# Design and Multi-Objective Optimization of Fiber-Reinforced Polymer Composite Flywheel Rotors
## 6 Conclusions  
In this study, a multi-objective optimization strategy for multi-rim composite rotors was developed. Three objectives were optimized: energy capacity, specific costs and productivity. To examine the impact of manufacturing, the manufacturing process was analyzed. It consists of four production steps, of which curing the polymer composite is usually the most time-consuming and filament winding the most costly process. The examination of the manufacturing processes led to mathematical expressions for the manufacturing time and costs. With these formulas, the models for costs and productivity were created. An analytical stress calculation for multi-rim rotors was employed which also accounts for residual stresses and interference fits between adjacent rims. Since the compressive stresses occurring directly after press fitting may be higher than during operation, these load cases were considered separately. To safely predict rotor failure, three different failure criteria were considered simultaneously: Maximum Strength, Maximum Strain and the Tsai-Wu criterion.  
The multi-objective optimization, which returns optimal rim thicknesses, the optimal number of rims, the optimal material selection, the optimal speed considering a safety factor and the optimal interferences between each rims, was classified. Since the optimization problem was found to be subject to strongly non-linear constraints and to be discrete, a global optimization technique was used. Due to its beneficial performance for multi-objective optimization, the GA was chosen. Domain knowledge was applied by a local improvement to further increase the optimization performance, resulting in  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Name**} & \multirow{2}{*}{**Materials**} & **Total Cost** & \multicolumn{2}{c}{**Share of**} & **Energy** & **Productivity** & **Cost/Energy** \\  & & **[CAD]** & **Manufacturing Cost** & **[kWh]** & **[units/h]** & **[CAD/kWh]** \\ \hline ACME (1) & AL & 66 & 0\% & 0.09 & - & 720 \\ ACME (2) & AL,C,C,C,C & 1244 & 49\% & 0.46 & 0.04 & 2698 \\ ACME (3) & AL,A & 269 & 57\% & 0.13 & 0.37 & 2105 \\ Rosesta T2 (1) & AL & 706 & 0\% & 0.9 & - & 782 \\ Rosesta T2 (2) & AL,C,C & 5976 & 6\% & 2.96 & 0.12 & 2018 \\ Rosesta T2 (3) & AL,G & 995 & 16\% & 0.92 & 0.36 & 1079 \\ \hline \hline \end{tabular}
\end{table}
Table 9: Summary of case study results: Optimal material choice and objective values for different rotor designs. (1): lowest costs, (2): highest energy, (3): most cost-efficient composite rotor, AL: aluminum, A: aramid, C: carbon.  
a hybrid optimization strategy. The local improvement was realized by solving a non-linear but continuous sub-problem applying the SQP algorithm. The advantageous performance of the hybrid optimization algorithm was shown by comparing it to the pure GA.  
Further, case studies were presented to examine two existing rotor configurations of which one is available in academia and one in industry. The obtained results are similar to the existing solutions. The impact of manufacturing costs became smaller the larger the rotor volume or the more expensive the used materials are. Therefore, larger flywheels were more cost-efficient.