Suppose that a flat belt is placed on the side of a double cone, Fig. 95, and that we start to rotate the cone in the direction of the arrow. The edge E, which is stretched more tightly than F, has a greater grip on the surface of the cone, and will climb up the incline as shown by the dotted lines. With continued rotation of the cone, the belt, if not prevented, will move farther up the incline, will finally pass the crest, and start down on the other side until the two edges E and F have equal tension, or the pull to the right is balanced by an equal pull to the left. The center line of the belt will now run in the central plane X Y of the pulley.
As long as this condition is maintained, the belt will run true and will stay on the pulley. Also, if the pulley faces were perfectly flat, the belt a perfectly homogeneous piece of leather, and the shafts perfectly parallel, the belt would stay in the pulley. Such perfect conditions, however, cannot be produced or maintained, and it is therefore necessary in practice to imitate the conditions of Fig. 95, and "crown" either one or both pulleys, so that the belt will not develop any tendency to run off. On the contrary, it will constantly seek to keep its center line in the central plane of the pulleys, any tendency of one edge to slacken and run off being instantly counteracted by the tightening up of the other as it starts to climb, thus pulling the belt back until the balance is secured. A very slight amount of crowning will accomplish this result, and as little crown as possible, consistent with good running, should be provided, that too great inequality of tension in the belt may not be introduced.
In Fig. 93, if the shafting be not parallel, the center line of the belt will not run in the central plane of the pulley, and the belt will climb towards the high part of the pulley, as in the above case of the cone, and we may expect the belt to run off.
The above discussion reduces to one fundamental working condition for belt transmission, viz, The center line of the belt leaving a pulley must lie in the central plane of the pulley to which the belt is delivered.
This principle is applicable to all cases of belt transmission, however complicated, whether the shafts be parallel or at an angle. The use of guide pulleys is merely a means of controlling the delivery of the belt according to the principle. The student should commit this principle to memory, and go over its application until he is sure that he understands it; for without it he cannot solve complicated belt problems, and he cannot feel sure of his solution of even the simplest ones. In the pages of discussion and illustration which follow, the student should constantly note the recurrence and application of this principle, as it is really all there is to the solution of belt problems, except familiar knowledge of how to make the drawing projections, which he already is supposed to possess.
Fig. 95. Theory of Crowning a Pulley.
Tight and loose pulleys are provided for cases in which a machine is to be thrown in and out of service without stopping the driving shaft.
A common arrangement is shown in Fig. 96, where a pulley with a straight face is located on the line shaft, and two pulleys with crowned faces are on the countershaft. Pulley B is loose on the shaft, and C is fast to the shaft. A collar D is placed on left of B, to prevent its end motion. Shifting the belt is accomplished by pushing on the advancing side of belt, close to the receiving pulley.
Fig. 96. Diagram of Tight and Loose Pulley Drive.
The shifter F has two iron pegs, one on each side of the belt, and is operated by hand. The belt is readily guided by pressure on the advancing side, for the motion of the receiving pulley aids the motion of the belt; but if pressure were applied to the retreating side it would be necessary to use enough force to shift the belt bodily sidewise on the face of the pulley. As excessive tension on the belt decreases its life, the diameter of the loose pulley is often slightly decreased, thus permitting the belt, when doing no useful work, to be under less tension than when driving.
Another arrangement is to provide a clutch to throw into a loose pulley on the line shaft, the belt standing idle when not in service.