FEM Analysis of Stress Distribution in Force-Balanced Coils

Distributions of stress in force-balanced coils (FBCs) for the superconducting magnetic energy storage (SMES) are analyzed numerically by a finite element method (FEM). Recently, we had developed the FBC concept using the virial theorem, and derived the winding pitch of helical coils as a function of a coil aspect, where a distribution of stress is nearly uniform and working stress is minimized. Coils with the winding pitch were named as FBCs with the virial-limit condition or simply virial-limit coils (VLC), and their excellent characters of stress were confirmed by experiments of a two-layered helical coil which can simulate arbitrary winding pitch numbers. Measurements of distributions of stress on the winding form of the coil proved that a minimum working stress and uniform stress were achieved under the VLC condition. In this work, stress distributions in FBCs with a monolithic winding form were investigated by FEM, and the results by FEM were compared with the experiments and the analytic solutions of a two-dimensional ideal shell model. Although the shell model could not explain the experimental results, qualitative agreements between FEM and the experiment were obtained.