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What is envelope analysis, and how is it done for bearings?

Short answer

Envelope analysis reveals amplitude modulation in a high-frequency resonance band. The signal is band-pass filtered, its envelope (the amplitude curve) is extracted with the Hilbert transform, and the FFT of that envelope is computed. Bearing defects then show up as peaks at their defect frequencies in the envelope spectrum.

October 5, 20263 minKutup · ASP Dijital

Why the defect hides in the raw spectrum

Each time a ball strikes a bearing defect, it produces a short impact. These impacts excite the machine's structural resonances, creating bursts of vibration in a resonance band that repeat at the defect frequency.

So the defect appears as amplitude modulation: the amplitude of a high-frequency carrier varies at the defect frequency. In a raw spectrum, that information can sit below low-frequency machine components and noise. Envelope analysis moves the modulation down to a low frequency, where an FFT can read it.

The method depends on where the resonance is. If the band is chosen badly, the defect impacts are not captured at all.

A step-by-step hypothetical example

A hypothetical bearing has an outer-race defect frequency BPFO = 90 Hz. An accelerometer samples at fs = 20,000 Hz for 1 second, so N = 20,000 and the bin width is 1 / T = 1 Hz.

  • Band-pass filter: 3,000 to 5,000 Hz. The upper edge is below fs/2 = 10,000 Hz, and 2.56 × 5,000 = 12,800 Hz fits under fs = 20,000 Hz.
  • Build the analytic signal with the Hilbert transform and take its magnitude. That is the envelope.
  • Remove the envelope mean (DC). Otherwise a large peak at 0 Hz hides the result.
  • Take the FFT of the envelope. Expect a peak at 90 Hz and another at 180 Hz. Even if it is small in the raw spectrum, it can stand out in the envelope.

Common mistakes

Most errors come from band choice and skipped steps:

  • Guessing the band. A band that is too wide mixes in other impacts and noise; one that is too narrow misses the defect impacts. Find the band with a resonance scan.
  • Forgetting to remove the DC component. The envelope mean creates a large 0 Hz peak that distorts the spectrum.
  • Reading with a fixed-width frequency grid while speed changes. Defect frequencies move with shaft speed; for large speed changes, order analysis is the better choice.
  • Applying the Hilbert transform to the raw signal. Without a band-pass filter, the envelope is a mix of all components.

Follow-up questions

What does the Hilbert transform actually do?

It produces a 90-degree phase-shifted partner of the signal. The magnitude of the analytic signal, made of the signal and its partner, gives the envelope. That envelope contains the amplitude variation, which is the modulation.

How do I choose the band?

There is no fixed rule. Find the resonance region that the impacts excite most strongly, using a spectrum scan or indicators such as kurtosis. Also check whether the same defect frequency appears in more than one band.

Sources

Example numbers are hypothetical, not measured field results.

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