Page 147 - Tribology in Machine Design

Friction, lubrication and wear in lower kinematic pairs 133

where a is the angle of lap of the smaller pulley. Hence

If F = the mean belt speed in ms *,

Alternatively:

4.10.4. Relationship between belt tension and modulus

In the foregoing treatment a linear elastic law for the belt material has been
assumed. It has already been mentioned that such materials do not in
general adhere closely to the simple law of direct proportionality. This is
illustrated in Fig. 4.37, which shows the stress-strain curves for samples of
leather- and fabric-reinforced rubber belts. Broadly speaking, the curves
may be divided into two classes:
(a) those which are approximately linear within the range of stress
corresponding to the driving tensions T l and T 2 (Fig. 4.37, case (a));
(b) those which are approximately parabolic in form (Fig. 4.37, case (b)).
In the former case we may write

where e\ and e 2 are the strains corresponding to the tensions T 1 and T 2,
respectively, and E is the slope of the stress-strain curve between these
limits. The value of E determined in this way is referred to as the chord
modulus of elasticity. If this value of E is used, it readily follows that the
expressions for the calculation of creep and initial tension so far obtained
are valid when the belt material falls into this group.
In the latter case let h m and e m denote a point on the stress-strain curve
corresponding to the mean belt tension T m. Then, if the curve is assumed
truly parabolic

and for any other point

Figure 4.37