Bearing Fault Frequencies Explained: BPFO, BPFI, BSF, and FTF

In one line: Every rolling-element bearing defect vibrates at a frequency set by the bearing's own geometry: BPFO, BPFI, BSF, and FTF. Learn to read them and a spectrum tells you not just that a bearing is failing, but exactly which part: the difference between a two-hour bearing swap and an unplanned line stop.

A bearing broadcasts exactly where it's failing

A healthy rolling-element bearing produces a broadband, unremarkable vibration signature. A degrading one does something far more useful: it broadcasts, at a specific and calculable frequency, exactly which part of itself is breaking down.

That's not a metaphor. When a spall forms on the outer raceway, every rolling element that rolls over it produces a small impact, repeating at a fixed rate set by the bearing's geometry and shaft speed. An inner-race defect impacts at a different rate; a ball or roller defect, different again; a cage problem, different again: four fault mechanisms, four predictable frequencies, usually written BPFO, BPFI, BSF, and FTF.

Our companion post on bearing failure prediction covers the four-stage degradation curve these frequencies belong to. This one goes deeper: the geometry behind the math, why the signatures are so hard to see, and what it takes to read them reliably at scale.

The four bearing defect frequencies

Every bearing defect frequency is a function of two things: the bearing's internal geometry and the shaft's rotational speed. The geometry inputs are the same four numbers on every bearing datasheet:

n: the number of rolling elements (balls or rollers)
Bd: the rolling-element diameter
Pd: the pitch diameter (the diameter of the circle traced by the centers of the rolling elements)
θ (theta): the contact angle (0° for a standard deep-groove ball bearing, larger for angular-contact designs)

Combine those with the shaft's rotational speed (fr, in Hz: RPM divided by 60) and you get the four standard formulas:

BPFO = (n/2) × fr × [1 − (Bd/Pd) cos θ]
BPFI = (n/2) × fr × [1 + (Bd/Pd) cos θ]
BSF  = (Pd / 2Bd) × fr × [1 − (Bd/Pd)² cos² θ]
FTF  = (fr/2) × [1 − (Bd/Pd) cos θ]

Four resulting defect frequencies, each pointing at a different failure mechanism:

BPFO (Ball Pass Frequency, Outer race): the rate at which rolling elements strike a defect on the stationary outer raceway. Outer-race defects are the single most common bearing failure mode.
BPFI (Ball Pass Frequency, Inner race): the rate at which rolling elements strike a defect on the inner raceway, which rotates with the shaft. Always higher than BPFO for the same bearing.
BSF (Ball Spin Frequency): the rate a rolling element spins about its own axis, typically the lowest of the four base frequencies, at roughly 1.5–3× shaft speed. A defect on the element itself typically peaks at twice BSF, since it strikes both the inner and outer race once per rotation: two impacts per revolution.
FTF (Fundamental Train Frequency): the rotational frequency of the cage that holds the rolling elements in position. Cage and lubrication problems live here. FTF is always sub-synchronous, typically around 0.4× shaft speed (roughly 0.35–0.45× across most standard designs).

You'll rarely calculate these by hand: bearing manufacturers publish defect-frequency tables, and vibration software computes them from a bearing model number and shaft speed. But the formula shape matters: all four scale linearly with shaft speed, and two of them (BPFO and BPFI) also scale with the number of rolling elements (BSF and FTF depend on the ball-to-pitch-diameter ratio instead). Two field-friendly rules of thumb hold up well for standard ball bearings: BPFO ≈ 0.4 × n × shaft speed, and BPFI ≈ 0.6 × n × shaft speed, good to within a few percent, though never a substitute for the manufacturer's number on a report you're going to act on.

A worked example. Here's a concrete case: an SKF 6205 deep-groove ball bearing (9 rolling elements, 7.94 mm ball diameter, 38.5 mm pitch diameter, 0° contact angle, so cos θ = 1 and drops out) on a motor running at 1,800 RPM, 30 Hz shaft speed.

| Frequency | Calculation | Result | |---|---|---| | BPFO | (9/2) × 30 × [1 − (7.94/38.5)] | ≈ 107 Hz | | BPFI | (9/2) × 30 × [1 + (7.94/38.5)] | ≈ 163 Hz | | BSF | (38.5 / (2×7.94)) × 30 × [1 − (7.94/38.5)²] | ≈ 70 Hz (defect energy at ≈ 140 Hz, i.e., 2×BSF) | | FTF | (30/2) × [1 − (7.94/38.5)] | ≈ 11.9 Hz |

Two sanity checks are worth knowing, since they catch a mistyped bearing number before it costs you a wrong diagnosis: BPFO + BPFI always equals n × shaft speed (107 + 163 = 270, and 9 × 30 = 270), and FTF × n always equals BPFO (11.9 × 9 ≈ 107). If those don't reconcile, you're looking at the wrong bearing's geometry.

Why these signatures are buried

Knowing a defect frequency exists doesn't mean you can see it. In a raw, direct vibration spectrum, a stage-two bearing defect is a small amount of energy at one specific frequency, sitting in the same plot as everything else the machine is doing, and everything else is usually much bigger.

Running speed (1×) and its harmonics dominate almost every industrial vibration spectrum: residual imbalance, a bit of misalignment, a slightly bent shaft. These peaks are often ten or a hundred times larger than an early bearing defect. A raw FFT plotted on a linear scale can make a real, growing BPFO peak essentially invisible next to 1× and 2× running-speed energy.

There's a second problem underneath the first: the actual mechanical event (a rolling element striking a spall) is an extremely short, sharp impact. That impact doesn't ring at the defect frequency itself; it excites the bearing and housing assembly's own natural resonances, typically well up in the kHz range. Early on, this shows up as a subtle broadband hump (sometimes called a "haystack") of raised energy around that resonance band, before any individual defect-frequency line is clean enough to read on its own.

This is exactly the problem envelope analysis (also called demodulation, or high-frequency enveloping) is built to solve. The technique band-pass filters the signal around the excited resonance band, extracts the envelope of that high-frequency energy, and runs an FFT on the envelope itself, separating the low-frequency rate of impacting from the high-frequency ringing the impacts excite. What comes out is a clean, low-frequency spectrum where BPFO, BPFI, BSF, and FTF stand out sharply against a near-silent background, because smooth running-speed vibration contributes almost nothing in that high-frequency band. Our vibration-analysis primer covers the broader metric set this builds on.

How to read them in a spectrum

Finding the right frequency is step one. What the peak looks like around it tells you as much as its amplitude, because BPFO, BPFI, and BSF each fail differently, and the spectrum shows it.

Outer-race defects (BPFO) are the cleanest signature. The outer race is stationary, and on most machines the load direction is fixed, so a defect on it sits in a constant position relative to the load zone: every impact is roughly the same severity. The result is a sharp peak at BPFO and its harmonics, without significant sidebands. Somewhat counterintuitively, this makes outer-race defects the easiest of the four to detect and confirm.

Inner-race defects (BPFI) are amplitude-modulated. The inner race rotates with the shaft, so a defect on it moves into and out of the load zone once per revolution: severe impact under load, faint outside it. That modulation produces sidebands: smaller peaks spaced at exactly ±1× running speed on either side of BPFI and its harmonics. Several evenly-spaced sidebands around a central peak (sometimes called a "picket fence") is close to a signature for an inner-race fault specifically.

Rolling-element defects (BSF) get the same treatment, at a different rate. A defective ball or roller travels around the bearing with the cage, cycling into and out of the load zone once per cage revolution. So a ball defect (typically dominant at 2×BSF) carries sidebands spaced at FTF, not running speed. That spacing is what separates a rolling-element fault from an inner-race fault when the two peaks land close together.

FTF does double duty. As a standalone peak, a rising FTF points to a cage or lubrication problem, a different failure mode from raceway pitting. As a sideband spacing, it's the ruler for reading a BSF-family defect correctly.

The diagnostic logic: find a peak, match it to one of the four frequencies, then read the sidebands (or their absence) to confirm which mechanism is actually responsible.

Why this doesn't scale by hand

The math above is exact, but it isn't generic: every bearing model has its own n, Bd, Pd, and θ, and every asset has its own shaft speed. A pump and a fan ten meters apart, with different bearing part numbers, have four different frequency sets to calculate, and, if either is VFD-driven, a shaft speed that moves, taking the frequencies of interest with it.

Do that correctly for one bearing, once, and it's solved. Do it for 200 bearings, every week, running envelope analysis and reading sidebands on each, and it's a staffing problem, not a solved one. Most plants don't have that many analyst-hours to spend, and the ones that do would rather spend them investigating a real finding than screening machines that are still healthy.

This is exactly the kind of narrow, repetitive, pattern-matching task machine learning is well suited to. A model that ingests raw multi-sensor time series doesn't need a human to pre-calculate a bearing's defect frequencies or run a manual demodulation: it learns what this bearing's normal vibration, temperature, and current signature looks like, and flags the moment reality starts drifting from it, on every asset, continuously. The analyst's job shifts from routinely screening mostly-healthy spectra to confirming the handful the model actually flagged.

What this looks like with Prevly

Prevly doesn't ask your team to run envelope analysis on every asset every week. It watches continuously and tells you when something changes:

Read-only ingestion. Prevly Edge connects to your existing vibration, temperature, and current sensors over read-only OPC-UA, on-premise by default: no new hardware, no writes back to your PLCs.
A learned baseline per asset. An LSTM-autoencoder anomaly model, conformal-calibrated on each machine's own operating history, learns normal for that specific bearing at that specific speed and load, and flags reconstruction error rising well before an overall vibration number would trip.
A defensible time estimate, not a guess. Once degradation is detected, Prevly's remaining-useful-life model (LightGBM with SHAP, validated on real NASA C-MAPSS data) reports a conformal prediction interval: a range to plan a shutdown window around, not a single false-precision number.
Every alert shows its work. Attribution (Integrated Gradients on the deep models, SHAP on the RUL model) reports exactly which sensors drove the finding, so your analyst can verify the pattern instead of trusting a black-box score.
Detection becomes a work order. A flagged prediction can draft a work order (asset, evidence, recommended action) directly alongside your existing CMMS.

Frequently asked questions

What is BPFO? BPFO (Ball Pass Frequency, Outer race) is the rate at which rolling elements strike a defect on a bearing's stationary outer raceway. Because the outer race and load zone are both fixed, BPFO impacts are consistently severe, producing a clean spectral peak without significant sidebands, usually the easiest defect frequency to detect.

How do you calculate bearing defect frequencies? From the bearing's geometry (number of rolling elements, ball diameter, pitch diameter, and contact angle) combined with shaft speed, using the standard BPFO/BPFI/BSF/FTF formulas. In practice, most analysts pull the numbers from a manufacturer's bearing table or vibration software rather than computing them by hand for every asset.

Why do inner-race defects show sidebands? Because the inner race rotates with the shaft, a defect on it moves into and out of the load zone once per revolution: the impact is severe under load, faint outside it. That once-per-revolution amplitude modulation produces sidebands spaced at exactly running speed on either side of BPFI and its harmonics.

Do you need envelope analysis? For inner-race and rolling-element defects, essentially yes: the modulated impact energy sits in a high-frequency resonance band that a raw velocity spectrum won't show clearly. Outer-race defects are sometimes visible without it, but envelope analysis (demodulation) remains standard practice for catching any bearing defect reliably at an early stage.

See your bearings' defect frequencies

You don't need a certified analyst screening every asset by hand to benefit from this diagnostic vocabulary. Prevly watches the raw signal continuously, flags the moment a bearing starts drifting from its own normal, and shows you exactly which sensors moved.

Request a Prevly demo and see what your bearings are already broadcasting.