittle fracture of surfaces take place. On the contrary, if we have ( ), then the thermal damage and wear with ductile fracture of surfaces take place. All the intermediate values of the components are associated with quasi-brittle or quasi-ductile fracture of solids. In the most general case, the energy balance at dry friction (1) should be written as 3 2 1 3 2 1 Q Q Q U U U W e e e f + + + D + D + D = . (7) In the special case, where the friction is localized into volume of the "third body" equation (7) develops into . (8) According to thermodynamic theory of strength [4], the damageability parameter and the fracture criterion are defined in terms of the internal energy density accumulated within the strained element of a solid body. A solid body is assumed to suffer fracture if the internal energy density has reached a critical value in at least a single macrovolume that is responsible for fracture. 3. Energy interpretation of Leonardo da Vinci (Amonton’s) friction coefficient According to thermodynamic theory of strength [4], the structure parameter should be related to the portion of the accumulated plastic deformation that is responsible for strain hardening. This portion is uniquely and integrally defined by the density of the potential component of internal energy (that is, the latent energy density ) of various defects and damages that accumulate in a plastically strained material. With this in mind, if we neglect the heat effect of friction, one will infer from the thermodynamic analysis of friction of equations (1)-(6) that the Amonton (Leonardo da Vinci) friction coefficient is ; ; , . (9) Consequently, the coefficient of friction has a very deep physical sense. On the one hand, it is the parameter which generally characterizes the resistance of relative displacement (movement) of surfaces, for it reflects the portion of energy, which «is done by friction away» as accumulated latent energy , by relation to parameter of external forces work (energy of external relative movement). On the other hand, it is the generalized characteristic of damage, for it is defined of the latent energy density as integral characteristic of the structure defectiveness measure, because this energy is the generalized parameter of damage. Here too, coefficient of friction generally reflects the structural order (disorder) of deforming contact volume, since the parameter is defined of the energy of defects and damages of different types, that are accumulated into contact volumes solids. Therefore, coefficient of friction is a true and generalized parameter of tribosystem state. From this conclusion we can say that the analysis of the evolution of the states of a tribosystem is primarily an analysis of the latent deformation energy accumulated within the contact friction volumes. 4. Energy regularities of rubbing surfaces evolution An analysis of modern experimental data using equations (1)-(9) has shown that the experimental friction curves of type are the generalized friction curves that reflect the evolution (the change in the friction coefficient) of tribosystem. We propose an energetic interpretation of the experimental friction curves (Figure 3). Figure 3. Structural-energy diagram for evolution of rubbing surfaces [1-3]. ; ; ; - static, dynamic, elastic, plastic friction coefficients correspondingly; ; - ignition (flash) temperature in contact friction volume in point 3 and melting temperature. According to our concept [1-3], the ascending portion of the friction coefficient curve is mainly controlled by processes associated with the accumulation of latent energy in various structural defects and damages. Here the increase in is due to the increasing density of latent (potential) energy and the increasing adaptive friction volume . The descending portion of the friction curve is mainly controlled by processes associated with the zero ( ) and the internal energy variation at damage and wear be defined only by variation of the potential component. Then, the mechanical damage and wear with brittle fracture of surfaces take place. On the contrary, if we have ( ), then the thermal damage and wear with ductile fracture of surfaces take place. All the intermediate values of the components are associated with quasi-brittle or quasi-ductile fracture of solids. In the most general case, the energy balance at dry friction (1) should be written as . (7) In the special case, where the friction is localized into volume of the "third body" equation (7) develops into . (8) According to thermodynamic theory of strength [4], the damageability parameter and the fracture criterion are defined in terms of the internal energy density accumulated within the strained element of a solid body. A solid body is assumed to suffer fracture if the internal energy density has reached a critical value in at least a single macrovolume that is responsible for fracture. 3. Energy interpretation of Leonardo da Vinci (Amonton’s) friction coefficient According to thermodynamic theory of strength [4], the structure parameter should be related to the portion of the accumulated plastic deformation that is responsible for strain hardening. This portion is uniquely and integrally defined by the density of the potential component of internal energy (that is, the latent energy density ) of various defects and damages that accumulate in a plastically strained material. With this in mind, if we neglect the heat effect of friction, one will infer from the thermodynamic analysis of friction of equations (1)-(6) that the Amonton (Leonardo da Vinci) friction coefficient is N F Nl U e = D = * m m ; l U F e D = ; 0 @ Q , 1 = * m . (9) Consequently, the coefficient of friction has a very deep physical sense. On the one hand, it is the parameter which generally characterizes the resistance of relative displacement (movement) of surfaces, for it reflects the portion of energy, which «is done by friction away» as accumulated latent energy , by relation to parameter of external forces work (energy of external relative movement). On the other hand, it is the generalized characteristic of damage, for it is defined of the latent energy density as integral characteristic of the structure defectiveness measure, because this energy is the generalized parameter of damage. Here too, coefficient of friction generally reflects the structural order (disorder) of deforming contact volume, since the parameter is defined of the energy of defects and damages of different types, that are accumulated into contact volumes solids. Therefore, coefficient of friction is a true and generalized parameter of tribosystem state. From this conclusion we can say that the analysis of the evolution of the states of a tribosystem is primarily an analysis of the latent deformation energy accumulated within the contact friction volumes. 4. Energy regularities of rubbing surfaces evolution An analysis of modern experimental data using equations (1)-(9) has shown that the experimental friction curves of type are the generalized friction curves that reflect the evolution (the change in the friction coefficient) of tribosystem. We propose an energetic interpretation of the experimental friction curves (Figure 3). Figure 3. Structural-energy diagram for evolution of rubbing surfaces [1-3]. ; ; ; - static, dynamic, elastic, plastic friction coefficients correspondingly; ; - ignition (flash) temperature in contact friction volume in point 3 and melting temperature. According to our concept [1-3], the ascending portion of the friction coefficient curve is mainly controlled by processes associated with the accumulation of latent energy in various structural defects and damages. Here the increase in is due to the increasing density of latent (potential) energy and the increasing adaptive friction volume . The descending portion of the friction curve is mainly controlled by processes associated with the zero ( ) and the internal energy variation at damage and wear be defined only by variation of the potential component. Then, the mechanical damage and wear with brittle fracture of surfaces take place. On the contrary, if we have ( ), then the thermal damage and wear with ductile fracture of surfaces take place. All the intermediate values of the components are associated with quasi-brittle or quasi-ductile fracture of solids. In the most general case, the energy balance at dry friction (1) should be written as . (7) In the special case, where the friction is localized into volume of the "third body" equation (7) develops into 3 3 Q U W e f r + D = . (8) According to thermodynamic theory of strength [4], the damageability parameter and the fracture criterion are defined in terms of the internal energy density accumulated within the strained element of a solid body. A solid body is assumed to suffer fracture if the internal energy density has reached a critical value in at least a single macrovolume that is responsible for fracture. 3. Energy interpretation of Leonardo da Vinci (Amonton’s) friction coefficient According to thermodynamic theory of strength [4], the structure parameter should be related to the portion of the accumulated plastic deformation that is responsible for strain hardening. This portion is uniquely and integrally defined by the density of the potential component of internal energy (that is, the latent energy density ) of various defects and damages that accumulate in a plastically strained material. With this in mind, if we neglect the heat effect of friction, one will infer from the thermodynamic analysis of friction of equations (1)-(6) that the Amonton (Leonardo da Vinci) friction coefficient is ; ; , . (9) Consequently, the coefficient of friction has a very deep physical sense. On the one hand, it is the parameter which generally characterizes the resistance of relative displacement (movement) of surfaces, for it reflects the portion of energy, which «is done by friction away» as accumulated latent energy , by relation to parameter of external forces work (energy of external relative movement). On the other hand, it is the generalized characteristic of damage, for it is defined of the latent energy density as integral characteristic of the structure defectiveness measure, because this energy is the generalized parameter of damage. Here too, coefficient of friction generally reflects the structural order (disorder) of deforming contact volume, since the parameter is defined of the energy of defects and damages of different types, that are accumulated into contact volumes solids. Therefore, coefficient of friction is a true and generalized parameter of tribosystem state. From this conclusion we can say that the analysis of the evolution of the states of a tribosystem is primarily an analysis of the latent deformation energy accumulated within the contact friction volumes. 4. Energy regularities of rubbing surfaces evolution An analysis of modern experimental data using equations (1)-(9) has shown that the experimental friction curves of type are the generalized friction curves that reflect the evolution (the change in the friction coefficient) of tribosystem. We propose an energetic interpretation of the experimental friction curves (Figure 3). Figure 3. Structural-energy diagram for evolution of rubbing surfaces [1-3]. ; ; ; - static, dynamic, elastic, plastic friction coefficients correspondingly; ; - ignition (flash) temperature in contact friction volume in point 3 and melting temperature. According to our concept [1-3], the ascending portion of the friction coefficient curve is mainly controlled by processes associated with the accumulation of latent energy in various structural defects and damages. Here the increase in is due to the increasing density of latent (potential) energy and the increasing adaptive friction volume . The descending portion of the friction curve is mainly controlled by processes associated with the T+S_3_16 05.04.16 09: 01 Seite 7 8 Tribologie + Schmierungstechnik 63. Jahrgang 3/ 2016 ally the same) to the decrease of the adaptive friction volume V adapt (u e = u *e ) and to the increase of the dissipative volume V dis (q →* = u e* ). Tribosystem evolution presented as a diagram (Figure 3), has adaptive-dissipative character (1) and reflects competitive (dialectical) nature of friction. Evolution curve has a set of principal points (1-5) of transitive states of tribosystem, which strongly obey a balance principle of friction. The most characteristic areas between these points reflect general properties of its non-linear dynamics. So, in Figure 3 it is possible to see the following conventionally designated points and stages: 0-1 - a stage of static friction and deformational strengthening; 1 - a point of limit for deformational strengthening; 1-2 - a stage of pumping of excess energy; 2 - a point of gripping (adhesion) and transition of outer friction into internal (critical non-stability): 2-3 - a stage of forming dissipation structures (formation of heat fluctuation in friction volume); 3 - a point of minimum compatibility (maximum friction); 1-2-3 a stage of self-organization; 3-4 - a stage of compatibility; 4 - a point of wear free condition (abnormal-low friction); 5 - a point of thermal adhesion. An ideal evolution of a tribosystem is symmetrical. The process starts and finishes within areas of elastic behavior. A plastic maximum (a super-activated condition) exists between them as a condition of self-organization and adaptation. In the most general case evolution (adaptation) regularities of tribosystems may be presented as a 2-stage (Figure 3). At the first stage (0-2) of adaptation the evolution of friction contact rushes to form some critical volume of friction V * f (point 2). It is elementary tribosystem, i. e. it is the elementary and self-sufficient energy transformer. The first stage - latent energy density growth ∆u e to a limited magnitude ∆u e* within critical friction volume V * f . This friction volume V * f is constant at the second stage of evolution, but here it is evolutionary developed owing to structural transformation; by this one may realize wide spectrum of compatibility friction structures (Figure 3). The second stage (2-4) - structural transformation of critical friction volume (elementary tribosystem) V * f into adaptive V adapt and dissipative V dis volumes. The limit (point 4) of this stage is characterized by a full transformation of adaptive critical volume V * adapt into V * dis dissipative. The volumes mentioned above characterize different regularities of transforming energy of outer mechanical movement at friction. Adaptive volume V adapt is connected with non-reversible absorption of deformation energy. It is in this volume where latent deformation energy ∆u e accumulates and where the centers of destruction initially emerge (birth). Dissipative volume V dis is capable of reversible transformation (dissipate) of outer movement energy. It doesn’t accumulate latent de- Aus Wissenschaft und Forschung zero ( ) and the internal energy variation at damage and wear be defined only by variation of the potential component. Then, the mechanical damage and wear with brittle fracture of surfaces take place. On the contrary, if we have ( ), then the thermal damage and wear with ductile fracture of surfaces take place. All the intermediate values of the components are associated with quasi-brittle or quasi-ductile fracture of solids. In the most general case, the energy balance at dry friction (1) should be written as . (7) In the special case, where the friction is localized into volume of the "third body" equation (7) develops into . (8) According to thermodynamic theory of strength [4], the damageability parameter and the fracture criterion are defined in terms of the internal energy density accumulated within the strained element of a solid body. A solid body is assumed to suffer fracture if the internal energy density has reached a critical value in at least a single macrovolume that is responsible for fracture. 3. Energy interpretation of Leonardo da Vinci (Amonton’s) friction coefficient According to thermodynamic theory of strength [4], the structure parameter should be related to the portion of the accumulated plastic deformation that is responsible for strain hardening. This portion is uniquely and integrally defined by the density of the potential component of internal energy (that is, the latent energy density ) of various defects and damages that accumulate in a plastically strained material. With this in mind, if we neglect the heat effect of friction, one will infer from the thermodynamic analysis of friction of equations (1)-(6) that the Amonton (Leonardo da Vinci) friction coefficient is ; ; , . (9) Consequently, the coefficient of friction has a very deep physical sense. On the one hand, it is the parameter which generally characterizes the resistance of relative displacement (movement) of surfaces, for it reflects the portion of energy, which «is done by friction away» as accumulated latent energy , by relation to parameter of external forces work (energy of external relative movement). On the other hand, it is the generalized characteristic of damage, for it is defined of the latent energy density as integral characteristic of the structure defectiveness measure, because this energy is the generalized parameter of damage. Here too, coefficient of friction generally reflects the structural order (disorder) of deforming contact volume, since the parameter is defined of the energy of defects and damages of different types, that are accumulated into contact volumes solids. Therefore, coefficient of friction is a true and generalized parameter of tribosystem state. From this conclusion we can say that the analysis of the evolution of the states of a tribosystem is primarily an analysis of the latent deformation energy accumulated within the contact friction volumes. 4. Energy regularities of rubbing surfaces evolution An analysis of modern experimental data using equations (1)-(9) has shown that the experimental friction curves of type are the generalized friction curves that reflect the evolution (the change in the friction coefficient) of tribosystem. We propose an energetic interpretation of the experimental friction curves ) , ( v N m m = (Figure 3). Figure 3. Structural-energy diagram for evolution of rubbing surfaces [1-3]. ; ; ; - static, dynamic, elastic, plastic friction coefficients correspondingly; ; - ignition (flash) temperature in contact friction volume in point 3 and melting temperature. According to our concept [1-3], the ascending portion of the friction coefficient curve is mainly controlled by processes associated with the accumulation of latent energy in various structural defects and damages. Here the increase in is due to the increasing density of latent (potential) energy and the increasing adaptive friction volume . The descending portion of the friction curve is mainly controlled by processes associated with the Figure 3: Structural-energy diagram for evolution of rubbing surfaces [1-3]. µ st at ; µ dyn ; µ elast ; µ plast - static, dynamic, elastic, plastic friction coefficients correspondingly; T f ; T S - ignition (flash) temperature in contact friction volume in point 3 and melting temperature. T+S_3_16 05.04.16 09: 01 Seite 8 Tribologie + Schmierungstechnik 63. Jahrgang 3/ 2016 formation energy owing to reversible elastic-viscousplastic deformation. Suggested theoretical and calculation assessments [3, 7- 8] showed that dissipative friction volume performs reversible elastic energy transformation of outer mechanical movement with density q → * equal to critical density of latent energy u *e . Culmination of tribosystem evolution is its final and limited condition of point 4 - a state of anomalously low friction and wear free condition (maximum efficient). Calculation shows [3] that at an ideal tribosystem evolution an adaptive (Amonton’s) friction coefficient µ adapt in a point 2 of a diagram falls abruptly down, reaching in a point 4 the value of elastic friction coefficient µ elast . For point 4 of compatibility area 3-4 an equation of energy balance (1) can be put in the following way: (10) Thus, point 4 stands for an ideal evolution of contact friction volume a condition of ideal elastic-viscous-plastic deformation. Equation (10) shows as a matter of fact exactly that Amonton’s friction coefficient µ adapt being in its essence plastic friction coefficient µ plast has a minimum value equal to zero. It follows then, that plastic friction became elastic with friction coefficient µ elast . It means that plastic deformation of contact volume friction is implemented with the maximum dynamic dissipation (Q → = max) of accumulated latent energy. That is why the value of accumulated energy in point 4 is equal to zero (∆U e = 0). This fact proves an ideal condition at full evolution of contact volume. From the physical point of view this condition may be explained by the full dissipation of accumulated energy ∆U * e in point 2 on newly emerged structures of point 4 in the form of elastic energy of interaction between them (dynamic dissipation energy Q → ). Here µ dis = 1,0. The structural elements themselves are free of defects - µ adapt = 0, and friction is elastic - µ = µ elast . It has been demonstrated [3] that the value of minimum adaptive friction volume V min adapt corresponding to the zero meaning of plastic friction component µ adapt is not equal to zero, but is equal to some minimum structural element of deformed solid body. 5 The idea of mechanical (nano) quantum of dissipative friction structures The result of ideal elementary tribosystem (contact) evolution is forming of unique nanostructure - a mechanical (nano) quantum. Strict notions about mechanical quantum have been obtained [3] considering equation of quasi-ideal solid body for point 4 of diagram of friction evolution (11) which is particular case of solving equation of energy friction balance (1) at µ adapt = 0 and µ dis = 1 = µ * dis . Here S →Q - inertia entropy of compatible friction volume; T - characteristic temperature of contact friction volume; l f - linear size of elementary contact. Correspondingly, in conditions of maximum compatibility (point 4) when tribosystem implements full evolution cycle of adaptation with formation of most perfect dissipative structure, the behavior of structure is subject to equation of quasi-ideal solid body condition. So, it is to be presumed that interaction between elements of this structure are minimized - a condition of ideal elasticity in dynamics. Equation (3) with taking into account Plank- Boltzmann formula S = k lnW and real number of atoms oscillators N f in the volume of elementary tribosystem (contact) V * f is brought to the form explaining friction regularities from the point of view of system evolution: (12) (13) where k - Boltzmann constant; W - condition probability; S U - configuration entropy of friction (contact) volume. Tribosystem always tends to some optimal condition, characterized, i. e. to a most probable condition W’ = N f lnW for the given friction conditions. Analysis and solution of these equations [3] allows to demonstrate the principle of constant probability value (parameter of tribosystem condition (order)) W for the whole range of compatible friction precisely lnW = 3 and W = e 3 = 20,08553696... The value of thermodynamic probability W equal to 20,08553696... was interpreted [3] as a minimum value of linear, atomic oscillators in one of three directions of minimum adaptive friction volume V min adapt corresponding to condition of practically absolute elastic friction - anomalously-low friction (safe deformation threshold). Then the number of atomic oscillators in this volume equals V Q = (e 3 ) 3 = (20,08553695...) 3 = 8103,083969…atom’s oscillators. It is the universal size (volume) of mechanical quantum [3, 9]. 9 Aus Wissenschaft und Forschung release and dissipation of energy . Here the decrease in is due to the decrease in latent energy density within the friction volume or (which is virtually the same) to the decrease of the adaptive friction volume ) and to the increase of the dissipative volume ). Tribosystem evolution presented as a diagram (Figure 2), has adaptive-dissipative character (1) and reflects competitive (dialectical) nature of friction. Evolution curve has a set of principal points (1-5) of transitive states of tribosystem, which strongly obeys a balance principle of friction. The most characteristic areas between these points reflect general properties of its non-linear dynamics. So, in Fig.2 it is possible to see the following conventionally designated points and stages: 0-1 - a stage of static friction and deformational strengthening; 1 - a point of limit for deformational strengthening; 1-2 - a stage of pumping of excess energy; 2 - a point of gripping (adhesion) and transition of outer friction into internal (critical nonstability): 2-3 - a stage of forming dissipation structures (formation of heat fluctuation in friction volume); 3 - a point of minimum compatibility (maximum frictionness); 1- 2-3 a stage of selforganization; 3-4 - a stage of compatibility; 4 - a point of wearlessness (anormal-low friction); 5 - a point of thermal adhesion. An ideal evolution of tribosystem is symmetrical. The process starts and finishes within areas of elastic behavior. A plastic maximum (a superactivated condition) exists between them as a condition of selforganisation and adaptation. In the most general case evolution (adaptation) regularities of tribosystems may be presented as a 2-stage (Figure 2). At the first stage (0-2) of adaptation the evolution of friction contact rushes to form some critical volume of friction (point 2). It is elementary tribosystem that is the elementary and self-sufficient energy transformer. The first stage latent energy density growth to a limited magnitude within critical friction volume . This friction volume is constant at the second stage of evolution, but here it is evolutionary developed owing to structural transformation; by this one may realize wide spectrum of compatibility friction structures (Figure 3). The second stage (2-4) - structural transformation of critical friction volume (elementary tribosystem) into adaptive and dissipative volumes. The limit (point 4) of this stage is characterized by a full transformation of adaptive critical volume into dissipative. The volumes mentioned above characterize different regularities of transforming energy of outer mechanical movement at friction. Adaptive volume is connected with non-reversible absorption of deformation energy. It is in this volume where latent deformation energy accumulates and where the centres of distruction initially emerge (birth). Dissipative volume is capable of reversible transformation (dissipate) of outer movement energy. It doesn’t accumulate latent deformation energy owing to reversible elastic-viscousplastic deformation. Suggested theoretical and calculation assessments [3, 7-8] showed that dissipative friction volume performs reversible elastic energy transformation of outer mechanical movement with density equal to critical density of latent energy . Culmination of tribosystem evolution is its final and limited condition of point 4 - a state of anomalously low friction and wearlessness (maximum efficient). Calculation show [3] that at an ideal tribosystem evolution an adaptive (Amontons) friction coefficient in a point 2 of a diagram falls abruptly down, reaching in a point 4 the value of elastic friction coefficient . For point 4 of compatibility area 3-4 an equation of energy balance (1) showed be put in the following way: = - = * dis adapt m m m elast plast dis m m m = = = - = 0 1 ; 0 , 1 = * m . (10) Thus, point 4 stands for an ideal evolution of contact friction volume a condition of ideal elastic-viscous-plastic deformation. Equation (10) shows as a matter of fact exactly it, i.e. Amontons friction coefficient being in its essence plastic friction coefficient has a minimum value equal to zero. It follows then, that plastic friction became elastic with friction coefficient . It means that plastic deformation of contact volume friction is implemented with the maximum dynamic dissipation ( ) of accumulated latent energy. That is why the value of accumulated energy in point 4 is equal to zero ( ). This fact proves an ideal condition at full evolution of contact volume. From the physics point of view this condition may be explained by the full dissipation of accumulated energy in point 2 and by newly emerged structures of point 4 in the form of elastic energy of interaction between them (dynamic dissipation energy ). Here . The structural elements themselves are defectlessness - , and friction is elastic - . It has been demonstrated [3] that value of minimum adaptive friction volume corresponding to the zero meaning of plastic friction component is not equal to zero, but is equal to some minimum structural element of deformed solid body. release and dissipation of energy . Here the decrease in is due to the decrease in latent energy density within the friction volume or (which is virtually the same) to the decrease of the adaptive friction volume ) and to the increase of the dissipative volume ). Tribosystem evolution presented as a diagram (Figure 2), has adaptive-dissipative character (1) and reflects competitive (dialectical) nature of friction. Evolution curve has a set of principal points (1-5) of transitive states of tribosystem, which strongly obeys a balance principle of friction. The most characteristic areas between these points reflect general properties of its non-linear dynamics. So, in Fig.2 it is possible to see the following conventionally designated points and stages: 0-1 - a stage of static friction and deformational strengthening; 1 - a point of limit for deformational strengthening; 1-2 - a stage of pumping of excess energy; 2 - a point of gripping (adhesion) and transition of outer friction into internal (critical nonstability): 2-3 - a stage of forming dissipation structures (formation of heat fluctuation in friction volume); 3 - a point of minimum compatibility (maximum frictionness); 1- 2-3 a stage of selforganization; 3-4 - a stage of compatibility; 4 - a point of wearlessness (anormal-low friction); 5 - a point of thermal adhesion. An ideal evolution of tribosystem is symmetrical. The process starts and finishes within areas of elastic behavior. A plastic maximum (a superactivated condition) exists between them as a condition of selforganisation and adaptation. In the most general case evolution (adaptation) regularities of tribosystems may be presented as a 2-stage (Figure 2). At the first stage (0-2) of adaptation the evolution of friction contact rushes to form some critical volume of friction (point 2). It is elementary tribosystem that is the elementary and self-sufficient energy transformer. The first stage latent energy density growth to a limited magnitude within critical friction volume . This friction volume is constant at the second stage of evolution, but here it is evolutionary developed owing to structural transformation; by this one may realize wide spectrum of compatibility friction structures (Figure 3). The second stage (2-4) - structural transformation of critical friction volume (elementary tribosystem) into adaptive and dissipative volumes. The limit (point 4) of this stage is characterized by a full transformation of adaptive critical volume into dissipative. The volumes mentioned above characterize different regularities of transforming energy of outer mechanical movement at friction. Adaptive volume is connected with non-reversible absorption of deformation energy. It is in this volume where latent deformation energy accumulates and where the centres of distruction initially emerge (birth). Dissipative volume is capable of reversible transformation (dissipate) of outer movement energy. It doesn’t accumulate latent deformation energy owing to reversible elastic-viscousplastic deformation. Suggested theoretical and calculation assessments [3, 7-8] showed that dissipative friction volume performs reversible elastic energy transformation of outer mechanical movement with density equal to critical density of latent energy . Culmination of tribosystem evolution is its final and limited condition of point 4 - a state of anomalously low friction and wearlessness (maximum efficient). Calculation show [3] that at an ideal tribosystem evolution an adaptive (Amontons) friction coefficient in a point 2 of a diagram falls abruptly down, reaching in a point 4 the value of elastic friction coefficient . For point 4 of compatibility area 3-4 an equation of energy balance (1) showed be put in the following way: elast plast dis m m m = = = - = 0 1 ; 0 , 1 = * m . (10) Thus, point 4 stands for an ideal evolution of contact friction volume a condition of ideal elastic-viscous-plastic deformation. Equation (10) shows as a matter of fact exactly it, i.e. Amontons friction coefficient being in its essence plastic friction coefficient has a minimum value equal to zero. It follows then, that plastic friction became elastic with friction coefficient . It means that plastic deformation of contact volume friction is implemented with the maximum dynamic dissipation ( ) of accumulated latent energy. That is why the value of accumulated energy in point 4 is equal to zero ( ). This fact proves an ideal condition at full evolution of contact volume. From the physics point of view this condition may be explained by the full dissipation of accumulated energy in point 2 and by newly emerged structures of point 4 in the form of elastic energy of interaction between them (dynamic dissipation energy ). Here . The structural elements themselves are defectlessness - , and friction is elastic - . It has been demonstrated [3] that value of minimum adaptive friction volume corresponding to the zero meaning of plastic friction component is not equal to zero, but is equal to some minimum structural element of deformed solid body. 5. The idea of mechanical (nano) quantum of dissipative friction structures The result of ideal elementary tribosystem (contact) evolution is forming of unique nanostructure - a mechanical (nano) quantum. Strict notions about mechanical quantum have been obtained [3] considering equation of quasiideal solid body for point 4 of diagram of friction evolution , (11) which is particular case of solving equation of energy friction balance (1) at and . Here - inertia entropy of compatible friction volume; characteristic temperature of contact friction volume; linear size of elementary contact. Correspondingly, in conditions of maximum compatibility (point 4) when tribosystem implements full evolution cycle of adaptation with formation of most perfect dissipative structure, the behaviour of structure is subject to equation of quasiideal solid body condition. So, it is to be presumed that, interaction between elements of this structure, are minimized - a condition of ideal elasticity in dynamics. Equation (3) with taking into account Plank-Boltzmann formula and real number of atoms oscillators in the volume of elementary tribosystem (contact) is brought to the form explaining friction regularities from the point of view of system evolution: f f f Q Nl W kTN Nl T S diss ln = = r m ; (12) (13) where - Boltzmann constant; condition probability; configuration entropy of friction (contact) volume. Tribosystem always tends to some optimal condition, characterized, i.e. to a most probable condition for the given friction conditions. Analysis and solution of these equations [3] allows to demonstrate the principle of constant probability value (parameter of tribosystem condition (order)) for the whole range of compatable friction precisely and . The value of thermodynamic probability equal to was interpreted [3] as a minimum value of linear, atomic oscillators in one of three directions of minimum adaptive friction volume corresponding to condition of practically absolute elastic friction - anomalously-low friction (safe deformation threshold). Then the number of atomic oscillators in this volume equals atom’s oscillators. It is the universal size (volume) of mechanical quantum [3,9]. On the other hand, adopting the meaning of Boltzmann entropy , a universal friction constant [3,8] is obtained, which characterizes in physical meaning «energetical size» of elementary tribosystem (TS), containing in ideal conditions the same number of atomic oscillators (mechanic quanta ): ( ); (14) , ( ), (15) where universal constant of deformation at friction. As it follows from calculations [3] the size of minimum adaptive friction volume coincides in its value with the size of submicroscopic area in crevice mouth, which is equal for metals mm, i.e. of critical volume size responsible to fracture. Thus the size of minimum adaptive friction volume , can be presented as the size of some mechanical quantum. This mechanical quantum constitutes a minimum number of atoms capable to provide such a configurational distribution (structure) which obtains the property of reversibly taking and dissipating (recovering) energy of outer mechanical movement. It also constitutes minimum structure in conditions of plastic deformation and it is formed at tribosystem transition (deformed volume) through an ultimately activated (critical) condition (see Figure 2) due to development of selforganisational tribosystem adaptation processes. Mutual rotationoscillation movement of these mechanical quanta in respect of each other within elementary tribosystem (contact) determines condition of most perfect dissipative friction structure. Properly speaking, such condition is described by equation of quasiideal solid body condition (9), a condition when interaction between structural elements (mechanical quanta) is minimized - a condition of ideal elasticity of quasiviscous flow. Calculation friction coefficient between quanta equals about [3,7-8]. A conclusion that mechanical quantum constitutes a minimum structural form at plastic deformation (friction) is supported by calculation. If values of elasticity modules correspond to atomic (true) elastisities then values equal to are obtained, where can be interpreted as a characteristic of volume elasticity of one 5. The idea of mechanical (nano) quantum of dissipative friction structures The result of ideal elementary tribosystem (contact) evolution is forming of unique nanostructure - a mechanical (nano) quantum. Strict notions about mechanical quantum have been obtained [3] considering equation of quasiideal solid body for point 4 of diagram of friction evolution * * * * * * = = = = q V u V Nl T S Q f e f f dis Q r r r m , (11) which is particular case of solving equation of energy friction balance (1) at and . Here - inertia entropy of compatible friction volume; characteristic temperature of contact friction volume; linear size of elementary contact. Correspondingly, in conditions of maximum compatibility (point 4) when tribosystem implements full evolution cycle of adaptation with formation of most perfect dissipative structure, the behaviour of structure is subject to equation of quasiideal solid body condition. So, it is to be presumed that, interaction between elements of this structure, are minimized - a condition of ideal elasticity in dynamics. Equation (3) with taking into account Plank-Boltzmann formula and real number of atoms oscillators in the volume of elementary tribosystem (contact) is brought to the form explaining friction regularities from the point of view of system evolution: ; (12) (13) where - Boltzmann constant; condition probability; configuration entropy of friction (contact) volume. Tribosystem always tends to some optimal condition, characterized, i.e. to a most probable condition for the given friction conditions. Analysis and solution of these equations [3] allows to demonstrate the principle of constant probability value (parameter of tribosystem condition (order)) for the whole range of compatable friction precisely and . The value of thermodynamic probability equal to was interpreted [3] as a minimum value of linear, atomic oscillators in one of three directions of minimum adaptive friction volume corresponding to condition of practically absolute elastic friction - anomalously-low friction (safe deformation threshold). Then the number of atomic oscillators in this volume equals atom’s oscillators. It is the universal size (volume) of mechanical quantum [3,9]. On the other hand, adopting the meaning of Boltzmann entropy , a universal friction constant [3,8] is obtained, which characterizes in physical meaning «energetical size» of elementary tribosystem (TS), containing in ideal conditions the same number of atomic oscillators (mechanic quanta ): ( ); (14) , ( ), (15) where universal constant of deformation at friction. As it follows from calculations [3] the size of minimum adaptive friction volume coincides in its value with the size of submicroscopic area in crevice mouth, which is equal for metals mm, i.e. of critical volume size responsible to fracture. Thus the size of minimum adaptive friction volume , can be presented as the size of some mechanical quantum. This mechanical quantum constitutes a minimum number of atoms capable to provide such a configurational distribution (structure) which obtains the property of reversibly taking and dissipating (recovering) energy of outer mechanical movement. It also constitutes minimum structure in conditions of plastic deformation and it is formed at tribosystem transition (deformed volume) through an ultimately activated (critical) condition (see Figure 2) due to development of selforganisational tribosystem adaptation processes. Mutual rotationoscillation movement of these mechanical quanta in respect of each other within elementary tribosystem (contact) determines condition of most perfect dissipative friction structure. Properly speaking, such condition is described by equation of quasiideal solid body condition (9), a condition when interaction between structural elements (mechanical quanta) is minimized - a condition of ideal elasticity of quasiviscous flow. Calculation friction coefficient between quanta equals about [3,7-8]. A conclusion that mechanical quantum constitutes a minimum structural form at plastic deformation (friction) is supported by calculation. If values of elasticity modules correspond to atomic (true) elastisities then values equal to are obtained, where can be interpreted as a characteristic of volume elasticity of one 5. The idea of mechanical (nano) quantum of dissipative friction structures The result of ideal elementary tribosystem (contact) evolution is forming of unique nanostructure - a mechanical (nano) quantum. Strict notions about mechanical quantum have been obtained [3] considering equation of quasiideal solid body for point 4 of diagram of friction evolution , (11) which is particular case of solving equation of energy friction balance (1) at and . Here - inertia entropy of compatible friction volume; characteristic temperature of contact friction volume; linear size of elementary contact. Correspondingly, in conditions of maximum compatibility (point 4) when tribosystem implements full evolution cycle of adaptation with formation of most perfect dissipative structure, the behaviour of structure is subject to equation of quasiideal solid body condition. So, it is to be presumed that, interaction between elements of this structure, are minimized - a condition of ideal elasticity in dynamics. Equation (3) with taking into account Plank-Boltzmann formula and real number of atoms oscillators in the volume of elementary tribosystem (contact) is brought to the form explaining friction regularities from the point of view of system evolution: f f f Q Nl W kTN Nl T S diss ln = = r m ; (12) = - = - = f f Nl W kTN diss adapt ln 1 1 m m (13) where - Boltzmann constant; condition probability; configuration entropy of friction (contact) volume. Tribosystem always tends to some optimal condition, characterized, i.e. to a most probable condition for the given friction conditions. Analysis and solution of these equations [3] allows to demonstrate the principle of constant probability value (parameter of tribosystem condition (order)) for the whole range of compatable friction precisely and . The value of thermodynamic probability equal to was interpreted [3] as a minimum value of linear, atomic oscillators in one of three directions of minimum adaptive friction volume corresponding to condition of practically absolute elastic friction - anomalously-low friction (safe deformation threshold). Then the number of atomic oscillators in this volume equals atom’s oscillators. It is the universal size (volume) of mechanical quantum [3,9]. On the other hand, adopting the meaning of Boltzmann entropy , a universal friction constant [3,8] is obtained, which characterizes in physical meaning «energetical size» of elementary tribosystem (TS), containing in ideal conditions the same number of atomic oscillators (mechanic quanta ): ( ); (14) , ( ), (15) where universal constant of deformation at friction. As it follows from calculations [3] the size of minimum adaptive friction volume coincides in its value with the size of submicroscopic area in crevice mouth, which is equal for metals mm, i.e. of critical volume size responsible to fracture. Thus the size of minimum adaptive friction volume , can be presented as the size of some mechanical quantum. This mechanical quantum constitutes a minimum number of atoms capable to provide such a configurational distribution (structure) which obtains the property of reversibly taking and dissipating (recovering) energy of outer mechanical movement. It also constitutes minimum structure in conditions of plastic deformation and it is formed at tribosystem transition (deformed volume) through an ultimately activated (critical) condition (see Figure 2) due to development of selforganisational tribosystem adaptation processes. Mutual rotationoscillation movement of these mechanical quanta in respect of each other within elementary tribosystem (contact) determines condition of most perfect dissipative friction structure. Properly speaking, such condition is described by equation of quasiideal solid body condition (9), a condition when interaction between structural elements (mechanical quanta) is minimized - a condition of ideal elasticity of quasiviscous flow. Calculation friction coefficient between quanta equals about [3,7-8]. A conclusion that mechanical quantum constitutes a minimum structural form at plastic deformation (friction) is supported by calculation. If values of elasticity modules correspond to atomic (true) elastisities then values equal to are obtained, where can be interpreted as a characteristic of volume elasticity of one 5. The idea of mechanical (nano) quantum of dissipative friction structures The result of ideal elementary tribosystem (contact) evolution is forming of unique nanostructure - a mechanical (nano) quantum. Strict notions about mechanical quantum have been obtained [3] considering equation of quasiideal solid body for point 4 of diagram of friction evolution , (11) which is particular case of solving equation of energy friction balance (1) at and . Here - inertia entropy of compatible friction volume; characteristic temperature of contact friction volume; linear size of elementary contact. Correspondingly, in conditions of maximum compatibility (point 4) when tribosystem implements full evolution cycle of adaptation with formation of most perfect dissipative structure, the behaviour of structure is subject to equation of quasiideal solid body condition. So, it is to be presumed that, interaction between elements of this structure, are minimized - a condition of ideal elasticity in dynamics. Equation (3) with taking into account Plank-Boltzmann formula and real number of atoms oscillators in the volume of elementary tribosystem (contact) is brought to the form explaining friction regularities from the point of view of system evolution: ; (12) = - = - = f f Nl W kTN diss adapt ln 1 1 m m , 1 f U f Q Nl T S Nl T S = - = r (13) where - Boltzmann constant; condition probability; configuration entropy of friction (contact) volume. Tribosystem always tends to some optimal condition, characterized, i.e. to a most probable condition for the given friction conditions. Analysis and solution of these equations [3] allows to demonstrate the principle of constant probability value (parameter of tribosystem condition (order)) for the whole range of compatable friction precisely and . The value of thermodynamic probability equal to was interpreted [3] as a minimum value of linear, atomic oscillators in one of three directions of minimum adaptive friction volume corresponding to condition of practically absolute elastic friction - anomalously-low friction (safe deformation threshold). Then the number of atomic oscillators in this volume equals atom’s oscillators. It is the universal size (volume) of mechanical quantum [3,9]. On the other hand, adopting the meaning of Boltzmann entropy , a universal friction constant [3,8] is obtained, which characterizes in physical meaning «energetical size» of elementary tribosystem (TS), containing in ideal conditions the same number of atomic oscillators (mechanic quanta ): ( ); (14) , ( ), (15) where universal constant of deformation at friction. As it follows from calculations [3] the size of minimum adaptive friction volume coincides in its value with the size of submicroscopic area in crevice mouth, which is equal for metals mm, i.e. of critical volume size responsible to fracture. Thus the size of minimum adaptive friction volume , can be presented as the size of some mechanical quantum. This mechanical quantum constitutes a minimum number of atoms capable to provide such a configurational distribution (structure) which obtains the property of reversibly taking and dissipating (recovering) energy of outer mechanical movement. It also constitutes minimum structure in conditions of plastic deformation and it is formed at tribosystem transition (deformed volume) through an ultimately activated (critical) condition (see Figure 2) due to development of selforganisational tribosystem adaptation processes. Mutual rotationoscillation movement of these mechanical quanta in respect of each other within elementary tribosystem (contact) determines condition of most perfect dissipative friction structure. Properly speaking, such condition is described by equation of quasiideal solid body condition (9), a condition when interaction between structural elements (mechanical quanta) is minimized - a condition of ideal elasticity of quasiviscous flow. Calculation friction coefficient between quanta equals about [3,7-8]. A conclusion that mechanical quantum constitutes a minimum structural form at plastic deformation (friction) is supported by calculation. If values of elasticity modules correspond to atomic (true) elastisities then values equal to are obtained, where can be interpreted as a characteristic of volume elasticity of one T+S_3_16 05.04.16 09: 01 Seite 9 10 Tribologie + Schmierungstechnik 63. Jahrgang 3/ 2016 On the other hand, adopting the meaning of Boltzmann entropy S, a universal friction constant R f = kN f [3,8] is obtained, which characterizes in physical meaning «energetical size» of elementary tribosystem (TS), containing in ideal conditions the same number of atomic oscillators N f (mechanic quanta N Q ): (14) (15) where R MQ - universal constant of deformation at friction. As it follows from calculations [3] the size of minimum adaptive friction volume V min adapt coincides in its value with the size of submicroscopic area in crack mouth, which is equal for metals (4…9) ·10 -6 mm, i. e. of critical volume size responsible to fracture. Thus the size of minimum adaptive friction volume V min adapt = V elast , can be presented as the size of some mechanical quantum. This mechanical quantum constitutes a minimum number of atoms capable to provide such a configurational distribution (structure) which obtains the property of reversibly taking and dissipating (recovering) energy of outer mechanical movement. It also constitutes minimum structure in conditions of plastic deformation and it is formed at tribosystem transition (deformed volume) through an ultimately activated (critical) condition (see Figure 2) due to development of self-organizational tribosystem adaptation processes. Mutual rotation-oscillation movement of these mechanical quanta in respect of each other within elementary tribosystem (contact) determines condition of most perfect dissipative friction structure. Properly speaking, such condition is described by equation of quasi-ideal solid body condition (9), a condition when interaction between structural elements (mechanical quanta) is minimized - a condition of ideal elasticity of quasi-viscous flow. Calculation friction coefficient between quanta equals about 10 -8 [3, 7-8]. A conclusion that mechanical quantum constitutes a minimum structural form at plastic deformation (friction) is supported by calculation. If values of elasticity modules E correspond to atomic (true) elasticities E r then values equal to 60 are obtained, where 60 = 3W can be interpreted as a characteristic of volume elasticity of one mechanical quantum - minimum adaptive friction volume V min adapt . Calculation assessment of parameter W : 20 = E / ̸̸ 3E r , done for various metals and steels gives an average value 20,77 ((Table 1)); ∆H S = 3E r entalpy of melting. ∆H S = 3E r , E/ 3E r = 20,77 A conclusion is made [3] that the number of atoms (mechanical quantum (MQ)) within volume of one elementary tribosystem (TS) in conditions of ideal tribosystem evolution is a constant value. Thus, it is possible to speak about the quantity of substance equal by mass to one elementary tribosystems and to one mechanic quantum. 6 Synergism of tribosystem and state of optimum Mechanical quantum is the dynamic oscillator of dissipative friction structure. An ideal quasi-elastic contact Aus Wissenschaft und Forschung 5. The idea of mechanical (nano) quantum of dissipative friction structures The result of ideal elementary tribosystem (contact) evolution is forming of unique nanostructure - a mechanical (nano) quantum. Strict notions about mechanical quantum have been obtained [3] considering equation of quasiideal solid body for point 4 of diagram of friction evolution , (11) which is particular case of solving equation of energy friction balance (1) at and . Here - inertia entropy of compatible friction volume; characteristic temperature of contact friction volume; linear size of elementary contact. Correspondingly, in conditions of maximum compatibility (point 4) when tribosystem implements full evolution cycle of adaptation with formation of most perfect dissipative structure, the behaviour of structure is subject to equation of quasiideal solid body condition. So, it is to be presumed that, interaction between elements of this structure, are minimized - a condition of ideal elasticity in dynamics. Equation (3) with taking into account Plank-Boltzmann formula and real number of atoms oscillators in the volume of elementary tribosystem (contact) is brought to the form explaining friction regularities from the point of view of system evolution: ; (12) (13) where - Boltzmann constant; condition probability; configuration entropy of friction (contact) volume. Tribosystem always tends to some optimal condition, characterized, i.e. to a most probable condition for the given friction conditions. Analysis and solution of these equations [3] allows to demonstrate the principle of constant probability value (parameter of tribosystem condition (order)) for the whole range of compatable friction precisely and . The value of thermodynamic probability equal to was interpreted [3] as a minimum value of linear, atomic oscillators in one of three directions of minimum adaptive friction volume corresponding to condition of practically absolute elastic friction - anomalously-low friction (safe deformation threshold). Then the number of atomic oscillators in this volume equals atom’s oscillators. It is the universal size (volume) of mechanical quantum [3,9]. On the other hand, adopting the meaning of Boltzmann entropy , a universal friction constant [3,8] is obtained, which characterizes in physical meaning «energetical size» of elementary tribosystem (TS), containing in ideal conditions the same number of atomic oscillators f N (mechanic quanta Q N ): × × = × × = × = Q MQ Q f f N R N W k N k R 3 ( TS grade J × ); (14) , ( ), (15) where universal constant of deformation at friction. As it follows from calculations [3] the size of minimum adaptive friction volume coincides in its value with the size of submicroscopic area in crevice mouth, which is equal for metals mm, i.e. of critical volume size responsible to fracture. Thus the size of minimum adaptive friction volume , can be presented as the size of some mechanical quantum. This mechanical quantum constitutes a minimum number of atoms capable to provide such a configurational distribution (structure) which obtains the property of reversibly taking and dissipating (recovering) energy of outer mechanical movement. It also constitutes minimum structure in conditions of plastic deformation and it is formed at tribosystem transition (deformed volume) through an ultimately activated (critical) condition (see Figure 2) due to development of selforganisational tribosystem adaptation processes. Mutual rotationoscillation movement of these mechanical quanta in respect of each other within elementary tribosystem (contact) determines condition of most perfect dissipative friction structure. Properly speaking, such condition is described by equation of quasiideal solid body condition (9), a condition when interaction between structural elements (mechanical quanta) is minimized - a condition of ideal elasticity of quasiviscous flow. Calculation friction coefficient between quanta equals about [3,7-8]. A conclusion that mechanical quantum constitutes a minimum structural form at plastic deformation (friction) is supported by calculation. If values of elasticity modules correspond to atomic (true) elastisities then values equal to are obtained, where can be interpreted as a characteristic of volume elasticity of one 5. The idea of mechanical (nano) quantum of dissipative friction structures The result of ideal elementary tribosystem (contact) evolution is forming of unique nanostructure - a mechanical (nano) quantum. Strict notions about mechanical quantum have been obtained [3] considering equation of quasiideal solid body for point 4 of diagram of friction evolution , (11) which is particular case of solving equation of energy friction balance (1) at and . Here - inertia entropy of compatible friction volume; characteristic temperature of contact friction volume; linear size of elementary contact. Correspondingly, in conditions of maximum compatibility (point 4) when tribosystem implements full evolution cycle of adaptation with formation of most perfect dissipative structure, the behaviour of structure is subject to equation of quasiideal solid body condition. So, it is to be presumed that, interaction between elements of this structure, are minimized - a condition of ideal elasticity in dynamics. Equation (3) with taking into account Plank-Boltzmann formula and real number of atoms oscillators in the volume of elementary tribosystem (contact) is brought to the form explaining friction regularities from the point of view of system evolution: ; (12) (13) where - Boltzmann constant; condition probability; configuration entropy of friction (contact) volume. Tribosystem always tends to some optimal condition, characterized, i.e. to a most probable condition for the given friction conditions. Analysis and solution of these equations [3] allows to demonstrate the principle of constant probability value (parameter of tribosystem condition (order)) for the whole range of compatable friction precisely and . The value of thermodynamic probability equal to was interpreted [3] as a minimum value of linear, atomic oscillators in one of three directions of minimum adaptive friction volume corresponding to condition of practically absolute elastic friction - anomalously-low friction (safe deformation threshold). Then the number of atomic oscillators in this volume equals atom’s oscillators. It is the universal size (volume) of mechanical quantum [3,9]. On the other hand, adopting the meaning of Boltzmann entropy , a universal friction constant [3,8] is obtained, which characterizes in physical meaning «energetical size» of elementary tribosystem (TS), containing in ideal conditions the same number of atomic oscillators (mechanic quanta ): × × = × × = × = Q MQ Q f f N R N W k N k R 3 ( TS grade J × ); (14) , ( ), (15) where universal constant of deformation at friction. As it follows from calculations [3] the size of minimum adaptive friction volume coincides in its value with the size of submicroscopic area in crevice mouth, which is equal for metals mm, i.e. of critical volume size responsible to fracture. Thus the size of minimum adaptive friction volume , can be presented as the size of some mechanical quantum. This mechanical quantum constitutes a minimum number of atoms capable to provide such a configurational distribution (structure) which obtains the property of reversibly taking and dissipating (recovering) energy of outer mechanical movement. It also constitutes minimum structure in conditions of plastic deformation and it is formed at tribosystem transition (deformed volume) through an ultimately activated (critical) condition (see Figure 2) due to development of selforganisational tribosystem adaptation processes. Mutual rotationoscillation movement of these mechanical quanta in respect of each other within elementary tribosystem (contact) determines condition of most perfect dissipative friction structure. Properly speaking, such condition is described by equation of quasiideal solid body condition (9), a condition when interaction between structural elements (mechanical quanta) is minimized - a condition of ideal elasticity of quasiviscous flow. Calculation friction coefficient between quanta equals about [3,7-8]. A conclusion that mechanical quantum constitutes a minimum structural form at plastic deformation (friction) is supported by calculation. If values of elasticity modules correspond to atomic (true) elastisities then values equal to are obtained, where can be interpreted as a characteristic of volume elasticity of one 5. The idea of mechanical (nano) quantum of dissipative friction structures The result of ideal elementary tribosystem (contact) evolution is forming of unique nanostructure - a mechanical (nano) quantum. Strict notions about mechanical quantum have been obtained [3] considering equation of quasiideal solid body for point 4 of diagram of friction evolution , (11) which is particular case of solving equation of energy friction balance (1) at and . Here - inertia entropy of compatible friction volume; characteristic temperature of contact friction volume; linear size of elementary contact. Correspondingly, in conditions of maximum compatibility (point 4) when tribosystem implements full evolution cycle of adaptation with formation of most perfect dissipative structure, the behaviour of structure is subject to equation of quasiideal solid body condition. So, it is to be presumed that, interaction between elements of this structure, are minimized - a condition of ideal elasticity in dynamics. Equation (3) with taking into account Plank-Boltzmann formula and real number of atoms oscillators in the volume of elementary tribosystem (contact) is brought to the form explaining friction regularities from the point of view of system evolution: ; (12) (13) where - Boltzmann constant; condition probability; configuration entropy of friction (contact) volume. Tribosystem always tends to some optimal condition, characterized, i.e. to a most probable condition for the given friction conditions. Analysis and solution of these equations [3] allows to demonstrate the principle of constant probability value (parameter of tribosystem condition (order)) for the whole range of compatable friction precisely and . The value of thermodynamic probability equal to was interpreted [3] as a minimum value of linear, atomic oscillators in one of three directions of minimum adaptive friction volume corresponding to condition of practically absolute elastic friction - anomalously-low friction (safe deformation threshold). Then the number of atomic oscillators in this volume equals atom’s oscillators. It is the universal size (volume) of mechanical quantum [3,9]. On the other hand, adopting the meaning of Boltzmann entropy , a universal friction constant [3,8] is obtained, which characterizes in physical meaning «energetical size» of elementary tribosystem (TS), containing in ideal conditions the same number of atomic oscillators (mechanic quanta ): ( TS grade J × ); (14) 3 W k R MQ × = , ( MQ grade J × ), (15) where universal constant of deformation at friction. As it follows from calculations [3] the size of minimum adaptive friction volume coincides in its value with the size of submicroscopic area in crevice mouth, which is equal for metals mm, i.e. of critical volume size responsible to fracture. Thus the size of minimum adaptive friction volume , can be presented as the size of some mechanical quantum. This mechanical quantum constitutes a minimum number of atoms capable to provide such a configurational distribution (structure) which obtains the property of reversibly taking and dissipating (recovering) energy of outer mechanical movement. It also constitutes minimum structure in conditions of plastic deformation and it is formed at tribosystem transition (deformed volume) through an ultimately activated (critical) condition (see Figure 2) due to development of selforganisational tribosystem adaptation processes. Mutual rotationoscillation movement of these mechanical quanta in respect of each other within elementary tribosystem (contact) determines condition of most perfect dissipative friction structure. Properly speaking, such condition is described by equation of quasiideal solid body condition (9), a condition when interaction between structural elements (mechanical quanta) is minimized - a condition of ideal elasticity of quasiviscous flow. Calculation friction coefficient between quanta equals about [3,7-8]. A conclusion that mechanical quantum constitutes a minimum structural form at plastic deformation (friction) is supported by calculation. If values of elasticity modules correspond to atomic (true) elastisities then values equal to are obtained, where can be interpreted as a characteristic of volume elasticity of one Table 1: Parameter W for Metals and Steels [3] Metals E # 10 -3 , (u * e )∆H s # 10 -3 E/ 3E r and steels MPa MJ/ m 3 Cr 235,4 8,5 27,69 Mg 44,4 1,9 23,37 Ag 79,0 3,7 21,35 Au 78,7 4,0 19,67 Co 200,1 10,6 18,88 Fe 211,4 9,9 21,35 Ta 184,4 10,6 17,39 Ti 105,9 6,7 15,8 Nb 104,0 9,2 11,3 Zr 95,6 5,7 16,77 Mo 316,9 12,0 26,4 W 392,4 14,4 27,25 Ni 201,1 9,4 21,39 Iron 210,9 10,1 20,88 20 200,1 9,5 21,06 1Kh13 206,0 8,9 23,14 3Kh13 218,8 9,2 23,78 Kh18N9T 199,1 9,4 21,19 Kh18M9 199,1 9,6 20,74 30Kh 214,1 10,2 20,99 30N3 207,5 10,3 20,11 40 209,4 9,7 21,58 30G2 207,2 10,0 20,72 30KhGN3 208,0 10,2 20,4 G13 204,0 10,0 20,4 50S2G 196,2 10,3 19,05 U8 198,0 10,3 19,22 U12 198,0 10,4 19,04 T+S_3_16 05.04.16 09: 01 Seite 10 Tribologie + Schmierungstechnik 63. Jahrgang 3/ 2016 condition at its full evolution constitutes effect of most fully dissipated energy of outer mechanical movement throughout newly formed (by mechanism of self-organization) structural elements - mechanical quantums (dynamic oscillators) which most fully realize their rotationary - oscillatory behavior in relation to each other within elementary tribosystem volume. Their resistance to relative interaction here is minimally elastic and corresponds to elasticity of ideal atomic (thermodynamically balanced) interactions at the level of electron orbits. Universal constants of mechanical quantum and elementary tribosystem (material point) determine quantum model of surface damping: (16) taking into account destruction quantums n dest (non-reversible process component) and damping quantums n i (reversible, elastic component - fatigue number), and also probability evolution tribosystem model to a most ordered condition: (17) where 3R MQ T = U 1Q - energy of one mechanical quantum; W i and W * - current and ultimate probabilities of tribosystems compatibility conditions. According to a model of quantum surface damping at friction in state of most complete evolution (adaptation) of elementary tribosystem all mechanical quantums with the exception of one elasticity and reversibly transform energy of outer impact (mechanic movement). One mechanical quantum of radiation ( : 8103 atoms) - is a minimum loss (essence of „wear free“ condition or other wear standard). Linear size of quantum is equal to diameter of a spherical ideal crystal with atomic roughness: (18) Here d- a - mean atomic diameter for metals; W = e 3 - parameter of state for mechanical quantum [3]. Mechanical quantum (Figure 4) can be examined as the elementary nanostructure of metal’s solid body. Calculations have shown [3] the number N Q of such mechanical «quanta» (sub-tribosystems) within the elemen- 11 Aus Wissenschaft und Forschung mechanical quantum - minimum adaptive friction volume . Calculation assessment of parameter , done for various metals and steels gives an average value ((Table)); entalpy of melting. Table. Parameter for Metals and Steels [3] MPa MJ/ m 3 , A conclusion is made [3] that the number of atoms (mechanical quantum (MQ)) within volume of one elementary tribosystem (TS) in conditions of ideal tribosystem evolution is a constant value. Thus, it is possible to speak about the quantity of substance equal by mass to one elementary tribosystems and to one mechanic quantum. 6. Synergism of tribosystem and state optimum Mechanical quantum is dynamic oscillator of dissipative friction structure. An ideal quasielastic contact condition at its full evolution constitutes effect of most fully dissipated energy of outer mechanical movement throughout newly formed (by mechanism of selforganization) structural elements -mechanical quantums (dynamic oscillators) which most fully realize their rotationary - oscillatory behavior in relation to each other within elementary tribosystem volume. Their resistance to relative interaction here is minimally elastic and corresponds to elasticity of ideal atomic (thermodynamically balanced) interactions at the level of electron orbits. Universal constants of mechanical quantum and elementary tribosystem (material point) determine quantum model of surface damping: adapt i Q i Q f i MQ dis n n n U n U l N n T R m m - = = = = * * 1 3 1 1 ; * * = - = n n n n dest i adapt 1 m , (16) taking into account destruction quantums (nonreversible process component) and damping quantums (reversible, elastic component - fatique number), and also probability evolution tribosystem model to a most ordered condition: . (17) where energy of one mechanical quantum; and current and ultimate probabilities of tribosystems compatibility conditions. According to a model of quantum surface damping at friction in state of most complete evolution (adaptation) of elementary tribosystem all mechanical quantums with the exeption of one elasticity and reversibly transform energy of outer impact (mechanic movement). One mechanical quantum of radiation ( atoms) - is a minimum loss (essence of wearlessness or other wear primary standart). Linear size of quantum is equal to diameter of spherical ideal crystal with atomic roughness : . (18) Here mean atomic diameter for metals; parameter of state for mechanical quantum [3]. Mechanical quantum (Figure 4) can be examined as the elementary nanostructure of metal’s solid body. Calculations have shown [3] the number of such mechanical «quanta» (subtribosystems) within the elementary tribosystem’s volume to be , which is close to the safe number of fatigue cycles. mechanical quantum - minimum adaptive friction volume . Calculation assessment of parameter , done for various metals and steels gives an average value ((Table)); entalpy of melting. Table. Parameter for Metals and Steels [3] MPa MJ/ m 3 , A conclusion is made [3] that the number of atoms (mechanical quantum (MQ)) within volume of one elementary tribosystem (TS) in conditions of ideal tribosystem evolution is a constant value. Thus, it is possible to speak about the quantity of substance equal by mass to one elementary tribosystems and to one mechanic quantum. 6. Synergism of tribosystem and state optimum Mechanical quantum is dynamic oscillator of dissipative friction structure. An ideal quasielastic contact condition at its full evolution constitutes effect of most fully dissipated energy of outer mechanical movement throughout newly formed (by mechanism of selforganization) structural elements -mechanical quantums (dynamic oscillators) which most fully realize their rotationary - oscillatory behavior in relation to each other within elementary tribosystem volume. Their resistance to relative interaction here is minimally elastic and corresponds to elasticity of ideal atomic (thermodynamically balanced) interactions at the level of electron orbits. Universal constants of mechanical quantum and elementary tribosystem (material point) determine quantum model of surface damping: adapt i Q i Q f i MQ dis n n n U n U l N n T R m m - = = = = * * 1 3 1 1 ; * * = - = n n n n dest i adapt 1 m , (16) taking into account destruction quantums (nonreversible process component) and damping quantums (reversible, elastic component - fatique number), and also probability evolution tribosystem model to a most ordered condition: . (17) where energy of one mechanical quantum; and current and ultimate probabilities of tribosystems compatibility conditions. According to a model of quantum surface damping at friction in state of most complete evolution (adaptation) of elementary tribosystem all mechanical quantums with the exeption of one elasticity and reversibly transform energy of outer impact (mechanic movement). One mechanical quantum of radiation ( atoms) - is a minimum loss (essence of wearlessness or other wear primary standart). Linear size of quantum is equal to diameter of spherical ideal crystal with atomic roughness : . (18) Here mean atomic diameter for metals; parameter of state for mechanical quantum [3]. Mechanical quantum (Figure 4) can be examined as the elementary nanostructure of metal’s solid body. Calculations have shown [3] the number of such mechanical «quanta» (subtribosystems) within the elementary tribosystem’s volume to be , which is close to the safe number of fatigue cycles. mechanical quantum - minimum adaptive friction volume . Calculation assessment of parameter , done for various metals and steels gives an average value ((Table)); entalpy of melting. Table. Parameter for Metals and Steels [3] MPa MJ/ m 3 , A conclusion is made [3] that the number of atoms (mechanical quantum (MQ)) within volume of one elementary tribosystem (TS) in conditions of ideal tribosystem evolution is a constant value. Thus, it is possible to speak about the quantity of substance equal by mass to one elementary tribosystems and to one mechanic quantum. 6. Synergism of tribosystem and state optimum Mechanical quantum is dynamic oscillator of dissipative friction structure. An ideal quasielastic contact condition at its full evolution constitutes effect of most fully dissipated energy of outer mechanical movement throughout newly formed (by mechanism of selforganization) structural elements -mechanical quantums (dynamic oscillators) which most fully realize their rotationary - oscillatory behavior in relation to each other within elementary tribosystem volume. Their resistance to relative interaction here is minimally elastic and corresponds to elasticity of ideal atomic (thermodynamically balanced) interactions at the level of electron orbits. Universal constants of mechanical quantum and elementary tribosystem (material point) determine quantum model of surface damping: ; , (16) taking into account destruction quantums (nonreversible process component) and damping quantums (reversible, elastic component - fatique number), and also probability evolution tribosystem model to a most ordered condition: * - = - = - = W W l N W T R i f i f dis adapt ln ln 1 ln 1 1 m m . (17) where energy of one mechanical quantum; and current and ultimate probabilities of tribosystems compatibility conditions. According to a model of quantum surface damping at friction in state of most complete evolution (adaptation) of elementary tribosystem all mechanical quantums with the exeption of one elasticity and reversibly transform energy of outer impact (mechanic movement). One mechanical quantum of radiation ( atoms) - is a minimum loss (essence of wearlessness or other wear primary standart). Linear size of quantum is equal to diameter of spherical ideal crystal with atomic roughness : . (18) Here mean atomic diameter for metals; parameter of state for mechanical quantum [3]. Mechanical quantum (Figure 4) can be examined as the elementary nanostructure of metal’s solid body. Calculations have shown [3] the number of such mechanical «quanta» (subtribosystems) within the elementary tribosystem’s volume to be , which is close to the safe number of fatigue cycles. mechanical quantum - minimum adaptive friction volume . Calculation assessment of parameter , done for various metals and steels gives an average value ((Table)); entalpy of melting. Table. Parameter for Metals and Steels [3] MPa MJ/ m 3 , A conclusion is made [3] that the number of atoms (mechanical quantum (MQ)) within volume of one elementary tribosystem (TS) in conditions of ideal tribosystem evolution is a constant value. Thus, it is possible to speak about the quantity of substance equal by mass to one elementary tribosystems and to one mechanic quantum. 6. Synergism of tribosystem and state optimum Mechanical quantum is dynamic oscillator of dissipative friction structure. An ideal quasielastic contact condition at its full evolution constitutes effect of most fully dissipated energy of outer mechanical movement throughout newly formed (by mechanism of selforganization) structural elements -mechanical quantums (dynamic oscillators) which most fully realize their rotationary - oscillatory behavior in relation to each other within elementary tribosystem volume. Their resistance to relative interaction here is minimally elastic and corresponds to elasticity of ideal atomic (thermodynamically balanced) interactions at the level of electron orbits. Universal constants of mechanical quantum and elementary tribosystem (material point) determine quantum model of surface damping: ; , (16) taking into account destruction quantums (nonreversible process component) and damping quantums (reversible, elastic component - fatique number), and also probability evolution tribosystem model to a most ordered condition: . (17) where energy of one mechanical quantum; and current and ultimate probabilities of tribosystems compatibility conditions. According to a model of quantum surface damping at friction in state of most complete evolution (adaptation) of elementary tribosystem all mechanical quantums with the exeption of one elasticity and reversibly transform energy of outer impact (mechanic movement). One mechanical quantum of radiation ( atoms) - is a minimum loss (essence of wearlessness or other wear primary standart). Linear size of quantum is equal to diameter of spherical ideal crystal with atomic roughness : nm d W D a MQ 177 , 7 ) ( 3 1 4 3 2 = × × × × = p . (18) Here mean atomic diameter for metals; parameter of state for mechanical quantum [3]. Mechanical quantum (Figure 4) can be examined as the elementary nanostructure of metal’s solid body. Calculations have shown [3] the number of such mechanical «quanta» (subtribosystems) within the elementary tribosystem’s volume to be , which is close to the safe number of fatigue cycles. Figure 4: Model of elementary nanostructure of friction (8103 atomic cubical cells) [7, 9, 10] tary tribosystem’s volume V * f = V * dis to be 0,63 ·10 8 , which is close to the safe number n * of fatigue cycles. In these terms (point 4) only one mechanical quantum [3, 10] is the lost - standard of wear. The tribosystem (friction contact) has the ideal damping properties - «wear free condition». The principle of mechanical quantum determines nanoquantum levels of all friction parameters of compatible tribosystems and other. 7 Self-organized nano-quantum solid lubricant Information above allows us to consider new self-organized surface layer as follows: 1. The layer that separates the two original surface (alloys) of friction from each other; 2. Layer, which has a low coefficient of internal friction; 3. Layer, which has a high capacity for work, i. e. very small wear; 4. Layer, which may be seen as a solid lubricant. Now you need to determine a value for the coefficient of friction of this self-organized solid lubricant and compare it with the coefficient of friction, for example, the most effective, or hydrodynamic lubrication. It is known that the hydrodynamic lubrication in the stationary condition (Figure 5) has coefficients of friction µ down to 0,005 ÷ 0,001 values. For nano-quantum self-organized solid lubricant friction coefficient will be calculated in the following order: 1. It is known [3] that between the nano-quantums the coefficient of friction is equal to µ MQ = 1,587 ·10 -8 . 2. It is known [11] that the size of the critical volume of frictional contact (elementary tribosystem) is equal to D TS = 2,85·10 -6 m. T+S_3_16 05.04.16 09: 01 Seite 11 12 Tribologie + Schmierungstechnik 63. Jahrgang 3/ 2016 3. Let’s picture an elementary tribosystem in the plane as a circle with a diameter of D TS = 2,85 mkm (Figure 6). 4. Next, let’s define the number of mechanical (nano) quantums n’ MQ on a length D TS of elementary tribosystem (Figure 6): 5. Let’s define the coefficient of friction for a single equilibrium critical volume of friction (elementary tribosystem), the length of which is 397 mechanical quantums (Figure 6). 6. Let’s take the average friction surface wavelength equal to L w : 1 ·10 -3 m. Now define a number of elementary tribosystems on this wave length (Figure 7) 7. Now define friction coefficient at a wavelength of friction surface As a result, we have a full conformity (Figure 8) of friction coefficient values for hydrodynamic lubrication - 0,005 ÷ 0,001 and solid lubricant - 0,0022. Thus, it is fair to talk about nano-quantum self-organized solid lubrication. Aus Wissenschaft und Forschung Figure 5: Notional scheme of hydrodynamic lubrication Figure 7: Notional scheme of friction on the wavelength, structured elementary tribosystems. At the surface friction wavelength is 351 elementary tribosystems Figure 8: Notional scheme of self-organized nanoquantum contact with unsteady hydrodynamic lubrication Figure 6: Conditional scheme for equilibrium elementary tribosystem, structured mechanical quantums. At length of this tribosystem there are 397 mechanical quantums. Figure 4 Model of elementary nanostructure of friction (8103 atomic cubical cells) [7,9,10] Calculations have shown [3] the number of such mechanical «quanta» (subtribosystems) within the elementary tribosystem’s volume to be , which is close to the safe number of fatigue cycles. In these terms (point 4) only one mechanical quantum [3,10] is the lost - standard wear. The tribosystem (friction contact) has the ideal damping properties - «wearlessness». The principle of mechanical quantum determines nanoquantum levels of all friction parameters of compatible tribosystems and other. 7. Selforganized nanoquantum solid lubricant Information above allows us to consider new selforganised surface layer as follows: 1. The layer that separates the two original surface (alloys) of friction from each other; 2. Layer, which has a low coefficient of internal friction; 3. Layer, which has a high capacity for work, i.e. very small wear; 4. Layer, which may be seen as a solid lubricant. Now you need to determine a value for the coefficient of friction of this self-organized solid lubricant and compare it with the coefficient of friction, for example, the most effective, or hydrodynamic lubrication. Figure 5. Notional scheme of hydrodynamic lubrication. It is known that the hydrodynamic lubrication when the stationary condition (Figure 5) has coefficients of friction down to values. For nanoquantum self-organized solid lubricant friction coefficient will be calculated in the following order: 1. It is known [3] that between the nanoquantums coefficient of friction is equal to . 2. It is known [11] that the size of the critical volume of frictional contact (elementary tribosystem) is equal to . 3. Let's picture an elementary tribosystem in the plane as a circle with a diameter of (Figure 6). Figure 6. Conditional scheme for equilibrium elementary tribosystem, structured mechanical quantums. At length of this tribosystem there are 397 mechanical quantums. 4. Next, let's define the number of mechanical (nano) quantums on a length of elementary tribosystem (Figure 6): 397 10 177 , 7 10 85 , 2 9 6 = × × = = ¢ - - MQ TS MQ D D n . 5. Let's define the coefficient of friction for a single equilibrium critical volume of friction (elementary tribosystem), the length of which is 397 mechanical quantums (Figure 6). . 6. Let's take the average friction surface wavelength equal to . Now define a number of elementary tribosystems on this wave length (Figure 7) . Figure 4 Model of elementary nanostructure of friction (8103 atomic cubical cells) [7,9,10] Calculations have shown [3] the number of such mechanical «quanta» (subtribosystems) within the elementary tribosystem’s volume to be , which is close to the safe number of fatigue cycles. In these terms (point 4) only one mechanical quantum [3,10] is the lost - standard wear. The tribosystem (friction contact) has the ideal damping properties - «wearlessness». The principle of mechanical quantum determines nanoquantum levels of all friction parameters of compatible tribosystems and other. 7. Selforganized nanoquantum solid lubricant Information above allows us to consider new selforganised surface layer as follows: 1. The layer that separates the two original surface (alloys) of friction from each other; 2. Layer, which has a low coefficient of internal friction; 3. Layer, which has a high capacity for work, i.e. very small wear; 4. Layer, which may be seen as a solid lubricant. Now you need to determine a value for the coefficient of friction of this self-organized solid lubricant and compare it with the coefficient of friction, for example, the most effective, or hydrodynamic lubrication. Figure 5. Notional scheme of hydrodynamic lubrication. It is known that the hydrodynamic lubrication when the stationary condition (Figure 5) has coefficients of friction down to values. For nanoquantum self-organized solid lubricant friction coefficient will be calculated in the following order: 1. It is known [3] that between the nanoquantums coefficient of friction is equal to . 2. It is known [11] that the size of the critical volume of frictional contact (elementary tribosystem) is equal to . 3. Let's picture an elementary tribosystem in the plane as a circle with a diameter of (Figure 6). Figure 6. Conditional scheme for equilibrium elementary tribosystem, structured mechanical quantums. At length of this tribosystem there are 397 mechanical quantums. 4. Next, let's define the number of mechanical (nano) quantums on a length of elementary tribosystem (Figure 6): . 5. Let's define the coefficient of friction for a single equilibrium critical volume of friction (elementary tribosystem), the length of which is 397 mechanical quantums (Figure 6). 5 8 10 63 , 0 397 10 587 , 1 - - × = × × = ¢ × = MQ MQ TS n m m . 6. Let's take the average friction surface wavelength equal to . Now define a number of elementary tribosystems on this wave length (Figure 7) . Figure 4 Model of elementary nanostructure of friction (8103 atomic cubical cells) [7,9,10] Calculations have shown [3] the number of such mechanical «quanta» (subtribosystems) within the elementary tribosystem’s volume to be , which is close to the safe number of fatigue cycles. In these terms (point 4) only one mechanical quantum [3,10] is the lost - standard wear. The tribosystem (friction contact) has the ideal damping properties - «wearlessness». The principle of mechanical quantum determines nanoquantum levels of all friction parameters of compatible tribosystems and other. 7. Selforganized nanoquantum solid lubricant Information above allows us to consider new selforganised surface layer as follows: 1. The layer that separates the two original surface (alloys) of friction from each other; 2. Layer, which has a low coefficient of internal friction; 3. Layer, which has a high capacity for work, i.e. very small wear; 4. Layer, which may be seen as a solid lubricant. Now you need to determine a value for the coefficient of friction of this self-organized solid lubricant and compare it with the coefficient of friction, for example, the most effective, or hydrodynamic lubrication. Figure 5. Notional scheme of hydrodynamic lubrication. It is known that the hydrodynamic lubrication when the stationary condition (Figure 5) has coefficients of friction down to values. For nanoquantum self-organized solid lubricant friction coefficient will be calculated in the following order: 1. It is known [3] that between the nanoquantums coefficient of friction is equal to . 2. It is known [11] that the size of the critical volume of frictional contact (elementary tribosystem) is equal to . 3. Let's picture an elementary tribosystem in the plane as a circle with a diameter of (Figure 6). Figure 6. Conditional scheme for equilibrium elementary tribosystem, structured mechanical quantums. At length of this tribosystem there are 397 mechanical quantums. 4. Next, let's define the number of mechanical (nano) quantums on a length of elementary tribosystem (Figure 6): . 5. Let's define the coefficient of friction for a single equilibrium critical volume of friction (elementary tribosystem), the length of which is 397 mechanical quantums (Figure 6). . 6. Let's take the average friction surface wavelength equal to . Now define a number of elementary tribosystems on this wave length (Figure 7) 351 10 85 , 2 10 1 6 3 = × × = = - - TS W TS D L n . Figure 7. Notional scheme of friction on the wavelength, structured elementary tribosystems. At the surface friction wavelength is 351 elementary tribosystems. 7. Now define friction coefficient at a wavelength of friction surface 0022 , 0 351 10 63 , 0 5 = × × = × = - TS TS W n m m . As a result, we have a full conformity (Figure 8) of friction coefficient values for hydrodynamic lubrication and solid lubricant - . Figure 8. Notional scheme of self-organized nanoquantum contact with unsteady hydrodynamic Lubrication Thus, it is fair to talk about nanoquantum self-organized solid lubrication. 8. Summary 8.1 Energy analysis of the friction process allows us to examine the friction process as the evolution process; 8.2 From the energy balance equations of friction follows that the evolution of tribosystem has an adaptivedissipative character. 8.3. The fuller evolution of tribosystem has symmetrical view the friction process is started and finished within elastic area. 8.4 Under fuller evolution of friction contact (elementary tribosystem) the unique nanostructure is formed; the basis of this structure is the mechanical (nano) quantum and the contact (material point of mechanics) consists of about such quantums. 8.5 We can examine the mechanical quantum as the least structural form of solid material body and the standard of wear. 8.6 All parameters of compatibility (optimal) friction have to be in quanta levels commensurable with the parameters of the one mechanical quantum. 8.7 Interaction between nanoquantums is nature the net elasticity. The value of the coefficient of friction between mechanical quantums has order . 8.8 Coefficient of friction surfaces formed most fully selforganized nano contacts can achieve the value of 0.0022. As a result, we have a full conformity of friction coefficient values for hydrodynamic lubrication and solid lubricant - . 8.9 Contact friction, structured mechanical quantums, should be regarded as a selforganized nanoquantum solid lubricant. Antifriction properties of such contact is adequate liquid properties of hydrodynamic lubrication. References [1] Fedorov S. V.: General Model of Friction. Trenie i Iznos 1 , vol. 14, no. 3: 1986 Page. 460-470. [2] Fedorov, S.: Method for the Energy Optimisation of Tribosystems. In: 9th International Tribology Colloquium, Esslingen. Germany. 11-13 January, 1994. Vol.2. Page. 9.3-1-10. [3] Fedorov S.V.: The Foundations of Triboergodynamics and Physico-Chemical Prerequisits of Compatibility Theory. Kaliningrad State Technical University Press [in Russian], Kaliningrad, 2003, Page. 416. [4] Fedorov V. V.: Thermodynamic Aspects of Strength and Fracture of Solid Bodies. Science [in Russian], Tashkent, 1979. Page 168. [5] Fedorov V. V.: Kinetics of Damage and Fracture of Solid Bodies. Science [in Russian], Tashkent, 1985. Page 186. [6] Fedorov, V.V.: Ergodynamic concept of failure. 1. Basic statements of the ergodynamics of deformed bodies. Criteria of failure ductility. Strength Of Materials (Translated from Russia), Vol. 23, no. 8: 1991. Page. 883-889. [7] Fedorov S.V.: Some Aspects of the Ergodynamics of Deformed Bodies and Triboergodynamics, Supplement to T+S_3_16 05.04.16 09: 01 Seite 12 Tribologie + Schmierungstechnik 63. Jahrgang 3/ 2016 8 Summary 8.1 Energy analysis of the friction process allows us to examine the friction process as the evolution process; 8.2 From the energy balance equations of friction follows that the evolution of tribosystem has an adaptive-dissipative character. 8.3. The fuller evolution of tribosystem has symmetrical view the friction process is started and finished within elastic area. 8.4 Under fuller evolution of friction contact (elementary tribosystem) the unique nanostructure is formed; the basis of this structure is the mechanical (nano) quantum and the contact (material point of mechanics) consists of about 0,63 ·10 8 such quantums. 8.5 We can examine the mechanical quantum as the least structural form of solid material body and the standard of wear. 8.6 All parameters of compatibility (optimal) friction have to be in quanta levels commensurable with the parameters of the one mechanical quantum. 8.7 Interaction between nano-quantums is in the nature the net elasticity. The value of the coefficient of friction between mechanical quantums has the order µ MQ = 1,587 ·10 -8 . 8.8 Coefficient of friction surfaces formed most fully self-organized nano contacts can achieve the value of 0.0022. As a result, we have a full conformity of friction coefficient values for hydrodynamic lubrication - 0,005 ÷ 0,001 and solid lubricant - 0,0022. 8.9 Contact friction, structured mechanical quantums, should be regarded as a self-organized nano-quantum solid lubricant. Antifriction properties of such contact is adequate liquid properties of hydrodynamic lubrication. References [1] Fedorov S. V.: General Model of Friction. Trenie i Iznos , vol. 14, no. 3: 1986, Page 460-470. [2] Fedorov, S.: Method for the Energy Optimisation of Tribosystems. In: 9th International Tribology Colloquium, Esslingen. Germany. 11-13 January, 1994. Vol.2., Page 9.3-1-10. [3] Fedorov S.V.: The Foundations of Triboergodynamics and Physico-Chemical Prerequisits of Compatibility Theory. Kaliningrad State Technical University Press [in Russian], Kaliningrad, 2003, Page 416. [4] Fedorov V. V.: Thermodynamic Aspects of Strength and Fracture of Solid Bodies. Science [in Russian], Tashkent, 1979, Page 168. [5] Fedorov V. V.: Kinetics of Damage and Fracture of Solid Bodies. Science [in Russian], Tashkent, 1985, Page 186. [6] Fedorov, V.V.: Ergodynamic concept of failure. 1. Basic statements of the ergodynamics of deformed bodies. Criteria of failure ductility. Strength Of Materials (Translated from Russia), Vol. 23, no. 8: 1991, Page 883-889. [7] Fedorov S.V.: Some Aspects of the Ergodynamics of Deformed Bodies and Triboergodynamics, Supplement to HANDBOOK. An Engineering Journal. [in Russian], no. 8: 2010, Page 28. [8] Fedorov S.V.: The Friction Coefficient and its Relation to the Contact Fatigue Characteristics of Materials. Industrial Laboratory. Translated From Zavodskaja Laboratorija. Vol. 61. no. 1: 1995, Page 41-49. [9] Fedorov, S. V.: The mechanical quantum of dissipative friction structures is the elementary tribonanostructure. In: IV WTC2009. Kyoto. Japan. 2009, Page 926. [10] Fedorov, S. V.: Generalized Energy Model of Sliding Friction Coefficient and Regularities of Tribosystem Evolution. In: Transactions of V World Tribology Congress 2013. Turino, Italy. 2013. ISBN 9788890818509. [11] Fedorov, S. V.: Calculation of the true friction volume. Friction & Lubrication in Machines and Mechanisms. No.5 2010, Page 3-7. 13 Aus Wissenschaft und Forschung Aktuelle Informationen über die Fachbücher zum Thema „Tribologie“ und über das Gesamtprogramm des expert verlags finden Sie im Internet unter www.expertverlag.de Anzeige T+S_3_16 05.04.16 09: 01 Seite 13