In a modern wind turbine, the gearbox is an expensive and fault-prone subsystem. Currently, condition monitoring, based on comparison of data of healthy baseline measurement and online measurement, followed by feature analysis and decision making, is the main approach of diagnosis and prognosis. Although having been employed in many practical implementations, such methods have limitations. For example, a huge database is needed when operating conditions change and normal variations are significant. Traditionally, first-principle-based modeling of gearboxes is considered very challenging, primarily due to their dynamic characteristics that exhibit time-periodicity and encompass a very wide frequency range. In this research, aiming at achieving the predictive modeling capability, a lumped-parameter model of a two-stage laboratory gearbox testbed is constructed based on the assumed mode method. This model can characterize the gearbox dynamic effects including the time-varying mesh stiffness and backlash. The Floquet theory and harmonic balance method are then applied to analytically investigate the system dynamics, where the eigenvalues of the time-periodic gearbox are extracted and correlated to the spectral analysis results of the time-domain response prediction. This modeling approach and the associated analysis lay down a foundation for establishing hybrid dynamic model of complex gearbox systems which will further be utilized in model-based diagnosis and prognosis.
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