Belt friction is a term describing the friction forces between a belt and a surface, such as a belt wrapped around a bollard. When one end of the belt is being pulled only part of this force is transmitted to the other end wrapped about a surface. The friction force increases with the amount of wrap about a surface and makes it so the tension in the belt can be different at both ends of the belt. Belt friction can be modeled by the Belt friction equation.
Contents
- Equation
- Generalization for a rope lying on an arbitrary orthotropic surface
- Friction coefficient
- Applications
- References
In practice, the theoretical tension acting on the belt or rope calculated by the belt friction equation can be compared to the maximum tension the belt can support. This helps a designer of such a rig to know how many times the belt or rope must be wrapped around the pulley to prevent it from slipping. 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 has no mass and its material is a fixed composition:
where
The tension on the pulling side of the belt and pulley has the ability to increase exponentially if the magnitude of the belt angle increases (e.g. it is wrapped around the pulley segment numerous times).
Generalization for a rope lying on an arbitrary orthotropic surface
If a rope is laying in equilibrium under tangential forces on a rough orthotropic surface then three following conditions (all of them) are satisfied:
1. No separation – normal reaction
2. Dragging coefficient of friction
3. Limit values of the tangential forces:
The forces at both ends of the rope
with
�where
If
This generalization has been obtained by Konyukhov A.,
Friction coefficient
There are certain factors that help determine the value of the friction coefficient. These determining factors are:
Applications
An understanding of belt friction is essential for sailing crews and mountain climbers. Their professions require being able to understand 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 slip. Misjudging the ability of a rope and capstan system to maintain the proper frictional forces may lead to failure and injury.