Lokesh Chennuru What the literature says
A rolling-element bearing has four characteristic defect frequencies, fixed by its geometry and the shaft speed. With the number of rolling elements N, shaft rotational frequency fr, rolling-element diameter Bd, pitch diameter Pd, and contact angle α:
| Frequency | Formula | A fault here means |
|---|---|---|
| BPFO — ball pass, outer race | (N/2) · fr · (1 − (Bd/Pd) · cos α) | Defect on the outer raceway |
| BPFI — ball pass, inner race | (N/2) · fr · (1 + (Bd/Pd) · cos α) | Defect on the inner raceway |
| BSF — ball spin | (Pd/2Bd) · fr · (1 − ((Bd/Pd) · cos α)²) | Defect on a rolling element |
| FTF — fundamental train | (fr/2) · (1 − (Bd/Pd) · cos α) | Cage problem |
Manufacturers publish these as multipliers of shaft speed (orders), so nobody computes them by hand in the field — SKF and Schaeffler both maintain free calculators keyed to their catalogues. ISO 13373-3 frames how these tones are used inside a structured vibration diagnosis.
One worked example: a 6205 at 1,800 RPM
The 6205 deep-groove ball bearing is one of the most common bearings in industry. Geometry: 9 balls, ball diameter 7.94 mm, pitch diameter 38.5 mm, contact angle 0°. At 1,800 RPM the shaft frequency is 30 Hz, and Bd/Pd = 0.206.
| Frequency | Multiplier (× shaft speed) | At 1,800 RPM |
|---|---|---|
| BPFO | 3.57 | 107.2 Hz |
| BPFI | 5.43 | 162.8 Hz |
| BSF | 2.32 | 69.7 Hz |
| FTF | 0.40 | 11.9 Hz |
Two properties make these tones diagnostic gold. First, they are non-integer multiples of shaft speed — 3.57×, not 3× or 4× — so a bearing tone cannot be confused with the ordinary harmonic series produced by imbalance, misalignment, or looseness. Second, each tone names a component: the spectrum is telling you which part of the bearing is degraded before anyone opens the housing.
What it means on the plant floor
- BPFO is the workhorse. Outer-race defects are the most common failure location because the outer race carries the load in a fixed zone. A clean BPFO tone with harmonics, trending upward, is the classic early-warning pattern.
- BPFI arrives dressed in sidebands. An inner-race defect rotates through the load zone once per revolution, so its tone is amplitude-modulated at shaft speed — BPFI flanked by ±1× sidebands. The sideband family growing is itself a severity signal.
- BSF often shows at twice itself. A ball defect strikes both races per spin, so energy frequently appears at 2×BSF. Seeing the pair is more convincing than either line alone.
- FTF is rare and serious. Cage tones at ~0.4× shaft speed usually mean lubrication breakdown or advanced damage. An FTF that modulates other bearing tones late in life is a strong signal that the decision window is closing.
The honest sequence for a maintenance team: a defect tone appears in the envelope spectrum → confirm it against the calculated frequency for that bearing and speed → watch the trend and the sideband growth → schedule inspection inside a planned stop, with the spare staged. The frequencies turn “the bearing is noisy” into “the outer race of the drive-end 6205 is degrading, and here is the trend.”
The three decisions this should change
- Inspection triggers become component-specific. Alarm on the appearance and growth of identified defect tones, not only on overall level — the broadband number can stay inside its ISO zone while a BPFO line doubles. This is the practical bridge from severity screening to defect-driven planning.
- Spares staging follows the tone. BPFO/BPFI families say “stage the bearing and plan the swap”; strong cage or ball tones with lubrication evidence say “also fix the lubrication practice or the fit, or the replacement repeats the failure.” ISO 15243’s failure-mode classes pair naturally with which tone appeared first.
- Measurement setup is dictated by the frequencies. The tones for this small bearing already reach 163 Hz at modest speed, and their harmonics and envelope carriers reach far higher. Sensor bandwidth, mounting quality, and sampling rate must cover the family you intend to detect — a low-rate temperature-style data path cannot carry this job.
Where it stops being useful
- Slip moves the lines. The formulas assume pure rolling contact. Real bearings slip slightly, so measured tones typically sit 1–2% below calculated values. Search in a window; do not reject a match for missing by a hertz.
- Speed must be known. All four frequencies scale linearly with shaft speed. On variable-speed drives, a tone smears unless speed is captured with the measurement or order-tracking is used.
- Identical bearings are indistinguishable by frequency alone. Two 6205s on the same shaft line produce the same tones; locating the defective one needs measurement-point comparison, not arithmetic.
- Envelope amplitude is not a portable severity scale. Demodulated amplitudes depend on sensor position, resonance, and machine structure. Trend each point against itself; never compare absolute envelope numbers across machines as if they were a health score.
Sources
- Bearing defect frequency formulas and worked examples IoT Bearings
- SKF Bearing Frequency Calculator SKF Group
- Bearing Frequency Calculator Schaeffler medias
- ISO 13373-3: Condition monitoring and diagnostics of machines — vibration condition monitoring, Part 3: Guidelines for vibration diagnosis International Organization for Standardization
Frequently asked
What is the difference between BPFO and BPFI?
BPFO is the rate at which rolling elements pass a fixed point on the outer race; BPFI is the rate for the inner race. With the inner ring rotating, BPFI is always the higher frequency and typically appears with sidebands at shaft speed because the defect rotates in and out of the load zone — a useful clue when separating the two.
Why don't my measured bearing frequencies match the calculated values exactly?
The formulas assume pure rolling. Real bearings slip slightly, so measured tones usually sit one to two percent below the calculated values, and they smear when machine speed varies during the measurement. Treat the calculated frequency as the centre of a search window, not an exact line.
Do I need vibration analysis to use defect frequencies?
The frequencies come from bearing geometry, so any monitoring path that resolves frequency content can use them — a portable analyser, an online system, or an envelope-capable sensor. What matters is that the measurement bandwidth covers the tones and that speed is known at the time of capture.