Bearing Defect Frequency Calculator (BPFO, BPFI, BSF, FTF)
Every rolling element bearing has four characteristic frequencies that depend only on its geometry and the shaft speed. When a spectrum shows energy at one of them, it points to the damaged part. This calculator returns BPFO, BPFI, BSF and FTF in Hz.
Your numbers
Running speed of the shaft carrying the bearing.
From the bearing data sheet or catalogue.
Diameter of the circle through the rolling element centres.
The select stores the cosine of the angle.
Your results
Theoretical frequencies assume pure rolling with no slip. Real defects show slight variation, so look for peaks within a percent or two and for sidebands at shaft speed (BPFI) or cage speed (BSF).
BPFO and BPFI versus shaft speed
Sweeps Shaft speed from 300 to 3600, holding your other inputs fixed.
Link bearing data to your asset records
Optional review of how to hold bearing geometry on equipment records in your ERP or CMMS.
Optional. The tool and every export work without this. No spam.
How to use the calculator
Read the number of rolling elements, the rolling element diameter and the pitch diameter from the bearing manufacturer data or a bearing frequency catalogue. Enter the shaft speed measured with a tachometer or taken from the drive, because a nameplate speed can be off by the slip of an induction motor. Pick the contact angle, with 0 deg for deep groove and cylindrical roller bearings. The results show frequencies in Hz and as orders of running speed, so you can overlay them on either a Hz axis or an order axis of your analyzer.
- BPFO: outer race defect, often the first to appear
- BPFI: inner race defect, usually with 1X sidebands
- BSF: rolling element defect, often at twice BSF
- FTF: cage or separator problems, below 1X
The formulas
With shaft frequency fr, Nb rolling elements, ball diameter Bd, pitch diameter Pd and contact angle phi: BPFO is Nb/2 times fr times (1 minus Bd/Pd cos phi). BPFI is Nb/2 times fr times (1 plus Bd/Pd cos phi). BSF is Pd/(2 Bd) times fr times (1 minus (Bd/Pd cos phi) squared). FTF is fr/2 times (1 minus Bd/Pd cos phi). BPFO plus BPFI equals Nb times fr, which is a quick sanity check on your result.
Reading the spectrum
Defects rarely show up at the fundamental alone. Look for harmonics at 2X and 3X of the defect frequency and, for inner race faults, sidebands spaced at shaft speed. Early damage excites bearing resonances in the kilohertz range, so envelope or demodulation spectra reveal BPFO and BPFI long before the overall velocity changes. Compare against a baseline from when the bearing was healthy rather than relying on one reading.
Common mistakes
Using motor nameplate rpm instead of actual speed shifts every line and can make peaks miss their markers. Taking the bore or outer diameter instead of the pitch diameter is another frequent slip. Variable frequency drives change speed continuously, so use the speed at the time of the measurement. Finally, check that the bearing is the exact designation fitted, as suffixes can change ball count.
Frequently Asked Questions
What is the difference between BPFO and BPFI?
BPFO is the rate at which rolling elements pass a point on the outer race, and BPFI is the rate at which they pass a point on the inner race. BPFI is higher because the inner race rotates against the elements. Their sum equals the number of elements times shaft frequency.
Where do I find the bearing geometry?
Use the bearing manufacturer catalogue or online bearing database for the exact designation. Many analyzers also include a bearing library. If you only know the bore size, you cannot compute the frequencies reliably because ball count and pitch diameter vary between series.
Why does my peak not match the calculated value exactly?
Rolling elements slip slightly, speed is not perfectly constant and measurement resolution limits accuracy. A peak within a percent or two of the calculated line is normally a match. Larger gaps usually mean the wrong bearing data or the wrong speed.
Does this work for tapered roller bearings?
The same equations apply with the correct pitch diameter, roller diameter and contact angle, but use the effective values from the manufacturer. For thrust or tapered designs the contact angle is not zero, so pick the closest option or calculate its cosine and verify the result against the catalogue.
If you want bearing frequencies stored with each asset record in your ERP or CMMS and used to annotate spectra automatically, Netray can help design that data flow.
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