Modal Synthesis of a Non-Proportionally Damped, Gyroscopically Influenced, Geared Rotor System via the State-Space

Modal synthesis provides for degree-of-freedom reduction and model simplification. This report presents a method for conducting modal synthesis on a geared rotor dynamic system under the influences of non-proportional damping and gyroscopic effects. Based on the familiar first-order, state-space methodology, a coordinate transformation is developed for diagonalizing the state-space equations of motion for each substructure of the system. A modal synthesis procedure then assembles the system equations of motion from the individual substructures. The coupling between the substructures occurs via the gear mesh. Using this methodology, the size and complexity of the model are reduced without incurring any significant loss in accuracy. The reduced model still allows for traditional methods of system analysis: Eigen-solution analysis, frequency domain response, and time domain response. Validation of this methodology occurs through its application to a finite element analysis of a geared system already published in the literature. The application illustrates that the results of the reduced system match almost exactly with the full finite element model. Additionally, the topics of gearing and gyroscopic effects are discussed with respect to limitations that arise from the analysis. In addition to model simplification, this technique also exhibits further potential for use in optimization and system identification schemes. Prepared in collaboration with the Department of Mechanical and Aerospace Engineering, University of Virginia, Charlottesville, VA. The original document contains color images.