Due to the complex structure and wide excitation of the range extender, the misalignment and stator short-circuit coupling fault can easily occur. Therefore, it is necessary to study the coupling fault mechanism of the range extender, analyze the cause of the fault and the fault evolution law, and research the coupling fault characteristics. To reveal the mechanism of misalignment and stator-short-circuit coupling fault, the misalignment mechanism was analyzed and the bending and torsion electromagnetic stiffness of the generator in the stator short-circuit fault was derived. Then the dynamic model of bending and torsion coupling for the generator was established. Furthermore, we used the Runge-Kutta method to study the vibration response characteristics of generator rotor under coupling fault. Then through finite element analysis, the feasibility of coupled fault diagnosis was verified. The results show that the response of the generator rotor not only has the frequency component of single faults, but also new frequency components such as 4.0 and 6.0 harmonic amplitudes of radial vibration and 3.0 harmonic amplitudes of torsional vibration, respectively.