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An investigation on a flywheel is presented based on finite element modelling simulations for different geometries. The goal was to optimise the energy density (rotational energy-to-mass ratio) and, at the same time, the rotational energy of a flywheel rotor. The stress behaviour of flywheel rotors under the rotational speed at the maximum stress achievable by the flywheel was analysed. Under this condition, the energy density was obtained for the different geometries, as well as the rotational energy. The best energy density performance due to geometry was achieved with a flywheel rotor presenting a new Gaussian section, which is different from the known Laval disk shape. The best results using a single disk involved a rotational speed of nearly 279,000 rpm and a rotational energy density around 1584 kJ/kg (440 Wh/kg). These values still yielded low total energy; to increase its value, two or three rotors were added to the flywheel, which were analysed in regard to stability. In particular, the triple rotor energy density was ≈ 1550 kJ/kg (431 Wh/kg). As some instability was found in these rotors, a solution using reinforcement was developed to avoid such instabilities. The energy density of such a reinforced double rotor neared 1451 kJ/kg (403 Wh/kg), and the system achieved higher total energy. The material assumed for the devices was carbon fibre Hexcel UHM 12,000, a material kept constant throughout the simulations to allow comparison among the different geometries. [ABSTRACT FROM AUTHOR]