Augmented Lagrangian approach for multi-objective topology optimization of energy storage flywheels with local stress constraints

Flywheel energy storage systems (FESS) used in short-duration grid energy storage applications can help improve power quality, grid reliability, and robustness. Flywheels are mechanical devices that can store energy as the inertia of a rotating disk. The energy capacity of FESS rotors can be improved by choosing the optimal rotor geometry, operation conditions, rotor materials, and by tailoring the material properties. A multi-objective formulation is presented in this article to simultaneously improve the energy capacity and reduce the weight of energy storage flywheels using stress-constrained topology optimization to determine the material placement and optimize the stress distribution in the rotor. A Pareto-front of optimal solutions to the multi-objective problem demonstrates that the rotors with the best specific energy content have volume fractions of 55-65%. Local stress constraints with an Augmented Lagrangian formulation are introduced to improve the stress distribution and optimal design and are compared to designs obtained with global stress constraints based on P-norm aggregation approach. We show that designs with local stress constraints have a more uniform stress distribution and fewer stress concentrations compared to stress using P-norm.