title: ÐÐ½Ð°Ð»Ð¸ÑÐ¸ÑÐµÑÐºÐ¾Ðµ Ð¸ ÑÐ¸ÑÐ»ÐµÐ½Ð½Ð¾Ðµ ÑÐµÑÐµÐ½Ð¸Ðµ Ð·Ð°Ð´Ð°ÑÐ¸ Ð¾ Ð´Ð¸ÑÑÑÐ·Ð¸Ð¸ Ð²Ð¾Ð´Ð¾ÑÐ¾Ð´Ð° Ð²Ð¾ Ð²ÑÐ°ÑÐ°ÑÑÐ¸Ñ ÑÑ ÑÐ¸Ð»Ð¸Ð½Ð´ÑÐ¸ÑÐµÑÐºÐ¸Ñ ÑÐ¿ÑÑÐ³Ð¸Ñ ÑÐµÐ»Ð°Ñ
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¼Ð°Ð³Ð¸ÑÑÑÐ°
titleType: Subtitle
title: Analytical and numerical solution of the problem of hydrogen diffusion in rotating cylindrical elastic bodies
Creators: name: ÐÐ°Ð»ÑÑÑÐ´Ð¸Ð½Ð¾Ð²Ð°, ÐÐ»Ð¸Ñ
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2022
Subjects: ÐÐ¸ÑÑÑÐ·Ð¸Ñ
ÐÐ¾Ð´Ð¾ÑÐ¾Ð´
ÐÐ¾Ð´ÑÐ¸Ð¿Ð½Ð¸ÐºÐ¸ ÐºÐ°ÑÐµÐ½Ð¸Ñ
Ð½Ð°Ð¿ÑÑÐ¶ÐµÐ½Ð½Ð¾Ðµ ÑÐ¾ÑÑÐ¾ÑÐ½Ð¸Ðµ
ÑÑÐ´ Ð¤ÑÑÑÐµ
ÑÐµÐ½ÑÑÐ¾Ð±ÐµÐ¶Ð½ÑÐµ ÑÐ¸Ð»Ñ
stress state
Fourier series
centrifugal forces

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description: The subject of the graduate qualification work is âAnalytical and numerical solution of the problem of hydrogen diffusion in rotating cylindrical elastic bodiesâ. The given work is devoted to the solution of the problem of hydrogen diffusion in a rotating cylindrical elastic body compressed by two distributed loads. The study included finding the stress state of the body, obtaining the hydrogen diffusion equation in a rotating elastic cylindrical body in the field of elastic stresses, numerical solution of the hydrogen diffusion equation and analyzing the stress state of the body taking into account the influence of centrifugal forces. The determination of the stress state of the body was carried out on the basis of known stresses from the Hertz contact problem of the compression of two cylinders. The means of the theory of functions of a complex variable was used. And approximating methods were used to obtain an approximate analytical expression for average normal stresses. The numerical solution of the diffusion equation was carried out by the finite difference method, and the tridiagonal matrix algorithm was used to solve the problem.In this research, the stress field in the body loaded with distributed forces was obtained, as well as in the case of loading the body with concentrated forces taking into account the influence of the centrifugal forces. The numerical solution of the diffusion equation showed the effect of localization of hydrogen concentration near the outer boundary. This result is consistent with experiments and physical concepts of the distribution of hydrogen concentration in rolling elements of bearings. This problem is important for diagnosing failures of rolling bearings due to hydrogen embrittlement.