Gear mesh and sidebands: finding the shaft that carries a worn gear
The gear mesh frequency, the sidebands around it, and how a spacing in hertz points to one shaft and one gear.
The gear mesh frequency
Two gears in mesh produce a vibration at the gear mesh frequency (GMF): the number of teeth on the gear times the speed of its shaft. Both gears of a pair give the same GMF.
Formulas
| Quantity | Formula |
|---|---|
| Gear mesh frequency | GMF = Z × shaft speed (Hz) |
| Speed of the other shaft | Z1 × n1 ÷ Z2 |
| Sideband spacing | The speed of the shaft with the damaged gear |
What sidebands mean
Damage on one tooth, or on every tooth of one gear, changes the mesh force once per turn of that gear. This modulates the mesh frequency and puts sidebands on either side of it. The spacing between the sidebands equals the speed of the shaft with the damaged gear.
Reading the pattern
| What you see | Likely cause |
|---|---|
| Sidebands at one shaft speed around the GMF | A worn, eccentric or cracked gear on that shaft |
| Sidebands at the speed of the other shaft | The mating gear is the damaged one |
| Many sidebands, growing in number and height | Wear or damage spread over several teeth |
| GMF alone, no sidebands | Load-related or normal. Check the trend. |
| Sidebands plus a high floor | Late wear with debris or poor lubrication |
A method that works
- Draw the gear map with the tooth counts and calculate the speed of every shaft.
- Find the GMF of each stage. Compare in orders when the speed changes.
- Measure the sideband spacing and match it to a shaft speed.
- Confirm in at least two views, such as the envelope spectrum, the shock pulse spectrum and the velocity spectrum.
- Check the time signal for the modulation once per turn.
- Check the oil for particles, water and wear debris.
Common causes
- Abrasive particles in the oil, such as cement dust.
- Poor lubrication or the wrong viscosity.
- Misalignment or an overloaded stage.
- Tooth damage left from an earlier overload.
Case
A cement mill gearbox showed sidebands at 8.52 Hz around the first-stage mesh, which was the speed of the intermediate shaft. The teardown found worn gear teeth and cement in the oil. See the field case for the spectra and photographs.