Bearing defect frequencies are the four characteristic vibration frequencies a rolling-element bearing generates when a specific part is damaged: BPFO (ball pass frequency, outer race), BPFI (ball pass frequency, inner race), BSF (ball spin frequency), and FTF (fundamental train frequency, the cage). Each is a fixed, non-integer multiple of shaft speed set by the bearing's geometry.
These four numbers are the reason a vibration analyst can point at a spectrum and say "outer race spall on the drive-end bearing" weeks before the bearing runs hot. This guide covers what each frequency means, how to calculate all four from a datasheet, a fully worked example, and a five-step workflow for turning a spectrum into a diagnosis. It sits underneath the broader predictive maintenance and condition-based maintenance programs that vibration analysis feeds.
What are the four bearing defect frequencies?
Each frequency corresponds to one surface inside the bearing. When a rolling element rolls over a defect on that surface, it produces a small impact; those impacts repeat at a rate fixed by geometry and shaft speed.
- BPFO, outer race. The rate at which rolling elements pass a single point on the stationary outer race. Outer-race defects are the most common finding and usually the cleanest signal, because the fault stays in the load zone.
- BPFI, inner race. The rate at which elements pass a point on the rotating inner race. Because the inner-race defect moves in and out of the load zone once per shaft turn, BPFI peaks carry running-speed sidebands.
- BSF, ball (or roller) spin. How fast a single rolling element rotates about its own axis. A spalled element strikes both races, so the impact often shows up at 2×BSF, modulated by the cage frequency.
- FTF, cage. The rotational speed of the cage assembly, always a fraction of shaft speed (typically 0.35–0.45×). A low-frequency FTF peak points to cage wear or a broken cage pocket.
How do you calculate bearing defect frequencies?
Each frequency is computed from four geometry values plus shaft speed. The four geometry values come from the bearing manufacturer's datasheet or catalog:
- N = number of rolling elements
- d = rolling-element (ball) diameter
- D = pitch diameter (the circle through the ball centers)
- θ = contact angle (0° for a deep-groove ball bearing)
Let n be shaft speed in Hz (RPM ÷ 60). The standard formulas, published in the same form by every major bearing manufacturer, are:
| Frequency | Formula | What a peak means |
|---|---|---|
| BPFO | (N/2) × n × [1 − (d/D)cosθ] | Defect on the outer race |
| BPFI | (N/2) × n × [1 + (d/D)cosθ] | Defect on the inner race |
| BSF | (D/2d) × n × [1 − (d/D)²cos²θ] | Defect on a rolling element |
| FTF | (1/2) × n × [1 − (d/D)cosθ] | Cage wear or damage |
Two properties are worth internalizing. First, these are orders of running speed, multiply the bracketed value by shaft speed and you get frequency in Hz. Second, they are almost never whole numbers. A gear mesh or a loose foot lands on integer multiples of running speed; a bearing defect lands at 3.58× or 5.42×. That non-integer signature is how you tell a bearing fault from everything else on the shaft.
A worked example
Take a common deep-groove ball bearing with illustrative geometry: N = 9 elements, ball diameter d = 7.94 mm, pitch diameter D = 39.0 mm, contact angle θ = 0°, running at 1,750 RPM (n = 29.17 Hz). The ratio d/D = 0.204.
- BPFO = 4.5 × 29.17 × (1 − 0.204) = 104.5 Hz (3.58 orders)
- BPFI = 4.5 × 29.17 × (1 + 0.204) = 158.0 Hz (5.42 orders)
- BSF = (39.0/15.88) × 29.17 × (1 − 0.204²) = 68.7 Hz (2.35 orders; the impact usually shows at 2× = 137 Hz)
- FTF = 0.5 × 29.17 × (1 − 0.204) = 11.6 Hz (0.40 orders)
Sanity check: BPFO + BPFI = 3.58 + 5.42 = 9.0 orders = N. If your calculated pair does not sum to the ball count, you entered the geometry wrong. When contact angle or exact ball diameter is unknown, two field rules of thumb get you close for ball bearings: BPFO ≈ 0.4 × N × n and BPFI ≈ 0.6 × N × n. They are approximations, not substitutes for the datasheet, but they will tell you whether a peak is plausibly a bearing tone.
How do you read a defect frequency in the spectrum?
A single peak at a calculated frequency is suggestive; the surrounding pattern is what confirms a bearing fault and grades its severity. Three features matter.
- Harmonics. A real spall produces a sharp, repeating impact, so the spectrum shows the fundamental plus a series of harmonics (2×, 3×, 4× the defect frequency). One isolated peak with no harmonics is more likely a coincidence than a fault.
- Sidebands. Peaks spaced at running speed (or at FTF, for element faults) around the defect harmonics indicate the fault is being amplitude-modulated as it moves through the load zone. Growing sidebands mean a growing defect.
- Envelope / demodulation. Early defects are buried under louder low-frequency noise. Envelope detection (high-pass filter, then demodulate) pulls the repetitive bearing impacts out of the noise floor and is the standard tool for catching a fault at stage one, long before amplitude rises in the raw velocity spectrum.
How fast does a bearing defect grow once you see it?
A detected defect frequency is the start of a race against a clock, and knowing roughly how much time you have is what turns a scary spectrum into a calm plan. Reliability engineers describe this window with the P-F interval: the time from the point a defect first becomes detectable (P, potential failure) to the point of functional failure (F). For rolling bearings, ultrasonic and envelope methods catch the defect earliest, followed by vibration, then heat, then audible noise, and finally catastrophic failure, each stage leaving less runway than the last.
Practically, that means the value of defect-frequency analysis is proportional to how early in the P-F interval you catch it. An outer-race spall found by envelope analysis at stage one might give you weeks of planning time; the same fault first noticed because the bearing is now hot to the touch might give you days. This is the entire economic argument for routine vibration routes over run-to-failure: the earlier the P, the more of the interval you get to spend planning instead of scrambling. It is also why a single alarming reading should trigger a shortened re-measurement interval, not an immediate teardown, you want to see the trend so you can place the repair in the cheapest possible window rather than the first available one. This is the same logic that governs every condition-based maintenance trigger and keeps unplanned events off the maintenance backlog.
A 5-step workflow to diagnose a bearing from vibration data
- Get the exact bearing number and speed. Pull N, d, D, and θ from the manufacturer datasheet for that part number, and record actual running speed at the moment of measurement. Guessed geometry produces confident nonsense.
- Calculate all four frequencies. BPFO, BPFI, BSF, FTF in Hz. Verify the sanity check (BPFO + BPFI = N×n) before trusting the numbers.
- Match peaks to frequencies. Overlay the calculated frequencies on the measured spectrum. A match at a non-integer order that is not a known gear-mesh or blade-pass tone is your candidate fault.
- Confirm with harmonics and sidebands. Require a family of harmonics and speed-spaced sidebands, and use envelope analysis to catch it early. Grade severity by how many harmonics appear and how fast amplitude and sidebands are trending, not by a single reading.
- Trend, then plan the fix. One spectrum is a snapshot; the trend is the diagnosis. Rising BPFO energy over successive routes means schedule the change-out in a planned window and stage the parts, the whole point of catching it early. Feed the finding into your MTBF history and spare-parts plan.
What the standards and numbers say
- Bearing geometry, defect frequencies, and measurement practice are governed by international standards. Overall machine vibration is evaluated against ISO 20816 (which superseded ISO 10816), using RMS velocity in the 10–1000 Hz band and zones A–D, where Zone A is a newly commissioned machine and Zone D is dangerous (ISO 20816-3:2022). Bearing damage itself is classified by ISO 15243 (ISO 15243:2017).
- The defect-frequency formulas above are published in identical form by bearing manufacturers and vibration-analysis references (Schatz Bearing, ball-bearing frequencies; Acoem, bearing fault frequencies). Because they depend only on geometry and speed, they are deterministic, the uncertainty is in reading the spectrum, not in the math.
Defect frequencies are only useful if someone is collecting and trending the data on a route, and if the finding actually reaches the planner. That is the connective-tissue problem Harmony is built for: it pulls machine signals, condition readings, and maintenance history into one operational data layer, surfaces the developing pattern, and can draft the work order for a human to approve, layered onto the CMMS and machines you already run, with no rip-and-replace. See how the platform works or the CLS case study for one plant's path to trustworthy floor data. For the bigger picture on where vibration analysis fits, start with the equipment reliability maturity ladder, and pair defect-frequency work with the bearing failure modes guide so the vibration tells you not just which surface but why it is failing.