# Research on the Multi-Angle Seismic Spectrum Response Law of Auxiliary Feedwater Electric Pumps
###### Abstract  
The auxiliary feedwater electric pump, which is vital in nuclear power units, demands exceptional seismic reliability. The impact of the seismic excitation direction on the seismic response of the complex auxiliary feedwater electric pump structure remains inadequately understood, thereby introducing uncertainties into seismic analysis and equipment installation procedures. To address this challenge, this study centers on a representative horizontal multi-stage centrifugal pump based on the finite element model and modal analysis. Utilizing the response spectrum method and the square root of the sum of the squares (SRSS) vibration pattern superposition principle, the research comprehensively explores the seismic response characteristics of individual pressure-bearing components and key rotor positions under seismic excitation from various angles. Findings reveal intricate variations in maximum stress and displacement responses for each pressure-bearing component under safe shutdown earthquake (SSE) level seismic excitation, corresponding to different input angles of seismic spectra. In assessing the seismic operability of the clearance between the impeller and the stator, the direction near 45 deg exhibits the maximum displacement response, highlighting the need for focused attention in testing and verification checks. The methodologies and conclusions presented in this paper offer valuable insights for designing, optimizing, and installing horizontal multi-stage centrifugal pumps, including auxiliary feedwater electric pumps, providing valuable guidance for future applications in the field. seismic response; horizontal multi-stage centrifugal pump; modal analysis; seismic spectrum input direction +
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loads. The integral calculation method proposed by them markedly enhances efficiency, ensuring target accuracy in seismic analysis. [PERSON] et al. [9] performed a seismic analysis on the reactor coolant system, employing both the single-point response spectrum (SPRS) method and the multi-point response spectrum (MPRS) method. Comparative studies indicated that the MPRS method demonstrates superior applicability, particularly for equipment with multiple supports. [PERSON] et al. [10] utilized a combined approach involving finite element simulation and prototype vibration testing to analyze the vibration characteristics of a nuclear centrifugal pump. Their investigation revealed that hydraulic disturbances exert a substantial influence on the frequency of the blades, and they identified the underlying reasons for this phenomenon. [PERSON] et al. [11] conducted impact tests on a two-stage centrifugal pump within a designated nuclear power plant. Through an assessment of the stress distribution across various components, they identified the maximum acceleration threshold that the pump could withstand. Current research on seismic analysis of auxiliary feedwater pumps predominantly focuses on reliability assessments and seismic analysis methodologies. In the evaluation of the seismic performance of pump bodies, a prevalent methodology entails employing finite element models in conjunction with response spectrum analysis. As an illustration, [PERSON] et al. [12] introduced a rotor stiffness model for an electric auxiliary feedwater pump, conducting seismic analyses using finite element methods. [PERSON] et al. [13] and [PERSON] et al. [14] calculated seismic responses, considering load combinations, to assess the structural integrity and operability of an auxiliary feedwater electric pump during an SSE earthquake. In the realm of seismic analysis methods, certain researchers have put forth pioneering approaches, including harmonic response analysis and the integration of computational fluid dynamics (CFD) simulation with monitoring data. For instance, [PERSON] et al. [15] integrated vibration monitoring data and computational fluid dynamics to analyze the response patterns of auxiliary feedwater pump casings. [PERSON] et al.