PeacheyPlx

I'm a first year Electrical Engineering Major in the College of Engineering at UCSB and will contribute to the Wikipedia project through a project in my Technical Writing Class.

The actual article: Belt Friction(Physics)

File:Beltfric.jpg

A typical belt drive attached to a pulley

Belt Friction is a physical property observed from the forces acting on a belt wrapped around a pulley, when one end is being pulled. The resulting tension, which acts on both ends of the belt, can be modeled by the Belt Friction Equation. This is also known as Eytelwein's formula or the Capstan equation.
In practice, the theoretical tension acting on the belt or rope calculated by the Belt Friction Equation can be compared to the belt's maximum tension it can support. This helps a designer of such a rig know how many times the belt or rope must be wrapped around the pulley to prevent it from snapping. Mountain climbers and sailing crews demonstrate a standard knowledge of belt friction when accomplishing basic tasks.

Equation

The equation used to model belt friction is, assuming the belt component of the setup has no mass< and its material is a fixed composition :

$T_{2}=T_{1}e^{\mu _{s}\beta }$

where $T_{2}$ is the tension of the pulling side, which is typically the greater force, $T_{1}$ is the tension of the resisting side, $\mu _{s}$ is the static friction coefficient, which has no units, and $\beta$ is the angle, in radians formed by the first and last spots the belt touches the pulley, with the vertex at the center of the pulley.

The tension on the pulling side has the ability to increase exponentially if the size of the angle increases (e.g. it is wrapped around the pulley segment numerous times) and as the coefficient of friction grows.

Friction Coefficient

There are certain factors that help determine the value of the friction coefficient. These determining factors are:

The Belting Material Used
The age of the material also plays a part, where worn out and older material tends to be more rough and therefore experience greater friction when sliding.
The Construction of the Drive-Pulley System
This involves strength and stability of the material used, like the pulley, and how greatly it will oppose the motion of the belt or rope.
The Conditions the Test is Being Performed In
The friction between the belt and pulley will decrease immensely if the belt happens to be muddy or wet, as it acts as lubricant to the force. This also applies to extremely dry or warm conditions which will evaporate any water naturally found in the belt, making friction much greater.
The Overall Design of the Setup
The setup involves the initial conditions of the construction, such as the angle which the belt is wrapped around and the maximum amount of tension that can be sustained by the belt.

Application

An understanding of belt friction is essential for sailing crews and mountain climbers. Their professions require being able to maximize the amount of weight a rope with a certain tension capacity can hold versus the amount of wraps around a pulley. Too many revolutions around a pulley make it inefficient to retract or release rope, and too few may cause the rope to snap. Misjudging the ability of a rope to sustain itself against a certain force will ultimately lead to failure or serious injury.