# Research on the Multi-Angle Seismic Spectrum Response Law of Auxiliary Feedwater Electric Pumps
## 5 Calculations and Analyses
### Rotor Analysis Results  
Figures 12 and 13 depict the maximum displacement curves of the impeller cover's inlet surface and the impeller's outlet surface, respectively, under various seismic spectrum input angles. Both response curves exhibit a consistent pattern: a peak between 0\({}^{\circ}\) and 90\({}^{\circ}\), a trough between 90\({}^{\circ}\) and 180\({}^{\circ}\), and a maximum value at 45\({}^{\circ}\). The maximum displacement of the impeller cover's inlet surface with the sealing ring measures 0.1118 mm, significantly smaller than the actual clearance between the impeller and the sealing ring. Similarly, the maximum deformation of the impeller's outlet is 0.1319 mm, below the practical clearance between the impeller and the guide vane, ensuring adherence to RCC-M2000 code. Notably, the maximum displacement at the inlet's front end surpasses that at the rear end across all input angles, indicating a reduction in the inlet's deformation along the flow direction,  
Figure 11: Maximum displacement response of the pressure-bearing components at different angles. especially between 0\({}^{\circ}\) and 90\({}^{\circ}\). Furthermore, the impeller cover's maximum displacements at the impeller outlet exceed those at the hub, indicating the higher fluid excitation force experienced by the impeller cover in comparison to the hub. Figures 14 and 15 illustrate the deformation factor curves of the impeller cover's inlet and impeller outlet surface monitoring points, respectively. Comparative analysis reveals a significant influence of the seismic spectrum input angle on the impeller outlet compared to the impeller cover inlet, underscoring the importance of careful consideration during the design and calibration processes. Generally, the absolute values of the deformation factors at points 1 and 3 are slightly larger than those at points 2 and 4, indicating a minor impact of the input angle on the front and rear ends of the impeller cover inlet. In contrast, the absolute values of the deformation factors at points 5 and 7 are significantly greater than those at points 6 and 8, signifying that the impeller cover is more responsive to displacement changes and fluctuations at different input angles than the impeller hub. Notably, the absolute values of the deformation factors at points 5 and 6 exceed those at points 7 and 8 due to the greater distance of points 5 and 6 from the seismic spectrum loading location, resulting in a more pronounced displacement response. These findings emphasize the need for meticulous attention to these factors in the design and calibration processes. Figure 12: Maximum displacement of impeller cover inlet surface. Figure 13: Maximum displacement of impeller outlet surface. From the above calculation results, it can be seen that the seismic response characteristics of the rotor in the auxiliary feedwater electric pump exhibit significant variations depending on different directions of seismic spectral input. Notably, distinct extreme values are observed in maximum displacements at 45\({}^{\circ}\) and 135\({}^{\circ}\), with 45\({}^{\circ}\) representing the peak value. This indicates that for future seismic analyses of auxiliary feedwater electric pumps, prioritizing seismic spectral inputs at this specific angle is crucial to conservatively assess the clearance between their rotors and stators. Moreover, for optimal seismic resilience, the installation angle of the pumps within the nuclear island can be strategically set between 120\({}^{\circ}\) to 150\({}^{\circ}\), aligning with the direction of frequent earthquakes. Conversely, angles within 30\({}^{\circ}\) to 60\({}^{\circ}\) should be avoided whenever possible to mitigate the deformation effects induced by seismic excitation. These insights provide valuable guidance for the design and operational strategies of auxiliary feedwater electric pumps in nuclear power plants, ensuring their robust performance under seismic conditions. Figure 14: Deformation factor of the monitoring point of the impeller cover inlet.