Taking the rigid support of the rotor installed vertically at both ends as the research object, the differential equation of unbalanced rotor bending and torsional coupling vibration is derived, the nonlinear differential equation is analyzed theoretically and qualitatively, the frequency components contained in the bending and torsional vibration response are solved, and the bending and torsional vibration characteristics of the unbalanced rotor are numerically simulated: under the external excitation of the rotor with an angular frequency of ω1, the torsional vibration with a frequency of |ω-ω1| is mainly excited through bending and torsional coupling, when the rotor has an external torque action with an angular frequency of ωt1. The main excitation generates the bending of the |ω±ωt1|frequency. The simulation results are consistent with the theoretical analysis, and the analysis results provide a theoretical basis for the fault diagnosis of vertical rotor bending torsion coupling resonance.