What is gear mesh frequency?

Gear mesh frequency (GMF) is the rate at which gear teeth engage. It equals the number of teeth on a gear multiplied by its rotational frequency (RPM/60). GMF = Z × RPM/60. Both meshing gears produce the same GMF.

What do sidebands indicate?

Sidebands around GMF are spaced at shaft rotational frequencies. They indicate gear faults like eccentricity, tooth wear, or cracking. Sidebands at the input shaft frequency suggest a fault on the input gear, while sidebands at the output shaft frequency suggest a fault on the output gear.

How to identify gear faults using vibration?

Common gear fault indicators: elevated GMF with sidebands indicates tooth wear or damage; non-synchronous sidebands suggest a cracked tooth; ghost frequencies (non-integer multiples) indicate manufacturing errors; natural frequency excitation with GMF modulation suggests advanced damage.

What is hunting tooth frequency?

Hunting tooth frequency (HTF) is the rate at which a specific tooth on one gear meshes with a specific tooth on the other gear. HTF = GMF / (Z1 × Z2 / GCD(Z1, Z2)). It is used to detect assembly-related faults and pattern wear.

What are assembly phase considerations for gears?

Assembly phasing refers to the specific tooth-to-tooth alignment when gears are installed. Marking and maintaining the original phasing during maintenance ensures the same wear pattern continues. Incorrect phasing can introduce new vibration patterns and accelerate wear on previously unloaded teeth.

Free Engineering Tool #036

Gear Mesh Frequency Calculator

Calculate gear mesh frequency (GMF), gear ratio, driven shaft speed, and sideband frequencies for vibration diagnostics.

GMF Sidebands Gear Ratio

Results

Gear Mesh Frequency (GMF)

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GMF as Order of Shaft 1

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Shaft 2 Speed

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Gear Ratio (Z₂/Z₁)

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Shaft 1 Frequency

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Shaft 2 Frequency

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Sideband Frequencies

Sideband	GMF − n×f₁ (Hz)	GMF + n×f₁ (Hz)	GMF − n×f₂ (Hz)	GMF + n×f₂ (Hz)

Gear Mesh Frequency

The gear mesh frequency (GMF) is the rate at which teeth engage between two meshing gears. It is the same for both gears:

Gear Ratio & Shaft 2 Speed

Sidebands

Sidebands appear around GMF spaced at shaft rotational frequencies. They are key indicators of gear health:

Sidebands at f₁: Indicate a fault on the driving gear
Sidebands at f₂: Indicate a fault on the driven gear
Asymmetric sidebands: Suggest cracked or broken teeth

Practical Example

Example — Helical Gear Pair 23/67, 1500 RPM

Given: Z₁ = 23, Z₂ = 67, RPM₁ = 1500

f₁ = 1500/60 = 25 Hz

GMF = 23 × 25 = 575 Hz

Gear ratio = 67/23 = 2.913:1

RPM₂ = 1500 × 23/67 = 514.9 RPM → f₂ = 8.58 Hz

Sidebands: 575 ± 25 Hz, 575 ± 8.58 Hz, etc.

Tip: A healthy gear typically shows GMF with low-amplitude, symmetric sidebands. Growing sidebands, especially asymmetric ones, indicate developing faults.

Gear Mesh Frequency Calculator | GMF & Sidebands

Published by Nikolai Shelkovenko on February 15, 2026 February 15, 2026