Dynamics of a torsional system with harmonically varying dry friction torque

Nonlinear dynamics of a single degree of freedom torsional system with dry friction is studied in this paper. First, the nonlinear system with a periodically varying normal load is formulated. Second, a multi-term harmonic balance method (MHBM) is re-formulated to directly solve the nonlinear time-varying problem in frequency domain. The feasibility of MHBM is demonstrated with a periodically varying friction and its accuracy is validated by numerical integration using Runge-Kutta scheme. Then, nonlinear frequency response is calculated by assuming classical Coulomb friction law under harmonically varying normal load. Effects of harmonic order and phase lag of normal load are then examined with the proposed approach. Our analysis shows that a change in the harmonic order of the normal load affects responses at both off-peak and peak frequencies while the phase lag has minimal influence on peak frequency responses