Optimum design of multi-ring composite flywheel rotor using a modified generalized plane strain assumption

Abstract

A numerical method for calculating the stress and strength ratio distribution of the hybrid rim-type composite flywheel rotor is presented with a consideration of the thermally induced residual stresses. The axisymmetric rotor is divided into several rings and the stiffness matrix for each ring is derived by solving the radial equilibrium equation and the stress–strain–temperature relations. The ring stiffness matrices are assembled into a symmetric global matrix satisfying the continuity equations at each interface with the assumptions of a modified generalized plane strain (MGPS). In the MGPS, the z-directional axial strains are assumed to vary linearly along the radial direction; ε z = ε 0+ ε 1 r. The conditions that the z-directional force and the circumferential moment resultants vanish are thus used to solve the z-directional axial strains as well as the radial and circumferential strains. After solving the strain distributions, the on-axis stresses and the strength ratios are calculated at each ring. Three-dimensional finite element method (3D FEM) is then used to verify the accuracy of the present method. The results are also compared with those based on the assumption of a plane stress (PSS). In this case, the analysis of MGPS better matches with 3D FEM results than PSS. An optimum design is then performed maximizing total stored energy (TSE) with the thickness of each composite rim as design variables. The optimal design obtained in this study, which considers material sequence, provides a more effective way of maximizing TSE. It is found that the consideration of the residual stress in the design of the hybrid flywheel rotor is crucial. The result of the optimal designs shows that TSE with consideration of Δ T reduces by about 30%.