Super-harmonics in a torsional system with dry friction path subject to harmonic excitation under a mean torque

The nonlinear frequency response characteristics of a two-degree-of-freedom torsional system with a significant dry friction controlled path are studied, when excited by sinusoidal torque under a mean load. An analytical solution is first developed for a simplified system subjected to continuous slipping motions. The nature of super-harmonic peaks as generated by the dry friction nonlinearity is efficiently found. The effect of a non-zero mean load is also determined and qualitatively understood. Further, a refined multi-term harmonic balance method (MHBM) is proposed that includes up to 12 terms. It is used to study an automotive drive train system that experiences significant stick-slip motions. Associated computational issues including the selection of initial conditions are addressed. Studies show that the mean load could induce asymmetric stick-slip motions and accordingly it has significant effect on time and frequency domain responses. Reasons for the occurrence of super-harmonic resonant peaks and transitional peaks are investigated. Finally, our MHBM is applied to the conventional single-degree-of-freedom system where the spring path exists in parallel with a dry friction damper (Den Hartog's problem). Our predictions match well with Den Hartog's analytical solution. Den Hartog's system differs, in terms of the dynamic behavior, from our torsional system (with a sole dry friction path).