Bearing fault frequencies: BPFO, BPFI, BSF and FTF explained

Why a damaged bearing has its own frequencies

A rolling element bearing is a small planetary gearbox: the rolling elements orbit inside the cage while the inner race turns with the shaft. When a spall or crack forms on one of the surfaces, every rolling element that passes over it produces a short impact. Those impacts repeat at a rate set by the bearing's geometry and the shaft speed, so each defect location has its own frequency.

That is what makes bearing faults diagnosable from vibration: if a peak and its harmonics sit exactly at one of these frequencies, you know not only that a bearing is failing but which part of it.

The four frequencies

Formulas

For a bearing with a stationary outer race and a rotating inner race, with n rolling elements, rolling element diameter d, pitch diameter D, contact angle φ and shaft speed f_r in Hz (rpm / 60):

BPFO = (n / 2) · fr · (1 − (d / D) · cos φ)
BPFI = (n / 2) · fr · (1 + (d / D) · cos φ)
BSF  = (D / 2d) · fr · (1 − ((d / D) · cos φ)²)
FTF  = (fr / 2) · (1 − (d / D) · cos φ)

Two quick checks follow from the formulas: BPFO + BPFI = n · f_r, and BPFO = n · FTF. If your numbers don't satisfy them, the geometry was entered wrong.

Many analysts track 2 × BSF rather than BSF: a defect on a ball strikes both the inner and the outer race once per spin, so the impacts repeat twice per ball revolution.

Worked example: a 6205 bearing at 1480 rpm

A deep groove 6205 bearing has 9 balls, a ball diameter of about 7.94 mm, a pitch diameter of about 39.04 mm and a contact angle of 0°. So d / D ≈ 0.2034. At 1480 rpm the shaft turns at f_r = 24.67 Hz.

Geometry varies between manufacturers and bearing series, so take d, D and the contact angle from the bearing maker's data, or use the defect frequencies they publish. The bearing fault frequency calculator does the arithmetic for any bearing.

Reading them in a spectrum

• Outer race: a series of harmonics at BPFO, usually without sidebands, because the defect stays in the load zone.
• Inner race: harmonics of BPFI with sidebands spaced at shaft speed (1 ×), because the defect moves in and out of the load zone once per revolution.
• Rolling element: peaks at BSF or 2 × BSF, often with sidebands at FTF, since the damaged element travels with the cage.
• Cage: FTF itself is low and hard to see directly; it more often shows up as sidebands or as modulation of other bearing frequencies.

The calculated values are a starting point, not an exact target. Slip between the rolling elements and the races, and load changes that alter the contact angle, shift the real frequencies by a percent or so, which is why analysts look for a family of harmonics near the expected value rather than a single exact line.

Catching them early: envelope analysis

In the early stages the impacts are tiny and hidden under the machine's normal vibration in a velocity spectrum. Envelope analysis (demodulation) high-pass filters the signal around the bearing's resonances, extracts the repetition rate of the impacts and shows it as a spectrum. Bearing defect frequencies often appear there weeks or months before they are visible in velocity.

How Misoki uses this

Misoki Prism AI looks for these bearing defect patterns in your vibration data, names the fault, grades how serious it is and gives the repair steps. Findings that matter are checked by a vibration analyst through specialist review before they reach your team.