Analytical and numerical solution to the problem of hydrogen diffusion in rotating cylindrical elastic bodies

The work is devoted to the solution of the problem of hydrogen diffusion in rotating cylindrical elastic bodies compressed by two distributed loads. The study includes the analytical determination of the stress state of the body on the basis of known stresses from the Hertz contact problem, the derivation of the hydrogen diffusion equation in a rotating body in the found field of elastic stresses, and the numerical solution of the obtained hydrogen diffusion equation. The numerical solution of the diffusion equation was carried out by the method of finite differences. According to the numerical solution of the diffusion equation, the effect of hydrogen concentration localization near the outer boundary was detected. This result is consistent with experimental studies of the distribution of hydrogen concentration in roller bearings. This problem is important for diagnostics of failures of rolling bearings due to hydrogen embrittlement.