Belt flex frequency

Technical article

Understand Belt flex frequency

This calculator finds how often one point on a circulating belt passes a pulley and flexes each second. Flex frequency is an important service-life parameter alongside pulley diameter, speed and tension.

What does this quantity describe?

A belt point takes L/v seconds per circuit. If it passes zs pulleys each circuit, it experiences zs flex events. Therefore fB = zs/(L/v) = zs·v/L.

Mark one point on the belt. At 10 m/s and 2 m length it returns five times per second. Passing two pulleys each circuit means ten flexes per second.

Formula and variables

fB = zs · v / L

Circuit frequency fU = v/L
Flex frequency fB = zs·fU = zs·v/L
L = zs·v/fB

Symbol / input	Meaning
Flex frequency fB	Number of pulley passes or flex events per second.
Pulleys passed zs	Number of pulleys a belt point passes during one complete circuit.
Belt speed v	Linear running speed of the belt.
Effective belt length L	Path length of one complete belt circuit along the neutral layer.

Choose the inputs correctly

L is complete effective endless-belt length, v its linear speed and zs the number of pulleys passed per circuit, including relevant idlers. Enter zs as a whole count.

How to use the calculator

Count every pulley touched by a marked belt point per circuit and enter L and v. Compare fB with the specific belt datasheet and pay special attention to backside idlers that reverse bending.

Worked example

L = 2 m, v = 10 m/s and zs = 2 give circuit frequency 5 Hz and flex frequency 10 Hz. A third idler raises it to 15 Hz with other values unchanged.

Understand the result and units

10 Hz means ten pulley passes each second. It is not a direct life prediction: a small pulley causes more severe strain per cycle and reverse bending can be more damaging.

v/L gives 1/s or Hz. Values convert internally to metres and metres per second. Shaft rpm alone is insufficient until converted to belt speed.

Why idlers influence belt life

An added idler increases zs and directly raises flex cycles. A backside idler also reverses bend direction. Dubbel and current manufacturer manuals therefore recommend adequate idler diameter and avoiding unnecessary reverse bends.

Typical applications

Use flex frequency to check fast V-, flat- and timing-belt layouts, assess extra idlers, and compare layouts with equal power but different lengths or pulley counts.

Assumptions, limits and common mistakes

Every pass is counted equally. The model does not distinguish diameters, wraps, bend direction, material or temperature. Manufacturer limits and minimum diameters determine actual suitability.

Common mistake: Include tensioners and idlers, do not confuse L with center distance, and do not interpret tooth-meshing frequency as flex frequency.

Frequently asked questions

What is belt flex frequency?

The number of pulley passes experienced by a belt point each second: fB = zs·v/L.

Does a tensioner count?

Yes if the belt passes over it each circuit. A backside idler may be additionally severe because it reverses bending.

Is flex frequency the same as circuit frequency?

Only with one pulley per circuit. Normally fB is circuit frequency v/L multiplied by zs.

What flex frequency is allowable?

It depends on profile, construction, diameters and temperature. The current manufacturer rating is decisive.

How can fB be reduced?

Lower belt speed, increase belt length or reduce pulley count, while checking the effects on the complete drive.