Abstract
In this work two methods for gearrattling detection in mechanical systems are studied. For this purpose, an experimental quickreturn mechanism was constructed with gears driven by an electric motor. Rattling is detected from the mechanical vibrations acceleration and the electric motor current. Vibrations signal is measured by a biaxial accelerometer and electrical current is obtained from the motor electronic driver. Signals are processed in timedomain and timefrequency domain. Rattling level is measured through a proposed performance evaluation index that is obtained from the application of bandpass filters and the RMS value of the signal for the timedomain processing. For the timefrequency analysis, the wavelet transform is used to isolate the rattling and the signal is postprocessed to compute the RMS value. It is shown that the use of the electric motor current for the detection of rattling produce better results than the mechanical vibrations acceleration. With respect to the timedomain method versus the timefrequency method, it was found that the application of the wavelet transform significantly improves the indexes that are used for gearrattle detection.
1. Introduction
Rotating machines are widely used in various industry applications. These machines must run safely and reliably under different operational conditions to ensure the quality of manufactured products and prevent any catastrophic failure. Condition monitoring systems are commonly adopted for diagnosis of the mechanical systems based on the history and evolution of the operating characteristics of the system. Various monitoring and analyses techniques are reported in the literature. Acoustic emission monitoring is an approach that has been adopted for earlier fault detection in mechanical elements such as rolling bearings. It allows the user to monitor the rate of degradation on the bearings and defect size [1]. Mechanical systems with gear elements have also been studied from vibration signals, which give information of the evolution of gear faults and crack magnitude [2]. Reliable realtime monitoring tools to prevent gear systems degradation based on the measurement of mechanical vibrations have also been proposed [3].
Mechanical transients can occur during the machine’s regular operation. These transients are the result of disturbances events. Mechanical transient analyses require online monitoring to detect problems for decision making. Machine vibration analysis is a common practice, and timefrequency methods of analysis are used to detect transient events that are buried in continuous machinery vibration data. Short time Fourier transform and wavelet transform are two valuable timefrequency diagnostics methods [4]. The wavelet transform has been applied successfully to the detection of gear condition, and specifically for crack detection in comparison with other timefrequency techniques [5]. However, wavelets have not achieved a standard status, and there is not a standard method to select the wavelet function for a particular problem. It is difficult to obtain information directly from the wavelet transform and results are not easily understood [6]. Despite this, the wavelet is a robust technique of analysis and it is, for some applications, the most important nonstationary signal processing tool today [7]. It has also led to the development of customized wavelets, designed to match the transient properties of the studied fault for improving the diagnosis methods [8]. Not only wavelets are used to detect mechanical transients, but also for feature extraction in noisy vibration signals with noise canceling and clean up techniques for gear damage diagnosis [9], multifault detection and classification [10], and to detect local and distributed faults [11]. New methods derived from the conventional wavelet transform have demonstrated robust and superior detection capabilities in damaged tooth gears [12].
Additionally, the low complexity, high sensitivity and robustness of statistical techniques have been applied successfully in gear failure prediction [13]. Statistical methods can be found today in combination with the wavelet transform for analyzing mechanical systems [14]. Gear fault and damage classification approaches based on wavelets are also under development [15, 16]. To our knowledge no reports have been found in the literature regarding the application of timefrequency analyses to feature extraction and detection of faults in quickreturn mechanisms.
2. Methodology and experimental setup
Mechanical vibrations produced under gearrattling were studied with the quickreturn mechanism shown in Fig. 1 [17]. In this mechanical system a servomotor drives a pinion or secondary gear (G1), while a main gear (G2) drives a slotted bar (2) by means of a driving pin (3). Rigid linkages (1) (2) were used to transfer a linear motion to a ram. The pinion gear was composed of 11 teeth and the main gear of 67 teeth.
A biaxial accelerometer was used to measure the mechanical vibrations in the directions of the ram displacement and normal to the floor. The beginning of each working cycle of the mechanism was detected with a proximity transducer operating as a phase signal detector. The electrical motor controller provided the information of the electrical current by means of an analog output signal. The analog signals were recorded with a LabVIEW program and NI USB6251 DAQ data acquisition system. Experiments were carried out with the motor operating at a speed of 600 rpm and data was acquired at a sampling rate of 10 kHz. The experimental rig is shown in Fig. 2. The picture inset at bottom left has been used to show details of the proximity and accelerometer transducers location.
Fig. 1Experimental quick return mechanism
Fig. 2Experimental system layout
Rattling signal was postprocessed with bandpass filters to isolate the characteristic frequencies of the phenomenon, and a local rootmeansquare (RMS) estimation technique was used to obtain and index for detecting the rattle development and to establish threshold levels for rattling identification. The frequency function of the filter used is given by:
The bandpass of the filter is from ${B}_{1}$ to ${B}_{2}$, with a time delay ${t}_{d}$. And the root mean square (RMS) is given by:
The wavelet transform was used as a second processing technique for rattling development identification. In mathematical terms, a wavelet is a function $\psi $ with zero average:
Which is dilated by a scale parameter $s$, and translated by $u$:
The continuous wavelet transform of a function $f$ at the scale $s$ and position $u$ is computed by correlating $f$ with a wavelet function:
Wavelet transforms can measure timefrequency variations of spectral components with a different timefrequency resolution. A wavelet transform correlates $f$ with ${\psi}_{u,s}$.
The implementation of the continuous wavelet transform is impractical because it consumes a significant amount of time and resources. The discrete wavelet transform DWT can be used to overcome this problem and it consists of a subband codification which can be implemented with a very high computational efficiency. Under this scheme, successive lowpass and highpass filters are applied to the discrete timedomain signal as shown in Fig. 3. Lowpass filters are related to the scaling function while highpass filters are related to the wavelet function, decomposing a signal in subbands that provide the low and high frequency information contained in a signal. In this work the 1D Daubechies wavelet transform was used to decompose the signal and obtain the timefrequency information.
Fig. 3Discrete wavelet transform subband codification
3. Analysis and discussion of results
Mechanical vibrations data and electric motor current are shown in Figs. 4, 5. Although these signals are not directly related, some coincidences can be noticed. A regular change in amplitude can be observed for the entire length of the time recorded in the timedomain plots, showing the twostroke cycle of the mechanism. A nonstationary event can also be distinguished at 4.5 s which corresponds to the instant when rattling occurs.
However, the frequency plots clearly show differences associated with the measured physical quantities. In the case of the acceleration records, mechanical vibrations are produced by the physical structure that supports the gear system. High frequency vibrations (mainly 800 Hz) are produced in response to the different modes of vibration of the mechanical elements when the quickreturn mechanism is operated. However, the spectral analysis of the electrical current that drives the motor shows a peak at a frequency slightly larger than 200 Hz. This frequency is in concordance with the oscillatory phenomenon produced by the rattling of the gears.
Fig. 4Timedomain and frequencydomain of mechanical vibrations signal
Fig. 5Timedomain and frequencydomain electrical motor current signal
Simple statistical analysis techniques for online detection of abnormal operating conditions in mechanical systems may be implemented. For the present work, a statistical technique for rattling development identification has been tested. This technique is based in the application of filters to the timedomain signals, and the construction of an index based on the RMS value of the filters output, according to the description given in the methodology section.
The timedomain signals have been passbandfiltered with a center frequency set to the main excited frequencies. In correspondence to Figs. 4 and 5, frequencies were set to 771 Hz for the vibrations acceleration signal and 224 Hz for the electrical current signal. Finally, the RMS value of the signal was obtained. This process was applied to data packets comprising 0.02 s to include various rattling cycles. Results are shown in Figs. 67. Various operational regions have been defined to establish the limits of the threshold values for rattling identification. Three zones may be observed: The lower zone comprising the signal produced under normal operation, when rattling is not present; a transition zone, where the uncertainty in the rattling identification process may be considerable, depending on the signal of interest; and the upper zone, which defines the developed rattling state. The threshold value that indicates the boundary between normal operation and the transition zone is set to the maximum index value obtained from the signal under normal operation of the system, and the extent of the transition zone was set to the same value of the normal operation zone. This prevents that transitory signals result in falsepositive identification.
For the case of the acceleration signal, rattling vibrations correspond to the structural frequencies that are also excited for each working cycle for normal operation of the mechanism. This results in index value variations that fall within the transition zone when rattling is present, with a significant uncertainty on the identification process. However, RMS values obtained from the electrical current signal are well defined with variations that fall far apart from the transition zone from the beginning to the end of the rattling occurrence. The result is a more reliable identification process technique based on the electrical current.
Fig. 6Rattling development detection from vibrations acceleration signal
Fig. 7Rattling development detection from electrical current signal
Since rattling can be considered a nonstationary phenomenon, a wavelet approach was also evaluated as a second method for detecting the rattling occurrence. Results obtained for the wavelet transform are shown in Figs. 8, 9, where the first four decomposition levels are depicted. Each level is labeled SB, and as a result of the procedure of transformation, it can be noticed that half of the data array is retained for each subsequent sublevel, evidencing the multiresolution analysis, characteristic of the wavelet transform.
The wavelet transform coefficients for the mechanical vibrations acceleration are shown in Fig. 8. Each subband is associated with a frequency range of values, and wavelet coefficients grow in the middle of each subband when rattling occurs. Coefficients associated to rattling are present in all subbands due to the presence of a mechanical vibrations spectrum rich in low and high frequencies. Results for the electrical current signal transformation are shown in Fig. 9. In contrast to the mechanical vibrations, the electrical current frequencies are more clearly defined, particularly in relation to the rattling signal that can be observed within SB1 segment. Lower frequencies are present in response to the signal variations produced by the ram forward and backward movements.
The first four subbands, extracted from the transformed wavelet coefficients array, are shown in Fig. 10. Highamplitude coefficients in subband 1 clearly show the rattling occurrence, in comparison to the lowamplitude coefficients for the adjacent time segments where this phenomenon is not present. This plot shows that the wavelet method is suitable for identifying the gear rattle.
Fig. 8Wavelet transform of acceleration signal
Fig. 9Wavelet transform of electrical motor current signal
The RMS of the wavelet transform was processed to obtain the index and be able to compare both methodologies. Results are shown in Fig. 11. Significant differences arise with respect to Fig. 7. Wavelet processing offers a shorter transition zone, and a wider zone for the rattling developed state. It can also be noticed that the index values for normal operation of the system are almost imperceptible, due to the excellent results obtained by the subband coding of the wavelet approach in the isolation of the rattling. This means that the wavelet function is able to identify more precisely the rattling phenomenon, and it represents a more confident method of identification of the rattling development.
Fig. 10Four subbands extracted from the wavelet coefficients array
Fig. 11Rattling development detection with the wavelet approach
4. Conclusions
Two methodologies have been tested in a quick return mechanism for rattling development detection. A timedomain analysis method was compared to a timefrequency domain analysis method. The acceleration of the mechanical vibrations and the electric motor current were used as the source signals. It was found that, for both methods, the variations in the electrical current produced by the rattling offers a better way of identification of the gearrattle, since frequencies are more localized in the spectrum. However, the wavelet approach, which consisted in the transformation of the signal to the timefrequency domain, and the extraction of the subband with the rattling occurrence, resulted in better discrimination indexes and therefore a superior technique for rattling detection. This represents a very useful tool for online detection of rattling in mechanical systems, since the wavelet transform can be implemented with a highcomputational efficiency.
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