Type of brake
A band brake is a primary or secondary brake, consisting of a band of friction material that tightens concentrically around a cylindrical piece of equipment or train wheel to either prevent it from rotating (a static or "holding" brake), or to slow it (a dynamic brake). 
Uses.
Band brakes were common on winch drums and chain saws and is also used for some bicycle brakes.
Band brakes were commonly used to control the winding drum on railway inclines that lowered loaded wagons while raising empty ones over a steep slope. 
A former application was the locking of gear rings in epicyclic gearing. In modern automatic transmissions this task has been largely taken over by multiple-plate clutches or multiple-plate brakes.
Features.
A band brake is a flexible band which warps around part or all of the outside surface of a wheel or drum. One end of the band is anchored in place, while the other is attached to a lever. Pressing on the lever brings the band into contact with the surface of the wheel and the friction causes the wheel's rotation to slow.
Band brakes can be simple, compact, rugged, and can generate high force with a light input force. However, band brakes are prone to grabbing or chatter and loss of brake force when hot. These problems are inherent with the design and thus limit where band brakes are a good solution.
Effectiveness.
One way to describe the effectiveness of the brake is as formula_1, where formula_2 is the coefficient of friction between band and drum, and formula_3 is the angle of wrap. With a large formula_4, the brake is very effective and requires low input force to achieve high brake force, but is also very sensitive to changes in formula_2. For example, light rust on the drum may cause the brake to "grab" or chatter, water may cause the brake to slip, and rising temperatures in braking may cause the coefficient of friction to drop slightly but in turn cause brake force to drop greatly. Using a band material with low formula_2 increases the input force required to achieve a given brake force, but some low-formula_2 materials also have more consistent formula_2 across the range of working temperatures.
References.
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