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Contact problems of thermoelasticity taking account of heat production

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Abstract

We give a survey of papers that discuss the mathematical statement and methods of solution of contact problems of thermoelasticity taking account of heat production due to frictional forces on the surface of contact.

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Literature cited

  1. V. M. Aleksandrov, “The contact problem taking account of wear caused by local smoothing,”Fiz. Khim. Mekh. Mater., No. 1, 111–124 (1986).

    Google Scholar 

  2. V. M. Aleksandrov, “The axisymmetric contact problem of wear by smoothing,”Izv. Akad. Nauk SSSR. Mekh. Tver. Tela, No. 6, 36–42 (1990).

    Google Scholar 

  3. V. M. Aleksandrov and G. K. Annakulova, “The contact problem of thermoelasticity taking account of wear and frictional heat production,”Trenie i Iznos,11, No. 1, 24–28 (1990).

    Google Scholar 

  4. V. M. Aleksandrov, V. A. Babeshko, A. V. Belokon', et al., “Computation of the thermoelastic contact pressures in a bearing with a polymer coating,” inContact Problems and their Engineering Applications [in Russian], NIIMash, Moscow (1969), pp. 214–226.

    Google Scholar 

  5. V. M. Aleksandrov and E. V. Kovalenko, “Methods of solving contact problems of thermoelasticity taking account of wear of interacting surfaces,”Zh. Prikl. Mat. Teor. Fiz., No. 3, 126–131 (1985).

    Google Scholar 

  6. G. K. Annakulova, “The thermoelastic contact problem of two interacting layers,” Preprint, VINITI, No. 7253-V89.

  7. S. M. Belotserkovskii and I. K. Lifanov,Numerical Methods in Singular Integral Equations [in Russian], Nauka, Moscow (1985).

    Google Scholar 

  8. O. B. Bogatin, V. A. Morov, and I. N. Cherskii,Foundations of the Computation of Polymer Friction Nodes [in Russian], Nauka, Novosibirsk (1983).

    Google Scholar 

  9. I. I. Borovich and Yu. A. Ustinov, “On certain results of the study of contact effects in polymer bearings,” in:Contact Problems and their Engineering Applications [in Russian], NIImash, Moscow (1969), pp. 193–199.

    Google Scholar 

  10. M. B. Generalov, B. A. Kudryavtsev, and V. Z. Parton, “The contact problem of thermoelasticity for rotating bodies,”Izv. Akad. Nauk SSSR. Mekh. Tver. Tela, No. 3, 46–52 (1976).

    Google Scholar 

  11. M. B. Generalov, B. A. Kudryavtsev, and V. Z. Parton, “The axisymmetric contact problem of thermoelasticity for a rotating finite die,”Izv. Akad. Nauk SSSR. Mekh. Tver. Tela, No. 6, 133–143 (1977).

    Google Scholar 

  12. D. V. Grilits'kii, “A system of singular integral equations for the two-dimensional contact problem of thermoelasticity with steady-state heat production on the regions of contact,”Visnik L 'viv Univ. Ser. Mekh.-Mat, No. 22, 29–34 (1984).

    Google Scholar 

  13. D. V. Grilits'kii and V. P. Baran, “On the statement of contact problems of thermoelasticity with nonideal thermal contact of bodies,”Visnik L'viv Univ. Ser. Mekh.-Mat., No. 27, 10–13 (1987).

    Google Scholar 

  14. D. V. Grilits'kii, V. P. Baran, and A. A. Evtushenko, “Problems of friction with heat emission for elastic cylindrical bodies,” in:Friction, Wear, and Lubricating Materials. Proceedings of the International Scientific Conference [in Russian], Tashkent, 22–26 May 1985, Academy of Sciences Press, Moscow (1985), Vol. 1, pp. 24–27.

    Google Scholar 

  15. D. V. Grilitskii and B. S. Okrepkii, “The axisymmetric thermoelastic contact problem of the pressure exerted on a layer by a rotating die,”Izv. Akad. Nauk SSSR. Mekh. Tver. Tela, No. 1, 22–30 (1984).

    Google Scholar 

  16. D. V. Grilits'kii and V. I. Pauk, “The contact problem for a thick rigid layer taking account of wear and heat production,”Fiz.-Khim. Mekh. Mater., No. 3, 78–83 (1989).

    Google Scholar 

  17. D. V. Grilits'kii and V. I. Pauk, “The two-dimensional thermoelastic problem for a layer taking account of roughness, heat production, and wear,” in:Final Session on Contemporary Problems of the Theory of Contact Interactions [in Russian], Armenian Academy of Sciences Press, Yerevan (1988), pp. 41–44.

    Google Scholar 

  18. D. V. Grilitskii and V. I. Pauk, “The contact thermoelastoplastic problem for a layer taking account of frictional heat production,”Trenie i Iznos,12, No. 2, 246–251 (1981).

    Google Scholar 

  19. V. G. Gromov, “Thermoviscoelastic deformations of a polymer bearing,” in:Contact Problems and their Engineering Applications [in Russian], NIImash (1969), pp. 227–233.

  20. A. A. Dmitriev, “The two-dimensional problem of the cutting temperature of metals,”Zh. Teor. Fiz.,21, No. 7, 832–841 (1951).

    Google Scholar 

  21. K. Johnson,Contact Mechanics, Cambridge University Press, New York (1985).

    Google Scholar 

  22. A. B. Efimov, Yu. N. Drozdov, A. I. Gasanov, et al., “Mathematical simulation of contact interaction in a cylindrical sliding bearing,”Trenie i Iznos,9, No. 2, 223–230 (1988).

    Google Scholar 

  23. A. B. Efimov, Yu. N. Drozdov, N. M. Naumov, et al., “Contact interaction in a cylindrical sliding bearing taking account of thermal deformations,”Trenie i Iznos,10, No. 3, 389–394 (1989).

    Google Scholar 

  24. M. V. Korovchinskii, “Local thermal contact with quasistationary heat production in a friction process,” in:The Theory of Friction and Wear [in Russian], Nauka, Moscow (1965), pp. 73–80.

    Google Scholar 

  25. M. V. Korovchinskii, “The two-dimensional contact problem of thermoelasticity with stationary heat production on the contact surface,” in:Contact Durability of Machine-tool Materials [in Russian], Nauka, Moscow (1964), pp. 2–27.

    Google Scholar 

  26. M. V. Korovchinskii, “Foundations of the theory of thermal contact under local friction,” in:Innovations in the Theory of Friction [in Russian], Nauka, Moscow (1966), Pt. 1, pp. 98–145.

    Google Scholar 

  27. M. V. Korovchinskii, “Foundations of the theory of thermal contact under local friction,” in:Problems of Friction and Lubrication [in Russian], Nauka, Moscow (1968), Pt. 2, pp. 5–72.

    Google Scholar 

  28. M. V. Korovchinskii, “Axisymmetric thermoelastic contact with frictional heat production,” in:Problems of Nonstationary Friction in Machinery, Equipment, and Apparatus [in Russian], Nauka, Moscow (1978), pp. 62–92.

    Google Scholar 

  29. M. V. Korovchinskii, “Thermoelastic local contact of high-loaded machine parts taking account of wear and frictional heat production,” Dissertation, Dr. Tekh. Nauk. Moscow (1983).

    Google Scholar 

  30. R. D. Kul'chitskii-Zhigailo, “The axisymmetric thermoelastic contact problem for rotating transversally isotropic bodies,” in:Proceedings of the 15th Scientific Conference of Young Scholars of the Institute of Mechanics of the Ukrainian Academy of Sciences [in Russian], Kiev (1990), Pt. 3, pp. 466–470.

  31. I. K. Lifanov and A. V. Saakyan, “Methods of numerical solution of the problem of pressing a moving die into an elastic half-plane taking account of heat production,”Prikl. Mat. Mekh.,46, No. 3, 494–501 (1982).

    Google Scholar 

  32. V. N. Maksimovich, Yu. N. Babei, P. B. Kratyuk, et al., “The two-dimensional thermoelastic contact problem taking account of heat production,”Fiz.-Khim. Mekh. Mater., No. 3, 76–81 (1986).

    Google Scholar 

  33. A. A. Merzlyakov and Yu. K. Mashkov, “Simulation of the thermal regime in a metal-polymer piston ring-cylinder tribosystem,”Trenie i Iznos,11, No. 3, 411–446 (1990).

    Google Scholar 

  34. V. A. Morov, A. Z. Ermolaeva, and A. S. Kondakov, “Diagrams of the thermoelastic states of cylindrical sliding bearings. 1. Analysis of the stationary solutions,”Trenie i Iznos,12, No. 6, 12–23 (1991).

    Google Scholar 

  35. B. S. Okrepkii and L. M. Tsebrii, “The axisymmetric thermoelastic contact problem of the pressure exerted on a layer by a rotating die taking account of the anisotropy of the materials,” Preprint. Ternopol' (1987), UkrNIITI, Uk-874.

  36. Ya. S. Pidstrigach, “Conditions of thermal contact of solid bodies,”Dop. Akad. Nauk Ukr. RSR, No. 7, 872–874 (1963).

    Google Scholar 

  37. Ya. S. Podstrigach, “The temperature field in a system of solid bodies coupled through a thin interface,”Inzh.-Fiz. Zh.,1, No. 10, 129–136 (1963).

    Google Scholar 

  38. A. Azarkhin and J. R. Barber, “Transient contact of two sliding half-planes with wear,”Trans. ASME. J. Tribology,109, No. 3, 598–603 (1987).

    Google Scholar 

  39. A. Azarkhin and J. R. Barber, “Transient thermoelastic contact problem of two sliding half-spaces,”Wear,102, No. 1–2, 1–13 (1985).

    Google Scholar 

  40. A. Azarkhin and J. R. Barber, “Thermoelastic instability for the transient contact problem of two sliding half-planes,”J. Appl. Mech. Sci.,53, No. 9, 565–572 (1985).

    Google Scholar 

  41. J. R. Barber, “Distribution of heat between sliding surfaces,”J. Mech. Eng. Sci.,9, No. 5, 351–354 (1967).

    Google Scholar 

  42. J. R. Barber, “The influence of thermal expansion on the friction and wear process,”Wear,10, No. 2, 155–159 (1967).

    Google Scholar 

  43. J. R. Barber, “Thermoelastic instabilities in the sliding of conforming solids,”Proc. Roy. Soc,A312, 381–394 (1969).

    Google Scholar 

  44. J. R. Barber, “The effect of thermal distortion on construction resistance,”Intern. J. Heat and Mass Transfer,14, No. 5, 751–766 (1971).

    Google Scholar 

  45. J. R. Barber, “Frictionally excited thermoelastic instabilities,”Wear,26, No. 3, 425–427 (1973).

    Google Scholar 

  46. J. R. Barber, “Thermoelastic contact of a rotating sphere and a half-space,”Wear,35, No. 1, 283–289 (1975).

    Google Scholar 

  47. J. R. Barber, “Some thermoelastic contact problems involving frictional heating,”Quart. J. Mech. Appl. Math.,29, No. 1, 1–13 (1976).

    Google Scholar 

  48. J. R. Barber, “The transient thermoelastic contact of a sphere sliding on a plane,”Wear,59, No. 1, 21–29 (1980).

    Google Scholar 

  49. J. R. Barber, “Stability of thermoelastic contact for the Aldo model,”Trans. ASME. J. Appl. Mech.,48, No. 3, 555–558 (1981).

    Google Scholar 

  50. J. R. Barber, “Stability of thermoelastic contact,”Proc. Inst. Mech. Eng.,2, No. 5, 981–986 (1987).

    Google Scholar 

  51. J. R. Barber and C. J. Martin-Moran, “Green's functions for transient thermoelastic contact problems for the half-plane,”Wear,79, No. 1, 11–19 (1982).

    Google Scholar 

  52. G. A. Berry and J. R. Barber, “The division of frictional heat—a guide to the nature of sliding contact,”Trans. ASME. J. Tribology,106, No. 2, 405–415 (1984).

    Google Scholar 

  53. J. L. Bishop and C. M. McCettles, “The seizure of journal bearings by thermoelastic mechanisms,”Wear,79, No. 1, 37–52 (1982).

    Google Scholar 

  54. R. A. Burton, “Thermal deformation in frictionally heated contact,”Wear,59, No. 2, 1–20 (1980).

    Google Scholar 

  55. R. A. Burton, “An axisymmetric contact patch configuration for two dies in frictionally heated contact,” in:Mechanics of Contact between Deformable Bodies, Delft University Press (1975), pp. 191–205.

  56. R. A. Burton, “Thermal aspects of bearing seizure,”Wear,8, No. 3, 157–172 (1965).

    Google Scholar 

  57. R. A. Burton and S. R. Heckmann, “The thermoelastic transition from line to point contact,”Wear,59, No. 1, 79–87 (1980).

    Google Scholar 

  58. R. A. Burton and V. Nerlikar, “Large disturbance solutions for initially flat frictionally heated thermoelastically deformed surfaces,”Trans. ASME. J. Lub. Tech.,97, No. 2, 546–551 (1975).

    Google Scholar 

  59. R. A. Burton and V. Nerlikar, “Clearing leakage and contact temperature in a thermoelastically deformed seal-like configuration,”Trans. ASME. J. Lub. Tech.,97, No. 2, 546–551 (1975).

    Google Scholar 

  60. R. A. Burton and V. Nerlikar, “Effect of initial surface curvature on frictionally excited thermoelastic phenomena,”Wear,27, No. 1, 195–207 (1974).

    Google Scholar 

  61. R. A. Burton, V. Nerlikar, and S. R. Kilaparti “Thermoelastic instability in a seal-like configuration,”Wear,27, No. 1, 177–188 (1974).

    Google Scholar 

  62. C. P. Chen and R. A. Burton, “Thermoelastic effect in brushes with high current and high sliding speed,”Wear,27, No. 1, 277–288 (1974).

    Google Scholar 

  63. T. A. Dow, “Thermoelastic effects in brakes,”Wear,27, No. 1, 213–221 (1974).

    Google Scholar 

  64. T. A. Dow, “Thermoelastic effects in a thin sliding seal-a review,”Wear,27, No. 1, 31–52 (1974).

    Google Scholar 

  65. T. A. Dow and R. A. Burton, “Thermoelastic instability of sliding contact in the absence of wear,”Wear,19, No. 2, 315–328 (1972).

    Google Scholar 

  66. T. A. Dow and R. A. Burton, “The role of wear in the initiation of thermoelastic instabilities of rubbing contact,”Trans. ASME. J. Lub. Tech.,95, No. 1, 71–75 (1973).

    Google Scholar 

  67. T. A. Dow and J. W. Kannel, “Thermomechanical effects in high current density electrical slip rings,”Trans. ASME. J. Lub. Tech.,79, No. 1, 93–105 (1982).

    Google Scholar 

  68. D. A. Hills and J. R. Barber, “Steady motion of an insulating rigid flat-ended punch over a thermally conducting half-plane,”Trans. ASME. J. Lub. Tech.,102, No. 1, 15–22 (1985).

    Google Scholar 

  69. D. A. Hills and J. R. Barber, “Steady sliding of a circular cylinder over a dissimilar thermally conducting half-plane,”Int. J. Mech. Sci.,28, No. 9, 613–622 (1986).

    Google Scholar 

  70. D. A. Hills, D. Dowell, and A. Sackdield, “The state of stress by cylindrical sliding contacts with frictional heating,”Int. J. Mech. Sci.,32, No. 9, 767–778 (1990).

    Google Scholar 

  71. J. H. Huang and F. D. Ju, “Thermomechanical cracking due to moving frictional loads,”Wear,102, No. 1, 81–84 (1985).

    Google Scholar 

  72. B. Gesim, “Transient hot spot temperatures at a sliding ceramic contact including surface coating effects,”Wear,123, No. 1, 59–76 (1988).

    Google Scholar 

  73. T. Coshima and L. M. Keer, “Thermoelastic contact between a rolling rigid indenter and damaged elastic body,”Trans. ASME. J. Tribology,112, No. 1, 382–391 (1990).

    Google Scholar 

  74. R. R. Johnson, T. A. Dow, and Y. Y. Zhang, “Thermoelastic instability in elliptic contact between two sliding surfaces,”Trans. ASME. J. Tribology,110, No. 1, 80–86 (1988).

    Google Scholar 

  75. F. D. Ju and J. R. Huang, “Heat checking in the contact zone of a bearing seal (a two-dimensional model of a single mowing asperity),”Wear,79, No. 1, 102–108 (1982).

    Google Scholar 

  76. J. W. Kannel and S. A. Barber, “Analysis of scuffing temperatures with considerations of wear,”Trans. ASME. J. Tribology,112, No. 1, 123–127 (1990).

    Google Scholar 

  77. J. W. Kannel and S. A. Barber, “Estimate of surface temperatures during rolling contact,”Trans. ASLE,32, No. 3, 305–310 (1989).

    Google Scholar 

  78. S. R. Kilaparti and R. A. Burton, “A moving hot-spot configuration for a seal-like geometry with frictional heating, expansion, and wear,”Trans. ALSE,20, No. 1, 64–70 (1977).

    Google Scholar 

  79. S. R. Kilaparti and R. A. Burton, “The thermoelastic path contact problem for large Peclet number,”Trans. ASME. J. Lub. Tech.,100, No. 1, 65–69 (1978).

    Google Scholar 

  80. S. R. Kilaparti and R. A. Burton, “Pressure distribution for patchlike contact in seals with frictional heating, thermal expansion, and wear,”Trans. ASME. J. Lub. Tech.,98, No. 3, 596–601 (1976).

    Google Scholar 

  81. F. F. Ling,Surface Mechanics, Wiley, New York (1973).

    Google Scholar 

  82. I. L. Maksimov, “Thermal instability of sliding and oscillations due to frictional heating effect,”Trans. ASME. J. Tribology,110, No. 1, 69–72 (1990).

    Google Scholar 

  83. J. P. Netzel, “Observations of thermoelastic instability in mechanical face seal,”Wear,59, No. 1, 139–148 (1980).

    Google Scholar 

  84. S. Oh, M. D. Bryant, and R. A. Burton, “The complete stress field produced by frictional heating of a thin conductor sliding against an insulator,”J. Thermal Stresses,6, No. 2–4, 307–321 (1983).

    Google Scholar 

  85. M. Wisniewski, “Temperatura tarcia w obszarach styku nierownosci powierzchni,”Trybologia, No. 1, 10–14 (1987).

    Google Scholar 

  86. M. Wisniewski, “Thermoelastical aspect of mixed frictional in concentrated contact,”Wear,111, No. 2, 259–274 (1986).

    Google Scholar 

  87. W. Y. D. Yuen, “Heat conduction in sliding solids,”Int. J. Heat and Mass Transfer,31, No. 3, 637–646 (1988).

    Google Scholar 

  88. W. Y. D. Yuen, “A new formulation of heat transfer between two moving bodies in contact over a finite region with different bulk temperatures,”Math. Eng. Ind.,1, No. 1, 1–19 (1987).

    Google Scholar 

  89. W. Y. D. Yuen, “On the heat transfer of moving composite strip compressed by two rotating cylinders.”Trans. ASME. J. Heat Transfer,107, No. 3, 541–548 (1985).

    Google Scholar 

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  1. D. V. Grilits'kii
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  2. O. O. Evtushenko
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Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 35, 1992, pp. 93–100.

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Grilits'kii, D.V., Evtushenko, O.O. Contact problems of thermoelasticity taking account of heat production. J Math Sci 67, 2904–2911 (1993). https://doi.org/10.1007/BF01095867

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