How are bearing defect frequencies (BPFO, BPFI, BSF, FTF) calculated?

What the four defect frequencies mean

A defect on a race or a ball produces a short impact at each contact. The repetition rate of those impacts depends on the bearing geometry; that rate is the defect frequency.

• BPFO (ball pass frequency, outer race): how often balls strike an outer-race defect.
• BPFI (ball pass frequency, inner race): the same idea for the inner race.
• BSF (ball spin frequency): how often a defect on one ball touches the races.
• FTF (fundamental train frequency): the rotation rate of the cage.

In the formulas, fr is the shaft frequency in Hz, Nb is the number of balls, d is the ball diameter, D is the pitch diameter and φ is the contact angle. Because BPFO and BPFI differ, the spectrum helps tell an outer-race defect from an inner-race defect.

Calculation for a hypothetical bearing

Consider a hypothetical bearing with Nb = 9, d/D = 0.2, φ = 0° and a shaft speed of 1,500 rpm, so fr = 1,500 / 60 = 25 Hz. Since cos 0° = 1:

• BPFO = (9/2) × 25 × (1 − 0.2) = 4.5 × 25 × 0.8 = 90 Hz
• BPFI = (9/2) × 25 × (1 + 0.2) = 4.5 × 25 × 1.2 = 135 Hz
• FTF = (25/2) × (1 − 0.2) = 12.5 × 0.8 = 10 Hz
• BSF = (D / 2d) × 25 × (1 − 0.2²) = 2.5 × 25 × 0.96 = 60 Hz

D / 2d equals 2.5 because d/D = 0.2. Measured values rarely match these exactly, since the rollers slip. Look for a peak close to a calculated value. If no peak is near any of them, first check the shaft speed and the rpm-to-Hz conversion.

Common mistakes

The most frequent errors are these:

• Entering degrees as radians. In radian mode, cos 15 gives a different value from cos 15°. Enter the angle in degrees or convert it.
• Using rpm where the formula needs Hz. fr must be in Hz: 1,500 rpm is 25 Hz.
• Swapping d/D and D/d. If D/d = 5 is entered, BPFO = 4.5 × 25 × (1 − 5) = −450 Hz, which is not physical.
• Declaring a defect from a calculated frequency alone. These frequencies are a lead; envelope analysis and trends must confirm them.

Follow-up questions