Page 145 - Tribology in Machine Design

Friction, lubrication and wear in lower kinematic pairs 131

Referring to Fig. 4.35, suppose AB represents the active arc on the driving
pulley. Consider a length of belt r/? extending backwards from the point A
into the straight portion. Friction plays no part over the idle arc; there is no
change in tension and no relative movement. Hence for the length r/?:

During the time interval in which the point A on the pulley moves to
position B, the corresponding point A on the belt will move to B'. The arc
BB' is the contraction of a length r/? of the belt in passing from a condition
of uniform tension 7\ to its position AB' on the active arc. Hence

The second term of this expression follows from eqn (4.84). Similarly for the
driven pulley the arc DD' is the increase in elastic extension of a length r/? in
passing from a condition of uniform tension T 2 to its position CD' on the
active arc, so that

Again, let the surface of the driving pulley travel a peripheral distance /, then

Corresponding travel of periphery of the driven pulley

Hence for pulleys of equal size, if
V l = peripheral velocity of surface of the driving pulley,
V 2= peripheral velocity of surface of the driven pulley,

and substituting for BB' and DD' from eqns (4.85) and (4.86)