Stress constrained topology optimization of energy storage flywheels using a specific energy formulation

Vaishnavi Kale, Niels Aage, Marc Secanell*

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review


A variable density, stress-constrained topology optimization approach is used, along with the solid isotropic material with penalization (SIMP) power law and a P-norm aggregated global stress measure to optimize the rotor of a flywheel energy storage systems (FESS). A new specific energy maximization optimization formulation is proposed which eliminates the need to impose an arbitrary volume fraction constraint to the optimization problem as it is done in traditional kinetic energy maximization approaches. The FESS rotors obtained with the specific energy formulation achieved a 15.8% increase in the specific energy compared to the kinetic energy based approach which improved the specific energy by 12.8%. Factors such as the operating speed, maximum stress, rotational symmetry and rotor material also influence the moment of inertia and stress distribution in the flywheel, and the effects of these parameters on the optimal topology and its energy capacity are investigated. At low speeds, the topology is seen to have elongated holes, which become rounded and move away from central shaft as the speed is increased. The reverse effect is seen when the upper limit on the stress constraint is increased. While the choice of rotor material affects the kinetic energy and mass of the flywheel, its optimal topology and specific energy is seen to be nearly identical for rotor materials with the same [Formula presented] ratio, and slightly different for other cases. The size of the circular sections used as the topology design domain is seen to affect the number of spokes in the rotor, but the overall specific energy is unaffected, so manufacturing considerations can be used to choose the rotational symmetry of the rotor. Due to the frequent charge–discharge cycles associated with short term storage, both centrifugal and acceleration forces might play an important role in determining the peak stresses in the flywheel. Therefore, the influence of acceleration loads on the optimal rotor topology is also studied and shown to only have an impact for very large instantaneous accelerations of 5235.9 rad/s2 or higher.

Original languageEnglish
Article number106733
JournalJournal of Energy Storage
Number of pages21
Publication statusPublished - 2023


  • Flywheel energy storage
  • Rotor design
  • Specific energy
  • Stress-constrained topology optimization


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