Dynamic vibratory motion analysis of a multi-degree-of-freedom torsional system with strongly stiff nonlinearities

Physical driveline systems have inherent nonlinearities such as multiple piecewise linear springs, gear backlashes, and drag torques. The multi-staged clutch dampers, in particular, cause severe problems in simulating the nonlinear dynamic behaviors of multi-degree-of-freedom systems. In order to analyze the nonlinear dynamic behaviors of the system, the harmonic balance method has been employed. This study suggests a method to overcome the convergence problems with strong nonlinearities by employing two distinct smoothening factors for stiffness and hysteresis. First, the dynamic behaviors of the multi-degree-of-freedom torsional system are investigated by employing multi-staged clutch dampers subjected to a sinusoidal excitation. Second, the effects of system parameters are examined with respect to dynamic characteristics of torsional vibration. The regimes of resonance frequencies along with the relevant parameters of the system are investigated by calculating backbone curves, which reduce the calculation time significantly. In order to validate harmonic balance method simulation, the simulated results are compared with those of numerical simulation. Harmonic balance method is shown to be more efficient than numerical simulation in calculating the nonlinear frequency response, as well as in simulating the steady-state responses without transient response effect.