Time Synchronous Averaging Research Articles

Optimal filtering of gear signals for early damage detection based on the spectral kurtosis

In this paper, we propose a methodology for the enhancement of small transients in gear vibration signals in order to detect local tooth faults, such as pitting, at an early stage of damage. We propose to apply the optimal denoising (Wiener) filter based on the spectral kurtosis (SK). The originality is to estimate and apply this filter to the gear residual signal, as classically obtained after removing the mesh harmonics from the time synchronous average (TSA). This presents several advantages over the direct estimation from the raw vibration signal: improved signal/noise ratio, reduced interferences from other stages of the gearbox and easier detection of excited structural resonance(s) within the range of the mesh harmonic components. From the SK-based filtered residual signal, called SK-residual, we define the local power as the smoothed squared envelope, which reflects both the energy and the degree of non-stationarity of the fault-induced transients. The methodology is then applied to an industrial case and shows the possibility of detection of relatively small tooth surface pitting (less than 10%) in a two-stage helical reduction gearbox. The adjustment of the resolution for the SK estimation appears to be optimal when the length of the analysis window is approximately matched with the mesh period of the gear. The proposed approach is also compared to an inverse filtering (blind deconvolution) approach. However, the latter turns out to be more unstable and sensitive to noise and shows a lower degree of separation, quantified by the Fisher criterion, between the estimated diagnostic features in the pitted and unpitted cases. Thus, the proposed optimal filtering methodology based on the SK appears to be well adapted for the early detection of local tooth damage in gears.

Fault degradation assessment of water hydraulic motor by impulse vibration signal with Wavelet Packet Analysis and Kolmogorov–Smirnov Test

The machinery fault diagnosis is important for improving reliability and performance of systems. Many methods such as Time Synchronous Average (TSA), Fast Fourier Transform (FFT)-based spectrum analysis and short-time Fourier transform (STFT) have been applied in fault diagnosis and condition monitoring of mechanical system. The above methods analyze the signal in frequency domain with low resolution, which is not suitable for non-stationary vibration signal. The Kolmogorov–Smirnov (KS) test is a simple and precise technique in vibration signal analysis for machinery fault diagnosis. It has limited use and advantage to analyze the vibration signal with higher noise directly. In this paper, a new method for the fault degradation assessment of the water hydraulic motor is proposed based on Wavelet Packet Analysis (WPA) and KS test to analyze the impulsive energy of the vibration signal, which is used to detect the piston condition of water hydraulic motor. WPA is used to analyze the impulsive vibration signal from the casing of the water hydraulic motor to obtain the impulsive energy. The impulsive energy of the vibration signal can be obtained by the multi-decomposition based on Wavelet Packet Transform (WPT) and used as feature values to assess the fault degradation of the pistons. The kurtosis of the impulsive energy in the reconstructed signal from the Wavelet Packet coefficients is used to extract the feature values of the impulse energy by calculating the coefficients of the WPT multi-decomposition. The KS test is used to compare the kurtosis of the impulse energy of the vibration signal statistically under the different piston conditions. The results show the applicability and effectiveness of the proposed method to assess the fault degradation of the pistons in the water hydraulic motor.

Time domain averaging across all scales: A novel method for detection of gearbox faults

The vibration signal of a gearbox carries the signature of the fault in the gears. As such early fault detection of the gearbox is possible by analyzing the vibration signal using different signal processing techniques. Time synchronous averaging can extract the periodic waveforms of a noisy vibration signal, whereas Wavelet transformation is able to characterize the local features of the signal at different scales. This paper proposes a new technique, time domain averaging across all scales, which combines the time synchronous average and wavelet transformation together to extract the periodic waveforms at different scales from noisy vibration signals. The technique efficiently cleans up noise and detects both local and distributed faults simultaneously. A pilot plant case study is presented to demonstrate the efficacy of the proposed technique.

An automated methodology for performing time synchronous averaging of a gearbox signal without speed sensor

In this paper we extend a sensorless algorithm proposed by Bonnardot et al. for angular resampling of the acceleration signal of a gearbox submitted to limited speed fluctuation. The previous algorithm estimates the shaft angular position by narrow-band demodulation of one harmonic of the mesh frequency. The harmonic was chosen by trial and error. This paper proposes a solution to select automatically the mesh harmonic used for the shaft angular position estimation. To do so it evaluates the local signal-to-noise ratio associated to the mesh harmonic and deduces the associated low-pass filtering effect on the time synchronous average (TSA) of the signal. Results are compared with the TSA obtained when using a tachometer on an industrial gearbox used for wastewater treatment. The proposed methodology requires only the knowledge of an approximate value of the running speed and the number of teeth of the gears. It forms an automated scheme which can prove useful for real-time diagnostic applications based on TSA where speed measurement is not possible or not advisable due to difficult environmental conditions.

FAULT DETECTION OF ROTATING MACHINERY FROM BICOHERENCE ANALYSIS OF VIBRATION DATA

The vibration signal carries the signature of faults in most rotating equipments, and early fault detection is possible by analyzing the signal using different signal processing techniques. In this paper we consider a gearbox as a typical representation of a rotating or cyclo-stationary process. Faults in gearboxes leave their signature on the vibration signal and generally manifest themselves as a non-linear transformation in the signal. Bicoherence analysis detects and quantifies the presence of non-linearity in the signal and thus indicates the severity of the fault in the gearbox. In this work, time synchronous averaging is used to find the proper representation of one period of the cyclo-stationary vibration signal. A pilot scale gearbox case study is presented to demonstrate the practicality and utility of the proposed technique.

A robust diagnostic model for gearboxes subject to vibration monitoring

This paper presents a robust model-based technique for the detection and diagnosis of gear faults under varying load conditions using the gear motion residual signal. Since the majority of energy in the healthy state of the gear of interest is concentrated at the meshing fundamental and its harmonics, the gear motion residual signal, obtained by the removal of the regular gear meshing fundamental and its harmonics from the time-synchronous average (TSA) signal, will be much less sensitive to the varying load conditions than the TSA signal. Also, the gear motion residual signal usually shows evidence of faults earlier and more clearly than the TSA signal. Therefore, less load dependence and an earlier indication of incipient faults can be obtained simultaneously. A noise-adaptive Kalman filter-based auto-regressive (AR) model is fitted to the gear motion residual signals in the healthy state of the gear of interest. By the selection of a proper model order which provides a compromised model for the healthy gear under various load conditions with the aid of a specific AR model order selection method proposed in this study, further enhancement in load independence can be obtained in the AR model residuals. Consequently, a robust statistical measure, which takes the percentage of outliers exceeding the three standard deviation limits of the baseline AR model residuals, is applied to evaluate the state of the gear of interest. The proposed diagnostic model is validated using full lifetime vibration signals of gearbox operating from new to breakdown under a variety of failure modes and demonstrates remarkable advantages over other newly proposed techniques.

Comparison of localised spalling and crack damage from dynamic modelling of spur gear vibrations

This paper presents a 26 degree of freedom gear dynamic model of three shafts and two pairs of spur gears in mesh for comparison of localised tooth spalling and damage. This paper details how tooth spalling and cracks can be included in the model by using the combined torsional mesh stiffness of the gears. The FEA models developed for calculation of the torsional stiffness and tooth load sharing ratio of the gears in mesh with the spalling and crack damage are also described. The dynamic simulation results of vibration from the gearbox were obtained by using Matlab and Simulink models, which were developed from the equations of motion. The simulation results were found to be consistent with results from previously published mathematical analysis and experimental investigations. The difference and comparison between the vibration signals with the tooth crack and spalling damage are discussed by investigating some of the common diagnostic functions and changes to the frequency spectra results. The result of this paper indicates that the amplitude and phase modulation of the coherent time synchronous vibration signal average can be effective in indicating the difference between localised tooth spalling and crack damage.

Compensation for encoder geometry and shaft speed variation in time interval torsional vibration measurement

Digital time interval techniques for the measurement of torsional vibrations in rotating shafts have been used in a variety of applications. The techniques use high-speed timers to detect the passage times (often referred to as “zero crossings”) in a carrier signal from a multiple pulse per revolution encoder on the shaft. Next, a reference array is created by computing the passage times for an encoder with geometrically uniform segments rotating at a constant speed. The measured times are compared against the reference array and the time difference processed to yield the shaft torsional vibration. If the reference array differs from the encoder passage times, the calculated torsional vibration will be subject to bias errors manifested as high-level order content. There are two potential causes for inconsistency in the reference signal: (1) geometric variation in angular encoding device and (2) a non-constant shaft speed. Procedures to handle these situations are addressed. An in situ encoder calibration method is presented that creates a reference array representative of the actual encoder angular intervals. The method uses time synchronous averaging of the encoder zero crossing over many shaft revolutions. The process causes the time passage variations induced by the torsional vibration to average to zero, ultimately yielding the time stamps caused by the passage of each respective encoder segment. The synchronous averaged encoder passage times are then used to correct the reference array to calculate the torsional vibration. Variation of the encoder geometry and changes in shaft running speed cause the torsional vibration be sampled on a non-uniform time interval basis. The non-uniform time sampling would cause errors if used with fixed sampling interval algorithms such as the DFT. A resampling algorithm is applied to create an array sampled with a constant time interval basis to minimize the error. The background and implementation details of time interval torsional vibration measurement enhancements are first presented. The capabilities are then demonstrated with experimental results from several pieces of rotating equipment. The tests show the successive improvement in the torsional vibration data as the proposed compensation methods are sequentially applied.

VIBRATION MONITORING FOR FAULT DIAGNOSIS OF HELICOPTER PLANETRY GEARS

In this paper, vibration data analysis techniques are investigated for fault diagnosis of helicopter planetary gears. A data pre-processing technique is introduced that achieves the same result as the commonly used Time Synchronous Averaging with much lower computational complexity since interpolation is not required. A notion of using raw vibration data instead of the Time Synchronous Averaged data is also presented that is more suitable for the analysis of vibration data produced by planetary gearboxes and for the purposes of detecting carrier plate crack fault. Based on this notion, features such as the Harmonic Index in the frequency domain and the Intra-Revolution Energy Variance in the wavelet domain are derived. The features are used as inputs to fault classifiers and are shown to detect the fault successfully based on the test data that is available.

EFFECTIVENESS AND SENSITIVITY OF VIBRATION PROCESSING TECHNIQUES FOR LOCAL FAULT DETECTION IN GEARS

This paper deals with gear condition monitoring based on vibration analysis techniques. The detection and diagnostic capability of some of the most effective techniques are discussed and compared on the basis of experimental results, concerning a gear pair affected by a fatigue crack. In particular, the results of new approaches based on time-frequency and cyclostationarity analysis are compared against those obtained by means of the well-accepted cepstrum analysis and time-synchronous average analysis. Moreover, the sensitivity to fault severity is assessed by considering two different depths of the crack. The effect of transducer location and processing options are also shown. In the case of the experimental results considered in this paper, the power cepstrum is practically insensitive to the crack evolution. Conversely, the spectral correlation density function is able to monitor the fault development and does not seem to be significantly influenced by the transducer position. Analysis techniques of the time-synchronous average, such as the ‘residual’ signal and the demodulation technique, are able to localise the damaged tooth; however, the sensitivity of the demodulation technique is strongly dependent on the proper choice of the filtering band and affected by the transducer location. The wavelet transform seems to be a good tool for crack detection; it is particularly effective if the residual part of the time-synchronous averaged signal is processed.

49 Variable age of onset in an alzheimer family with a His163Tyr mutation in the presenilin 1 gene

Fault diagnosis of gearbox at an early stage is very important to avoid catastrophic failures. Condition indicators (CI) are used to quantify the level of vibration generated by the defected gears. A comprehensive comparison of various CIs, i.e., RMS, kurtosis, crest factor, FM0, FM4, M6A, NB4, energy ratio, NA4, energy operator and two new proposed condition indicators (PS-I and PS-II), have been performed for no crack, initial crack and advanced crack for different fluctuating profiles of input speed. This comparative analysis shows the responsiveness of indicators towards crack detection. Limited speed fluctuations and instantaneous high speed fluctuations are considered. Results suggest that newly proposed condition indicators are more robust, stable and effective towards crack detection under fluctuating profiles of speed. A modified time synchronous averaging (MTSA) is also proposed to increase signal-to-noise ratio (SNR).

Pressure mapping under an operating lawn mower deck

The use of relatively quiet engines and electric motors on lawn mowers has shifted much of the emphasis on noise reduction to the under deck flow-induced noise sources. However, the environment under an operating mower deck makes it difficult to either model or directly measure the pressure field. This presentation will detail a rather simple scheme which was used to first measure, then animate the pressure field in a plane directly below an operating deck, using an inertial frame of reference. Time synchronous averaging was employed to collect the data at discrete sample points. Individual data planes were then reconstructed representing all the sample points at specific blade locations. The measurement planes were contoured and used as separate frames in a slow-motion animation of the pressure field.

Time synchronous averaging of ball mill vibrations

This note presents an investigation into the problems of ball mill pinions. Pinion pitch measurements and vibration analysis were conducted to find a relationship between vibration signals and the errors. Analysis of time synchronous averaging (TSA) indicates the teeth with pitch error. TSA and sideband index (measure of sidebands in spectrum) allows the first estimation of the pinion quality and could be applied for commissioning new pinions and gears, and also in a routine procedure for progressive machine condition assessment. Valuable information on the gear condition is obtained from the sideband index.