23rd International Colloquium Tribology - January 2022 81 Theoretical And Computational Estimation Of The Value Of The Coefficient Of Friction Of The Synovial Fluid Of Human Joints Sergey Vasiliy Fedorov Kaliningrad State Technical University, Kaliningrad, Russia, fedorov@klgtu.ru 1. Introduction The principle of natural (living) and constructed machines and tribosystems is discussed. Machine tribosystems as machine subsystems possess basic functional meaning of objects transformation movement (energy) inside machine. So machine is taken as supertribosystem. Energy scheme of tribopair (Figure 1) has 1, 2 tribosurfaces and 3 third (compatible) body. Figure 1: Schematic view of friction’s contact (elementary tribosystem) in energy interpretation [1]. Friction process is analyzed as a global phenomenon of energy transformation and dissipation from the triboergodynamics [1-3] point of view. Regularities of structural-energy evolution of friction contact (tribosystem) demonstrate (Figure 2) that the friction process itself in the area of compatibility of rubbing surfaces (machine friction) is characterized by two friction coefficients - adaptive (Amontons) µ adapt and dissipative µ dis : . (1) Here ; ; V f is the deformable (friction) volume; V adapt -adaptive and V dis dissipative friction volumes; µ-friction coefficient; N normal load; h i , l f linear sizes of elementary contact. The latent (potential), accumulated energy density ∆u e of defects of structure is an integral parameter of tribostate and damageability (failure ( )). The dynamic dissipated energy density is an integral parameter of tribostate too and capacity for work. Here . Figure 2: Structural-energy diagram for evolution of rubbing surfaces [1-3]. Entropy interpretation of friction coefficients These friction coefficients have entropy interpreting: . (2) Here S U configuration entropy of friction (contact) volume; - inertia entropy of compatible friction volume (entropy of dissipative structures); S * critical entropy of elementary tribosystem (friction volume). Both these friction coefficients are probability parameters of tribosystem state. Adaptive friction coefficient - is parameter of resistance to movement and damage of volume contact probability: . (3) Dissipative friction coefficient - is a parameter of facilitating to movement and capacity for work of contact volume (elementary tribosystem) probability: . (4) 82 23rd International Colloquium Tribology - January 2022 Theoretical And Computational Estimation Of The Value Of The Coefficient Of Friction Of The Synovial Fluid Of Human Joints 2. The rule of natural machine (mechanism) Additive entropy principle of supertribosystem as an entropy sum of its subsystems - tribosystems is discussed. The rule of natural machine as a total sum of adaptive friction coefficients of its tribosystems which is equaled to unit is formulated. . (5) The generalized friction coefficients of natural machine as a natural supertribosystem are suggested. The most characteristic equation of natural machine as natural supertribosystem has the form: (6) (7) (8) , (9) Here ; ; the generalized friction coefficients of natural machine as a natural supertribosystem; n MACH number of machines or the degree of complexity. Quantitative row (Table 1) of possible natural tribosystems (adaptive and dissipative friction coefficients) forming natural machine, i.e. natural supertribosystem is constructed. Table 1: Quantitative row of possible tribosystems (adaptive and dissipative friction coefficients) forming natural machine (mechanism). 0,5 0,5 2 0,25 0,75 4 0,2 0,8 5 0,1 0,9 10 0,05 0,95 20 0,04 0,96 25 0,025 0,975 40 0,02 0,980 50 0,01 0,990 100 0,005 0,995 200 0,004 0,996 250 0,0025 0.9975 400 0,002 0,998 500 0,001 0,999 1000 0,0005 0,9995 2000 0,0004 0,9996 2500 0,00025 0,99975 4000 0,0002… 0,9998… 5000… 3. Synovia friction coefficient of natural machines To check the calculated set of living machines (Table 1) it is necessary to study living machines, e.g. structural, kinematic schemes of man and horse. These structural kinematic schemes are skeletons of man and horse. The basis of these skeletons for kinematic couples: links - bones and tribopairs - joint hinges. According to information [4,5] human skeleton is composed of 270 bones in the early age and of 220 bones in mature age. The horse skeleton is composed of 252 bones. As it is seen this number of links (n mach ) in these living machines correspond to a calculated set of natural machines with the machine number n mach =250. This result allows to assess the value of friction coefficient of synovial liquid of joint hinges of living organisms (machines). From Table 1 we have for n mach =250 the value of adaptive friction coefficient equal to µ adapt =0,004. This value should be taken for synovia friction coefficient. Modern tribology treats this level of friction coefficient as the level of superlubrication [6]. 23rd International Colloquium Tribology - January 2022 83 Theoretical And Computational Estimation Of The Value Of The Coefficient Of Friction Of The Synovial Fluid Of Human Joints Thus, the friction in live machines has the most optimal, i.e. the ideal level. The physical model of the behavior of synovial lubrication [7] can be represented by the essence of self-organizing processes during friction [8]. References [1] Fedorov, S.V., “Energy Balance of Friction and Friction Coefficient in Energetical Interpretation”, Tribology in Industry, 37, 3, 2015, 380-389. [2] Fedorov, S.V., “Nano-Structural Standard of Friction and Wear”, Tribology in Industry, 40, 2, 2018, 225-238. [3] Fedorov, S.V., “Friction Energy Balance Regularities And Tribology’s Nano-Structural Standard”, COMADEM, 23, 1, 2020, 13-30. [4] “Skeleton. Great Soviet Encyclopaedia” [in Russian], Vol. 23, Soviet Encyclopaedia, Moscow, 1976. [5] “Horse Skeleton”, available at: http: / / www.horseof-ream.vsau.ru/ inter/ bone.html [6] Erdemir A, Martin J.-M., Luo J., “Superlubricity”, Elsevier, 2020, Paperback ISBN: 9780444643131 [7] Chikama, H., “The Role of the Protein and the Hualuronic Acid in the Synovial Fluid in Animal Joint Lubrication”, J. Jpn. Orthop. Ass. - 1985 (59) №5, 559-572. [8] Fedorov, S., “Selforganized Nano-quantum Solid Lubricant”, Tribologue + Schmierungstechnik, 63, 3 2016, 5-13.