Page 142 - Tribology in Machine Design

128 Tribology in machine design

higher pairs is the kinematic equivalent of two lower pairs, and gives the
same conditions of motion as the higher pair of elements represented by the
two friction wheels in direct contact.

4.10.1. Belt drive

When two pulleys connected by a belt are at rest, the tensions in the two
straight portions are equal, and will be referred to as the initial tension. If a
torque is applied to the driving pulley, and the initial pressure between the
contact surfaces is sufficient, slipping will be prevented by friction, with the
result that the tensions in the straight portions will no longer be equal. The
difference between the two tensions will be determined by the resistance to
motion of the driven pulley and, if limiting friction is reached, slipping will
occur. Let
Figure 4.33
T! =the tension on the tight side of the belt,
T 2 =the tension on the slack side of the belt,
/=the limiting coefficient of friction, assumed constant.

Consider the equilibrium of an element of length r<50 when slipping is
about to commence and 0 being measured from the point of tangency of T 2
with the pulley surface (Fig. 4.34). Thus T is the belt tension at angle 0,
T + 5T is the belt tension at angle 0 + £0, R is the normal reaction exerted
by the pulley on the element passing through the intersection of T and
T + 6T and fR is the tangential friction force.
If motion of the driven pulley occurs it is assumed that the speed is low, so
that centrifugal effects may be neglected. The polygon of forces for the
element is shown in Fig. 4.34, and to the first order of small we may write

Figure 4.34

and in the limit

hence