## 5 Experimental Verification
### Experimental Results and Validation of Theoretical and Simulation Models  
Rigorous experimental validation confirms the remarkable accuracy of both theoretical and finite element models in predicting the electromagnetic loss mechanisms and thermal behavior of high-speed magnetic-field-modulated motors for flywheel energy storage systems. As shown in Figure 14a, total-loss validation across the entire speed range demonstrates strong agreement between analytical predictions, FEA simulations, and experimental measurements, with a mean absolute percentage error of only 4.2%. The experimental error band (\(\pm\)5%) encompasses most predicted values, confirming model credibility. At rated conditions, Figure 14b details the component-specific breakdown of losses into copper, core, and permanent magnet parts, revealing excellent agreement: 3.1% error for copper, 4.2% for core, and 6.8% for PM eddy-current losses compared to experimental results. Figure 14c further illustrates axial temperature distribution along the stator, with predicted temperature profiles closely matching measurements--maximum deviation limited to 5.8 \({}^{\circ}\)C--confirming hotspot prediction accuracy at both ends and center. Figure 14d validates the electromagnetic model's capability to capture harmonic behavior in the air-gap flux density, with a correlation coefficient of 0.967 between experimental and theoretical harmonic magnitudes, thus verifying precise implementation of the magnetic field modulation principle. Efficiency consistency across various load levels is demonstrated in Figure 14e, where deviations remain below 1.2 percentage points throughout the entire operating range, confirming the reliability of the model for optimization tasks. Figure 14: Experimental validation of theoretical and simulation models. Finally, Figure 14f shows transient thermal response behavior, in which the proposed modal-based prediction method achieves exceptional accuracy--temperature time constants deviate by only 7.3% compared to measured values--supporting the model's suitability for operational planning in vacuum-sealed environments. Together, these results comprehensively verify the integrated electromagnetic-thermal framework's predictive reliability and establish a robust basis for high-fidelity performance analysis and optimization in flywheel energy storage systems. This comprehensive validation establishes the reliability of the integrated multiphysics modeling framework, providing a solid foundation for optimizing high-speed magnetic field-modulated motors in flywheel energy storage applications. While the analytical and finite element models demonstrate remarkable agreement with experimental measurements, several factors contribute to the observed discrepancies in loss component prediction. The slightly higher deviation in permanent magnet eddy current losses (6.8%) compared to core and copper losses can be attributed to three primary factors. First, manufacturing tolerances in magnet positioning and segmentation create variations in flux paths not fully captured in the idealized simulation model, particularly affecting harmonic content at high frequencies. Second, the temperature-dependent properties of permanent magnet materials introduce additional complexity, as local temperature gradients during operation differ from the uniform temperature assumptions in the simulation, affecting both conductivity and magnetic properties. Third, the measurement methodology for isolating rotor losses relies on indirect calorimetric methods with inherent uncertainty margins of approximately \(\pm\)3%. For core losses, the deviation of 4.2% stems primarily from the simplified representation of material nonlinearity in the modified Bertotti model, particularly at the steep transition regions of the B-H curve where minor hysteresis loops occur during rapid field variations.