Demo essay — illustrative content

Gear-mesh frequency, in one line

A short note on the one number that anchors acoustic gearbox analysis.

Published 17 October 2026 · #mathematics#signal-processing

Demo essay — illustrative content. Layout placeholder, not written by Tathagat.

If a gear with NN teeth turns at fshaftf_{\text{shaft}} revolutions per second, its teeth mesh at

fmesh=N⋅fshaftf_{\text{mesh}} = N \cdot f_{\text{shaft}}

Sidebands appear at fmesh±k⋅fshaftf_{\text{mesh}} \pm k \cdot f_{\text{shaft}} when the shaft wobbles or a tooth is damaged. That is why the shaft frequency is the first thing to pin down from the tachometer: without it, every other feature drifts with engine speed.