# Research on the Multi-Angle Seismic Spectrum Response Law of Auxiliary Feedwater Electric Pumps
## 4 Multi-Angle Response Spectrum Analysis Model  
The pump unit is strategically positioned within the reactor plant, a critical aspect for its functionality. In this study, the SSE seismic response spectrum at the pump's specific location was discretized into three orthogonal directions of acceleration: a vertical z-directionacceleration and two mutually perpendicular horizontal x-direction and y-direction accelerations, as shown in Figure 4. Adhering to the actual installation arrangement of the auxiliary feedwater electric pump, the seismic spectrum was meticulously applied to the pump base mounting surface, as visually represented in Figure 5. This meticulous approach ensures the precise consideration of the pump's mounting conditions and real-world installation scenario.  
The orientations of the seismic excitation inputs are illustrated in Figure 6. To accommodate various seismic spectrum input directions, both horizontal seismic spectra are concurrently rotated counterclockwise around the vertical z-direction. Throughout this rotation, the angle between the two horizontal seismic spectra is consistently maintained at 90\({}^{\circ}\). Calculations are conducted at 15\({}^{\circ}\) intervals spanning from 0\({}^{\circ}\) to 180\({}^{\circ}\). Meanwhile, the seismic spectrum input direction along the vertical z-direction remains unchanged in the downward direction. Upon individual computations of seismic responses in these three directions, the cumulative response under simultaneous seismic excitation from all three directions is determined through the SRSS method.  
Figure 4: Floor acceleration response spectrum. (**a**) Horizontal x-direction, (**b**) horizontal y-direction, (**c**) vertical z-direction.  
Figure 5: Seismic spectrum loading location.  
Specialized attention is directed towards the clearances between the rotating and fixed components of auxiliary feedwater electric pumps, a critical focus highlighted in previous studies [31; 32; 33]. It is imperative to prevent any instances of collision or wear between the impeller cover inlet and sealing ring, as well as between the impeller outlet and guide vane, emphasizing the need for precision engineering in these areas [34]. Seismic excitation can induce deformations, potentially leading to friction or interference, which must not exceed the limits outlined in the RCC-M 2000 standard [35]. Such scenarios pose significant risks, including the potential for nuclear leakage. To meticulously address these concerns, as illustrated in Figure 7, this study strategically establishes monitoring points at specific locations: points 1, 3 and 2, 4 are designated at the front and rear ends of the impeller cover inlet, where the sealing ring is fitted. Additionally, points 5, 7, and 6, 8 are identified on the surfaces of both the impeller cover and the hub at the outlet. These monitoring points serve as crucial markers for investigating displacement responses between the rotor and stator components during seismic excitation.  
To visualize the impact of seismic spectrum input angles on the displacement responses of monitoring points and to discern differences among these responses, a deformation factor is defined herein.  
\[D_{f}=\frac{D-\overline{D}}{\overline{D}} \tag{5}\]  
where \(D_{f}\) represents the deformation factor, \(\overline{D}\) denotes the average displacement value across all input angles for the monitoring point, and \(D\) signifies the displacement value of the monitoring point at each specific input angle.  
Figure 6: Schematic diagram of seismic spectrum input angle. (**a**) Coordinate direction diagram. (**b**) Input angle schematic.  
Figure 7: Impeller monitoring points.