bearing_defect_frequencies — ACOUSTICS bearing op

Data kinds: nonetable (an op determined by its arguments alone — it takes no image or data input)

Call: import acoustics; acoustics.bearing_defect_frequencies(rpm=1800.0, n_elements=9, element_diameter=8.0, pitch_diameter=40.0, contact_angle_deg=0.0) (or opsacoustics.get("bearing_defect_frequencies"))

Usage

The four characteristic rates of a rolling-element bearing, from geometry.

Derived, not tabulated. Under pure rolling the cage advances at half the sum

of the race surface speeds, which with `r = d/D cos(alpha)` gives, per

shaft revolution rate `f_r = rpm/60`:

• `FTF (cage / fundamental train) = f_r (1 - r) / 2`

• `BPFO (ball pass, outer race) = N f_r (1 - r) / 2 = N * FTF`

• `BPFI (ball pass, inner race) = N f_r (1 + r) / 2`

• `BSF (ball spin) = f_r (1 - r^2) D / (2 d)`

Two exact identities fall out and are asserted in the tests, because they

catch a transposed `d and D immediately: BPFO + BPFI = N f_r`

exactly, and `BPFO = N * FTF` exactly. Measured for the defaults

(1800 rpm, 9 elements, d = 8, D = 40, alpha = 0): `ratio = 0.200000`,

`f_r = 30.000000, FTF = 12.000000, BPFO = 108.000000`,

`BPFI = 162.000000, BSF = 72.000000` Hz, with

`BPFO + BPFI - 9 f_r = 0.000e+00 and BPFO - 9 FTF = 0.000e+00` —

exactly zero in float64, not merely small.

Returns a dict with `shaft_hz, ftf_hz, bpfo_hz, bpfi_hz`,

`bsf_hz, ratio (d/D cos alpha`), and the inputs echoed back.

Also `bsf_hz_2x`: a rolling element normally strikes *both* races per

spin, so a spall on the element itself is usually seen at `2 * BSF`, and

reporting only `BSF` is the classic way to miss it.

These are the no-slip kinematic rates. Real bearings slip by roughly a

percent, so an observed line within about 1 % of one of these is a match and

an exact match is a coincidence; that tolerance is the caller's to apply.

Raises `ValueError: non-real / string / bool scalars, rpm <= 0`,

`n_elements` not an int >= 2, non-positive diameters, an

`element_diameter >= pitch_diameter` (geometrically impossible — the

rolling elements would not fit inside the pitch circle, and the usual cause

is the two arguments being swapped, which otherwise returns a negative FTF

and a plausible-looking BPFI), and `|contact_angle_deg| >= 90`.

Detailed usage guide

acoustic_condition_monitoring family guide

References (sample data, literature)

• Sample-data catalog (download URLs / licences) — 2-D uses skimage.data (BSD/public domain) plus synthetic images; 3-D lists download URLs for real data sources (Stanford, PDS, …).

• Operator provenance and references — the sources of the research/methods this op family came from.

• The canonical algorithm (author, year) and its uses are named in the family usage guide above.

Runnable examples (verified samples that actually call this op)

acoustic_condition_monitoringpy -3.11 examples/acoustic_condition_monitoring.py

Ops the type connects to (they accept table as input)

istft

Same category (bearing)

envelope_spectrum · spectral_kurtosis · cepstrum


*Provenance: acoustics.py — ACOUSTICS operator registry. This per-op note is generated by tools/opdocs.py md (do not hand-edit).*

© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.