The torsional vibration of gear boxes with backlash

The study of vibration with backlash in geared systems has been a popular topic for academic research in recent years. A subset of this research deals with the subharmonic response of gear pairs with backlash. A review of this prior research reveals that it may be complemented in two ways. Firstly, there is a need for experimental work that allows external excitation of the gear pair at a frequency other than their own meshing frequency. Secondly, an analysis of the type of damping employed by the physical model (viscous and/or impact) is required, since including impact damping seems more appropriate and yet is not evident in prior work in this area. Mathematical models for both the impact damping and viscous damping cases have been programmed into Matlab's SIMULINK environment. Both models allow for external excitation at an arbitrary frequency and can (optionally) include the effects of time varying mesh stiffness of the gears on the system. Stable subharmonic motions were found to exist for both models; thus, the viscous damping model was favoured due to its simplicity - justifying its use in prior research. The simulation results show that subharmonic motions only develop if the system is given a certain initial energy input. An experimental rig has been constructed, but conclusive evidence of subharmonic motions is yet to be detected in it - probably because precise (and unknown) combinations of initial conditions are required for such motions to occur. These findings have implications for the designers of geared systems that may have backlash; subharmonic motions can lead to different-than-expected responses if linear models are employed that ignore backlash.