Bearings produce specific vibration frequencies that can be monitored for faults. The amplitude of these vibrations increase as the bearing nears failure.
Rather than wait for the amplified vibration levels to cause failure, it is helpful to try and detect bearing defects early before they become too severe. Early detection is done with a combination of band-pass filtering, envelope analysis, and spectral analysis.
This article outlines the processing steps to determine bearing defects in their early stages. A specific bearing with nine rolling elements and a fault on the outer race will be used throughout the article as an example.
Bearings are mechanical components used to support a rotating shaft in machinery. It is designed to allow the shaft to rotate as freely as possible to minimize wear and tear.
There are many different types of the bearings that have races and rolling elements (Figure 1).
Figure 1: Different bearing types.
Bearing types include:
Ball bearings
Roller bearings
Needle bearings
Tapered roller bearings
Spherical roller bearings
Thrust bearings
A typical bearing consists of rolling elements, an outer race, and an inner race as shown in Figure 2.
Figure 2: Bearing consisting of an inner race, outer race, and rolling elements.
These three components have the following functions:
Rolling elements: Cylindrical or spherical elements that roll and allow relative rotational motion between the inner race and outer race.
Inner race: Fixed to the rotating shaft or element.
Outer race: Fixed to the object that contains the rotating shaft.
2. Bearing Fault Frequencies
Based on the geometry of the bearings, “fault frequencies” can be predicted. These are the frequencies produced by the rotating bearing components that can be seen in the vibration signature.
Fault frequencies are calculated using the geometric information of the bearing elements shown in Figure 3.
Figure 3: Bearing geometry used for the calculation of fault frequencies.
Where:
Nb is the number of balls or rolling elements
α is the contact angle of the ball bearing or rolling element
Bd is the diameter of the ball bearing or rolling element
d2 is the outer diameter of the bearing
d1 is the inner diameter of the bearing
Pd is the pitch diameter
These geometric features and associated fault frequencies are typically provided by bearing manufacturers.
The frequency with which the balls roll against the outer race (BPFO) is shown in Equation 1.
Equation 1: Ball pass frequency on bearing outer race (BPFO)
The frequency with which the balls roll against the inner race (BPFI) is shown in Equation 2.
Equation 2: Ball pass frequency on bearing inner race (BPFI)
The ball spin frequency (BSF) is shown in Equation 3. It is the number rotations that a ball bearing makes per one rotation of the shaft.
Equation 3: Ball spin frequency (BSF) of bearing
The fundamental train frequency (FTF), or cage frequency, is shown in Equation 4. The cage holds the bearings in place and the frequency corresponds to the number of rotations the cage makes per one rotation of the shaft.
Equation 4: Fundamental train frequency (FTF) of bearing
3. Bearing Example
In this article, a bearing with the properties below (Figure 4) is used for an example.
Figure 4: The fault frequencies for a bearing with 9 balls, pitch diameter (Pd) of 1.548 inches, and ball diameter (Bd) of 0.3125 inches. The ball pass frequency on the outer race is highlighted which is where a defect was introduced in the example bearing used in this article.
Notice the fault orders are not a multiple of the nine balls (e.g., 9th, 18th, 27th order, etc.). Due to the interaction of the races and rolling elements, the orders and frequencies are not whole integer numbers. Without the fault frequency equations, the orders and frequencies associated with the rotating bearing would be difficult to guess.
For the rest of this article, vibration data taken from a bearing with and without a fault on the outer race will be used. The speed analyzed is 2000 rpm, which equates to approximately a 121 Hz fault frequency for the outer race.
When analyzing the data using only a Fourier Transform, there is little difference between the good and faulted bearing (Figure 5). There is nothing to clearly indicate that there is a fault in the outer race:
Figure 5: Good bearing (green) versus outer race faulted bearing (red) shows little difference. The fault frequency for the outer race is highlighted with a cursor.
When a bearing is very close to failing (bearing becomes loose, etc.), the amplitude of the fault frequency is much larger than the baseline condition. The result will be a large increase in overall vibration amplitudes which is not seen here.
In this case, the fault on the outer race is small pit which will become a larger fault over time. A small pit creates an impact as ball bearing passes over it. The impact has high frequency content which cannot be seen readily in the Fourier transform.
When trying to perform early detection of faults in bearings, a Fourier Transform alone is not enough to diagnose the issue as illustrated by the nine ball bearing with outer race defect. Filtering and enveloping are needed in addition to the Fourier transform. These additional processing steps are covered in the next sections.
4. Bearing Impacts
As discussed previously, bearing defects start as a series of small periodic impacts as shown in Figure 6.
Figure 6: As the bearings roll over the defect in the outer race they produce small periodic impacts.
The bearing race can develop a crack or become pitted in the early stages of bearing failure. The impacts caused as the bearing rolls over the defect are very small in amplitude and often buried in other vibration sources (imbalance gears, combustion, other bearings,…) of the rotating machinery.
An illustration of how impacts are “buried” in other vibration of the rotating machinery is shown in Figure 7.
Figure 7: Conceptual illustration of the small impacts (left of graph) that are “buried” in the operational vibration (right of graph) of a rotating system.
This makes the bearing defect difficult to identify for two reasons:
Amplitude: The vibration due to the impacts is very small compared to the overall vibration of rotating machinery. If there is a fault, the difference in the measured vibration levels does not change significantly.
Frequency: Impacts are short duration events that are broad in frequency. The impact energy is spread across the frequency domain instead of concentrated at a single frequency. This makes it difficult to diagnose in the frequency domain via the Fourier Transform.
5. Filtering
At very high frequencies (much higher than the fault frequencies), the defect impacts create an amplitude difference as shown in Figure 8. A filter can be applied to the vibration data in this high frequency range to better differentiate the good bearing from the bad bearing.
Figure 8: The good baseline bearing and the faulted bearing show significant differences in the 30 kHz to 35 kHz range which is far above the fault frequency for the outer race (~121 Hz).
Why does the bearing defect manifest between 30 kHz and 35 kHz in this case? Two reasons:
Impact Event Frequency Range: Impact events that are short in time but broad in frequency. They excite a wide frequency range. Other rotating machinery vibrations (gears, combustion, pulsations, imbalance orders, etc.) affect low frequencies of the rotating machinery while the impact energy can be seen at high frequencies.
Accelerometer Resonance: Accelerometers have resonances (Figure 9) at high frequencies which amplify the level of the impact events. In this example, the accelerometer resonance is from 30 kHz to 35 kHz (Note: different model accelerometers will have different resonant frequency ranges)
Figure 9: The internal resonance of accelerometer amplifies high frequencies containing the impact energy.
When measuring vibration in general, the desired frequency response of an accelerometer is flat. The accelerometer frequency response should not gain or attenuate the vibration versus frequency.
But at high frequencies, all accelerometers have a resonance which amplifies the incoming vibration. While the amplification is not ideal for general measurement of vibration, it is useful for the identification of early or small bearing defects.
In this case, the accelerometer resonance amplifies the impact energy of the bad bearing. By applying a band-pass filter (in this example from 30 kHz to 35 kHz) it is easier to distinguish the good bearing from the faulted bearing in the time domain (Figure 10):
Figure 10: Top – Difficult to differentiate the bearing with fault (red) and without fault (green) by viewing the time data. Bottom – After applying a bandpass filter, it is easier to distinguish between the bearing with (red) and without fault (green) in the time domain.
Vibration data gathered for bearing defects need to be measured in a consistent manner for analysis:
Consistent accelerometer types/models: The same accelerometer (with fixed resonance) should be used to measure the baseline versus the faulted condition. Changing accelerometer models that have different resonant frequencies is discouraged since the results will be unpredictable.
Permanently and well mounted: Accelerometers used to monitor bearings are typically installed in place permanently, so their response does not change over time due to remounting. They are also firmly mounted (no hot glue or bees wax) so that they do not come loose over long periods of time.
Structural Resonance: The structural resonances of the rotating machinery should not change over time. Resonances would alter the vibrations levels but not due to defects in the bearing.
Consistent Operating Conditions: The RPM and load measurement conditions of the machinery should be as identical as possible to make comparisons over time.
In this example, with the 30 kHz to 35 kHz band-pass filter, the time data now reflects the bearing defect. But the fault frequency of 121 Hertz has been removed from the data by the band-pass filter. The fault frequency can be “recovered” using envelope analysis which is covered in the next section.
In the previous section the data was band-pass filtered between 30 kHz and 35 kHz to accentuate the difference between the good and bad bearing. The fault frequencies for the bearing are below 200 Hertz. After band-pass filtering the signal from 30 kHz to 35 kHz, performing a Fourier Transform on the data will have no content below 30,000 Hertz. This would make it impossible to trace the defect to a particular part of the bearing (like the outer race at 121 Hz).
To get the fault frequencies (which are below 200 Hz) from the band-pass filtered data (30 kHz to 35 kHz), the solution is to perform an envelope analysis. An envelope is a mathematical function that outlines the maximum amplitude variations of a signal over time, essentially representing the "outline" of the signal.
The defect impacts are still “in” the data as seen in Figure 11. Even though the vibration data (green curve) has frequency content only in the 30 kHz to 35 kHz range, the envelope (blue) will contain frequency content of the fault frequencies.
Figure 11: The envelope (blue) of the faulted bearing overlaid with the band-pass filtered vibration (green).
Performing a Fourier Transform of the envelope of both the good bearing and faulted bearing shows a significant difference at the outer race fault frequency (Figure 12).
Figure 12: The Fourier transform of the envelope of the band-pass filtered data shows a difference between the good bearing (green) and the faulted bearing (red) at the outer race defect frequency. Performing only a Fourier Transform of the same measurements did not show a difference.
By band-pass filtering and enveloping before performing the Fourier transform, there is a significant difference between the baseline and faulted bearing data. No significant difference was present when only a Fourier transform was performed (Figure 5 previously) on the originally recorded data with and without fault.
7. Simplified Envelope Example
How does the envelope help identify the fault frequencies of a bearing? Consider a simplified example that has a series of impacts that occur at a regular interval in a similar manner to a bearing with a defect (Figure 13):
Figure 13: The green curve is a series of impact events that occur 1.66 times a second (inverse of 0.6 seconds).
The envelope (blue), which outlines the impact event time history (green), rises and falls 1.66 times a second. In this simplified example, the fault frequency is 1.66 Hertz instead of 121 Hertz.
The results of a Fourier Transform of the original impact time history (green) versus the envelope (blue) are shown in Figure 14 below.
Figure 14: Fourier Transform of the original impact time history (green) versus the envelope (blue). The spectrum of the impacts (green) does not contain 1.66 Hertz but the spectrum of the envelope does (blue).
In the case of the simplified example, the envelope rises and falls 0.6 seconds apart which corresponds to a frequency of 1.66 Hertz (inverse of 0.6 is 1.66).
The Fourier Transform of the envelope has a 1.66 Hertz peak as shown in Figure 15.
Figure 15: The Fourier transform of the envelope has a peak at 1.66 Hertz. 1.66 times a second is the rate at which the impact events occur in the original signal.
In a similar manner, the Fourier Transform of the band-pass filtered impacts of a bearing defect will contain the fault frequencies of the bearing. The impacts on the outer race (in the example bearing used in this article) occur approximately 121 times per second. The frequency and a proportional amplitude at which the defect impacts occur is reflected in the Fourier Transform of the envelope function. But the defect was not reflected in the amplitude of the peak at 121 Hertz in the Fourier Transform of the original data (Figure 5).
Envelope processing is often used to identify the rate of changes in a signal. The rate of change in the amplitude of a signal is often called a modulation frequency. For examples of how envelopes are used to identify modulation frequencies in a signal see the knowledge article: Simcenter Testlab Neo: Modulation Metrics
7. Simcenter Testlab Neo
The Process Designer of Simcenter Testlab Neo can be used to analyze bearing defects using an envelope analysis. An example process is shown in Figure 16 below.
Figure 16: Simcenter Testlab Neo process for bearing defect analysis includes filtering, envelope, and spectrum methods.
Process Designer (19 tokens)" Pre-requisite for processing data in Simcenter Testlab Neo
Interactive Analysis (19 tokens): For “Filter” and “Envelope” method
Signature Analysis (36 tokens) or Sound Quality Analysis (33 tokens): For “Spectrum Average” method
Add the bearing data to be processed to the input basket. Click on the “Processing” tab at the bottom of the screen. The Process Designer shown in Figure 17 will be ready to analyze the bearing data once the appropriate methods are added.
The output of the Filter Method is then connected to the Envelope method. The Envelope method produces a mathematical function that is the “outline” of the input signal as discussed previously in the article.
There is a low pass cutoff frequency parameter that can be set in the method properties (Figure 20):
Figure 20: Properties menu of the Envelope method in Simcenter Testlab Neo Process Designer.
The higher the cutoff frequency parameter, the more closely the envelope function follows the input signal as shown in Figure 21.
Figure 21: Input signal (green) and envelope function with 2000 Hertz cutoff (orange) and 6000 Hz cutoff (blue).
The Fourier Transform of the envelope will not contain frequency content higher than the cutoff frequency setting. If all the fault frequencies are 200 Hertz or lower, then the cutoff needs to be 200 Hertz or higher to show the fault frequencies.
In the last step, the “Spectrum Average” method is used to calculate a spectrum of the envelope. The properties of the method are shown in Figure 22.
Figure 22: Properties of Spectrum Average method in Simcenter Testlab Neo Process Designer.
If the time data being processed is at a steady state condition (constant rpm) for a duration of 20 seconds or greater, a frequency resolution of 1 Hz or less can be used. This will make it easier to identify the fault frequency in the spectral analysis.
In Simcenter Testlab, turn on the “Time Signal Calculator” (26 tokens) and “Signature Throughput Processing” (36 tokens) add-ins. This is all that is needed to be able to filter, envelope, and spectrally analyze bearing vibration data.
Two new tabs will appear called “Time Data Selection” and “Time Data Processing” as shown in Figure 23 below.
Figure 23: Simcenter Testlab with Time Signal Calculator and Signature Throughput Processing add-ins activated.
In the Time Signal Calculator, enter the formulas as shown in Figure 24:
Figure 24: Formulas for calculating an envelope of band-pass filtered data in Time Signal Calculator.
The formulas do the following:
FILTER_BP: Performs a band-pass filter operation on the bearing vibration data (CH0 is the bearing data, filtered data is stored into CH1)
HILBERT_ENVELOPE: Calculates the envelope on the filtered data (CH1 is filtered data, CH2 contains the envelope)
The Fourier transform of these time histories is then calculated in the “Time Data Processing” tab shown in Figure 25.
Figure 25: Perform spectral analysis in the “Time Data Processing” worksheet.
Under the “Acquisition Parameter” use the “Change Settings” button to set the spectral processing parameters. For example, using “Stationary” mode to process steady state data and set a spectral resolution of 1 Hertz or less.
For more information on using Time Signal Calculator and Signature Throughput Processing in Simcenter Testlab, see the knowledge articles:
