Timing-belt teeth in mesh

Technical article

Understand Timing-belt teeth in mesh

This calculator determines how many timing-pulley teeth lie within the belt wrap arc. Mesh count is a separate rating step because manufacturers derate power or torque when too few teeth carry load.

What does this quantity describe?

Wrap β is the fraction β/360° of a full circle. The same fraction of z pulley teeth is geometrically covered: ze = z·β/360°. Round the fraction down when counting fully engaged teeth.

At 180° wrap, the belt covers half the pulley and half its teeth. A 20-tooth pulley gives ten; at 160° it gives 8.889 pitches and conservatively eight whole teeth.

Formula and variables

ze = z · β / 360°

ze,geom = z·β/360°
ze,full = floor(ze,geom)
β = 360°·ze/z

Symbol / input	Meaning
Geometric teeth in mesh ze	Calculated, possibly fractional mesh count; round down for fully engaged load-carrying teeth.
Pulley teeth z	Total tooth count of the timing-belt pulley considered.
Wrap angle β	Timing-belt contact angle on the pulley considered.

Choose the inputs correctly

z is total teeth on the pulley considered, usually the critical small pulley. β is its actual wrap. For rating, use the smallest angle occurring across the full load case.

How to use the calculator

First obtain β from drive geometry, then enter β and z. Round down for whole load-carrying teeth and consult the current manual for the profile-specific teeth-in-mesh factor.

Worked example

z = 20 and β = 160° give ze,geom = 20·160/360 = 8.889, so eight fully engaged teeth may be counted conservatively.

Understand the result and units

More teeth distribute circumferential force across more contacts. Eight whole teeth is only geometry; the product method decides whether its factor is already 1.0.

z and ze are dimensionless. β is evaluated in radians internally and can be entered in degrees; one revolution is 360° or 2π rad.

What follows after mesh count?

Gates and Mitsuboshi use teeth in mesh as input to a product-specific correction factor. Mitsuboshi, for example, tabulates factors for two through six or more teeth. NormCalc deliberately returns transparent geometry; use the current product manual for rating.

Typical applications

Use mesh count in timing-belt preselection, rating correction, small-pulley checks and layouts with short centers or large ratios.

Assumptions, limits and common mistakes

The equation counts covered pitches but does not model unequal load distribution, tooth stiffness, pretension, profile error or tooth jump. Correction factors are product-specific.

Common mistake: Do not round a fractional result upward when whole teeth are required. Check the critical small pulley, and do not transfer one profile's minimum blindly to another.

Frequently asked questions

How many timing-belt teeth are in mesh?

Geometrically ze = z·β/360°. Round down when counting fully engaged load-carrying teeth.

Why round down?

A boundary tooth only partly covered by the contact arc should not conservatively count as one fully loaded tooth.

What is the minimum teeth in mesh?

It is profile- and manufacturer-specific. Many rating methods apply a factor below a stated count; consult the current manual.

Which pulley should be checked?

Usually the small pulley because it has fewer teeth and often less wrap.

How can mesh count be increased?

Use more pulley teeth or increase wrap through center-distance or idler changes, while checking bending and layout effects.