A tacholess order tracking methodology based on a probabilistic approach to incorporate angular acceleration information into the maxima tracking process

Abstract

Rotational speed or phase measurements are important in the rotating machine condition monitoring field. Rotating machines often operate in the presence of fluctuating rotational speeds and its components generate signals which are periodical in the angle domain. Hence, it is essential to perform order tracking when condition monitoring is performed under varying speed conditions. Computed order tracking is performed with a measured tachometer signal and it requires additional hardware to be installed on the machine, which may not be feasible nor practical. This article presents a tacholess order tracking method which is capable of accurately estimating the phase of a shaft of interest in the presence of large angular accelerations and noise. An improved maxima tracking procedure is used with an angular-displacement Vold-Kalman filter and the Hilbert transform to estimate the instantaneous phase of the shaft under consideration. The estimated instantaneous phase is used to resample the vibration signal from the time to the angle domain. The proposed tacholess order tracking technique is critically investigated on three numerical and three experimental rotational speed profiles. The minimum and maximum phase error obtained for the experimental data was 0.037697 and 0.05022 radians respectively, which highlights the potential of the technique.

An open set recognition methodology utilising discrepancy analysis for gear diagnostics under varying operating conditions

“…Hence, the Continuous Wavelet Transform (CWT), which is popular for analysing non-stationary signals for rotating machine diagnostics [4,12,23,40], is used with a Mexican hat basis function to obtain an angle-order distribution of the order tracked vibration signal, with the order tracking performed with the available rotational speed (or phase) information. The rotational speed can be estimated from measurement equipment [41] or estimated from the vibration signal [42,43] depending on the available equipment. The wavelet coefficients of the first three gear mesh components are extracted for different shaft angles, whereafter a windowing procedure is used to extract localised features from the wavelet coefficient signals.…”

Tacholess order tracking method for gearbox based on time-varying filter and energy centrobaric correction method

“…(2) Method based on VKF: as reported in Refs. [17,19], the pure harmonic component of gear meshing ( ) is extracted from the original vibration, which corresponds to IFE. The instantaneous phase of the reference shaft ( )is calculated based on Eq.…”

“…12(b). It can be seen that the characteristic order of the reference shaft (1 ) and its harmonics (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20) are quite abundant. The frequency change of the modulation component with the largest energy is the same as the change of the frequency of the reference shaft, thereby verifying that the fault gear is on the reference shaft.…”

“…The instantaneous frequency of filtered bearing signal obtained by the short-time Fourier transform (STFT), which filtered by the fast-spectrum kurtosis, then the angular domain signal and the order spectrum were obtained by a new resampling algorithm [18]. S. Schmidt et al [19] improved the maximum value tracking algorithm and combined VKF to extract the instantaneous phase information of the vibration signal. The instantaneous phase of the shaft can be obtained by integrating the instantaneous frequency, which is identified by dynamic path optimization [20].…”

A Similarity Comparison Method of Homologous Fault Response Fragments under Variable Rotational Speed

“…At present, the common methods to overcome the influence of rotational speed change are the OT [10][11][12] and the similarity calculation method of DTW. Firstly, the essence of OT is to resample the original vibration signal at a constant angle increment and transform the nonstationary signal in the time domain into the stationary signal in the angle domain [13,14]. In 2006, Saavedra and Rodriguez [15] carried out detailed analysis and verification of the algorithm for calculating order ratio analysis.…”