Autocorrelation: Identifying machine vibration signals
The autocorrelation is a defect identification tool in machines that, after the time domain analysis, correlates the waveforms to themselves to calculate a correlation factor at every instant of time.
The period characterization is the technical basis of the vibration analysis technique in predictive maintenance. When the rotating machines indicate signs of failure, most part of the defects present periodic characteristics, as:
● The passing of each rolling element over a crack on the outer race of a bearing.
● Each engagement of a defected tooth on a crown wheel and pinion gearing assembly.
● Each revolution of an unbalanced mass present in a rotor.
●The passing of each fan vane with cracks over a fixed reference point.
With the components’ geometrical, constructive and operational information, it becomes possible to determine the period and, therefore, the frequency in which these events occur.
From the period and frequency determination, the autocorrelation is used from the waveform, once it alters itself when a defect in a rotating machine emerges.
When the alteration is noticed, a more detailed level of analysis is put into action to confirm the existence of a defect and define the failure modes and the recommended course of actions.
The result of the tool’s usage is a form of an autocorrelated wave which indicates the presence of periodical events in the vibration signals, because the maximum value of the autocorrelation factor tends to 1 for a periodic signal and the autocorrelation is periodic.
On the other hand, if the signal is aleatory, the maximum value of the autocorrelation factor tends to 0 and the autocorrelation is aleatory.
Analyzing anomalies with waveform and autocorrelation
The figures below show the stages of progressive evolution of a defect on the outer race of a bearing located on the discharge pulley of a bucket wheel stacker-reclaimer, operating at 60 RPM. The effects can be observed on the acceleration waveform and its autocorrelation.
With flawless bearing, the RMS of the waveform in the axial axle is 0.0276g and the autocorrelation is of 0,0510g. The periodic events of the bearing don’t possess relevant energy in the vibration signal and the autocorrelation is predominantly random.
When the defect is in its incipient phase, no alteration becomes evident in the waveform. The RMS increase in the waveform is 6,5% in the axial direction. However, the autocorrelation signal is visibly altered: it becomes periodical, its RMS increases 91% in the axial direction and the pike of the correlation positive factor surpasses 0,25 in several moments.
In this stage, the defect begins to be noticed on the waveform, which also starts to exhibit a periodical characteristic and a relevant evolution of RMS – 411% related to the previous stage in the axial direction.
Despite it being a more evident and assertive defect characteristic, it was only noticed in the waveform around a month after the identified alterations in the autocorrelation.
This, nonetheless, becomes predominantly periodic and its positive peak exceeds the 0,85 value in all the cycles.
As it’s possible to observe, the autocorrelation is a great industrial condition of an industrial active monitoring tool, because it’s capable of alerting the vibration analyst about the existence of an anomalous condition with great antecedence.
When added to the other vibration analysis tools, such as the circular waveform, the autocorrelation power becomes even more evident. The picture below points out how the circular waveform of autocorrelation, from the case exemplified above, evolves from July 13th, flawless, to August 29th, with great severity defect.
The autocorrelation’s circular waveform does not present oscillations.
The circular waveform of the autocorrelation exhibits 4 oscillations in each 0,0686s turn. This turn’s duration equates to 14,5hz, which corresponds to the defect frequency on the bearing’s outer lane.
The 4 oscillations occur in a 0,97s period, equals 58hz, which is the 4th harmonic from the defect frequency in the bearing’s outer lane.
To allow analysis as these ones performed so far, Dynamox now provides the waveform correlation in the DynaPredict Web Platform, in the client’s navigator, using stored data in the cloud and completely online.
It allows the acceleration, speed and displacement signals, raw or digitally filtered, the period cursors’ usage and the graphic manipulation with different tools, facilitating the identification of periodic events and the frequency determination of these events. Furthermore, it is possible to visualize and manipulate the circular waveform autocorrelation, as described in this article.
The autocorrelation is available in the Spectral and Spectral Comparison pages. It can be enabled or disabled by clicking on the Toggle located on the right superior corner of these pages.
The circular waveform of autocorrelation can be enabled or disabled with the Toggle located on the left superior corner of these pages.
Signal Processing Tools
As the autocorrelation entirely depends on the waveform, when a determined processing is applied to the signal, it reflects on the autocorrelation. Therefore, if we apply a low-pass filter with a 300hz cut on the signal, the autocorrelation is resultant of the filtered signal.
Similarly, if a transformation to speed or displacement is performed, it reflects upon the autocorrelation.
All the available tools to aid the waveform analysis are also available to the autocorrelation analysis in the superior right corner of the graph.
Ergo, it’s possible to apply different kinds of zoom, drag, define axle limit, apply period cursor, add notes, show or hide the statistics and the reference grid.
Keep navigating and read more about the circular waveform tools and cascade spectrum, interactive and personalized graphics which aid in the analysis of industrial active flaws, via DynaPredict Web Platform.