| This dissertation presents a comprehensive investigation into the influence of sliding friction on the dynamic behavior of gears. New alternative techniques are proposed for modeling friction in gears and the corresponding governing equations are derived. A simplified linear time-varying (LTV) gear system is first considered with sliding friction and periodic mesh stiffness and damping. Analytical models based on Floquet theory and the Galerkin technique are developed and closed-form solutions are obtained for multiple excitations. These are then applied to investigate the dynamic interactions between friction, periodic mesh parameters and external excitation. An implicit non-linearity, arising out of sliding at the tooth surface, is introduced and the resulting non-linear time-varying (NLTV) system is numerically studied, with emphasis on the equivalent damping properties of sliding. For both the LTV and NLTV systems, the criteria for stability are refined, and the influence of sliding friction on regimes of instabilities is examined.; Subsequently, a higher dimensional geared system model is developed, incorporating mixed lubrication conditions, time-varying distributed mesh compliance and multi-directional dynamic coupling, as in the case of helical gears. With this model, the dynamic characteristics of the geared system are analyzed given the transmission error or transient torque excitation, and related phenomena like axial shuttling, friction coupling, energy losses and shaft wobble are identified. Appropriate formulations for the coefficient of friction are obtained by simulating the entire range of gear meshing conditions using two-disk and quasi-static gear experiments. Tribological conditions of gears are varied using alternate lubricants and surface topography, and their effect on noise and vibration is analyzed. Dynamic measurements with enhanced instrumentation and signal processing has revealed additional dynamic characteristics. The proposed analytical and experimental methodologies should lead to refined gear design and analysis guidelines especially when stringent specifications of noise and vibration exist. |
