Page 146 - Tribology in Machine Design
P. 146
132 Tribology in machine design
Also
It should be noted that the idle arc must occupy the earlier portion of the arc
of embrace, since contraction of the belt must be directed towards A in the
driving pulley and extension of the belt must be directed away-from C on the
driven pulley. It follows therefore that
velocity of the surface of the driving pulley
= velocity of the tight side of the belt,
velocity of the surface of the driven pulley
= velocity of the slack side of the belt.
Further, as the power transmitted by the driving pulley increases, the idle
arc diminishes in length until /? = oc and the whole arc of contact becomes
active. When this condition is reached, the belt commences to slip bodily
over the surface of the pulley. This is shown schematically in Fig. 4.36. Thus,
Figure 4.36 eqn (4.87) may be written
and if V l is constant, the velocity of slip due to creeping action is
proportional to (7\ — T 2) within the range /? ^ a. Since T l/T 2 is the same for
both pulleys, it follows that the angle /? subtended by the active arc must be
the same for both.
Thus for pulleys of unequal size, the maximum permissible value of /?
must be less than the angle of lap on the smaller pulley, if the belt is not to
slip bodily over the contact surface.
4.10.3. Power transmission rating
In approximate calculations it is usual to assume that the initial belt tension
is equal to the mean of the driving tensions, i.e.
If the belt is on the point of slipping, and the effects of centrifugal action are
neglected
