Belt Drive Theory and Example Calculation

Theory
Note that in the example below the belt is assumed to be flat. Most belts now have a 'V' cross section. The V belt does not run on the bottom of the belt groove, but the sides wedge into the sides of the pulley. If the semi-included angle of the V groove is B, then the theory below needs modifying as the maximum friction force is no longer F = mu R, (where mu is the coefficient of friction) but becomes:

F = mu R cosec(B) = mu R /[sin(B)]
A 'V' grooved pulley is the equivalent of having a flat pulley with a coefficient of friction mu cosec(B).

In the theory below it is assumed that the element of belt subtends a small angle and when resolving radially, sine of half the small angle is approximately equal to the angle in radians and (resolving in a tangential direction) the cosine is approximately equal to 1.