Electromagnetic force is an important excitation source of stator-core vibration in hydro-generators. The methodological novelty of this study lies in an order-specific spectral-attribution framework for electromagnetically induced stator vibration. Unlike conventional electromagnetic–structural analyses that focus mainly on response-amplitude prediction or resonance screening, the proposed framework links electromagnetic-field distribution, Maxwell stress-based force harmonics, experimentally validated modal frequencies, swept-frequency harmonic response, and normalized modal detuning to distinguish force-dominated components from components influenced or amplified by nearby structural modes. A full-scale three-dimensional electromagnetic model of an actual hydro-generator was established to calculate the electromagnetic surface force acting on the stator-core tooth surfaces. The electromagnetic-force spectrum was obtained using fast Fourier transform. The steady-periodic surface-force data were converted into complex harmonic load vectors through Maxwell–Mechanical coupling and mapped onto the structural model as distributed surface loads, while hammer-impact modal tests were used to validate the structural dynamic model. With an electrical fundamental frequency of 50 Hz, the force spectrum contained components from approximately 49.9 to 499.2 Hz, corresponding to the first ten electrical-frequency orders. The principal vibration responses occurred near 9.98, 99.78, 199.56–201.55, 299.33, and 399.11–399.16 Hz. The minimum modal detunings of the 4th-, 6th-, and 8th-order electrical-frequency components were 4.02–4.97%, 1.81%, and 2.41–2.42%, respectively. Accordingly, the 4th-order component was identified as a dominant electromagnetic forced response with possible influence from the 210 Hz mode, the 6th-order component exhibited modal amplification associated with the 294 Hz mode, and the 8th-order component was influenced by the nearby 409 Hz mode. Although the 9th- and 10th-order force components were present, their vibration responses remained weak. These results demonstrate that the vibration spectrum is shaped jointly by electromagnetic excitation and structural frequency-response effects, providing a quantitative basis for electromagnetic-source reduction, structural detuning, and damping enhancement.

Francis turbines are renowned for their high efficiency and adaptability across a wide range of head and discharge conditions. However, internal mechanical friction losses (IMFLs), resulting from rotational frictional resistance between the rotating runner and the surrounding fluid, remain a significant obstacle to further performance optimisation. This study introduced a CFD-derived integral friction torque framework, validated through theoretical analysis, that enables the spatially resolved quantification of IMFLs in Francis turbine runners. Building on this framework, a comprehensive computational approach was established to quantify IMFLs in a Francis turbine runner using a CFD-derived integral torque method combined with a theoretical verification model. Three runner configurations were analysed: the original runner model (ORM), a modified runner (RM1) with selective exit height reduction, and a modified runner (RM2) with uniform exit height reduction. Transient simulations were conducted at the best efficiency point (BEP) using the shear stress transport (SST) k–ω turbulence model and a sliding mesh approach. The numerical results were verified using the theoretical model and systematically evaluated to assess IMFL mechanisms and runner performance. The findings demonstrate that variations in runner geometry significantly influence internal frictional resistance and turbine efficiency. Compared with ORM, both RM1 and RM2 reduced the rotational friction torque, with RM2 exhibiting the greatest improvement: a 2.83% reduction in total friction resistance torque, a 14.74% reduction in total power losses, and a 1% absolute increase in efficiency. These improvements are primarily attributed to reduced wall shear stress and a more uniform pressure distribution across the runner surface.

Accurate identification of electromagnetically induced stator vibration frequency components is essential for the online condition monitoring of hydro-generators, particularly for assessing the dynamic state of the stator core under normal operating conditions. In engineering practice, the fast Fourier transform (FFT) is widely used for vibration spectrum analysis; however, because the measured vibration response is simultaneously affected by electromagnetic excitation, mechanical rotation, hydraulic disturbance, and external harmonic interference, FFT-based spectra often contain multiple frequency components whose structural relevance is difficult to determine directly. To address this issue, this paper proposes a coupled continuous wavelet transform and power spectral density transmissibility (CWT-PSDT) method for identifying key vibration frequency components with stable time-frequency energy and inter-sensor transmissibility in hydro-generator stator vibration signals. In the proposed framework, the analytic Morlet wavelet is first employed to localize dominant energy bands in the time-frequency domain, and PSDT is then used to screen frequency components with relatively stable inter-sensor transmissibility characteristics, thereby reducing the ambiguity caused by excitation-dominated spectral components. A clamped-clamped beam model is first used for numerical validation, and the maximum identification error of the first five natural frequencies is 4.22%. Experiments on a Francis turbine-generator test rig under five operating conditions further show that the proposed method can distinguish the mechanical rotational component near 10.3 Hz from the electromagnetic-related component near 50.8 Hz, while retaining higher-order electromagnetic-related components around 150 Hz and 250 Hz. The results demonstrate that the proposed CWT-PSDT method provides a physically interpretable and data-efficient approach for extracting stator-core-related spectral features, and offers a theoretical basis for spectrum-based online monitoring and future abnormal-condition comparison of hydro-generator stator responses.

The change of hydraulic factors would affect the vibration state of the hydro-turbine during operational condition. In order to ensure the stability of the hydro-turbine, it is necessary to study the vibration response characteristics under different operating conditions. In this study, the operational modal frequency of the Francis turbine under three different operating conditions of empty load, low load and high load were measured by experiments, and the Power Spectral Density Transmissibility (PSDT) method based on the Operational Modal Analysis (OMA) was used for data analysis. The results shown that the vibration frequency is distributed from low frequency to high frequency. In the operating state, the electromagnetic excitation force would cause changes in the frequency of 3rd, 4th and 6th modes of the unit. In addition, under high-load conditions when the hydraulic excitation force dominates, the 12th modal frequency of the unit would be excited. Furthermore, as the load gradually increases, due to the decrease of the equivalent stiffness, the vibration frequencies of each order of the unit show a decreasing trend.