Research on Mechanical Characteristics of Multi-Stage Centrifugal Pump Rotor Based on Fluid–Structure Interaction

This study investigates the mechanical characteristics of a multi-stage centrifugal pump rotor through fluid–structure interaction (FSI) analysis. A two-stage centrifugal pump equipped with back vanes on the trailing impeller is selected as the research object. Numerical simulations are performed based on the continuity equation and Reynolds-averaged Navier–Stokes (RANS) equations, with experimental data utilized to validate the numerical model’s accuracy. The internal flow field mechanisms are analyzed, and the effectiveness of two axial force calculation methods—formula-based and numerical simulation-based—for the rotor system is comprehensively evaluated. Employing an FSI-based modal analysis approach, the governing differential equations of motion are established and decoupled via Laplace transformation to introduce modal coordinates. Modal analysis of the pump rotor system is conducted, revealing the first six natural frequencies and corresponding vibration modes, along with critical speed calculations. The findings demonstrate that when the flow field near the back vanes exhibits complex characteristics, the formula-based axial force calculation shows reduced accuracy. In contrast, without back vanes, the hydraulic motion in the impeller rear chamber remains relatively stable, resulting in higher accuracy for formula-based axial force predictions. The calculation error between the two conditions (with/without back vanes) reaches 27.6%. Based on vibration mode characteristics and critical speed analysis, the pump is confirmed to operate within a safe region. The rotor system exhibits two similar adjacent natural frequencies differing by less than 1 Hz, with perpendicular vibration mode directions. Additionally, rotational speed fluctuations in the rotor system induce alternating critical speed phenomena when operating in this region. This study establishes a coupled analysis framework of “flow field stability–axial force calculation accuracy–rotor dynamic response”, quantifies the axial force calculation error patterns under different flow field conditions of a special pump type, supplements the basic data on axial force calculation accuracy for complex structure centrifugal pumps, and provides new theoretical insights and reference benchmarks for the study of hydraulic–mechanical coupling characteristics of similar fluid machinery. In engineering applications, it avoids over-design or under-design of thrust bearings to reduce manufacturing costs and operational risks. The revealed rotor modal characteristics, critical speed distribution, and frequency alternation phenomena can provide direct technical support for the optimization of operating parameters, vibration control, and structural improvement of pump units in industrial scenarios, thereby reducing rotor imbalance, bearing wear, and other failures.