Torsional dynamics and stability of automotive driveline considering cubic nonlinearity

Since the half-shaft is the main flexible part of the automotive driveline, the torsional dynamics of the simplified driveline considering the cubic nonlinearity of the half-shaft is discussed in the paper. The approximate solutions of the torsional shock response and the resonance response of the driveline are derived using the method of multiple scales. The stability and bifurcation condition of the responses are judged based on the Routh–Hurwitz criterion and the bifurcation theory, respectively. It is shown that the negative cubic nonlinear stiffness is propitious to suppress the torsional shock of the driveline while the positive is on the contrary. Meanwhile, the ability of the suppression of the torsional shock can be improved with the decrease in the linear stiffness. The resonance curve of the driveline may lose its stability when the value of the cubic nonlinear stiffness reaches the threshold. By properly designing the negative cubic nonlinear stiffness of the half-shaft, the instability of the resonance can be suppressed and the ability of the suppression of the torsional shock can also be improved.