One Chipped Tooth, Once per Revolution: Reading Gear Mesh and Its Sidebands

A healthy gearbox is not silent — it sings. Every time a pinion tooth rolls into contact with a gear tooth, the stiffness of the mesh changes slightly, and that tiny periodic push repeats once per tooth, teeth-times per shaft revolution. The result is the gear-mesh frequency, GMF: tooth count multiplied by shaft speed. A 23-tooth pinion on a shaft turning 1,475 rpm — 24.6 revolutions per second — engages 23 × 24.6 ≈ 565 teeth every second, so this gearbox hums at 565 Hz on the day it is commissioned and on every healthy day after.

That is the first thing to unlearn: a tall mesh peak is not, by itself, a fault. Its height moves with load, alignment, tooth finish, temperature, and the vibration path between mesh and sensor — it can double between two measurements on a gearbox that is perfectly fine. The diagnosis does not live in the height of the singing voice. It lives in the family of smaller peaks that appears on either side of it: the sidebands.

The two gears are locked together at the mesh, so teeth stream through the contact point at a single shared rate. Count it from either side and you must get the same number: pinion teeth × input shaft speed = gear teeth × output shaft speed. That equality is also the speed ratio — the output shaft turns at the input speed multiplied by pinion teeth over gear teeth. Our 23-tooth pinion at 1,475 rpm driving a 91-tooth gear gives an output of 1,475 × 23⁄91 ≈ 373 rpm, or 6.21 Hz; and sure enough 91 × 6.21 ≈ 565 Hz, the same GMF the pinion side gave us.

This is why the mesh peak alone can never tell you which gear is damaged: both shafts own that peak jointly. When something goes wrong on one tooth of one gear, you need a second piece of evidence to name the shaft it rides on — and the spectrum provides one, in the form of how the peaks around the GMF are spaced.

Now chip one tooth on the pinion. For most of each revolution the mesh is healthy and the tone is steady — but once per pinion revolution the damaged tooth carries the load, the contact stiffness dips, and the mesh vibration momentarily jumps and shifts. The gearbox is still singing at the GMF; the defect is rhythmically squeezing that song, once every turn of the shaft the bad tooth rides on. In signal terms, the mesh tone has become amplitude- and phase-modulated at that shaft's rotational frequency.

Modulation in time has an exact signature in frequency: sidebands. The spectrum keeps its carrier peak at the GMF and grows a family of smaller peaks at GMF ± 1, 2, 3… times the modulating frequency — and the modulating frequency is the rotational speed of whichever shaft carries the damaged gear. Chip a pinion tooth and the sidebands sit at shaft-input spacing; chip a gear tooth and they crowd in at the slower output-shaft spacing. The spacing is the fingerprint.

Set the tooth counts and the input speed, and the simulator does the arithmetic live: GMF = pinion teeth × input shaft frequency, output shaft speed = input × (pinion teeth ÷ gear teeth), and the readouts update as you drag. The spectrum is drawn from those same numbers — every peak sits exactly where the formulas put it, on a full-span view above and a zoom around the mesh peak below.

The severity slider grows a local defect on one tooth, and the two buttons choose which gear carries it. Watch what changes and what does not: the mesh peak itself barely moves, while the sideband family around it grows with severity — and when you move the fault from pinion to gear, the family keeps its shape but its spacing collapses from input-shaft speed to the slower output-shaft speed. The annotated Δ on the zoom plot is the number an analyst would read off with a sideband cursor.

Run the numbers for our example gearbox both ways. With the 23-tooth pinion chipped, the sidebands sit at 565.4 ± 24.6 Hz — at 540.8 and 590.0 Hz, then 516.3 and 614.6, marching outwards at input-shaft spacing. With one tooth of the 91-tooth gear chipped instead, the same mesh peak wears a much tighter family: 565.4 ± 6.2 Hz, at 559.2 and 571.6. Same carrier, same GMF, completely different verdict. The height of the mesh peak told you nothing either time; the spacing of its escort named the shaft — and with the shaft named, you know which gear to pull and inspect.

There is a practical catch: to read a 6.2 Hz spacing you must first resolve it. FFT line spacing is one over the capture time, so a 6.2 Hz spacing needs a record of at least 1 ÷ 6.2 ≈ 0.16 seconds merely to land the two peaks in different bins — and one bin apart is not readable. A window's main lobe is several bins wide, so you want the spacing to cover several lines: a one-second record gives 1 Hz lines, which puts six of them between the carrier and its first sideband and makes the family legible; a four-second record gives 0.25 Hz lines and makes it unambiguous. That is why gearbox work leans on long records and high line counts rather than quick snapshots. Once the resolution is there, a sideband cursor does the reading for you: anchor it on the mesh peak, set the spacing to a candidate shaft speed, and see which family the markers land on.

A representative example, not a specific customer: a single-stage reduction gearbox on a conveyor drive shows a mesh peak that has drifted upwards over three monthly readings. On height alone the finding is ambiguous — load had also changed. A zoomed spectrum around the GMF settles it: a clean sideband family has appeared, and the spacing matches the output shaft's rotational frequency, not the motor's. The wheel is pulled at the next planned stop and one tooth face shows spalling at mid-flank. The lesson is the sequence: the drifting peak raised the question, but the sideband spacing answered it — which shaft, therefore which gear, therefore which spare to have on the shelf before opening the case.

Pattern recognition like this builds fastest on faults you can trust. A TMFSS simulator's fault library includes gearbox faults among its 30+ conditions, with VFD speed control and a built-in tachometer — so you can seed a known gear fault, sweep the speed, and watch the GMF and its sidebands move exactly as the arithmetic predicts. For the theory, the free Bearing & Gear Analysis 101 primer at 101.tieraonline.in walks through mesh frequencies and sideband families step by step — it is a free primer, not an accredited ISO certification. When you want the formal credential, TIERA's TCAT programme runs structured analyst training (see /services), with proctored examinations conducted at exams.tieraonline.in.

Sideband work is a resolution problem before it is an interpretation problem: a 6 Hz spacing next to a 565 Hz carrier only appears if your capture is long enough and your FFT fine enough to separate the lines. PhonoVibe Q, O and HD record at 128 kHz sampling with 24-bit resolution across a 0.5 Hz – 60 kHz bandwidth, with IEPE sensor power built in — clean, long records with the dynamic range to keep small sidebands above the floor next to a large mesh peak. Every PhonoVibe ships with TVIB TSAP201, whose FFT runs up to 102,400 points with harmonic, band and sideband cursors — the sideband cursor is exactly the Δ annotation from the simulator above, laid over your own data — and recorded signals can be re-processed later as the picture develops.

If you want the pattern in your hands before a real gearbox provides it, the TMFSS simulator reproduces gearbox faults among its 30+ controlled conditions, with VFD speed control and a built-in tachometer, so an analyst can practise reading GMF and sideband spacing against a known truth.