How Do I Use Envelope Analysis and FFT Spectra to Find Bearing Faults?
Use envelope analysis when a bearing defect produces repeating impacts that are hidden beneath ordinary shaft, gear, or structural vibration in a raw FFT. Filter a high-frequency resonance band, extract its amplitude envelope, then run an FFT on that envelope and compare its peaks, harmonics, and sidebands with calculated bearing-fault frequencies rather than assuming every prominent peak is a defect.
The practical problem is not that a standard FFT is useless. It is that a bearing defect may announce itself as a high-frequency resonance whose amplitude rises and falls at a much lower repetition rate. The 2023 peer-reviewed study from Mechanical Systems and Signal Processing explains why direct low-frequency FFT interpretation can be difficult: impulses excite high-frequency resonance, while low-frequency fault-frequency energy can be weak. That distinction saves a lot of false confidence.
When should I use envelope analysis instead of a standard vibration FFT?
Use envelope analysis when the ordinary waveform or FFT does not clearly separate the expected bearing repetition rate from stronger machine vibration. Brüel & Kjær notes that early bearing-fault frequencies can be obscured by lower-frequency shaft, gear, and structural vibration in both the raw waveform and conventional spectrum. In that situation, a larger raw peak is not automatically a more useful peak.
Begin with the standard FFT anyway. It gives context: shaft-related components, gear-mesh content, broad structural activity, and other features that can affect the measurement. Then move to enveloping when the diagnostic question is specifically whether repeated rolling-element impacts are modulating a resonance.
Purdue University's research describes the sequence plainly: start with the raw accelerometer waveform, use a band-pass or high-pass filter to remove large low-frequency components, construct the rectified or otherwise extracted envelope, and apply an FFT to that envelope. The filtering step matters because it can remove synchronous rotor and gear-mesh vibration that would otherwise obscure bearing signatures.
The processing decision can be summarized this way: a raw FFT asks, “What frequencies are in the measured motion?” An envelope FFT asks, “At what rate is a selected high-frequency carrier being repeatedly excited?” Those are related questions. They are not interchangeable.
What does an envelope spectrum actually show?
An envelope spectrum shows the frequency content of the modulating signal extracted from a selected vibration band, not simply the original vibration spectrum viewed again. Brüel & Kjær defines envelope analysis as “the FFT (Fast Fourier Transform) frequency spectrum of the modulating signal.” National Instruments similarly defines envelope detection as extracting the modulating signal from an amplitude-modulated signal.
For a localized bearing defect, each rolling-element strike can excite a structural natural frequency. The resonance is the high-frequency carrier; the repeated impacts control its amplitude. After filtering and demodulation, the FFT of that changing amplitude can reveal a line at the impact repetition rate and harmonics of that rate.
That is why an envelope peak should be interpreted as a relationship, not a verdict. A credible diagnosis starts with an expected frequency, then looks for a matching fundamental and repeating harmonics. MathWorks illustrates the contrast in a constant-speed inner-race example: its raw power spectrum did not show a clear pattern at the known BPFI and harmonics, while the envelope spectrum concentrated most energy at BPFI and its harmonics.
| Expected component | Common label | What the label is used to check |
|---|---|---|
| Outer race | BPFO | Repeated impacts associated with an outer-race defect |
| Inner race | BPFI | Repeated impacts associated with an inner-race defect |
| Rolling element | BSF | Repeated rolling-element contact events |
| Cage | FTF | Cage-related repetition rate |
Names vary slightly across references. Brüel & Kjær also discusses ball-fault frequency as twice BSF in its terminology. The useful habit is to check the formula definition used by the instrument or software before assigning a label.
Which filter band should I choose for bearing envelope analysis?
Choose a band containing the resonance excited by impacts, not a band selected because it happens to include the suspected fault frequency. The suspected BPFO or BPFI is the modulation rate; the filter should isolate the higher-frequency carrier where impacts are most visible. This is the central idea behind the band-pass-before-demodulation approach described by Brüel & Kjær and Purdue.
There is no universal band expressed as one magic number. National Instruments documents an implementation with a default 4,800 Hz center frequency and 2,000 Hz span, meaning a passband from center frequency minus span to center frequency plus span. Those defaults are an example of configurable settings, not a rule for every motor, bearing, sensor, or installation.
A defensible workflow is to inspect the high-frequency acceleration content, select a resonance-dominated region rather than obvious low-frequency rotational content, calculate the envelope, and compare results across sensible bands. If the expected bearing family only appears in one arbitrary-looking setting and disappears when the band is adjusted, treat the diagnosis as unconfirmed. MathWorks recommends spectral kurtosis or a kurtogram to locate an impulsive band when noise masks outer-race information.
Frequency resolution also deserves a quick calculation. Brüel & Kjær recommends envelope-spectrum resolution five to ten times finer than the frequency separation that must be distinguished, with record length T greater than 1/df. In plain English: if two possible explanations are close together, collect a long enough record to separate them before declaring either one the winner.
Can I identify inner-race and roller faults from a time waveform alone?
No, a time waveform alone is usually insufficient to identify an inner-race or rolling-element fault with confidence. It may show impacts or modulation, but it does not reliably establish which component produced them; MathWorks shows a raw waveform whose approximate modulation period suggested about 111 Hz while the known BPFI was 118.875 Hz.
Calculate the expected frequencies first. Purdue and MathWorks both specify the needed inputs: shaft rotation frequency, number of rolling elements, rolling-element diameter, pitch diameter, and estimated contact angle. Using shaft frequency as fr, number of rolling elements as n, rolling-element diameter as d, pitch diameter as D, and contact angle as θ, common forms are:
| Frequency | Formula |
|---|---|
| BPFO | (n × fr / 2) × [1 − (d / D) × cos θ] |
| BPFI | (n × fr / 2) × [1 + (d / D) × cos θ] |
| FTF | (fr / 2) × [1 − (d / D) × cos θ] |
| BSF | (D × fr / 2d) × [1 − ((d / D) × cos θ)2] |
Then use the waveform as supporting evidence and the envelope spectrum as the discriminator. A real defect candidate should align with a calculated rate, show an intelligible harmonic pattern, and remain interpretable after the selected filter band and resolution are reviewed.
Speed variation is another reason not to rely on one stationary-looking waveform. The 2023 Iowa State study notes that fault frequencies shift with speed and uses computed order tracking to reduce those effects. A peak that moves with mechanical speed deserves a different investigation from a stationary electrical component. Nobody can settle that question from peak height alone.
Frequently Asked Questions
Why does a peak appear in an envelope spectrum but not in the normal spectrum?
A localized bearing defect can create weak, repeating impacts that excite a high-frequency structural resonance. In the raw spectrum, that impact repetition rate may be buried under stronger low-frequency machine vibration, while demodulation extracts the repeating amplitude pattern and makes its frequency and harmonics visible.
How can I tell a real bearing fault from line-frequency or VFD noise?
Start with calculated bearing frequencies and compare the peak against shaft-speed-related orders, BPFO, BPFI, BSF, and FTF rather than relying on peak height alone. Then repeat the analysis with a suitable resonance band and, where speed varies, account for the shift in fault frequency; a peak that does not follow the expected mechanical relationship needs more investigation.
Do bearing-fault frequencies require shaft speed and bearing geometry?
Yes. Purdue research and MathWorks both describe calculations that use operating speed, the number of rolling elements, rolling-element diameter, pitch diameter, and estimated contact angle. Without those inputs, a spectrum may still be suggestive, but it cannot reliably assign a peak to a specific bearing component.
Conclusion
The clean process is modest but demanding: collect a usable acceleration waveform, establish shaft speed and bearing geometry, calculate the candidate frequencies, select a resonance band, demodulate, and inspect the envelope FFT for the expected family of peaks. Use the raw FFT for context and the envelope spectrum for impact repetition.
Do not promote a peak to a bearing diagnosis until it survives those checks. Calculate first, filter deliberately, and validate the frequency relationship.