 Gear mesh frequency

Gear mesh frequency is the rate at which successive teeth pass through a mesh. For a fixed-axis gear with $N$ teeth rotating at $f_{\mathrm{rot}}$ revolutions per second,where $n$ is speed in revolutions per minute and $\omega$ is angular velocity in radians per second. The formula follows by counting $N$ tooth passages per complete turn. Both gears of one steady compatible mesh give the same result because their tooth-passage rates agree.^[ref]

For an original example, a24-tooth input rotating at1500 revolutions per minute gives $f_m=600\mathrm{Hz}$. Its60-tooth mate turns at600 revolutions per minute, also giving $60(600)/60=600\mathrm{Hz}$. The shaft rotation frequencies differ even though the mesh frequency agrees.

A compound gear train can have different mesh frequencies at successive stages. If that60-tooth gear is rigidly joined to a20-tooth gear driving an80-tooth output, the second mesh frequency is $20(600)/60=200\mathrm{Hz}$. The final output turns at150 revolutions per minute. By contrast, every mesh of an ideal fixed-axis simple gear train shares the same tooth-passage frequency: its intermediate gear engages both neighbors with the same tooth count and rotation rate.

A gear vibration spectrum may contain components at the mesh frequency and its integer multiples, together with other mechanical excitations. Measuring rotation with a rotary encoder lets a test compare observed frequency components with tooth-passage predictions. A spectral peak near $f_m$ does not by itself establish a structural natural frequency or identify a particular defect; the forcing and the system's frequency response both shape measured vibration.^[ref] For trains with moving gear axes, the simple fixed-axis formula requires the appropriate relative rotational rate rather than an unqualified absolute shaft speed.