A method for calculating surface mechanical stresses in axisymmetric magnetic systems

A method is proposed for calculating the mechanical stresses of magnetic and current systems calculated from the energy density of a uniformly magnetized cylinder. Volume-average demagnetizing factor of the cylinder $\bar N_z$ is introduced for the calculation, which is proportional to the ratio of cylinder diameter $2a$ to its length $h$. It is shown that demagnetization energy $E_p$, which is negligible for a “long” cylinder with $2a/h\ll1$ $(\bar N_z\approx0)$, becomes decisive in the formation of stresses at $\bar N_z\le0.5$. Radial $\sigma_r$ and axial $\sigma_z$ stresses are investigated in a wide range of variation of the ratio $2a/h$.