Open Access Kent State (OAKS)

The presence of damping, gyroscopic behavior, and gearing complicates traditional vibration analysis. This paper presents a methodology for conducting modal reduction on a geared rotor dynamic system under the influences of general damping and gyroscopic effects. Based on the first-order, state-space methodology, a coordinate transformation is presented for diagonalizing the state equations of motion for each substructure in the system. A modal synthesis procedure assembles the system equations from the individual substructures. The substructures are coupled via gear-mesh interactions. Using this technique, the size and complexity of a model can be reduced without incurring significant loss of accuracy. The reduced model allows for traditional methods of system analysis to include eigen-solution analysis, and frequency response. Validation occurs through application to a simple geared system widely discussed in the literature. The results of the modal reduction match closely with the full finite element model. A transmission system is also analyzed to illustrate the method’s usefulness to a complex system model of multiple shafts and gear interactions. Considerations arising from the analysis of geared systems are also discussed.