# Design and Multi-Objective Optimization of Fiber-Reinforced Polymer Composite Flywheel Rotors  
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FESS allow a very high number of charge/discharge cycles resulting in a useful lifetime of greater than 20 years. Further, FESS have a low environmental impact and the state of charge can be easily monitored. FESS excel in uninterruptible power supply (UPS) applications and electrical grid frequency regulation due to their high reliability, fast response and high-cycle charge-discharge capabilities [5; 7]. On the other hand, less experience with this technology and higher costs currently impede the application of FESS in other fields [8]. Finding a cost-efficient design for FESS is therefore crucial to make them more attractive to a wider range of applications.  
The flywheel rotor is the determining factor for the energy capacity as well as the typically most cost-intensive component. Dimensions and material choices for FESS rotors vary significantly depending on the application. Small rotors made of lightweight materials such as fiber-reinforced polymer composites having a mass in the order of a few tens kilograms can typically be found in mobility applications such as hybrid and electric vehicles, including energy recovery systems for some race cars. On the upper end, steel FESS rotors with mass in the order of tens of metric tons exist as stationary systems for the short-term energy supply for very high peak-power applications [7]. Flywheel rotors for various applications have been modeled and optimized in previous works [9; 10; 11; 12; 13; 14]. Considering fiber-reinforced polymer composite rotors, optimization models were restricted by circumferential stresses and radial stresses in the rotor. To determine whether the rotor will fail, failure criteria--such as the Maximum Strength, Maximum Strain or the Tsai-Wu criterion--were introduced. To increase the energy density of the flywheel, multi-rim rotors are often considered. Since the circumferential stresses are at their highest level at the outermost rim, it would be useful to employ high strength materials such as unidirectional carbon fiber polymer composites that are filament-wound to form the outer rim geometry. For the inner rims lower strength materials with lower cost are usually sufficient, such as glass or aamid fiber composites, because stresses are comparatively low. Please note that rims may also be made of isotropic materials such as metals. Therefore, cost efficiency will increase as expensive materials are not employed in each rim. Further, flywheel rotors may also fail due to radial stresses since these act transverse to circumferentially oriented fibers. Assembling the rims into a rotor via press fit improves the stress distribution due to residual compressive radial stresses [15]. One of the first analytical methods to calculate the rotor stresses was published in [9]. This model also considered interference between adjacent rims caused by press fits. The model was later supplemented by the consideration of residual stresses due to the curing process [10; 14], and a split-type hub [16]. Besides the analytical methods, there are also numerical methods to calculate the stresses [12; 13]. Numerical models using the finite element method can determine results with greater accuracy especially for complex geometries. However, these methods cause higher computation time, which is a significant disadvantage for optimization problems. Irrespective of the modeling approach, the design space for multi-rim rotors is significant and the challenge for optimization strategies is not only finding optimal design parameters, such as the number of rims, the rim thicknesses, the size of interference fits and the material selection, but also providing guidance to the designer by elucidating suitable designs within the design space.