Hydrogen diffusion in rotating cylindrical elastic bodies

In this paper, we study the distribution of the hydrogen concentration in a rotating cylindrical elastic body compressed by two concentrated forces. This problem is relevant for diagnostics of bearing failure due to the influence of hydrogen on the mechanical properties of structures. During the study, the plane stress state of a loaded cylindrical elastic body is determined by means of the theory of functions of a complex variable. We used the transition to a rotating coordinate system to obtain the static problem of hydrogen diffusion in a body loaded by the known stresses. The solution of the problem includes the methods of asymptotic analysis for the simplification of partial differential equation, the expansion in a Fourier series and the Galerkin approach for finding the expansion coefficients for several harmonics. The results can be useful for calculating the hydrogen concentration distribution in roller bearings.