Timing-belt tooth mesh frequency

What does this quantity describe?

Each revolution of a timing-belt pulley, exactly z teeth engage the belt in sequence. At rotational speed n this gives a base mesh frequency f = n·z/60, with n in rpm and f in Hz — the number of tooth engagements per second.

This is similar to a ratchet clicking through a gear: each tooth produces a short impulse, and the click rate rises with speed or tooth count. In timing belts, this impulse train shows up as a tonal excitation that, depending on frequency, can be heard as a hum or whine.

Formula and variables

f = n · z / 60

• f = n · z / 60
• n = f · 60/z
• z = f · 60/n

Choose the inputs correctly

Rotational speed n and tooth count z of the pulley considered set the mesh frequency. For a sizing question — at what speed a given excitation frequency should be avoided — n can be chosen as the target.

How to use the calculator

Enter speed and tooth count of the pulley considered to compute mesh frequency. To avoid a critical frequency such as a housing resonance, choose n as the target and enter the frequency to avoid along with tooth count.

Worked example

3,000 rpm and 20 teeth give f = 3,000 · 20 / 60 = 1,000 Hz.

Understand the result and units

A mesh frequency of 1,000 Hz falls in a clearly audible range; if it coincides with a resonance of the housing, mount or an attached component, noise can be markedly amplified.

Rotational speed is given in rpm, tooth count is dimensionless, and mesh frequency is given in Hz.

Why do both pulleys share the same mesh frequency?

Because a timing belt runs with constant tooth pitch throughout, the same number of belt teeth engages each pulley in the same time interval, regardless of that pulley's own tooth count. So n1·z1/60 at the driving pulley and n2·z2/60 at the driven pulley give the same numeric value, even though the two pulleys can have different speeds and tooth counts. This shared frequency is the base excitation present throughout the drivetrain.

Typical applications

The calculation is used for the acoustic design of timing-belt drives, for example choosing an operating speed whose mesh frequency avoids a known structural or housing resonance, and for diagnosing noise issues from a measured frequency.

Assumptions, limits and common mistakes

The model gives only the geometrically determined base frequency of tooth engagement. Actual noise generation additionally depends on belt tension, tooth profile geometry, misalignment and the natural frequencies of the surrounding structure, none of which are captured here.

Common mistake: A common mistake is confusing mesh frequency with the plain rotational frequency n/60 — only multiplying by tooth count gives the actual tooth-engagement excitation frequency. It is also easy to overlook that the driving and driven pulleys share the same mesh frequency despite different tooth counts and speeds, since both are driven synchronously by the same belt.