Consideration of wear in plane contact of rectangular punch and elastic half-plane

Authors

  • V. M. Onyshkevych Ukrainian National Forestry University, 79057, L’viv, General Chuprynka str., 103
  • G. T. Sulym Ivan Franko National University of L’viv, 79000, L’viv, Universytetska str., 1 https://orcid.org/0000-0003-2223-8645

DOI:

https://doi.org/10.17721/1812-5409.2019/1.31

Abstract

The plane contact problem on wear of elastic half-plane by a rigid punch has been considered. The punch moves with constant velocity. Arising thermal effects are neglected because the problem is investigated in stationary statement. In this case the crumpling of the nonhomogeneities of the surfaces and abrasion of half-plane take place. Out of the punch the surface of half-plane is free of load. The solution for problem of theory of elasticity is constructed by means of Fourier integral transformation. Contact stresses are found in Fourier series which coefficients satisfy the dual integral equations. It leads to the system of nonlinear algebraical equations for unknown coefficients by a method of collocations. This system is reduced to linear system in the partial most interesting cases for computing of maximum and minimum wear. The iterative scheme is considered for investigation of other nonlinear cases, for initial approximation the mean value of boundary cases is used. The evolutions of contact stresses, wear and abrasion in the time are given. For both last cases increase or invariable of vertical displacement correspondently is obtained. In the boundary cases coincidence of results with known is obtained.

Key words: contact, friction, wear.

Pages of the article in the issue: 138-141

Language of the article: Ukrainian

References

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KOROVCHINSKYI, M.V. (1971) Lokalnyi kontakt uprugih tel pri iznashivaniyi ih poverhnostey. Kontaktnoye vzaimodeystviye tverdyh tel i raschet sil treniya i iznosa eoryya reshetok. Moskva: Nauka.

ALEKSANDROV, V.M. (1983) O postanovke ploskih kontaktnyh zadach teoryi uprugosti pri iznose vzaimodeystvuyushchih tel. DAN SSSR. 271(4). p.827-831.

LEVYTSKYI, V.P. & ONYSHKEVYCH, V.M. (1993) Osesymetrychna kontaktna zadacha iz znoshuvannyam. Bulletin of Lviv University. Series: Mechanics & Mathematics. 38. p.60-63.

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

GAVRIKOV, M.V. & MAZING, R.I. (1988) Nasledstvenno-stareyushchaya model iznashivaniya i eyo primeneniye k zadacham s monotonno rastushchey zonoy kontakta. Treniye i iznos. 9(2). p.274-279.

No 1 (2019)

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How to Cite

Onyshkevych, V. M., & Sulym, G. T. (2019). Consideration of wear in plane contact of rectangular punch and elastic half-plane. Bulletin of Taras Shevchenko National University of Kyiv. Physical and Mathematical Sciences, (1), 138–141. https://doi.org/10.17721/1812-5409.2019/1.31

Issue

No. 1 (2019)

Section

Differential equations, mathematical physics and mechanics

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