SLIDING FRICTION-INDUCED NON-LINEARITY AND PARAMETRIC EFFECTS IN GEAR DYNAMICS

The mechanism of gear meshing entails a large amount of sliding between the mating teeth in contact. Friction forces act orthogonal to the line of action, and the resulting dynamic force and moment are governed by a number of parameters, such as the relative surface speed, instantaneous load and spatial location of the point of contact. Sliding resistance is inherently non-linear in nature, and due to the additional presence of periodic meshing properties like stiffness and viscous damping, dynamic interactions result between friction and system parameters. This combination leads to a non-linear time-varying (NLTV) system comprising implicit non-linear differential equations. Nevertheless, most researchers have treated friction as a linear time-varying (LTV) phenomenon. In this article, both of these models are critically analyzed. For the LTV system, the harmonic balance formulation is developed to predict the dynamic behavior and sub-harmonic instabilities in the system. The NLTV analysis leads to very complex and intractable equations, and hence numerical methods are applied. Using this analysis, the physical phenomena associated with the two models are compared and the essential differences in the system behavior are examined. Finally, the dynamic effects of friction-induced non-linearity are investigated and the critical parameters are identified.