industrial//maintenance//condition monitoring//vibration analysis//envelope analysis

Envelope analysis is a signal-processing technique that recovers the repetition rate of short impacts buried in a vibration signal, by band-pass filtering around a structural resonance, taking the envelope of what passes and computing the spectrum of that envelope, and it is the standard industrial method for detecting rolling-bearing defects early. In the result, the **envelope spectrum**, a damaged bearing shows a clean peak at its bearing defect frequency with harmonics, where the ordinary spectrum showed nothing.

Envelope analysis is a signal-processing technique that recovers the repetition rate of short impacts buried in a vibration signal, by band-pass filtering around a structural resonance, taking the envelope of what passes and computing the spectrum of that envelope, and it is the standard industrial method for detecting rolling-bearing defects early. In the result, the envelope spectrum, a damaged bearing shows a clean peak at its bearing defect frequency with harmonics, where the ordinary spectrum showed nothing.

The ordinary spectrum fails for a simple reason. Each impact of a ball on a pit lasts a fraction of a millisecond and rings the housing's resonances at several kilohertz; its energy is spread over a wide band and sits under the much larger lines of shaft rotation and gear mesh, so the defect rate itself, a hundred hertz or so, has almost no energy at its own frequency. What does repeat at that rate is the amplitude of the ringing. The method extracts it in three steps.

1Band-pass around a resonance the impacts excitea few kilohertz2Take the envelope of the filtered signalmagnitude of the analytic signal3Compute the spectrum of the envelopepeaks at the impact rate

shaft25.0 Hz defect, BPFO89.3 Hz peak in the spectrumno (+2 dB) peak in the envelopeyes (+24 dB) A machine at 1500 rpm with an outer-race defect at 50 % severity and 0.50 g of noise: the defect strikes at 89.3 Hz. In the plain spectrum its peak stands 2 dB over the floor (not detected); in the envelope spectrum of the band from 2 to 4 kHz, 24 dB (detected).

Look for the defect frequency in the plain spectrum and find nothing, then switch to the envelope spectrum and watch it appear with its harmonics; change the speed and see the peak move in proportion, then raise the noise and lower the severity until it is no longer detected.

The band is the one real choice. It must contain a resonance the impacts excite and avoid bands dominated by gear mesh or electrical noise; analysts pick it from a spectrum of the healthy machine, and automated methods choose the band where the filtered signal is most impulsive (its kurtosis is highest).

The sampling rate is set by the band: to see a 3 kHz resonance the accelerometer is sampled at 10 kHz or more behind an anti-alias filter, even though the answer is a peak near 100 Hz (sampling).

Edge gateways compute the envelope's energy at the expected defect frequencies, expressed in orders of shaft speed, and send that number, one of the most informative features a bearing can give (condition monitoring).