Over the past five sessions, we have discussed the fundamentals of vibration measurement, including free vibration, forced vibration, vibration transmissibility, vibration damping, natural frequency and damping ratio, as well as the amplitude, frequency, and phase of vibration waveforms, and how vibrations are represented (acceleration, velocity, displacement).
This time, I will talk about equipment diagnostics for rotating machinery using vibration methods.
There are many possible causes of malfunctions in rotating machinery, but most are related to frequency. By performing a frequency analysis and examining which frequency levels of vibration and noise are increasing, it is often possible to determine the cause of the malfunction.
The following are some of the typical causes of abnormal vibrations occurring in rotating machinery:
- Unbalance
- Misalignment
- rattle
- Bending of the shaft
- Bearing damage
- Gear damage
- Resonance with rotational order components
This time, I will briefly explain item number 5, "Bearing damage."
Rolling bearings are widely used in the rotating, slewing, and oscillating parts of machinery, and are one of the most important components of rotating machinery, as they deteriorate particularly quickly and require regular maintenance.
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Figure 1: Motion of a rolling bearing -
Figure 2: When damage occurs to the outer ring of a rolling bearing.
Figure 1 shows the motion of a rolling bearing. When the inner ring, which is directly connected to the rotating shaft, rotates, the rolling elements (balls) rotate on their own axis while revolving around the Earth. This motion is similar to that of the moon orbiting the Earth. This rotation of the rolling elements generates vibrations. This is called rolling element passage vibration. Figure 3 shows the vibration time waveform of a normal bearing. In this case, the vibration level of the rolling element passage vibration is relatively small. This time waveform was obtained by attaching a contact-type piezoelectric Accelerometer to the bearing casing and monitoring it with an FFT analyzer.
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Figure 3. Vibration time waveform of a normal bearing (vertical axis: acceleration, m/s²)
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Figure 4. Vibration time waveform of a bearing with damage (vertical axis: acceleration, m/s²)
For example, as shown in Figure 2, if there are spot scratches on the outer ring, an impact vibration occurs each time the rolling element rotates and collides with the spot scratches. This is as if the outer ring is being hammered, resulting in a high-frequency impact vibration (usually several kHz or higher) equivalent to the natural frequency of the workpiece. Furthermore, this impact vibration is clearly a repetitive vibration with a certain period.
Next, the spectral analysis of the time waveforms in Figures 3 and 4 is shown in Figure 5, "Vibration Power Spectrum of a Normal Bearing," and Figure 6, "Vibration Power Spectrum of a Damaged Bearing."
Compared to Figure 5, Figure 6 shows an increase in the vibration level at frequencies around 4 kHz, indicating that high-frequency shock vibrations dependent on damage to the outer ring are occurring.
In this way, by using the initial bearing data under normal conditions as a baseline and checking the changes, it is possible to determine the occurrence of an abnormality.
Specifically, by periodically monitoring vibration levels in a particular frequency band using a vibration comparator or FFT comparator, it becomes possible to construct an equipment diagnostic system.
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Figure 5. Vibration power spectrum of a normal bearing.
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Figure 6. Vibration power spectrum of a bearing with damage.
In vibration diagnosis due to bearing damage, a method to estimate the location of the bearing damage, namely precise diagnostic techniques using an FFT analyzer, is frequently employed.
When a localized scratch occurs in a rolling bearing, it results in repeated shock vibrations, as shown in Figure 4. The frequency of these shock vibrations varies depending on the location of the scratch in the rolling bearing (inner ring, outer ring, rolling elements).
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Figure 7 Shock vibrations generated in rolling bearings
Therefore, if the frequency, which is the reciprocal of the period of impact vibration, can be determined, as shown in Figure 7, the location of the injury can be identified.
Setting item
f0: Axis resonance frequency [Hz]
D: Pitch circle diameter of the bearing [mm]
d: Diameter of the rolling element [mm]
a: Contact angle of rolling elements [deg]
Z: Number of rolling elements
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Figure 8. Structure of rolling bearings and formula for calculating the frequency of shock vibrations caused by damage.
While I will omit a detailed explanation, as shown in Figure 8, the frequency of repeated shock vibrations caused by damage can be determined if the specifications of the bearing and the rotational speed of the rotating body are known (Note: Here, we assume that there is only one location for each cause of damage).
If we denote the frequencies of the shock vibrations caused by damage to the inner ring, outer ring, and rolling elements as f in, f out, and f ball, respectively, then generally, f out < f in < f ball.
So, how can we determine the repetition frequency of shock vibrations caused by damage to rolling elements?
As shown in Figure 7, the actual frequency of the shock waveform is high, several kHz or more, while the repetition frequency of the shock vibration we want to determine is usually very low, typically several tens of Hz. Therefore, if we analyze the original vibration waveform directly in a low frequency range, the high-frequency components will be lost, and we will not be able to obtain information about the repetition frequency. To address this, we perform envelope processing on the shock vibration waveform (Figure 9), converting it into a relatively simple time waveform and analyzing it in a low frequency range to determine the repetition frequency of the shock vibration.
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Figure 9: Time waveform (blue line) obtained by applying envelope processing to the shock waveform from Figure 7.
Figure 10 shows an example of a system configuration for actual envelope processing. Before performing envelope processing, rotational first-order components and low-frequency vibration components become noise when extracting the shock waveform. Therefore, using a bandpass filter to remove unwanted vibration components is a key technique in this measurement.
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Figure 10 Measurement configuration diagram for precise diagnosis of rolling bearings
Figure 11 shows an example of a time waveform obtained by applying envelope processing to an actual impact vibration time waveform, and it can be seen that the period of the damage has become clearer.
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Figure 11 Envelope waveform of a damaged bearing vibration
Furthermore, Figure 12 shows the results of frequency analysis of the envelope-processed time waveform. The frequency of the spectral peak at this time is 71 Hz, and the frequency calculated to indicate damage to the outer ring is 71.13 Hz. Therefore, it can be determined that this bearing has damage to the outer ring.
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Figure 12. Spectrum after envelope processing of bearing vibration with a scratch on the outer ring (fout on the right of the graph is a value obtained by calculation).
Finally, here's a summary.
- The causes of malfunctions in rotating machinery often manifest as differences in the frequency components of vibration and noise signals, making FFT analyzers an important application.
- If there is a spot scratch anywhere on the inner ring, outer ring, or rolling element (ball) of a rolling bearing, it will cause a series of shocking vibrations called rolling element passing vibrations.
- The shock vibration caused by spot scratches is a resonance phenomenon in the components that make up the bearing, and therefore its frequency range is high, at several kHz or higher.
- The repetition frequency of shock vibrations varies depending on which part of the bearing is damaged, so precise diagnostic techniques that analyze the frequency components are often used.
- To extract the repetition frequency of the shock vibration, bandpass filtering and envelope processing are performed as preprocessing steps, followed by frequency analysis.
【keyword】
Rolling bearings, inner rings, rolling elements, vibrations passing through rolling elements, FFT analyzers, piezoelectric Accelerometer, outer rings, spot scratches, natural frequencies, vibration comparators, precision diagnostic technology, envelopes, bandpass filters
【reference】
"How to Conduct Diagnostics for Rotating Machinery," by Toshio Toyoda, Japan Plant Maintenance Association (1991)
"FFT Analyzer User Manual," edited by Kenichi Kido, Japan Plant Maintenance Association (1984)
(Excerpt from the email newsletter issued on July 22, 2016)
