Modal Reduction of Geared Rotor Systems with General Damping and Gyroscopic Effects

Publication Title

Journal of Vibration and Control

Publication Date


Document Type





gearing effect, general damping systems, gyroscopic systems, modal reduction




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.