bearing-noise

name	bearing-noise
description	Bearing noise analysis — defect frequencies (BPFO/BPFI/BSF/FTF), envelope analysis, kurtosis, bearing signal processing, lubrication noise, ISO 15242, SKF bearing diagnostics.
metadata	{"priority":7,"promptSignals":{"phrases":["bearing noise","bearing vibration","bearing defect frequency","BPFO BPFI","envelope analysis bearing","bearing diagnosis"],"minScore":3}}

Bearing Noise and Vibration Diagnostics — Complete Skill

Bearing Defect Frequencies

Fundamental Bearing Frequencies (from geometry):

Ball Pass Frequency Outer Race (BPFO): BPFO = (N_b/2) × f_r × (1 - (d_ball/D_pitch) × cos α) [Hz] N_b = number of balls; f_r = shaft rotation frequency [Hz]; d_ball = ball diameter; D_pitch = pitch diameter; α = contact angle

Ball Pass Frequency Inner Race (BPFI): BPFI = (N_b/2) × f_r × (1 + (d_ball/D_pitch) × cos α) [Hz]

Ball Spin Frequency (BSF): BSF = (D_pitch / (2 × d_ball)) × f_r × (1 - (d_ball/D_pitch)² × cos²α) [Hz]

Fundamental Train Frequency (cage; FTF): FTF = (1/2) × f_r × (1 - (d_ball/D_pitch) × cos α) [Hz; FTF ≈ 0.35–0.45 × f_r]

Approximate (for quick estimate): BPFO ≈ 0.4 × N_b × f_r BPFI ≈ 0.6 × N_b × f_r Harmonics: 2×BPFO, 3×BPFO, etc. appear as defect develops

Example (6205 bearing, 1500 RPM, 8 balls, d/D = 0.33): f_r = 1500/60 = 25 Hz BPFO ≈ 0.4 × 8 × 25 = 80 Hz BPFI ≈ 0.6 × 8 × 25 = 120 Hz

Bearing Noise Sources

Raceway defect: spall or pit → impulsive excitation at defect frequency; modulated by load zone Rolling element defect: excitation at BSF (symmetric) or 2×BSF (one defect side) Cage defect: FTF; rattle or cracks Geometric imperfections: waviness → harmonics at Z × f_r (Z = number of balls) Lubrication: grease insufficient → metal contact → broad-band noise; starvation → high frequency hiss

Signal Processing Methods

Time Domain — Statistical Indicators

RMS vibration: X_rms = √(Σ x_i² / N) [m/s²; overall signal level; low sensitivity to impulsive]

Peak: X_peak = max|x_i| [high sensitivity to large impacts]

Crest factor: CF = X_peak / X_rms [> 6 → early bearing fault; > 12 → advanced]

Kurtosis K₄: K₄ = (1/N) Σ(x_i - μ)⁴ / σ⁴ Normal signal: K₄ ≈ 3.0 (Gaussian) Impulsive bearing signal: K₄ > 4–6 → early fault; > 8 → significant fault Limitation: kurtosis decreases when many impacts overlap (advanced damage)

Envelope (Demodulation) Analysis

Process:

1. Bandpass filter raw accelerometer signal around high-frequency bearing resonance (f_res = 2–20 kHz typically)
2. Rectify: |x(t)|
3. Low-pass filter (or compute envelope via Hilbert transform)
4. FFT of envelope signal → peaks at BPFO, BPFI, BSF, FTF

Why envelope: Defect impacts ring structural resonance → high-frequency burst → modulation at defect frequency Envelope analysis extracts modulation → defect frequency visible

Spectral Kurtosis (SK): Frequency-dependent kurtosis; identifies which frequency band has most impulsive content → optimal filter selection for envelope analysis

Frequency Spectrum Analysis

Fault indicators:

Fault	Spectrum feature
Outer race	BPFO harmonics; sidebands at f_r
Inner race	BPFI harmonics; sidebands at f_r
Ball	BSF (less common; variable load zone)
Cage	FTF; sidebands around bearing tones
Misalignment	1×, 2×, 3× running speed; axial component
Unbalance	1× running speed dominant
Looseness	0.5×, 1.5× running speed harmonics

ISO 15242 — Running Accuracy Tests

Vibration frequency bands: Low (50–300 Hz); medium (300–1800 Hz); high (1800–10,000 Hz) Measured as velocity [μm/s] or acceleration [m/s²] per band

V₁₂₅ test: test at 1800 RPM; velocity signal in each band Bearing quality grades: 4, 5, 6 (higher = quieter)

Condition Monitoring Approach

Trending: Measure: RMS overall vibration, BPFO amplitude, kurtosis — every 2 weeks or 1 month Plot trend vs. time → alert when parameter crosses alarm threshold

ISO 10816 vibration severity: Zone A: good (< 2.3 mm/s RMS); Zone B: acceptable; Zone C: alarm; Zone D: trip

Bearing remaining life estimation: Stage 1 (healthy): K₄ ≈ 3; no peaks at defect frequencies Stage 2 (early fault): K₄ > 4; BPFO visible in envelope spectrum Stage 3 (developed fault): K₄ > 8; multiple harmonics; sidebands Stage 4 (late fault): K₄ may decrease; RMS increasing; broadband noise

P-F interval: time from detectable defect to functional failure High-speed bearing: P-F = days to weeks Low-speed bearing: P-F = weeks to months

Lubrication-Related Noise

Metal-to-metal contact sound: Insufficient lubrication → high-frequency broad-band noise increase (> 2 kHz) Re-grease → noise drops → confirm lubrication effect

Grease noise: New grease (shear thickening): temporary high noise at startup; settles in 5–30 min Old/oxidized grease: crackling, high frequency → relubricate

Oil whirl (fluid film bearings): Instability at ~0.46 × f_r (sub-synchronous); distinct peak just below 0.5× If speed increases and peak tracks with 0.5× → oil whirl → oil whip (resonant) danger

Standards

Standard	Scope
ISO 15242	Bearing noise test methods
ISO 10816	Vibration limits for rotating machinery
API 670	Machinery protection (vibration measurement)
ISO 13373	Condition monitoring — vibration
SKF Bearing Technical Handbook	Diagnostic guidelines

Output

Provide: defect frequencies BPFO, BPFI, BSF, FTF [Hz] for given bearing at operating speed, measurement method (accelerometer bandpass + envelope, ISO 15242 velocity), diagnostic parameter thresholds (kurtosis alert/alarm, RMS ISO zone), spectrum interpretation for identified peaks, lubrication assessment (κ and noise correlation), remaining life stage assessment (1–4), recommended monitoring interval, and applicable standard (ISO 15242, ISO 10816, API 670).