## 4 Results and Discussion
### Viscoelastic Behavior
#### 4.2.2 Case 2
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **Phase** & **Day 1** & **Day 90** & **Day 180** & **Day 270** & **Day 365** \\ \hline Peak interface pressure & \(\omega_{\rm{Pmin}}\) & \(-41.04\) & \(-39.26\) & \(-39.03\) & \(-38.90\) & \(-38.80\) \\
[MPa] & \(\omega_{\rm{Pint}}\) & \(-38.76\) & \(-36.49\) & \(-36.17\) & \(-35.98\) & \(-35.84\) \\  & \(\omega_{\rm{Pmax}}\) & \(-34.78\) & \(-31.54\) & \(-31.05\) & \(-30.77\) & \(-30.55\) \\ \hline Peak radial tensile stress in CFRP rim & \(\omega_{\rm{Pmin}}\) & \(0.0\) & \(0.001\) & \(0.010\) & \(0.012\) & \(0.014\) \\
[MPa] & \(\omega_{\rm{Pint}}\) & \(10.19\) & \(10.35\) & \(10.37\) & \(10.38\) & \(10.39\) \\  & \(\omega_{\rm{Pmax}}\) & \(35.33\) & \(35.26\) & \(35.24\) & \(35.23\) & \(35.22\) \\ \hline Peak circumferential stress in CFRP rim [MPa] & \(\omega_{\rm{Pmin}}\) & \(207.9\) & \(207.3\) & \(207.2\) & \(207.1\) & \(207.1\) \\  & \(\omega_{\rm{Pint}}\) & \(426.8\) & \(420.2\) & \(419.3\) & \(418.7\) & \(418.3\) \\  & \(\omega_{\rm{Pmax}}\) & \(816.7\) & \(800.9\) & \(796.4\) & \(797.0\) & \(795.9\) \\ \hline SR for aluminum hub & \(\omega_{\rm{Pmin}}\) & \(0.271\) & \(0.256\) & \(0.255\) & \(0.253\) & \(0.253\) \\  & \(\omega_{\rm{Pint}}\) & \(0.044\) & \(0.056\) & \(0.057\) & \(0.058\) & \(0.059\) \\  & \(\omega_{\rm{Pmax}}\) & \(0.524\) & \(0.550\) & \(0.554\) & \(0.556\) & \(0.557\) \\ \hline SR for CFRP rim & \(\omega_{\rm{Pmin}}\) & \(0.160\) & \(0.155\) & \(0.154\) & \(0.153\) & \(0.153\) \\  & \(\omega_{\rm{Pint}}\) & \(0.242\) & \(0.236\) & \(0.235\) & \(0.235\) & \(0.234\) \\  & \(\omega_{\rm{Pmax}}\) & \(0.760\) & \(0.740\) & \(0. Akin to case 1, values for the interfacial pressure exhibit the most significant change during the case 2 simulation, as shown in Figure 8a. This observation again substantiates conclusions in previous work [30] which suggested that stress relaxation at the interface could pose a risk to a flywheel rotor's structural integrity. After 1 year of operation, the  
Figure 8: Stress results normalized by their initial value on day 1 for (**a**) interfacial pressure, (**b**) peak radial tensile stress, and (**c**) peak circumferential stress in the CFRP rim, (**d**) peak \(SR\) in the aluminum hub, and (**e**) peak \(SR\) in the CFRP rim. interfacial pressure is predicted to decrease by approximately 7%, 7.5%, and 12% at the minimum, intermediate, and maximum velocities, respectively. However, these reductions are significantly less compared to case 1, for which a decrease of 29% is predicted after year 1. Again, lower predicted interface pressures in case 2 are due to the rotor being subjected to lower average angular velocities than in case 1, and the rotor spending less time subjected to high velocity loading conditions. Since for each charge-discharge cycle the rotor transitions from low to high velocity and vice versa, high cycle rates will typically subject the rotor to reduced viscoelastic effects, as it will spend less time at or near maximum velocities. Considering Figure 8b,c, changes in peak stresses are rather benign. The peak radial tensile stress increases by a maximum of about 2%, which is comparable to the corresponding decrease seen in case 1. The peak circumferential stress shows a reduction of 0.5% at \(\omega_{\rm{Pmin}}\) and 3% at \(\omega_{\rm{Pmax}}\). Reductions in both peak stress components are less than those for case 1 for the same reasons as discussed earlier. In Figure 8d, peak \(SR\) values for the aluminum hub are indicated to decrease for \(\omega_{\rm{Pmin}}\) but to rise for the other two velocities. \(SR\) changes at \(\omega_{\rm{Pmin}}\) and \(\omega_{\rm{Pint}}\), being seemingly high at the latter velocity, are largely irrelevant given the comparatively low absolute \(SR\) values for the hub at these operating conditions (see Figure 7). The rise in \(SR\) at \(\omega_{\rm{Pmax}}\) is considerable but is still confined to below 10% and remains uncritical.