Вплив міжповерхневих рідинних містків на контактну взаємодію тіл з хвилястим рельєфом

• Date: 2018
• Main Authors: Козачок, Олег, Слободян, Богдан, Мартиняк, Ростислав
• Format: Article
• Language: Ukrainian
• Published: Інститут прикладних проблем механіки і математики ім. Я. С. Підстригача НАН України 2018
• Subjects: контактна взаємодія; хвилястий рельєф; міжповерхневі зазори; нестислива рідина; поверхневий натяг; сингулярне інтегральне рівняння
• Online Access: https://www.fmmit.lviv.ua/index.php/fmmit/article/view/39
• Journal Title: Physico-mathematical modeling and informational technologies

The frictional contact between two semi-infinite elastic bodies, one of which has a wavy surface, isconsidered for the case when there are an incompressible liquid wetting the surfaces of the bodiesat the edges of the intersurface gaps and a gas under constant pressure in the central parts of thegaps. Due to the surface tension of the liquid, a pressure drop occurs in the liquid and the gas,which is described by the Laplace formula. The formulated contact problem is reduced to asingular integral equation (SIE) with the Hilbert kernel, which is transformed into a SIE with theCauchy kernel for a derivative of a heigth of the gaps. A system of transcendental equations forwidths of gaps and regions with the gas is obtained from the condition of boundedness of the SIEsolution at the integration interval ends and the condition of liquid’s amount conservation, andthen it is solved numerically. The dependences of the width and shape of the gaps, the width of theregions with the gas, the contact approach of the bodies on the applied load and the surfacetension of the liquid are analyzed.