Stability Analysis of Torsional Vibration of Vehicle Powertrain Based on the Nonlinear Drive-shaft Model

The influence of the nonlinear terms on the torsional dynamics of the powertrain is studied by adding nonlinear stiffness and nonlinear damping on the traditional linear Drive-shaft model of the powertrain. The existence of the nonlinear stiffness is verified by experimental method. Based on the nonlinear Drive-shaft model, the quantified model is obtained by using Lagrange method. The stability condition and bifurcation condition, fold bifurcation and Hopf bifurcation, of the torsional vibration system with constant excitation are deduced. The averaged equations and the amplitude-frequency response equation of the torsional vibration system during resonance are obtained by using the method of multi-scale. The stability condition and the bifurcation condition, fold bifurcation and Hopf bifurcation, of the resonance curve of the torsional vibration system are also deduced by using bifurcation theories. The influence of the nonlinear stiffness and nonlinear damping on the torsional dynamics are studied by simulation. It is shown that the nonlinear damping coefficient can lead to Hopf bifurcation which can cause instability of the resonance response, and the nonlinear stiffness coefficient can lead to fold bifurcation which can also cause instability of the resonance response. It is also shown that the instability of the resonance response can be suppressed by avoiding the occurrence of fold and Hopf bifurcation.