Floquet Modal Analysis to Detect Cracks in a Rotating Shaft on Anisotropic Supports

Many systems can be approximated as linear with coefficients that vary periodically with time. For example, an anisotropic shaft rotating at constant speed on anisotropic bearings can be modeled as periodically time varying (PTV). Similar models can be obtained for wind turbines, some mechanisms, etc... However, the vast majority of modal analysis algorithms and techniques apply only to linear time invariant (LTI) systems. In this paper, two methods are demonstrated by which the free response of a periodically time varying system can be exactly parameterized by an LTI system. The parameters of the LTI representation can then be identified using standard techniques. The analysis techniques are demonstrated on a simple system, representing a rotor mounted on an anisotropic, flexible shaft, supported by anisotropic bearings. They are then applied to synthetic response data for a system with parameters that vary only weakly with time, as might be encountered when attempting to detect small cracks in a rotating shaft. These examples demonstrate the methods’ ability to characterize the anisotropy of the shaft, even when both the shaft and supports are anisotropic.