Jiannan Zhao

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.

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.