Tacholess Order Tracking Method Research Articles

A TLOT train gearbox fault diagnosis method based on ridge extraction under variable speed conditions

Owing to the rapidly varying working conditions of urban rail trains, the rotational speed conditions constantly shift in a short time span. As a key component of the running gear, the gearbox generates non-stationary vibration signals, making it challenging to monitor its health status. To address this challenge, a tacholess order tracking method (TLOT) based on ridge extraction method is proposed in this paper. This method determines the optimal search starting point using the time-frequency Gini coefficient and extracts the time-varying gearbox meshing frequency components from the time-frequency representation results. Furthermore, the TLOT method is utilized to process the strongly time-varying gearbox signal. In the order domain, multiple frequency components are extracted to reconstruct the signal. Simulation and experimental results demonstrate that the proposed method achieves a superior ridge extraction effect on gearbox experimental signals. It accurately converts unstable signals into angular domain stable signals, enhancing the energy aggregation of time-varying unstable signals in the order domain. This approach addresses the problem of weak harmonic component extraction from gearbox signals and effectively reduces interference in the resonance band, realizing fault diagnosis of the gearbox under unstable working conditions.

Tacholess Order Tracking Method Based on STFrFT for Fault Diagnosis of Wind Turbine Gearbox Under Variable Operating Conditions

Tacholess Order Tracking Method Based on STFrFT for Fault Diagnosis of Wind Turbine Gearbox Under Variable Operating Conditions

A Tacholess Order Tracking Method Based on the STFTSC Algorithm for Rotor Unbalance Fault Diagnosis Under Variable-Speed Conditions

Abstract Due to the fact that rotors usually operate in a non-stationary mode with changing speeds, the conventional rotor unbalance detection method based on the stationary signal will produce a major “spectrum ambiguity issue” and affect the accuracy of rotor unbalance detection. To this end, a tacholess order tracking method based on the STFTSC algorithm is suggested in this study, where the STFTSC algorithm is developed by combining the short-time Fourier transform and the seam carving algorithm. First, the STFTSC algorithm is utilized to accurately extract the instantaneous frequency (IF) of the rotor and calculate the instantaneous phase under variable-speed conditions. Subsequently, the original signal is resampled in the angular domain to transform the non-stationary time domain signal into a stable angle domain signal, eliminating the effect of the speed variations. Finally, the angular domain signal is transformed into the order domain signal, which uses the discrete Fourier transform and the discrete spectrum correction method to identify the amplitude and phase corresponding to the fundamental frequency component of the signal. The simulation results show that the IF extracted by the STFTSC algorithm has higher extraction accuracy compared with the traditional STFT spectral peak detection method and effectively eliminates the effect of speed fluctuations. A rotor dynamic-balancing experiment shows that the unbalance correction effect based on the STFTSC algorithm is remarkable, with the average unbalance amount decrease rate on the left and right sides being 90.02% and 92.56%, respectively, after a single correction.

Novel tacholess order tracking method for gear fault diagnosis under speed-up and speed-down conditions

Order analysis is a powerful technique for analysing the vibration signals of rotating machinery under a known variable rotational speed. It requires the installation of speed-measuring devices; however, these devices cannot be installed in most machines due to design or cost reasons. In this study, a new method based on a time delay and resampling technique is introduced to estimate the instantaneous frequency (IF) of the vibration signal of a gear system. Order analysis techniques are used to extract the gear fault features. The performance of the proposed method is validated using simulated data from a gear system under speed-up and speed-down conditions.

A Tacholess Order Tracking Method Based on Spectral Amplitude Modulation for Variable Speed Bearing Fault Diagnosis

Rolling bearings often work under nonstationary conditions, which will lead to spectrum smearing phenomenon and the failure of traditional diagnostic methods. Order tracking is a common technique to alleviate this problem by resampling the time-domain signal using the instantaneous rotation frequency. For tacholess applications, it is of great importance to obtain accurate rotation speeds. In this paper, a tacholess order tracking method based on spectral amplitude modulation (SAM) is proposed. Based on the fact that SAM can separate frequency components with different levels of energy, an appropriate weight is selected to highlight the instantaneous frequency, which is then extracted from the time-frequency representation by peak search algorithm. Moreover, entropy is employed to evaluate the valuable information in the time-frequency representation in order to select an optimal weight adaptively. A simulated signal and experimental signals of bearing outer and inner ring faults demonstrate that the proposed method can extract instantaneous rotation frequency and detect nonstationary bearing fault characteristics effectively.

A novel tacholess order tracking method for gearbox vibration signal based on extremums search of gearmesh harmonic

Computed order tracking (COT) is an effective vibration analysis method for mechanical equipment operating at time-varying speed. The principle is to resample the time-domain sampled vibration data under the guidance of angle information of reference shaft. The rotation angle obtained from numerical integration is generally limited by the deviation of integration on rotation speed. To address this problem, a novel acquisition method of rotation angle is proposed to improve the precision of order tracking analysis. Based on the equi-angular relationship between adjacent peaks of a single gearmesh harmonic, the discrete shaft phase vs time map is directly established by obtaining the peak time. The process error is thoroughly investigated, and a designed scheme is provided to eliminate the effects of discrete sampling and amplitude modulation. Theoretically, the rotation angle can be correctly depicted, which is useful for a highly precise order-tracking analysis. The accurate amplitude and high condensed spectral lines of order spectrum are achieved both in the simulation and experiment signals, which verified the effectiveness and robustness of the proposed method. It is helpful for the accurate reconstruction of speed-related vibration signal in the order spectrum, and enhances the capability of condition monitoring on gear systems.

A tacholess order tracking method based on extended intrinsic chirp component decomposition for gears under large speed variation conditions

Abstract Order tracking has been considered as the most effective non-stationary signal analysis technique for condition monitoring and fault diagnosis. Conventional order tracking is performed with a reference signal measured by the auxiliary device, which is expensive and inconvenient to install. In order to to break the constraint of the traditional order tracking technique, some tacholess order tracking methods have been developed in the past few years. However, current tacholess order tracking approaches are only applicable to slightly varying speed applications. To overcome the shortcoming above, a novel tacholess order tracking method is proposed in this paper. In the proposed method, each mode of the vibration signal is reconstructed by a method called extended intrinsic chirp component decomposition, and the Hilbert transform is used to estimate the instantaneous phase of reference shaft. Then the vibration signal is resampled to the angle domain, and the fault characteristic orders can be identified in the order spectrum accurately. The effectiveness of the proposed method has been validated by a simulated meshing gear vibration signal. The result illustrates that the proposed method can realize gears fault diagnosis under large speed variation conditions.

Adaptive tacholess order tracking method based on generalized linear chirplet transform and its application for bearing fault diagnosis

Bearing plays an important role in industrial equipment and it may operate under varying conditions. When the speed of shaft changes, whether monotonous or non-monotonous speed, common diagnostic approaches cannot effectively extract fault features. But encoders and tachometers are not always available. Therefore, tacholess order tracking methods which can directly extract the instantaneous rotating frequency (IRF) from vibration signal are very useful in bearing fault diagnosis under varying speed. Among these methods, the generalized linear chirplet transform (GLCT) can produce time–frequency representation without constructing any mathematical model, but there are two parameters must be set in advance. The parameters have great influence on the analysis result. To reduce the dependence on the prior knowledge of presetting the parameters in varying conditions, two different improved GLCT methods are proposed in this paper. To do with the situation where the trend of speed changes is monotonous, the scale-space is introduced to lift GLCT which can adaptively set a vital parameter, and the other parameter is set to default value. When faced with non-monotonous speed, the second method is proposed which the grey wolf optimizer (GWO) and Gini index are introduced to search the optimal parameters of GLCT without any prior knowledge. With the help of the proposed methods, the IRF can be extracted directly from vibration signal. Then, the raw signal can be resampled based on the IRF to eliminate the influences of speed. The morphological filtering is adopted to remove the noise and extract the fault characteristics order (FCO). Another two typical time–frequency analysis methods are used for comparisons. Three different signals are used for analysis to demonstrate the superiority of the proposed methods.

A Tacholess Order Tracking Method Based on Inverse Short Time Fourier Transform and Singular Value Decomposition for Bearing Fault Diagnosis.

Order tracking has been widely used to diagnose failures of variable speed rotating machines. The performance of the TOT (Time-Frequency Domain Tacholess Order Tracking) methods is based on the correct separation of the target component strictly related to the shaft rotation frequency. Currently, most of the methods have focused on obtaining the instantaneous frequency with accuracy. In this paper, a new TOT method has been proposed that combines the inverse short-time Fourier transform (ISTFT) with singular value decomposition (SVD). The target component closely related to the shaft rotation frequency is selected and filtered approximately in the time-frequency domain. Hence, the ISTFT is adopted to reverse the target component into the time domain. Next, SVD is used to refine the roughly filtered target component. Finally, the phase of the refined signal is extracted to resample the original signal. The performance of the method was tested using real vibration signals collected from a large-scale test rig of a high-speed train traction system.

An Adaptive Cross-Validation Thresholding De-Noising Algorithm for Fault Diagnosis of Rolling Element Bearings Under Variable and Transients Conditions

Developing a proper approach for extracting the fault characteristics of rolling element bearings is a significant behavior in variable operation conditions. Generally, without a tachometer, the tacholess order tracking method is well established by instantaneous rotation frequency curve estimation using time-frequency analysis. However, the fault features are often masked in strong background noises. An adaptive cross-validation thresholding de-noising algorithm is employed to improve the performance of the traditional envelope order spectrum method. First, the general linear chirplet transform is applied to estimate the instantaneous rotation frequency curve. Second, with the help of the instantaneous rotation frequency curve, the raw non-stationary signal is transferred to an angular domain by the re-sampling technique. Third, the adaptive cross-validation thresholding de-noising algorithm is employed to purify the angular domain signal to improve the fault feature extraction performance of the envelope order spectrum method. Comparisons using numerical simulations and experimental investigations of bearing faults under variable speed conditions are given to show the superiority of the present method.

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

Under the premise that the instantaneous speed can be accurately measured or precise estimated, order tracking is considered to be a classical and effective technique for non-stationary vibration analysis of rotating machinery. The meshing frequency components of the vibration signal measured from complex gearbox system interfere with each other mutually. The energy centrobaric correction method exhibits exact instantaneous frequency estimation (IFE) ability under the interference, but is susceptible to strong noise. Combining with time-varying filter and energy centrobaric correction method, a tacholess order tracking technique for gear fault diagnosis under the rotating frequency multi-linear fluctuation is proposed. The time-varying filter is designed to filter the strong noise signal, and then IFE could be accurately calculated from the filtered signal by energy centrobaric correction method. The instantaneous phase of reference shaft based on the Vold-Kalman filter (VKF) is used for angular resampling of the original vibration signal. The results show that the shaft rotating speed could be accurately identified from extracted gear meshing components. The order spectrum obtained by the proposed method with tacholess is substantially the same as the order spectrum obtained by a tachometer. Simulation analysis and experimental results verify the advantages of proposed tacholess order tracking technology for monitoring and fault diagnosis of gearbox vibration under the condition of strong noise and large speed variation.

A tacholess order tracking method for wind turbine planetary gearbox fault detection

Wind turbine (WT) usually works under a poor condition, its operating speed varies almost all the time, therefore, the transmission mechanism of planetary gearbox tends to occur fault to a large extent, and an effective fault detection method for WT planetary gearbox is urgently needed. However, the traditional fault detection methods which are based on constant operating speed assumption will be invalid in such a complex situation, this paper provides a novel tacholess order tracking method based on generalized demodulation (GD) for WT fault detection. Firstly, the conventional GD is modified with dual path optimization ridge estimation (DPORE) strategy, and the main innovative idea of the proposed method is that the phase reference information is obtained from the generator shaft vibration signal through GD and Hilbert transform rather than the gearbox vibration signal. Then the raw gearbox vibration signal could be resampled with uniform angle. Finally, the envelope order spectrum is obtained and the fault characteristic order (FCO) related to the WT planetary gearbox fault can be identified without auxiliary sensors. The effectiveness of the proposed method is demonstrated by real-world WT vibration signals, compound-faults on planetary gearbox can be effectively uncovered and a better performance is obtained when compared with the conventional method.

Order spectrogram visualization for rolling bearing fault detection under speed variation conditions

Abstract For rotating machinery condition monitoring and fault diagnosis under speed variation conditions, order tracking has been considered as a very powerful non-stationary vibration signal analysis method, when compared with the frequency analysis methods based on stationary assumption. However, the conventional order tracking methods require additional hardware to provide a phase reference signal. This constraint limits the conventional methods in industrial applications significantly. In order to further improve the applicability of the conventional order tracking methods, some tacho-less order tracking methods have been proposed in the past few years. Despite the tacho-less order tracking methods successfully getting rid of reference signal, the algorithms are very complex and the computational burden is increased correspondingly. To address the aforementioned shortcomings, a straightforward tacho-less order tracking method based on order spectrogram visualization is proposed in this paper. In the proposed method, a ridge extraction approach is used to estimate the instantaneous frequency of a certain rotating frequency harmonic. And then the vibration signal is resonance demodulated and the time-frequency distribution of the demodulated signal is obtained. A subsequent transform is conducted and the frequency axis of the time-frequency distribution is rescaled based on the estimated instantaneous frequency of rotating shaft. Then, an order spectrogram is constructed and thereby the non-stationary interference introduced by rotating speed fluctuation is suppressed. Finally, fault orders are uncovered and bearing fault type can be identified. The effectiveness of the proposed method has been validated by both simulated and experimental rolling bearing vibration signals. The results illustrate the improved features regarding previously developed tacho-less order tracking method in bearing diagnosis under speed variation conditions.

A modified tacho-less order tracking method for the surveillance and diagnosis of machine under sharp speed variation

Tacho-less order tracking (TLOT) is an effective technique to address the surveillance and diagnosis of mechanical fault on speed variation conditions without tachometers. Nevertheless, fault diagnosis with sharp speed fluctuations is still a challenging task, since the accurate instantaneous frequency (IF) cannot be obtained from the acquired condition signals. In this work, a modified TLOT method based on nonlinear compensating demodulation transform (NCDT) is proposed for fault diagnostics in extreme condition monitoring of machinery. During NCDT, the demodulation functions based on opposite cubic polynomial are investigated and performed to improve IF estimation. Then, a regression filter (RF) is employed to extract the interested harmonic component according to the estimated IF and instantaneous bandwidth for signal resampling. Finally, order spectrum analysis is used to analyze the resampled signal for mechanical fault diagnosis. Simulations, experiments and industrial cases are given to verify the effectiveness and efficiency of the proposed method. The results are as effective as those obtained by tacho-based method under sharp speed fluctuation.

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.

Tacholess order-tracking approach for wind turbine gearbox fault detection

Monitoring of wind turbines under variable-speed operating conditions has become an important issue in recent years. The gearbox of a wind turbine is the most important transmission unit; it generally exhibits complex vibration signatures due to random variations in operating conditions. Spectral analysis is one of the main approaches in vibration signal processing. However, spectral analysis is based on a stationary assumption and thus inapplicable to the fault diagnosis of wind turbines under variable-speed operating conditions. This constraint limits the application of spectral analysis to wind turbine diagnosis in industrial applications. Although order-tracking methods have been proposed for wind turbine fault detection in recent years, current methods are only applicable to cases in which the instantaneous shaft phase is available. For wind turbines with limited structural spaces, collecting phase signals with tachometers or encoders is difficult. In this study, a tacholess order-tracking method for wind turbines is proposed to overcome the limitations of traditional techniques. The proposed method extracts the instantaneous phase from the vibration signal, resamples the signal at equiangular increments, and calculates the order spectrum for wind turbine fault identification. The effectiveness of the proposed method is experimentally validated with the vibration signals of wind turbines.

A dual path optimization ridge estimation method for condition monitoring of planetary gearbox under varying-speed operation

Abstract Tacholess order tracking method is an effective tool for condition monitoring of planetary gearbox under varying-speed operation to reduce the measurement cost and avoid the inconvenience in the installation and adjustment. The robust ridge estimation is an indispensable procedure in the tacholess order tracking. However, conventional ridge estimation methods are difficult to extract the targeted ridge from the highly nonstationary signals. In this paper, we propose a novel method, termed dual path optimization ridge estimation (DPORE), which implants the idea of local integration to adapt with the intensively oscillated ridge. An in-situ vibration signal collected from a wind turbine planetary gearbox provided by the contest during the conference CMMNO December 2014 is employed to validate the proposed method. As a result, an important time-frequency ridge with weak energy and intricate shape is successfully extracted by the proposed method, while two popular ridge estimation methods cannot well track the complete time-frequency ridge. Moreover, the results obtained by the proposed method outperform those provided by the contestants in the conference contest. Finally, the accuracy of estimated ridge is further demonstrated by order analysis and one of the planet bearings in planetary gearbox with an inner race defect can be detected based on the order spectrum.

An online tacholess order tracking technique based on generalized demodulation for rolling bearing fault detection

Vibration analysis has been proved to be an effective and powerful tool for the condition monitoring and fault diagnosis of rolling bearings. During the past decades, the conventional envelope analysis has been one of the main approaches in vibration signal processing. However, the envelope analysis is based on stationary assumption, thus it is not applicable to the fault diagnosis of bearings under rotating speed variation conditions. This constraint limits the bearing diagnosis in industrial applications. In recent years, order tracking methods based on time–frequency representation have been proposed for bearing fault detection under speed variation operating conditions. However, the methods are only applicable for offline bearing fault detection. Aiming at the shortcomings of the current tacholess order tracking techniques, an online tacholess order tracking method is proposed in this paper. The proposed method is on the basis of extracting the instantaneous tachometer information from the collected vibration signal itself continuously, and resampling the original signal with equal angle increment. The envelope order spectrum is used for bearing fault identification. The effectiveness of the proposed method has been validated by both simulated and experimental bearing vibration signals.

A tacho-less order tracking technique for large speed variations

Order tracking is considered as a classic and effective technique of the non-stationary vibration analysis for rotating machinery. Traditionally, a tachometer is required to obtain a reference signal. Some tacho-less order tracking methods have been proposed in the past few years to improve the applicability of traditional order tracking technique. However, current tacho-less order tracking methods are only applicable to those with small speed fluctuations. A new tacho-less order tracking method is established for any speed variations including large speed variation such as run-up or run-down process of machinery. In this method, a Chirplet-based approach is proposed to estimate the instantaneous frequency of a certain harmonic of rotating frequency. The result is accurate and reliable since the chirp basis can be adjusted to match the vibration signal. After that, Vold–Kalman filter is employed to extract the harmonic, because it is particularly suitable for the harmonic extraction under large speed variations. Then, the shaft angular position is recovered from the vibration signal through demodulating the extracted harmonic. The order tracking is carried out by using the shaft angular position thereafter. Simulations and experiments are given to testify the proposed tacho-less method. The results obtained by the proposed method are almost the same as those obtained by a tachometer under large speed variation.