Ball Pass Frequency, Outer Race (BPFO)
Computes the ball pass frequency of the outer race (BPFO), the signature a localized defect on a bearing outer ring leaves in the vibration spectrum: BPFO = (number of elements ÷ 2) × shaft rotation frequency × (1 − element diameter ÷ pitch diameter × cosine of the contact angle). The result, in hertz, is the frequency at which a peak appears every time a ball or roller rides over the flaw; because it is not an integer multiple of shaft speed, it is distinguishable from unbalance and misalignment, which show up at 1× and 2× rotation. Since the races slip slightly, the measured frequency usually falls 1% to 2% below the theoretical one, so look for the band rather than the exact line. A 6205 deep-groove ball bearing has a BPFO near 3.6 times shaft speed, and it is always worth checking that BPFO plus the inner race frequency equals exactly the number of elements times the rotation frequency. Enter the number of rolling elements, the shaft rotation frequency, the rolling element diameter, the pitch diameter and the contact angle.
Result
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BPFO: pinning an outer race fault in the spectrum
A vibration analyst pulls a spectrum off a motor-pump, finds half a dozen peaks between 100 and 200 Hz, and has to decide whether the machine stops this weekend or waits for the next route. Without the theoretical BPFO worked out before the walk, that spectrum tells him nothing: every peak becomes a suspect and the call reverts to the mechanic's ear. Both mistakes bite — swapping a healthy bearing over a structural looseness peak, or missing an outer race spall while it still shows up only in the envelope band and the overall level has yet to move.
The math reads BPFO = (n ÷ 2) × fr × (1 − (d ÷ D) × cos α). Here n is the rolling element count, fr the shaft speed in hertz, d the ball or roller diameter, D the pitch diameter (the circle through the centres of the elements) and α the contact angle in degrees. Only the ratio d ÷ D enters, so millimetres or inches work equally well provided both fields share one unit. The answer usually lands near 0.4 × n times shaft speed; with the screen defaults, 4.93 times. The check that never fails: BPFO plus BPFI must equal n × fr exactly.
The formula assumes pure rolling with no slip, the outer race clamped in the housing and the inner race turning with the shaft. Flip that arrangement, with a rotating outer ring, and the two frequencies swap roles. Axial load and internal clearance shift the effective contact angle, which is why the measured line sits 1% to 2% under the computed one: the elements creep slightly on every revolution. The classic unit slip is typing shaft speed in rpm into a hertz field. 1500 rpm equals 25 Hz, and whoever forgets to divide by 60 goes hunting a peak at 7.4 kHz.
Frequently asked questions
How does the screen reach 123.251 Hz from the defaults?
Mine is a deep-groove ball bearing. Which contact angle?
Why did the message asking me to check the entries appear?
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The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.