In this paper, the axial nonlinear vibrations of the transformer winding under steady state operation case and short circuit case are studied in single degree and multi-degree models.

In the case of having ampere-turn balance, the steady state response of the former model is obtained by using multi-scale method and periodic shooting method, analytically and numerically. At the same time, the computing method of Jacobi matrix in the periodic shooting method has been modified, so that the computing CPU time is saved. For multi-degree mechanical model of a single phase transformer windings, the time domain response and relation between the response and various parameters are obtained by Runge-Kutta method.

For ampere-turn unbalance case, an electric-mechanical coupled problem, that the electric force depends the displacement of the winding are foomed, and the nonlinear forced Mathieu equation is established for this problem; and then the nonlinear dynamical response and global dynamical behaviors are analyzed.

Finally, for a 20 MVA single phase three windings transformer, a series of short circuit experiments have been performed and the axial dynamical response force, magnetic field, strain etc. have been measured. The theoretical results well agree with the experimental results.

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