Vibration Power Flow Modeling and Experimental Verification of a Multi-Substructure Centrifugal Pump Prototype

To enable consistent modeling and quantitative evaluation of vibration-energy transmission in centrifugal pumps with multiple coupled substructures and branches, this study develops a generalized transfer-matrix model. The method combines Craig-Bampton reduction with the four-terminal parameter method and the multibody system transfer matrix method. Dynamic-equilibrium and kinematic-compatibility constraints are incorporated at branch nodes so that chain-like and branched paths can be assembled within one formulation. A vibration-power-flow model was developed for three layouts of a prototype comprising an equivalent pump body, an extended casing, spring–damper connectors, and a support base. Its predictions of axial active power flow at the L6 mounting-foot connection were compared with measurements over 8–1000 Hz. The mean relative error for the first 12 natural frequencies was 4.38%. The power-flow-level RMSEs for Layouts 1–3 were 3.12, 2.71, and 2.28 dB, respectively, and the highest proportion of frequency points within a ±3 dB deviation band was 91.4%. The three layouts exhibited similar power-flow trends over approximately 8–80 Hz, whereas differences in amplitude and peak–valley locations became pronounced above 250 Hz as energy was redistributed among parallel paths. The proposed framework provides a quantitative basis for comparing centrifugal-pump layouts and controlling vibration-transmission paths.