Page 144 - Tribology in Machine Design
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130 Tribology in machine design
the pulley would be entirely prevented by friction. The first assumption is
correct for an inextensible belt. Bodily slip would then occur if/reaches its
limiting value. Investigations into the creeping action of a belt under
driving conditions do not support this view, since a certain measure of slip
occurs under all conditions of loading. Taking the latter assumption as
correct, it follows that the angle ft over which a change of tension occurs is
measured by the equation
where a is the angle subtended by the arc of contact, /? is the angle subtended
by the active arc and a — /? is the angle subtended by the idle arc.
Creep in an extensible belt is measured by elastic extension, or
contraction, as the belt passes from the straight path to the pulley surface.
Further, any relative movement of the belt over the pulley must be directed
towards the point of maximum tension.
To examine these changes in length, first consider the active arc, Fig. 4.35.
If 0 is measured from the position where growth of tension commences,
and T is the tension at angle 0
Figure 4.35
The extension of an element of length rSQ is then (g/E)r6®.
fli
and since (T 1/T 2) = e , this becomes
where E is the Young modulus of the belt's material.
