Belt friction is a term describing the friction forces between a belt and a surface, such as a belt wrapped around a bollard. When a force applies a tension to one end of a belt or rope wrapped around a curved surface, the frictional force between the two surfaces increases with the amount of wrap about the curved surface, and only part of that force (or resultant belt tension) is transmitted to the other end of the belt or rope. Belt friction can be modeled by the Belt friction equation.[1]
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 system determine how many times the belt or rope must be wrapped around a curved surface to prevent it from slipping. Mountain climbers and sailing crews demonstrate a working knowledge of belt friction when accomplishing tasks with ropes, pulleys, bollards and capstans.
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 is positive for all points of the rope curve:
, where is a normal curvature of the rope curve.
2. Dragging coefficient of friction and angle are satisfying the following criteria for all points of the curve
3. Limit values of the tangential forces:
The forces at both ends of the rope and are satisfying the following inequality
with ,
where is a geodesic curvature of the rope curve, is a curvature of a rope curve, is a coefficient of friction in the tangential direction.
If then .
This generalization has been obtained by Konyukhov A.,[4][5]