Nonlinear analysis on torsional vibration of misaligned rotor driven by universal joint

The nonlinear torsional vibration on rotor system driven by universal joint was studied considering both natural structure misalignment and actual error misalignment. Firstly, the equation with weakly nonlinear vibration was derived after analyzing the kinematic relation about driven shaft and driving shaft. Secondly, the periodic solution was obtained corresponding to principal resonance by multi-scale approach, including amplitude-frequency characteristic and phase-frequency characteristic curves. Then the stable region and unstable region on the amplitude and the phase of the periodic solution were deduce using Lyapunov´s approximate stability theory, which varied with the tunable parameter. At last, the driving shaft´s stable periodic motion of the first approximation and its calculation simulation were carried out according to the kinetic relation about driven shaft and driving shaft. The results above indicate the fundamental characteristic of the nonlinear dynamic on the misaligned rotor, also applying the foundation for advanced bifurcation analysis.