industrial//maintenance//condition monitoring//vibration analysis//bearing defect frequency
A bearing defect frequency is the rate at which a localized defect on one part of a rolling-element bearing is struck by the rolling elements, fixed by the bearing's geometry and the shaft speed, and it is the frequency a vibration analyst looks for to say *this is the bearing* and even which part of it. A pit on the outer race, which stays still in the housing, is hit once every time a ball passes over it; that rate is the **ball pass frequency of the outer race**, BPFO:
A bearing defect frequency is the rate at which a localized defect on one part of a rolling-element bearing is struck by the rolling elements, fixed by the bearing's geometry and the shaft speed, and it is the frequency a vibration analyst looks for to say this is the bearing and even which part of it. A pit on the outer race, which stays still in the housing, is hit once every time a ball passes over it; that rate is the ball pass frequency of the outer race, BPFO:
fBPFO=nb2 fr(1−dDcosϕ)f_{\mathrm{BPFO}}=\frac{n_b}{2}\,f_r\left(1-\frac{d}{D}\cos\phi\right)fBPFO=2nbfr(1−Ddcosϕ)
with nbn_bnb the number of balls, frf_rfr the shaft rotation frequency, ddd the ball diameter, DDD the pitch diameter and ϕ\phiϕ the contact angle. For common bearings it comes out at a few times the shaft frequency and, importantly, at a non-integer multiple of it, which separates it from imbalance and misalignment lines. The inner race (BPFI), the rolling elements and the cage each have their own formula, and the catalogue of any bearing maker lists all four as multiples of shaft speed.
A bearing failing in a pump crosses every level of a system.
The physics is an impact each time a ball rolls over the pit, at the rate above; the signal is a burst of high-frequency ringing at that rate, buried in everything else the machine does; the hardware is an accelerometer on the housing and a gateway that cannot send every sample; the algorithm is an envelope spectrum and a limit; the system is an alarm and a work order someone must believe; the business is a cheap replacement at the next stop against an expensive one mid-campaign.
The formula assumes pure rolling. Real bearings slip by a percent or two, so the measured peak sits slightly off the computed line and wanders; analysts look for a peak near the frequency, with its harmonics, rather than at an exact bin.
Each impact is brief and excites resonances of the housing at several kilohertz, so at low severity the defect frequency is nearly invisible in the plain spectrum and appears clearly only after demodulation (envelope analysis).
Expressed in orders of shaft speed, the defect lines stay put when the speed varies, the reason vibration features are computed in orders on variable-speed machines (vibration analysis).