## 4 Results and Discussion
### Viscoelastic Behavior
#### 4.2.1 Case 1
Conceivably, the initial rapid relaxation could be avoided by subjecting the composite rim to a suitable conditioning process prior to rotor assembly. In this case, only a relative minor decrease in interfacial pressure of about 7% would be expected. Based on present findings, while viscoelastic stress relaxation leading to hub-rim separation is a conceivable scenario, it is controllable provided adequate interfacial pressure is achieved during assembly, or substantial initial creep effects can effectively be mitigated otherwise (e.g., by CFRP rim conditioning). It is interesting to note that for a reduced press-fit interference of 0.45 mm between the hub and rim (instead of 0.8 mm), creep effects are sufficient to cause zero interfacial pressure over the considered operating time, that is, separation between hub and rim would occur. Clearly, these results demonstrate that a viscoelastic analysis is warranted for the engineering design of FESS rotors. The Tsai-Wu failure criteria were used to determine the \(SR\) data and predict the location and angular velocity associated with rotor failure. \(SR\) data facilitate predicting failure since these data are based on the combined stresses exceeding the strength threshold. In other words, the \(SR\) analysis provides an understanding of the total stress state of the rotor. \(SR\) data for the current rotor are provided in Figure 5. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Time [Year]** & **0** & **0.5** & **1** & **5** & **10** \\ \hline Interface pressure [MPa] & \(-26.98\) & \(-19.60\) & \(-19.01\) & \(-17.66\) & \(-17.08\) \\ Radial peak stress [MPa] & 50.96 & 50.86 & 50.83 & 50.75 & 50.71 \\ Circumferential peak stress [MPa] & 975.51 & 936.54 & 933.20 & 925.40 & 922.01 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Rotor peak stress values for interfacial stress, radial peak stress, and circumferential stress at 0, 0.5, 1, 5, and 10 years of continuous flywheel operation at limit velocity. Figure 4: Normalized rotor peak stress for interfacial pressure, radial stress, and circumferential stress over time for continuous flywheel operation at limit velocity. Values are normalized by the corresponding stress at time \(t=0\). The CFRP rim initially has the highest \(SR\) of 1.01 and is located at the midplane of the rim; however, viscoelastic stress relaxation improves the stress state of this rim, so \(SR\) decreases to 0.975 within 6 months, then continues to slowly decrease to about 0.96 after 10 years. The same cannot be said for the aluminum hub, which exhibits an evolution of stresses approaching failure. The \(SR\) for the hub, while initially substantially less than the composite rim, increases from 0.836 to 0.9 within 6 months, then continues to increase to 0.92 over the following 10 years. With an increase by 6.8%, changes in \(SR\) for the hub are rapid in the first year of operation, while the \(SR\) is predicted to increase by only another 2% over the next 9 years. Referring to Figure 3, this \(SR\) growth is caused by a rising circumferential stress in conjunction with a lessening of compression in the radial direction. This behavior can be understood recalling Equation (13), which is composed of radial, circumferential, axial, and coupled terms. The linear term for radial direction is \(SR_{\text{radial}}=F_{3}\sigma_{3}^{\text{app}}R\). Since the peak radial stress is compressive, a large negative value is introduced into Equation (13), thus reducing \(SR\) accordingly. As the CFRP rim undergoes viscoelastic deformation, the radial compressive load diminishes, so \(SR_{\text{radial}}\) diminishes as well, thus removing the negative term from the equation, causing the observed \(SR\) increase for the hub. In summary, viscoelastic stress relaxation of the CFRP rim can improve its stress state to the detriment of the aluminum hub. It is reasonable to conclude that for a given rotor geometry, changing stresses may lead to damage of the aluminum hub and/or separation between hub and rim components.