When power transformers operate in a hybrid AC-DC environment

the excitation current experiences half-wave distortion

and the core becomes excessively saturated

leading to increased transformer vibration and severely affecting operational reliability. To address the issue of intensified vibration under DC interference

this paper proposes a multi-field coupling method for electromagnetic-mechanical analysis of transformers based on the Jiles-Atherton (J-A) hysteresis theory. This method updates the core permeability using the hysteresis loop during the calculation process

constructs a three-dimensional electromagnetic-mechanical finite element model of the transformer

solves for changes in characteristic parameters of multiple physical fields under different DC disturbances

and investigates the intrinsic relationships among parameters of multiple physical fields. A Yd-connected three-phase three-limb transformer is taken as an example for simulation to study changes in electromagnetic and vibration parameters under various DC components and to summarize their variation patterns. Comparison with experimental results verifies the accuracy of the proposed method. Finally

a mapping relationship between electromagnetic parameters and vibration parameters during transformer operation under DC bias is established

allowing measurable electrical information to reflect abnormal changes in difficult-to-measure vibration parameters. This provides a new approach for monitoring and identifying DC bias in transformers.