Non-linear dynamics of gear-pair systems with periodic stiffness and backlash

The present work investigates dynamics of a gear-pair system involving back lash and time-dependent mesh stiffness. In addition, the system is under th e action of external excitation, caused by torsional moments and gear geome try errors. First, the equation of motion is established in a strongly non- linear form. Then, the emphasis is laid on a specific forcing frequency ran ge, corresponding to conditions of,simultaneous fundamental parametric reso nance and principal external resonance. For these conditions, several types of periodic steady state response are identified and determined by employi ng suitable methodologies, including techniques applicable to piecewise lin ear systems and to oscillators with time-periodic coefficients. Moreover, t hese methodologies are complemented by appropriate procedures revealing the stability properties of the located: periodic solutions. In the second par t of the work, numerical results are presented. These results verify the va lidity and effectiveness of the new analytical methodology and provide info rmation on the gear-pair dynamics. First, series of typical response diagra ms are obtained, illustrating the effect of the mesh stiffness variation,:t he damping and the forcing parameters on the gear-pair periodic response. T hese response diagrams are accompanied by results obtained with direct inte gration of the equation of motion,. In this way, it is demonstrated that fo r some parameter combinations, the dynamical system examined can exhibit mo re complicated and irregular response, including crises and intermittent ch aos. (C) 2000 Academic Press.