# Frictional heating of system punch-elastic half plane when sliding along creative line

## Authors

• V. M. Onyshkevych Ukrainian National Forestry University, L’viv https://orcid.org/0000-0002-4657-5462
• G. M. Barabash Ivan Franko National University of L’viv

## Keywords:

contact, friction, heating, thermal conductance

## Abstract

Friction heating of system punch-elastic half plane when sliding along creative line is considered. Model of so-called “third body”, i.e., thin near-surface and intermediate layers, the physical and mechanical properties of which differ from those of the interacting bodies, and by the microgeometry of their surfaces in the contact zone, used for mathematical description of contact. The method of determination of thermal contact conductance in mathematical modelling of contact interaction with considering friction and hear generation by “third body” is presented. Using of modified conditions of heat contact in mathematical model of contact thermoelasticity, taking into account of friction and heat generation is proposed. The solution of the problem of thermoelasticity for a half-plane is obtained by means of the Fourier integral transformation. Heat conductivity problem for the punch is solved by method of straight lines. The system obtained of dual integral equations is reduced to the system of linear algebraic equations by means of points collocation method. Formulas for thermal fields, heat fluxes and contact stresses are proposed. In order to obtain the unknown contact area, the iterative scheme based on a control of a sign of normal stresses in the immediate contact interaction zones is used. Method of moving line of separation of boundary conditions is proposed.

Pages of the article in the issue: 140 - 143

Language of the article: Ukrainian

## References

COMNINOU, M., BARBER, J. R. & DUNDURS, J. (1981) Heat conduction through flat punch. J. Appl. Mech. 48. pp. 871–874.

SHVEC, R. N. & MARTYNIAK, R. M. (1988) Termouprugoye kontaktnoye vzaimodejstviye tel pri nalichii poverhnostnyh teplofizicheskih neodnorodnostey. Mat. metody i fiz.-meh. polia. 27. p. 23-28.

ONYSHKEVYCH, V. M. & BARABASH, G. M. (2021) Modeliuvannya kontaktnoyi vzayemodii “tretim tilom” u trybologichnyh zadachah. Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics & Mathematics. 3. p. 85-88.

LEVYTSKYI, V.P. & ONYSHKEVYCH, V.M. (1999) Doslidjennya vplyvu vlastyvostey “tretiogo tila” na teploutvorennia vid tertia. Mat. metody ta fiz.-meh. polia. 42(1). p. 82-86.

ONYSHKEVYCH, V. M. & SULYM, G. T. (2017) Zadacha pro termopruzhnyi kontakt pivploshchyny z priamokutnym shtampom za teploutvorennia vid tertia. Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics & Mathematics. 3. p.165-168.

2023-12-23

## How to Cite

Onyshkevych, V. M., & Barabash, G. M. (2023). Frictional heating of system punch-elastic half plane when sliding along creative line. Bulletin of Taras Shevchenko National University of Kyiv. Physical and Mathematical Sciences, (2), 140–143. https://doi.org/10.17721/1812-5409.2023/2.23

## Section

Differential equations, mathematical physics and mechanics