Time-frequency domain construction of dual tree complex wavelets for assembly clearance detection of gear chains

To optimize the time-frequency localizability of discrete wavelet transform in extracting nonstationary and periodic fault signatures of mechanical equipment, a time-frequency domain constructing scheme of dual tree complex wavelet transform (DTCWT) is investigated. Frequency responses with imposed phase shift condition and reduced energy leakage are designed for the prototype filters of scaling functions in the frequency domain. Subsequently, in the time domain the orthogonality and the energy leakage of the constructed DTCWT are further addressed. The regularity of the constructed DTCWT can be guaranteed even at zero vanishing moment. The reduced energy leakage effect of the constructing method is validated via numerical simulations. The constructed DTCWT is utilized to analyze the vibration signal of the gear train of a heavy-duty lathe and to successfully extract the weak periodic modulation signatures induced by the assembly clearance of the sliding gears. The extracting performance is superior to Daubechies orthonormal wavelet and DTCWT constructed purely in the time domain.