TR Get a quote

Bearing Fault Frequency Calculator

Bearing defects produce vibration at characteristic frequencies determined by bearing geometry and shaft speed. This calculator returns the outer race (BPFO), inner race (BPFI), rolling element (BSF) and cage (FTF) frequencies.

Pick a bearing from the list or enter the number and diameters of the balls from the maker's catalogue.

HzCPMOrder
Shaft frequency———
FTF — Cage———
BSF — Ball spin———
BPFO — Outer race———
BPFI — Inner race———

Fault frequencies and harmonics

These tools are for preliminary assessment and training. Decisions on critical equipment must be based on on-site measurement and expert review.

Worked example

Geometry commonly quoted for a 6205-type deep groove ball bearing: Nb = 9, Bd = 7.94 mm, Pd = 39.04 mm, φ = 0°. The shaft turns at 1800 rpm (fr = 30 Hz); Bd/Pd = 0.2034.

BPFO = 9·30/2·(1 − 0.2034) ≈ 107.54 Hz (3.585X); BPFI ≈ 162.46 Hz (5.415X); BSF ≈ 70.70 Hz (2.357X); FTF ≈ 11.95 Hz (0.398X).

Internal geometry differs between manufacturers; use catalogue values from the manufacturer for diagnosis.

Assumptions and limits

The formulas assume pure rolling without slip, a stationary outer ring and a rotating inner ring. Measured fault frequencies are usually slightly below the theoretical values because of load and slip, so look for a nearby peak rather than the exact value.

How to use it

  1. Get the geometry from the bearing manufacturer's catalogue or data sheet.

  2. If the pitch diameter is unknown, (bore + outside diameter) / 2 is a good approximation.

  3. Enter the shaft speed; frequencies update instantly.

Theory and formulas

FTF = fr/2 · (1 − (Bd/Pd)·cosφ)

BPFO = Nb·fr/2 · (1 − (Bd/Pd)·cosφ)

BPFI = Nb·fr/2 · (1 + (Bd/Pd)·cosφ)

BSF = Pd/(2·Bd) · fr · (1 − ((Bd/Pd)·cosφ)²) — because a ball defect strikes both races each revolution, 2×BSF is often what appears in the spectrum.

Rough estimate without geometry: BPFO ≈ 0.4·Nb·fr, BPFI ≈ 0.6·Nb·fr.

For the 60, 62 and 63 series in the list, internal geometry is estimated from ISO 15 boundary dimensions: the ball is the largest standard ball that fits the ring section (about min(0.3·(D−d), 0.7·B)), pitch diameter (d+D)/2, ball count about 0.6·π·dm/Dw. The estimate is close to actual values for common deep groove bearings (e.g. 6205: 9 × 7.94 mm), but exact values are in the maker's catalogue.

Measured geometries come from open research datasets: CWRU Bearing Data Center, NASA PCoE / IMS, XJTU-SY and MFPT.

Frequently asked questions

What are BPFO and BPFI?

BPFO (Ball Pass Frequency Outer) is the rate at which rolling elements pass a defect on the outer race; BPFI (Ball Pass Frequency Inner) is the same for an inner race defect. Inner race defects usually appear with running speed (1X) sidebands.