Fig. 2679.
Thus suppose p, [Fig. 2679], represents a driven pulley, whose load is 1,000 pounds, and that from a to b, from b to c, from c to d, and from d to e, represent equal arcs of contact between belt and pulley, then arc a b will have on it the amount of stretch due to a pull of 250 pounds at b, diminishing to nothing at a. Arc c b will have on it the amount of stretch due to a pull of 500 pounds at c and 250 at b; arc d c will have on it the amount of stretch due to a load of 750 at d, and 500 at c; and arc d e will have the tension due to a load of 1,000 pounds at e, and 750 pounds at d. Suppose, then, that the amount of belt stretch is greater between b and c than it is between d and e, then the belt will travel faster between b c than between d e to an amount equal to the difference in stretch, and will at b c slip over the pulley to that amount; or if the friction of the belt at b c is sufficient to move the pulley in accordance with the stretch, then the belt must move the pulley at a greater velocity than the belt motion from d to e.
But since the friction of the belt is greatest at d e, it will hold the pulley with the greatest force, and hence the velocity of the belt and pulley will be uniform, or at least the most uniform, at d e.
Here arises another consideration, in that the stretch of the leather is not uniform, and the section of belt at c b may stretch more or less under its load than section c d does under its load, in which event the velocities of the respective belt sections cannot be uniform, and to whatever amount belt slip ensues the velocity of the driven wheel will be less than that of the driver.
Attention has thus far been directed to the relative velocities of the pulleys while under continuous motion. But let us now examine the relative velocities when the two pulleys are first put in motion. Suppose, then, the belt and pulley to be at rest with an equal degree of tension (independently of the weight of the belt, as before) on both sides of the belt. On motion being imparted to the driving pulley, the amount of belt elongation due to the stress of the load on the driving pulley has first to be taken up and transferred to the slack side of the belt, and during such transfer a creep is taking place on the arc of belt contact on the driving pulley.
Fig. 2680.
Furthermore, let it be noted that while under continuous motion the belt first receives full stress at point f, [Fig. 2677]; at starting it first receives it at point e, and there will be a period of time during which the belt stretch will proceed from e towards f, the pulley remaining motionless. The length of duration of this period will, in a belt of a given width, and having a given arc of contact on the driven pulley, depend on the amount of the load. Thus, referring to [Fig. 2680], if the amount of the load is such that the arc of contact between the top and the point b is sufficient to drive the pulley, the pulley will receive motion when the belt stretch has proceeded from a to b; but if the load on the pulley be increased the belt stretch will require to proceed farther towards c.
At the top the stretch will proceed simultaneously with that of the driving side of the belt, between the points f g, [Fig. 2677]; but from the friction between the belt and pulley, the stretch of the part enveloping the pulley will be subsequent and progressive from f towards e, [Fig. 2677].