KutupASP DijitalThis article shows how envelope analysis pulls repeating impacts out of a high-frequency vibration band, how to calculate the four defect frequencies, and how to read the result step by step.
In a rolling-element bearing, a defect such as a scratch on the inner race or a pit on the outer race creates a short impact each time a rolling element passes over it. Each impact excites the structural resonances of the machine, so a high-frequency band rings. The result is a signal whose amplitude rises and falls at the rate of the impacts. This is amplitude modulation. The repetition rate of the impacts depends on the bearing geometry and the shaft speed, not on the size of the defect, so the measured rate can be matched against calculated values.
In a raw low-frequency spectrum, that repetition is often masked by the strong peaks of gears, unbalance and motor components. Envelope analysis aims to extract the modulation from the raw signal, so that only its repetition rate remains visible.
The method has four steps. First, a band-pass filter isolates a band around a structural resonance. Second, the envelope is extracted by taking the magnitude of the analytic signal obtained from the Hilbert transform; this is demodulation. Third, the mean value, the DC component, is removed from the envelope. Last, the FFT of the envelope is computed and its peaks are compared with the defect frequencies.
The order of the steps and the band choice both matter. The sampling rate of the raw signal must also be high enough; otherwise the high-frequency resonance band has already folded before the envelope is taken. Check the sampling rate before you choose the band. A band that is too narrow can miss the impacts, and one that is too wide lets other impact sources into the envelope. For that reason, choose the band by inspecting the spectrum for resonance peaks, not at random. If resonances are hard to see, an impact hammer test or a comparison with a healthy machine's record can help.
Four defect frequencies follow from the bearing geometry and the shaft frequency fr. Nb is the number of rolling elements, d the ball diameter, D the pitch diameter (the diameter of the circle through the rolling-element centres), and φ the contact angle.
These formulas assume no slip and an ideal geometry. Real bearings slip, so a measured peak sits near the calculated value rather than exactly on it.
Hypothetical example. Take a bearing with Nb = 9, d/D = 0.2, φ = 0 and fr = 25 Hz. Since cos 0 = 1:
A peak near 90 Hz in the envelope spectrum, together with its harmonics, would be a reason to suspect an outer-race defect. Inner-race defects usually show sidebands spaced at fr, so around the 135 Hz peak you would look for pairs 25 Hz apart. This is a first check only; it does not replace a diagnosis.
Envelope analysis does not work in every case. The most common error is a band centred on the wrong resonance. The envelope then shows impacts from another source, and the peaks are misread. Repeating gear-mesh impacts can also appear as peaks in the envelope spectrum. If shaft speed changes during the record, the fixed defect frequencies smear across the spectrum and the peaks widen.
The record length matters too: it should contain several periods of the defect frequency, otherwise the lines do not separate in the envelope spectrum. For that reason, one record is not enough. Compare several records from the same measurement point, taken under similar load and speed. Decide whether a peak comes from the bearing by weighing the speed, the load and the mounting information together.
Practising on open data helps before you apply the method to your own machines. The Case Western Reserve University Bearing Data Center is an openly available source of bearing records that include known defects. Before you start on your own plant, check the following:
Start with one machine and one measurement point. If the method does not work in that narrow case, review the measurement direction and the band choice before widening the scope.
In a raw low-frequency spectrum, bearing impacts are often hidden among the strong gear and unbalance peaks. Envelope analysis extracts how the amplitude of the high-frequency resonance band changes, and makes the repetition rate of the impacts visible at low frequency.
BPFO is the repetition frequency of a defect on the outer race, and BPFI is the one for a defect on the inner race. The two formulas differ only in the sign of the (d/D) cos φ term. For a contact angle below 90 degrees, BPFI is higher than BPFO, so the peak position helps tell the two cases apart.
Pilot steps in this guide are proposed engineering workflows. Examples do not constitute measured field performance.
After reading, you can compute frequency resolution for a vibration record, justify your window choice, and read spectral peaks as clues rather than diagnoses, using a worked example.
After reading, you can set a sampling rate from your analysis band, recognise a false low-frequency peak caused by aliasing, and see why slow PLC or SCADA logs fall short for spectra.
After reading, you can track a machine's broadband vibration against its own baseline and read the ISO 20816 zones in the right context, without treating a zone as a fault diagnosis.
