Copyright © 2022 V.V. Aulin, A.V. Hrynkiv, S.V. Lysenko, O.M. Livitskyi This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Problems of Tribology, V. 27, No 1/103-2022,82-91 Problems of Tribology Website: http://tribology.khnu.km.ua/index.php/ProbTrib E-mail: tribosenator@gmail.com DOI: https://doi.org/10.31891/2079-1372-2022-103-1-82-91 Substantiation of conditions of effective working capacity of tribocouples of the details made of polymeric composite materials with high-modulus fillers V.V. Aulin*, A.V. Hrynkiv, S.V. Lysenko, O.M. Livitskyi Central Ukrainian National Technical University, Ukraine *E-mail: AulinVV@gmail.com Received: 25 February 2022: Revised: 10 March 2022: Accept: 29 March 2022 Abstract This work is devoted to the study of the conditions of effective performance of triad couplings of parts made of polymeric composite materials. The stress state of the material is associated with the characteristics of the accumulation of dislocations, the energy of activation of their movement. The average stress, friction stress is determined. Based on this, expressions for estimating critical stresses and loads on tribocouple parts are obtained. The distribution of the force on the tribocoupling of parts is determined taking into account the quality characteristics of the friction surfaces, modulus of elasticity and Poisson's constant of the components of the polymer composite material. This problem is considered for tribocouples of parts of various kinds. Expressions for calculation of nominal pressures at different types of contact of material of details of tribocoupling are received, and also the equations on which it is possible to estimate in them values of nominal critical pressure are resulted. The conditions for efficient operation of tribocoupling of parts made of polymer composite materials are clarified. It is determined that a significant increase in the nominal critical pressure on the tribocoupling is possible with the use of high-modulus fillers, the modulus of elasticity of which is greater than the modulus of elasticity of the polymer matrix. Key words: polymer composite material, macroheterophase material, high modulus filler, tribocoupling of parts, matrix, filler, stress field, elastic contact, critical pressure, nominal pressure Introduction The efficiency of using tribocouples of parts made of macroheterophase polymer composite materials depends on the content of the filler, its size, shape, nature and tribological properties of the structural components of the composite material and the strength of the bond between them. Today there is no single theory of reliability and efficiency of tribotechnical polymer composites and methods of substantiation of their optimal composition and structure. Existing methods for predicting the composition and structure of composites cover some cases due to practical application, but they do not take into account different types of contacts, the presence of an elastic component, which is achieved during the correct running of parts and critical pressure on the triad. There is also no criterion by which it is possible to assess a degree of efficiency of the triad couplings of systems and units of machines, parts of which are made of polymeric composite materials with high-modulus fillers. Literature review The use of tribocoupling of parts made of polymeric composite materials (PCM) has shown their effectiveness in increasing the durability of systems and units of machines [1-3]. However, there is a problem of optimizing the composition of polymer composites from the content of fillers, the distribution of stress fields in the polymer matrix, the geometric shape and concentration of the filler and the development of methods for http://creativecommons.org/licenses/by/3.0/ http://tribology.khnu.km.ua/index.php/ProbTrib https://doi.org/10.31891/2079-1372-2022-103-1-82-91 Problems of Tribology 83 evaluating the efficiency and reliability of such tribocouples [4,5]. Specific features of the work of PCM with a macroheterogeneous structure necessitate the analysis of the stress-strain state (SSS), which occurs under load conditions during operation [6-8] by friction forces. There is a need to take into account different types of triangular parts and different types of contacts of their work surfaces. The same amount of deformation of the components of PCM can lead to brittle destruction of one component, to viscous – the second component and tired – the third component [7]. The strength characteristics of each of the components of the PCM are decisive. Research on SSS of surface layers reinforced with PCM [8] revealed the need to take into account the interaction of neighboring contour and actual contacts in the process of sliding friction. In the scientific literature, this issue is insufficiently studied and not all types of wear in the conjugation of machine parts are considered [9,10]. PCM chipping and exfoliation processes should also be considered. Note that in the implementation of such performance properties of materials as their wear resistance, the task is complicated by the significant dependence of stresses on the volume ratio of components, their size, shape, as well as design features of conjugate parts and properties of working (technological) environment. The authors of [11-14] the main cause of destructive processes in the surface layers of PCM is SSS, which occurs as a result of contact stresses and deformations under the influence of loads on the tribocoupling of parts. This leads to a detailed study of the features in the surface layers of the materials of the tribocouples of parts. The study of the peculiarities of PCM in the process of functioning of three-part couplings allows to approach unsolved problems from a single position. The use of physical and mathematical models [7,8] is appropriate, and VAT estimates are carried out by load distribution in different types of contact by polarization- optical and other methods [9]. Attempts to compare the wear resistance and SSS of the surface layers of PCM made in [11]. According to research conducted in [15], there is a need for relaxation of local maximum stresses in the surface layers of tribocouple parts. It was found that with increasing volumetric content and filler size, the intensity of wear of parts decreases. However, the influence of these factors on the value of the maximum tangential stresses in the PCM is not sufficiently clarified [4,16]. The connection between the wear process of PCM and their mechanical properties is given in [6, 17]. The results of wear resistance studies of PCM with homogeneous and heterogeneous structure show that in the first case it is lower than in the second due to faster equalization of contact pressure. The phenomenon of spontaneous installation and maintenance of the stationary mode of wear of PCM is also revealed. This is due to the existence of feedback. Based on the ideal conditions of sliding contact, in [5] with the help of friction surface models, tribotechnical characteristics of PCM with different structure and different composition were calculated. The current results of research [4-6] do not allow to fully assess the effectiveness of the triad coupling of parts and the nature and amount of wear. There is a need to connect them with the types of contacts and the conditions of contact. It was found that in the operation of tribocouples of parts, elastic and plastic deformation of their materials are the main processes that initiate the emergence and development of physical, chemical and mechanical processes in the surface layers of PCM [17]. It is shown that in the PCM the main part of the load is received by the filler. Reinforcing fillers prevent the movement of dislocations in the matrix, which is subject to plastic deformation, limiting it [3]. Strengthening of PCM is carried out by increasing the content of the filler and reducing the distance between its particles. In [9] it was found that depending on the structural state of the PCM, the magnitude of the accumulated plastic deformation is not the same, which causes a different course of relaxation processes. The type and dispersion of filler particles (carbides, borides, oxides, intermetallics) in the polymer matrix, which are barriers to plastic deformation, significantly affect the inhibition of the relaxation process, but it is not known how the degree of dispersion of the filler affects the properties of PCM, filler – for stress relaxation, wear process and efficiency of triboconjugation of parts in general. Purpose The aim of this work is to identify the conditions for the effective operation of various truboconjugations of parts made of macroheterophase polymer composite materials with high modulus filler, taking into account different types of contact. Results Using different combinations of PCM, regarding the variation of high-modulus fillers in the polymer matrix, it is possible from a macroscopic point of view to ensure the predominant presence on the friction surfaces of parts of one or another type of contacts. Analytical methods for estimating the optimal structure of such PCM have not yet been developed. To determine the allowable force in heavy-duty tribocouples of parts made of macroheterophase PCM, one of the efficiency indicators can be the critical pressure, the value of which is estimated at the beginning of plastic deformation, brittle fracture or setting of friction surfaces. This uses the fact that in macroheterophase PCM the nature of deformation and fracture is similar to the nature of deformation and fracture of single-phase materials. It is quite clear. that in tribocouples of parts made of materials of macroheterophase structure, the contacts of the two surfaces of polymeric materials are the least effective. These materials should be used in reinforced 84 Problems of Tribology form and provide such structures and composition that the share of space occupied by the contacts of two plastic materials was minimal, and with high-modulus fillers – maximum. The quantitative efficiency of different types of contacts can be assessed by assuming that the main mechanism of setting of PCM materials is the formation of a common degree on the surface of physical contact. In this case, the stress created by the accumulation of dislocations in the area of the sources of dislocations, which is located beyond the contact boundary at a distance l, is:   dsffl ll / 2 1   , (1) where f – friction stress; sl – length of the sliding strip; dl – distance to the cluster of dislocations. If with increasing current voltage the value  reaches the value l at which the source of dislocations begins to work, we can assume that  l , cr  , where  is the average voltage; cr – critical value of voltage. In this case, the value of the critical voltage is equal to: 2/12/1 212                           s d f s d cr l l l l  , (2) where  f ; sd ll  . The value of the average voltage can be determined from the equation:  ТkU V Тkb b bd 3/exp 3 0 2/1           , (3) where db – constant, characterizing the degree of deformation, 0.2%, of this material;  – the rate of relative deformation of the material; V – activation volume; bk – became Boltzmann; T – absolute temperature; 0U – dislocation motion activation energy. Similar to equation (3), the amount of friction stress is determined:  ТkU V Тkb b f f b f d f 3/exp 3 0 2/1             . (4) Given expressions (3) and (4) in equation (2), we obtain:    ТkU V Тkb l l ТkU V Тkb l l b f f b f d s d b bd s d кр 3/exp 3 213/exp 3 2 0 2/12/1 0 2/12/1                                           , (5) Taking the critical load crР proportional cr , we have:                                                    ТkU V Тkb l l ТkU V Тkb l l CCР b f f b f d s d b bd s d ucrucr 3/exp 3 213/exp 3 2 0 2/12/1 0 2/12/1    , (6) where uC – is the coefficient that takes into account the shape and size of the contact irregularities of the working surfaces of the parts. The lack of data on the values of uC , dl , db , f db , 0U , f U 0 does not allow to determine the specific value of the critical load crР for a given triad of parts. From equation (16) it follows that the value crР of is greater the greater the energy of motion of dislocations 0U and f U 0 . Analysis of the influence of the structure and phase composition of PCM on the quality parameters of friction surfaces showed that when contacting tribocouples of parts made of macroheterophase composites, it is possible to provide the required share of friction surface area. In this case, you should use the laws of contact established for tribocoupling of the first kind, when single-phase material is in contact with single-phase. At the same time, the presence on the friction surface of areas with different composition of contact materials leads to a redistribution of contact pressures between contacts of different types. This causes a change in the critical load on the triad coupling of parts, and hence the coefficient of friction and wear resistance. It is found that while ensuring the process of minimal wear and stabilization of the friction force, it is necessary to create such conditions when in the process of operation of tribocouples of parts on their friction surfaces an elastic contact is realized. Note that in the simplified calculation of the triad of parts with PCM in the first approximation, the following is taken into account: – materials of tribocouples of the corresponding details consist of matrices M1 and M2 and fillers iН1 and jН2 ; – the number of fillers in the material of the first part is i, and in the second – j; – all parts of the total friction surface are real in triad conjugation; – the structure of the PKM and the mutual orientation of the details of the triad coupling ensure the Problems of Tribology 85 independence of the fraction of the area occupied by one type of contact from their displacement along the direction of friction; – the relative volume content of the filler in the surface layer of the parts is constant, the effect of their self-lubrication is absent, and secondary structures are not formed. In the case of flat surfaces, with a nominal contour area of contact, the proportion of the area occupied by a particular type of contact is found by the expressions:                                                               .,1;,1; ;1 ;1 ;11 21 2 1 2 2 1 1 1 2 1 1 21 2 21 21 mjnijiHH j m j jММ j n i iММ m j j n i iММ ji ij j     (7) We assume that the nominal area of the entire friction surface is equal to aA . The area occupied by contacts of the corresponding type (their nominal area) can be determined by multiplying the components of the system of equations (7) by aA . Since the friction surfaces of the parts conjugations are pressed by the force N, the different types of contacts account for the forces: 21 MM N  , jHM N 21  , jHMN 22  , ji HH N 21  . The equilibrium condition of the friction surfaces in the General case has the form: NNMNN m j n i HH n i HM m j HMMM jiij          1 111 21122221 . (8) Equation (8) makes it possible to obtain the equilibrium condition for any particular case of tribocontact with PCM material. For example, if both triad coupling parts are made of matrix single-phase materials M1 and M2, respectively, then 21 MM N  = N. In the case of contact of single-phase material M1 with multiphase М2 + jН2 , the equilibrium condition will look like: NNN m j HMMM j    1 2121 . (9) When estimating the forces 21 MM N  , jHM N 21 , jHM N 22  and ji HH N 21  , assume that the micro- irregularities on the friction surfaces are deformed elastically and are located on a rigid base. There is no mutual influence of conjugate surfaces of parts, as the contact of nominally flat surfaces is considered. Convergence of friction surfaces under the action of force N in this case can be determined from the equation:             cc cc cc accccccccccc ccccccfpc AbEEq EERRkN a                              23 2 2121 21 2 12 2 21maxmax ; 2 5 4 113 21 , (10) where cN – the force acting on the contacts; c R 1max , c R 2max – the maximum height of the irregularities in the contact areas of the surfaces of the first and second parts of the tribocoupling; cb , c – parameters of the reference curve of the equivalent surface; c1 , c2 , cE1 , cE2 , c1 , c2 – respectively, the radii of curvature of the vertices of micro-inequalities, the modulus of elasticity of Jung and the Poisson's ratios of the materials of the first and second parts of the tribocouple; c , fpk – coefficients that depend on the shape of the protrusions;        cc  ; 2 5 – beta function; cq – the number of protrusions per unit area of the equivalent surface; c – the proportion of the friction surface area in the corresponding types of contacts of expression (7) c; aA – nominal area of friction. Note that the number of equations of the form (10) is equal to the number of types of contacts in this triad of parts. Using the equilibrium condition (8) and expression (10), we can trace the influence of the phase composition of the PCM on the amount of pressure that develops in the contacts of each type under the total force N. For clarity, it is convenient 86 Problems of Tribology – single-phase material М1 is in contact with the second, (or the same М1) single-phase М2; – single-phase material М1 is in contact with multiphase М2 + jН2 ; – multiphase material М1 + iH1 is in contact with multiphase М2 + jH2 . During the operation of tribocouples of parts of the first kind, the external force N is balanced by the forces on the contacts M1 - M2, ie NN MM  21 . Dividing this equality by the nominal area of friction Aa, we obtain that in this case the pressure 21 MM P  is equal to the nominal pressure Ра. To eliminate the adhesion of materials in the tribocouple of this kind, it is necessary to reduce the force N until Pa is below the critical pressure 21 MM cr P  determined for the contact of the matrix M1 with the matrix M2 or experimentally by equation crucr CР  . During the operation of the tribocoupling of the second kind, the pressure in the contacts of different types in the general case should be different. To estimate it, it is necessary to use the equilibrium condition (9) and the equation of the form (10). Solving the system of equations of the form (10), giving values jHM N 21  through 21 MM N  and substituting them in equation (9), we can calculate the forces at the contacts of types M1 - M2 and M1 - jH2 . Analytically, a system consisting of expressions (9) and (j + 1) expressions of type (10) cannot be solved. However, using the appropriate experimental data, it is easy to do with application packages on a PC. If the tribocoupling of parts of the second kind and the composite consists of a matrix of M2 and j fillers, then solving the system of equations (9) and (j + 1) equations of type (4), find the forces at the contacts M1 - M2 and M1 - jH2 by the formulas:                    m j j jj m j j MM z z x x N N 1 2 1 2 1 1 1 1 21   ; (11)                         m j j jj jj m j jj HM z z zxzx zxN N j 1 2 2 2 1 1111 1 21    , (12) where 1 2 M M E E x  ; 1 2 M Н j E E z j  . (13) If PCM jHM 22  consists of two phases, j = 1; ij 12   , the equation of the form (10) has the form:                                           23 2 21 22 max ; 2 5 12 1123 21 221221 aMM MMMMфMM AbEEq EERkN а , (14) or                                         23 2 21 22 max ; 2 5 2 1123 21 1 21 21 21211 aHM HMMHфHM AbEEq EERkN а . (15) For two-phase PCM, based on formulas (12) and (13), we have:            2122 21 22 111 11 2 21 11 21 21 211221 211        MHMMH HMMMMMM HM EEE EEEN N . (16) Solving equations (16) and (9), we find:                   21222122 22 21 11111 111 2 21 11 2121 212 21 11 21 2 21      MHMMHHMMMM HMMHM MM EEEEEE EEEN N ; (17) Problems of Tribology 87                 21222122 22 21 11111 11 2 21 11 2121 212 21122 211       MHMMHHMMMM MMMMM HM EEEEEE EEEN N . (18) To calculate the nominal pressures in the considered types of contact, we accept: a a P A N  ; 12 MM xEE  ; 111 1 MH EZE  ; 2111 MMH   . Taking into account equation (7), we have the following formulas:        aaMM P ZxZx Zx PP 1 211211 1 111 1 21       ; (19)        aaHM P ZxZx xZ PP 2 211211 1 111 1 211        . (20) Analysis of expressions (19) and (20) shows that the triad coupling of parts with PCM will work effectively under the condition: 2121 MM crMM PP   and 211 211 HM crHM PP    , for the matrix M1 and filler 21H . Given the conditions for the existence of contacts of type М1 - М2 and M1 - 21H , equation (19) should be used at 0 ≤ 21 < 1, and equation (20) – at 0 < 21 ≤ 1. The use of PCM in the details of tribocouples of the second kind is appropriate in the following cases: х = Z1; Zl > х. In the first case, the nominal pressures in the contacts of different types do not depend on the content of the filler and are equal to the nominal pressure Pa, the limit value of which should be below 21 ММ cr P  and І НМ cr P 21  . For this filler, the force N on the tribocouple cannot be increased, because the pressure 21 ММ Р  will exceed the allowable pressure. It is determined that the use of high-modulus filler is appropriate if you can change the coefficient of friction in the contact of the filler from one of the matrices, which will be lower than the coefficient of friction in the contact М1 - М2. In the second case, when Z1 > х, the filler can be introduced only in the matrix that has in contact with the filler less critical pressure Pcr. If such a matrix is M2. Then, when introducing a filler with Z1 > х into this matrix, the value 1 < 1 and the voltage at the most dangerous contacts М1 - М2 can be reduced several times, which will increase the nominal force N acting on the tribocouples of parts. If in one of the details of the tribocoupling of the second kind to enter j – fillers, the feasibility of this procedure is determined by the same conditions as when introducing one filler (х = Zi і Zj > х). However, so that the pressure on them does not exceed the critical value when increasing N, you need to control a larger number of types of contacts. In order to simplify the previous expressions, we accept: 12 Мм хЕЕ  ; 1 2 MiН EzЕ j  ; 1 1 MiH EyE i  ; ij HHMM 12 21   and solving together equations (8) and (10), we express the forces on the contacts of different types through a set of data: N; х; Zj; Yj; ³1 ; j2 . Then we have:                                                                                        , 1 ; 1 11 ; 1 11 ; 11 21 2 1 1 1 21 1 2 1 1 21 21 12 21         j jiji HH j j n i ij HM i m j jii HM m j j n i i MM zy xzy N Z zx NN y yx NN x NN ji j i (21)         . 1 1 1 1111 1 1 1 2 1 1 1 2 1 2 1 1 1 2 1 1                                                          n i ji ii j m j j n i i ji m j j m j j jj n i i m j j n i i zy y z y y z z xx       (22) 88 Problems of Tribology Dividing equation (19) by the area of the surface occupied by contacts of different types, and accepting a a P A N  , we obtain expressions for calculating the pressure at the corresponding contacts:             . 1 ; 1 1 ; 1 1 ; 2112 21 21 Qzy zyx PP Qy yx PP Qz zx PP Q x PP ji ji aHH i i aHM j j aHMaMM jii j            (23) Experimental studies have shown that the tribocoupling of parts will be able to work if the pressure on the contacts of different types of this type does not exceed the critical value for its constituent materials tribocoupling of parts. Using equations (19), (20) and (23), we can quantify the dependence of the critical load on the tribocoupling of parts on the composition and tribological properties of structural components. As a criterion for the effectiveness of the filler in PCM, we take the ratio of the nominal critical pressure Pa cr in the triad of parts made of PCM to the nominal critical pressure ММcr Р  of the triad of parts made of the same matrix material. Assuming that in equations (19) and (20) ММcrММ РР   21 , a ММ НМ crcr РР     211 , the value of the nominal critical pressure for tribocoupling of parts of the second kind can be found by equations: 21 ;     ММММ cr crа cr crа Р Р Р Р   . (24) The calculation of Pa cr tribocouples of parts must be performed on both equations. The smaller of the two obtained values of Pa cr and will represent the limit value of Pa cr on the triad, one of the parts of which is made of PCM. We present equation (24) in the form: 1   ММcr crа Р Р ; (25) 2   ММcr crа Р Р . (26) A smaller value ММcr cr Р P  of the ratio can be taken as the value of the criterion of the effectiveness of the filler for a given critical load. It was found that the introduction of a high-modulus filler in a polymer matrix with a smaller modulus of elasticity 2121 5 ММj crНМ РР    can significantly increase the value of Pa cr tribocoupling of parts, but not higher 211 НМ cr Р  . In tribocouples of parts of the third kind, when two PCM are in contact with the macroheterophase structure, the criterion of filler efficiency ММcr crа Р Р  is selected by the minimum value of the ratio ММcr crа Р P  calculated for the contacts М-М, М-Н and Н-Н. If a matrix and a filler with different modulus of elasticity are used in triad couplings of parts with such a combination of contact types, the contacts made of materials with a smaller modulus of elasticity will be underloaded and the criterion value ММcr crа Р Р  will be lower. When Ен = 10Ем and 2121 5 ММj crНМ РР    , the criterion 4 8,0           Н ММcr crа Р Р  . This value, although lower ММcr crа Р Р  , with the same modulus of elasticity of the matrix and filler, but higher than in layered PCM with other combinations of contact types. Conclusions 1. The field of stresses in tribocouples of parts made of polymer-composite materials is considered, taking into account the properties of friction surfaces. It is revealed that the critical pressure in the tribocouples of parts is determined primarily by the energy of motion of dislocations in the surface layers of their materials. 2. It was found that to ensure the process of minimal wear in the triad of parts of polymer-composite Problems of Tribology 89 materials should create conditions when in the process of their operation are realized elastic contacts. For the case of flat conjugate surfaces of details the basic requirements are formulated, expressions for a share of the areas occupied by this or that contact of the details made of polymeric composite materials are received. 3. Efforts on different types of contacts of tribocouples of details taking into account the modulus of elasticity and Poisson's constant of matrix materials and fillers, share of the areas occupied by this or that type of contact are considered, and also nominal pressures in them are defined. 4. It is shown that the efficiency of tribocouples made of polymer-composite materials should be evaluated by the critical pressures at the contact surfaces of parts. 5. It is determined that for the manufacture of both antifriction and friction polymer composite materials it is more effective to use fillers whose modulus of elasticity is greater than the matrix. In order to increase the strength of the parts, it is advisable to use tribocoupling of parts of the third kind, and in terms of saving filler – the second kind. References 1. Aulin V.V., Derkach O.D., Makarenko D.O., Hrynkiv A.V. (2018) Vplyv rezhymiv ekspluatatsii na znoshuvannia detalei, vyhotovlenykh z polimerno-kompozytnoho materialu [Problems of tribology. №4] – S.65- 69. 2. Aulin V.V., Derkach O.D., Hrynkiv A.V., Makarenko D.O. (2021) Vyznachennia robochoi temperatury kompozytnykh elementiv rukhomykh ziednan v zoni tertia [Naukovyi visnyk Tavriiskoho derzhavnoho ahrotekhnolohichnoho universytetu: elektronne naukove fakhove vydannia - Vyp. 11, tom 1, stattia21]. 3. Aulin V.V., Hrynkiv A.V., Smal V.V., Lysenko S.V. ta in. (2021). Basic approaches and requirements for the design of tribological polymer composite materials with high-modulus fillers [Problems of Tribology, V. 26, No 4/102-2021] P.51-60. 4. Aulin V., Derkach O., Makarenko D., Hrynkiv A. ta in. (2019). Analysis of tribological efficiency of movable junctions "polymeric-composite materials – steel" [Eastern-European Journal of Enterprise Technologies. Vol. 4 (12-100)] - P. 6-15. 5. Aulin V.V., Derkach O.D., Kabat O.S., Makarenko D.O., Hrynkiv A.V., Krutous D.I. (2020). Application of polymer composites in the design of agricultural machines for tillage [Problems of Tribology, V. 25, No 2/96-2020] - P.49-58 6. Aulin V., Kobets A., Derkach O., Makarenko D., Hrynkiv A. ta in. (2020). Design of mated parts using polymeric materials with enhanced tribotechnical characteristics [Eastern-European Journal of Enterprise Technologies. Vol.5 (12-107)] - P. 49-57. 7. Aulin V.V. (2006). Pole napruzhen v kompozytsiinomu materiali ta kompozytsiinomu pokrytti v umovakh tertia kovzannia [Zb. nauk. prats LNAU. Seriia: Tekhnichni nauky. №.65(88)] S.13-20. 8. Aulin V.V. (2008). Vyznachennia obiemnoho vmistu napovniuvacha v antyfryktsiinomu kompozytsiinomu pokrytti [Mashynoznavstvo. №7(85)] S. 49-53. 9. Aulin V.V. (2006). Vplyv kharakterystyk komponentiv kontaktuiuchykh kompozytsiinykh materialiv i pokryttiv na parametry ta vlastyvosti zony tertia [Problems of tribology. №4 (42)] S. 110-112. 10. Bondarenko V.P. (1987). Tribotehnicheskie kompozityi s vyisokomodulnyimi napolnitelyami. [K.: Nauk. dumka] 232 s. 11. Aulin V.V. (2015). Trybofizychni osnovy pidvyshchennia znosostiikosti detalei ta robochykh orhaniv silskohospodarskoi tekhniky [dys. ... d-ra tekhn. nauk: 05.02.04] 360 s. 12. Aulin V.V., Brutskyi O.P. (2015). Pro dotsilnist vykorystannia polimernykh kompozytsii z nanonapovniuvachiv pry vidnovliuvanni ta vyhotovlenni resursovyznachalnykh detalei SHT. [Problemy konstruiuvannia, vyrobnytstva ta ekspluatatsii s.-h. tekhniky: materialy. Kirovohrad: KNTU] S.138-140. 13. Aulin V.V., Brutskyi O.P., Lysenko S.V. (2015). Doslidzhennia zakonomirnostei protsesiv tertia ta znoshuvannia v metalopolimernykh trybosystemakh. [Trybolohiia, enerho- ta resursozberezhennia: zb. tez. Mykolaiv: Vyd-vo ChDU im. Petra Mohyly] S.3-4. 14. Aulin V.V., Derkach O.D., Makarenko D.O., Hrynkiv A.V. (2018). Vplyv rezhymiv ekspluatatsii na znoshuvannia detalei, vyhotovlenykh z polimerno-kompozytnoho materialu [Problemy trybolohii. №4] S.65-69. 15. Sorokov S. (2003). Klasternyi pidkhid do rozrakhunku fizychnykh kharakterystyk kompozytnykh materialiv [Lviv: In-t fizyky kondens. system NANU] 23 s. 16. Aulin V.V., Kuzyk O.V. (2014). Dynamichne materialoznavstvo zon tertia detalei silskohospodarskoi tekhniky [Visnyk ZhNAEU: nauk.-teor. zbir. № 2(45), t.4, ch.II] S. 102-110. 17. Aulin V., Derkach O., Makarenko D., Hrynkiv A. et al. (2020). Krutous D., Muranov E. Development of a system for diagnosing bearing assemblies with polymer parts during operation [Technology audit and production reserves. № 5/1(55)] рр.18-20. 90 Problems of Tribology Аулін В.В., Гриньків А.В., Лисенко С.В., Лівіцький О.М. Обґрунтування умов ефективної працездатності трибоспряжень деталей, виготовлених з полімерних композитних матеріалів з високомодульними наповнювачами Дана робота присвячена дослідженню умов ефективної працездатності трибоспряжень деталей, виготовлених з полімерних композитних матеріалів. Напружений стан матеріалу пов'язано з характеристиками скупчення дислокацій, енергією активації їх руху. Визначено усереднене напруження, напруження тертя. На основі цього отримано вирази для оцінки критичних напружень та навантаження на трибоспряження деталей. Визначено розподіл зусилля на трибоспряження деталей з врахуванням характеристик якості поверхонь тертя, модулів пружності та сталої Пуассона компонентів полімерного композитного матеріалу. Цю задачу розглянуто для трибоспряжень деталей різного роду. Отримано вирази для розрахунку номінальних тисків у різних типів контакту матеріалу деталей трибоспряження, а також наведені рівняння, за якими можливо оцінити в них значення номінального критичного тиску. З'ясовано умови ефективного функціонування трибоспряження деталей з полімерокомпозитних матеріалів. Визначено, що значне підвищення номінального критичного тиску на трибоспряження можливе використанням високомодульних наповнювачів, модуль пружності матеріалу яких більший за модуль пружності полімерної матриці. Ключові слова: полімерний композитний матеріал, макрогетерофазний матеріал, високомодульний наповнювач, трибоспряження деталей, матриця, наповнювач, поле напружень, пружний контакт, критичний тиск, номінальний тиск