on the energy storage capacity and design optimization of compound flywheel rotors with prestressed hyperbolic disks

Flywheels used for energy storage may be assembled by press fitting or bonding of concentric rotor parts. during operation, each part is subjected to a superposition of stress fields associated with centrifugal loading and with contact at the component interfaces. to capture the highest overall energy storage capacity, design properties must be selected to achieve the maximum moment of inertia, subject to constraints on the stress occurring within each part at the maximum operating speed. this paper proposes a mathematical formulation for parametric shape optimization problems which can be used to design a multi-disk flywheel rotor to maximize the energy storage capacity. it is shown that the energy storage function for each part of the flywheel can be expressed as a product of two fundamental shape-factors: one that accounts for the stress distribution and the other accounts for the mass distribution. these factors are expressed analytically for cases involving hyperbolic disks, leading to a finite dimension shape optimization problem for a multi-disk rotor. case studies are presented based on the derived analytical solutions that show how the theory can be usefully applied in flywheel design optimization problems. the results from the case study show significant improvements in specific energy compared to previous research results. this advancement is particularly relevant to develop high-performance, cost-effective flywheel systems, offering potential for widespread application in energy storage technologies.