Page 143 - Tribology in Machine Design

Friction, lubrication and wear in lower kinematic pairs 129

Alternatively, if a denotes the total angle of lap for the driven pulley, this
result may be written as

The integration is based on the assumption that / is constant over the
contact surface. Under conditions of boundary friction this is not strictly
true as/may vary with the intensity of pressure on the bearing surface. Let
p=the normal pressure per unit area of the contact surface of
the belt and pulley at position 0,
b =the width of the belt,

then, for the element
R=pbrdQ = Td&
so that,

This pressure intensity is therefore directly proportional to the tensile stress
in the belt at the point considered. If g is the tensile stress in the belt at
position 0 and t is the belt thickness

4.10.2. Mechanism of action
The effect of elasticity on the frictional action between the belt and the
pulley surfaces is a vitally important factor in the solution of problems
relating to power transmission by belt drives. For a well-designed belt
under driving conditions, slip of the belt over the pulley should not occur,
fx
i.e. Ti/T 2 <e , where/is the limiting coefficient of friction and a is the angle
of wrap. There are two possible assumptions:
(i) frictional resistance is uniformly distributed over the arc of contact with
a reduced coefficient of friction,/;
(ii) the coefficient of friction,/, reaches its limiting value over an active arc
which is less than the actual arc of contact, and that over this arc T l falls
to T 2. For the remaining portion of the arc of contact, the tension
remains constant at either 7\ or T 2, depending upon the direction of
frictional action relative to the pulley.
If the former assumption were correct, relative movement of the belt over