Hilbert Envelope Demodulation for Bearing Diagnosis

Envelope demodulation separates hidden impact components from a normal vibration acceleration signal and turns periodic fault impacts that cannot be seen by eye into clear fault frequency lines in the envelope spectrum.

The main window has channel, band and bearing settings on the left and four plots on the right: raw waveform, raw spectrum, envelope waveform and envelope spectrum, with colored lines for bearing frequencies and a red alarm threshold.

In the early stage of a bearing fault the impact energy is very small, and the normal spectrum often shows nothing: the impacts are amplified by structural resonance and buried in broadband noise.

• Reveal early faults: each impact of a defect excites a structural resonance. Demodulation detects this high-frequency resonance and recovers the repetition rate of the impacts — the fault characteristic frequency.
• Locate the fault: outer race, inner race, rolling element and cage impacts repeat at different rates. A peak in the envelope spectrum that coincides with BPFO or its harmonics points to outer race damage, giving a direct basis for spare parts before the machine is opened.
• Quantify severity: the ratio of the envelope peak to the noise floor, the presence of harmonic families and exceedance of the alarm threshold support decisions to continue, monitor more closely or replace.
• Distinguish sources: in a normal spectrum unbalance, misalignment and bearing faults are easily confused. The envelope spectrum responds only to impact modulation and naturally suppresses 1× and 2× faults; reading both together greatly reduces misdiagnosis.

The module uses the common Hilbert transform envelope method in five steps: raw acceleration → band-pass filter → FFT → analytic signal → envelope → envelope spectrum.

Bearing characteristic frequencies

fr is the running frequency, Z the number of rolling elements, d the rolling element diameter, D the pitch diameter and α the contact angle.

BPFO = (Z/2) · fr · (1 − (d/D) · cos α) BPFI = (Z/2) · fr · (1 + (d/D) · cos α)

BSF = (D/2d) · fr · (1 − ((d/D) · cos α)²) FTF = (1/2) · fr · (1 − (d/D) · cos α)

The software calculates and marks these in real time, so no manual calculation is needed. FFTs run in the platform's DSP acceleration library, with continuous phase between refreshes for smooth waveform scrolling.

Test mode set-up: when test mode is enabled, the software derives all parameters from the built-in impact train (100 Hz impact rate, 1500 Hz resonance carrier): bearing set to the built-in 6204 parameters (Z = 8), speed 1883 rpm so that BPFO is 100 Hz, and band 1000–2000 Hz.

• Four views on one screen make the whole process visible from raw waveform to envelope spectrum, rather than a black-box result.
• Characteristic frequencies calculated and marked automatically from speed and bearing parameters.
• Harmonic families shown in one step, so baseline-plus-harmonics fault patterns are not missed.
• Automatic alarm threshold adapted to the noise floor, with no repeated threshold tuning.
• Built-in fault signal with automatic parameters for exhibitions, training and acceptance without faulty machines.
• Eight-channel comparison and batch export of all four views.
• DSP-accelerated FFT for smooth refreshing, also with long records.
• Chinese and English interface.

Step 1: preparation

1. Acquire vibration acceleration data or open a recorded project.
2. Select the channels to analyze (several for comparison).
3. Enter the speed from the nameplate or a tachometer.
4. Enter the rolling element diameter, pitch diameter, number of rolling elements and contact angle from the bearing catalog.

Step 2: select the demodulation band (key step)

1. Look at the raw acceleration spectrum and find a clearly raised resonance band.
2. Place the band there: lower limit clear of the region below 10 × running frequency, upper limit no more than 40 % of the sampling rate, and enough bandwidth for the highest fault frequency (commonly 1000–5000 Hz).
3. If unsure where to start, try 1000–2000 Hz and adjust according to the envelope spectrum quality.

Step 3: read the envelope spectrum

1. Switch to the envelope spectrum.
2. Enable bearing frequency markers and the display of harmonics up to 3×.
3. Read against the colored lines: a significant peak (or harmonic family) at a characteristic frequency means periodic impacts from that component.
4. Highlight peaks above the red threshold, and compare several measurements over time to confirm how fast the fault develops.

Step 4: report

Export all four views or the data to Excel. State the measurement point, operating speed, bearing type, band setting and characteristic frequency conclusion in the report.