Library / Driveline and transmission / DRV-18
Driveline and transmission
Gear mesh frequency
Frequency at which gear teeth engage, equal to the number of teeth times the rotation frequency of that gear.
- Ref
- DRV-18
- Rev
- v1
- Field
- Driveline and transmission
- Result
- fmesh [Hz]
Each tooth engages once per revolution of its gear, so a gear with Z teeth turning at ngear rpm produces fmesh = Z ngear/60. This is the whine heard from a gearbox. It is the same number whichever gear of the pair you use, because meshing gears have tooth counts inversely proportional to their speeds. Sidebands spaced at the shaft frequency appear on either side of the mesh frequency when a gear is eccentric or damaged. Use the actual rotational speed of the gear, not the vehicle speed.
Frequency at which gear teeth engage, equal to the number of teeth times the rotation frequency of that gear. It sets the whine heard from a gearbox and appears with sidebands in gearbox vibration.
Calculator
- Rotation frequency of the gear, n/6025 Hz
- Second harmonic of the mesh frequency2,000 Hz
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- A 40-tooth gear at 1,500 rpm meshes at 1,000 Hz, the 40th order of the shaft. Sidebands at ±25 Hz appear around it if a gear is eccentric.
- The mesh frequency rises directly with speed and tooth count: a 60-tooth gear on the same shaft would mesh at 1,500 Hz.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (Hz) | Local step | Change in result |
|---|---|---|---|---|---|---|
| ngear Gear speed | 100 to 6,000 rpm | 66.67 | 4,000 | 3,933 | +10% | +10 % |
| Z Number of teeth | 10 to 120 | 250 | 3,000 | 2,750 | +1 | +2.5 % |
Sweep of Gear speed
| Gear speed (rpm) | Mesh frequency (Hz) |
|---|---|
| 100 | 66.67 |
| 837.5 | 558.3 |
| 1,575 | 1,050 |
| 2,313 | 1,542 |
| 3,050 | 2,033 |
| 3,788 | 2,525 |
| 4,525 | 3,017 |
| 5,263 | 3,508 |
| 6,000 | 4,000 |
Sweep one variable
Variables and how each one contributes
Mesh frequency
What the equation gives you. Everything else feeds it.
Number of teeth
The number of teeth on the gear, a whole number from 10 to 120. Raises the mesh frequency in proportion. Raising it by 5 (to 45) moves the result by +12.5 %, from 1,000 to 1,125 Hz.
Gear speed
The gear’s rotational speed, in rpm. Raises the mesh frequency in proportion. Raising it by 10 % (to 1,650) moves the result by +10 %, from 1,000 to 1,100 Hz.
Worked example with the values above
- Rotation frequency: ngear/60 = 1,500/60 = 25 Hz.
- Multiply by the number of teeth: 40 × 25.
- fmesh = 1,000 Hz.
Assumptions and limits
- Steady rotation and ideal gears with an integer number of teeth.
- The speed is that of the gear considered, not of the engine.
Common mistakes
- Using the engine speed rather than the gear’s own speed.
- Pairing the tooth count of one gear with the speed of the other gear in the pair.
Statistics and uncertainty
Gearbox noise peaks are narrow, so speed variation of 1 to 2 % moves the peak by the same fraction. In condition monitoring, a change of several dB in the mesh peak is a stronger sign of wear than a small change in its frequency.
Where it is used
- Identifying gear whine and finding the source in a gearbox.
- Checking the mesh frequency against structural resonances in the housing.
Maths you need
- Frequency: cycles per second, hertz
- Gear teeth: one engagement per tooth per revolution