Tools · Diagnostics
Gear mesh & belt frequencies
The frequencies to mark on a gearbox or belt-drive spectrum before you start looking for faults.
Gear pair
Belt drive
Belt drive uses the same input speed as the driver pulley.
| Gear pair | Hz | CPM |
|---|
| Belt drive | Hz | CPM |
|---|
The formulas
GMF = Z1 · f1 = Z2 · f2 f2 = f1 · Z1/Z2
Na = gcd(Z1, Z2) fHT = GMF · Na / (Z1·Z2)
fbelt = π · D1 · f1 / L
- Gear mesh (GMF) and its harmonics are always present. Watch their amplitude trend, and sidebands at the shaft speeds of each gear: sidebands at f1 point to the input gear, at f2 to the output gear.
- Hunting tooth frequency is how often the same pair of teeth meet again. A damaged tooth on each gear shows up as a low-frequency beat at fHT. Tooth counts with a common factor (Na > 1) make it repeat more often.
- Belt frequency is usually below running speed. A worn or damaged belt shows peaks at 1×, 2× and 3× belt frequency, often with 2× dominant.
Method & sources
What it calculates
- Gear mesh frequency GMF = Z1·f1; output speed f2 = f1·Z1/Z2.
- Assembly phase factor Na = gcd(Z1, Z2); hunting tooth frequency fHT = GMF·Na / (Z1·Z2); assembly phase frequency = GMF / Na.
- Belt frequency = π·D1·f1 / L (pitch diameter and pitch length); driven speed = f1·D1/D2.
Assumptions & limits
- Belt slip (typically 1–2%) is ignored.
- Planetary gearboxes need their own carrier and planet relationships.
Verified: 20/47 teeth at 1480 RPM gives GMF 493.3 Hz, output 10.50 Hz and hunting tooth 0.5248 Hz, matching Python.