Gearbox Dynamics in the Modeling of Rotating Machinery

The ability to accurately predict rotating machine resonant frequencies and to assess their stability and response to external forces is crucial from a reliability and preventive maintenance perspective. Resonant frequencies and forced response become more difficult to predict when additional complicated components such as gearboxes are present in the rotor system. Gearbox dynamics contain many complexities. No computationally straight forward methods are currently available in the literature that relate gear forces and moments acting in 3-D space to the deflections of a wide variety of shaft systems in gear trains. Several models for analyzing gear forces and deflections have been proposed, but they focus primarily on the dynamics of the gearbox itself and neglect vibration transmission through the remainder of the drive-train. More recent models have used the finite element method to couple the lateral and torsional degrees-of-freedom of shaft systems to the forces and moments of the gears through stiffness matrices. However, these models were limited to spur geared systems and could not account for the forces and moments produced by helical gears, which act not only in the lateral and torsional directions but also in the axial direction. A finite element formulation of gearboxes, which couples the axial, lateral, and torsional degrees-of-freedom of the connected shafts, is developed in this thesis. The thesis contains applications to two industrial gear trains. It has the capability to apply to a wide variety of both spur and helical geared systems set at arbitrary orientation angles.