How It's Calculated
The process follows these steps:
1. Raw Acceleration Signal Acquisition Collect the raw vibration signal using an accelerometer, typically in the high-frequency range (1–20 kHz depending on the machine).
2. High-Pass or Band-Pass Filtering Filter the raw signal to isolate a high-frequency resonance band — usually a structural resonance of the machine or sensor. This removes low-frequency noise (imbalance, misalignment) that would obscure the bearing impulses.
3. Rectification The filtered signal is full-wave rectified (absolute value taken), converting all negative values to positive. This exposes the amplitude modulation pattern embedded in the carrier frequency.
4. Low-Pass Filtering (Smoothing) A low-pass filter smooths the rectified signal, extracting the envelope — the outline of the high-frequency bursts. What remains is the modulating signal caused by the defect impacts.
5. FFT of the Envelope A Fast Fourier Transform is applied to the envelope signal to produce the Envelope Spectrum. Defect frequencies now appear as clear spectral peaks.
Mathematically:
Envelope(t) = LPF{ | BPF{x(t)} | }
Where:
- x(t) = raw vibration signal
- BPF = band-pass filter at resonance frequency
- |·| = rectification
- LPF = low-pass filter
Defect Frequencies Identified
Once in the envelope spectrum, you compare peaks against calculated bearing defect frequencies:
| Frequency | Defect |
|---|---|
| BPFO – Ball Pass Frequency Outer race | Outer race defect |
| BPFI – Ball Pass Frequency Inner race | Inner race defect |
| BSF – Ball Spin Frequency | Rolling element defect |
| FTF – Fundamental Train Frequency | Cage defect |
These are calculated from bearing geometry (pitch diameter, ball diameter, contact angle, RPM).
How It's Applied in Practice
Early Fault Detection Envelope analysis detects bearing defects weeks or months before they appear in overall vibration or standard FFT spectra. A small spall produces high-frequency impacts that standard analysis misses entirely.
Severity Trending The amplitude of defect frequency peaks in the envelope spectrum is trended over time. Rising amplitude = progressing damage.
Gear Mesh Analysis Enveloping can also isolate gear mesh modulation and tooth defects in gearboxes where background noise is high.
Selecting the Filter Band This is the most critical skill — the band-pass filter must be centered on a structural resonance to amplify the impacts. Tools like kurtogram or spectral kurtosis are used to automatically find the optimal filter band.
Integration with Overall Metrics
- SEE (Stress Wave Energy) – SKF's proprietary envelope metric
- PeakVue – Emerson's implementation
- gE (g-Envelope) – used in portable data collectors
Key Advantage Over Standard Vibration
| Standard FFT | Envelope Analysis |
|---|---|
| Detects imbalance, misalignment, looseness | Detects early-stage bearing/gear defects |
| Works at low frequency (10–1000 Hz) | Works at high frequency (1–20 kHz) |
| Defect peaks buried in noise | Defect frequencies clearly visible |
| Detects faults when already severe | Detects faults when still minor |
Envelope acceleration is most powerful when combined with standard spectrum analysis, time waveform review, and phase analysis — giving a complete picture from early warning through fault confirmation.