Use of non-Gaussian distribution for analysis of shaft components

The drive train of a helicopter is a flight critical system in which the transmission of power results in both lift and thrust via a complex set of gears and shafts. Maintenance cost of this aircraft system is typically high due to the large damaging forces directed through these components. Consequently, monitoring the health of the drive train can potentially enhance flight safety and reduce operating costs. Health and usage management systems (HUMS) monitor the drive train by using accelerometers to measure component vibration. Algorithms process the time domain vibration data into various condition indicators (CI), which are used to determine component health via thresholding. For the rotating machinery, a standard set of CI are shaft order one, two and three (i.e. 1, 2 or 3 times the shaft RPM). Shaft order one (SOI) is indicative of an unbalance, where as higher shaft order can be used to detect a bent shaft or misalignment condition. The magnitude of the shaft orders sometimes have maximum allowable values set by the manufacture. At other times, some method is used to set thresholds, and maintenance is recommended when that vibration exceeds that threshold. In this paper, we present evidence that the distribution of the magnitude vibration is Rayleigh for nominal (health components) and the Rice for components that are damaged. A model for shaft magnitude is used which describes the Rayleigh distribution. It is shown that the Rice distribution is the general case of the Rayleigh distribution when the component has nonzero centrality (e.g. an imbalance). Threshold setting procedures for the Rayleigh distribution are given for anomaly detection (e.g. component is no longer normal) and for failure detection (component is damaged) and compared to Gaussian model. Finally, examples are given against real world conditions. The Rayleigh and Rice distribution are beneficial for diagnostics and prognostics as it measures non-centrality (imbalance) and variance (stiffne- - ss) in shaft vibration better than Gaussian models. We feel that use of this class of non-Gaussian distributions may allow accurate calculation of useful life remaining because it is sensitive to changes in shaft stiffness that is a precursor to component failure