A multi-order FRFT self-adaptive filter based on segmental frequency fitting and early fault diagnosis in gears

• LMSS method is able to divide any signal with curved frequency into a minimal number of segments with nearly linear frequency.
• DFFPFF method is able to exactly determine the FRFT filter parameters of each signal segment.
• MFSFF is able to precisely extract feature components from a signal with curved frequency.
• A gear’s early failure can be exactly diagnosed by an order envelope analysis of the feature component extracted by MFSFF.

To effectively diagnose gear failure at an early stage, a multi-order Fractional Fourier transform (FRFT) self-adaptive filter based on segmental frequency fitting (MFSFF) is proposed to separate the feature components with curved frequency from the gearbox’s transient conditions. First, a linear multi-scale segmentation method (LMSS) is developed to divide the signal with curved frequency into segments with nearly linear frequency; then, a method for determining the FRFT filter parameters by fitting the frequency curve (DFFPFF) is developed to calculate the FRFT filter parameters for each signal segment, and the signal in each segment is filtered by an FRFT filter using these parameters to determine the MFSFF. The vibration of the gearbox’s acceleration and deceleration process is analyzed using an MFSFF and the filtered signal is demodulated. The experimental results show that LMSS is able to divide any signal with curved frequency into minimal segments with nearly linear frequency; DFFPFF is exact, fast, not influenced by the vibration source or the number of components, and able to determine the FRFT filter parameters for each signal segment accurately; the feature component of the gearbox’s transient condition is accurately extracted by an MFSFF, and the other components and noise are removed simultaneously. Early gear failure is diagnosed exactly by demodulation of the extracted feature component, which is difficult to identify using the traditional method.