Optimum design of thick-walled composite rings for an energy storage system

An optimum design has been performed to maximize the specific energy density (SED) of a composite flywheel rotor for an energy storage system. The flywheel rotor consists of multiple rings, and the interferences and ply angles vary in the radial direction. For the structural analysis the rotor is assumed to be an axisymmetric thick laminated shell with a plane strain state. Considering the ring-by-ring variation of fiber orientations, a symmetric local stiffness matrix was derived for each ring. Using the stiffness matrix, the continuity conditions of radial stresses and displacements between the rings with a consideration of the interferences can be easily incorporated. A symmetric global stiffness matrix is then obtained assembling the local stiffness matrices. Displacements are obtained by solving the global stiffness matrix, and the stresses in each ring are then calculated. Three-dimensional intra-laminar quadratic Tsai-Wu criterion for the strength analysis is used yielding the strength ratio for each ring. The optimization has been also performed maximizing the kinetic energy stored in the rotor. For that purpose the sensitivities of the strength ratios and displacements with respect to the design variables have been derived. As a result, the optimal design has attained 2.4 times of total energy compared to the case of 0 degree ply angle and no interference. The effects of interferences are found to be much more considerable than those of fiber orientations.