W. A. Dow

In placing a belt around two pulleys, no rule can be given which will account for the stretch in the belt, since the stretch of a belt is variable in different belts of the same length. A belt should be cut slightly shorter than the measured length around the pulleys and it is evident that the length of a belt cannot be obtained exactly by calculation. In practice, to obtain the necessary length of a belt which is to pass around two pulleys already on their places upon the shaft, it is usual to pass a tape measure around the pulleys, the stretch of the line or tape being allowed for the stretch of the belt.

If the length of a belt for pulleys not in position is required, it may be obtained as follows: Suppose Fig. 1 represents the condition where the diameter of the large wheel is 36 in. and the diameter of the small wheel 18 in. and the distance between centers is 50 in.; then, V502+92 = V2581 =50.79 in., the length of the belt on each side tangent to pulleys. This must be multiplied by 2 to get the length of both sides, to which must be added the half circumference of both the larger and smaller pulleys, or 50.79 x 2 = 101.58 in.; half circumference of larger pulley = 18 x 3.1416 = 56.54; half circumference of smaller pulley = 9x 3.1416 = 28.27; therefore 101.58 + 56.54 + 23.27=186.33 in. is the length of belt required.

Fig. 1

The rule, therefore, is: Square the distance between center of pulleys and square the difference in radii of the two pulleys, add together and extract the square root. Multiply this root by 2 and add half the circumference of each pulley. The result will be the length of the belt. This will give a belt a little too long, but allows for a small amount to be cut out of the belt to give the necessary tension. Another rule is as follows: Add the diameters of the two pulleys, divide the result by 2, multiply the quotient by 3 1/4 and add twice the distance between the center of the shafts. The result will be the length of belt required.

The grain side of the belt should be placed next to the pulley, for with the grain side out there is a tendency to stretch and crack; this occurs especially when small pulleys are used, whereas if the grain side was next to the pulley the tendency would be to compress it and prevent either cracking or tearing. Very little of the belt's strength is lost by wearing away its weak side.

When two pulleys are placed one above the other, the upper pulley will have a grip due to. the tension and weight of the belt, whereas if placed horizon-tally, the weight of the belt will fall equally on both pulleys and for this reason vertical belts of, large size require greater tension on the pulleys to transmit the same power than belts placed horizontally.

Fig. 2

As soon as motion is transmitted by a belt from one pulley to another, one side of the belt is under.greater tension than the other. The side of the belt to be the most strained is the drive side, which is the side that approaches the driving pulley. The slack side is always that which recedes from the pulley. In some cases the sag of the belt is so great that the arc of contact on the drive pulley is not sufficient to prevent slipping of the belt. When this occurs, which is usually when the slack side is the lower side of the belt, an idle pulley is placed between the two main pulleys, as shown in Fig. 2.

As will be noticed, this pulley takes up the sag of the belt and allows a longer arc of contact to,be made on the drive pulley. When the direction of rotation of the driven pulley is required to be reversed from that of the driving pulley, the belt must be crossed, as shown in Fig. 3. It is evident that cross belts have a greater arc of contact and a greater transmitting power than open belts and the slip is less, but the life of the belt is shortened on account of the two sides of the belt being in constant use.

When a belt connects two pulleys whose planes of rotation are at an angle one to the other, it is necessary to have the center line of the belt approach the pulley in the plane of the pulley's revolution irrespective of the line of motion of the belt when receding from the pulley, as shown in Fig. 4. This figure represents what is known as a quarter-twist belt. A and B are the two pulleys whose planes of revolutions are at right angles, the belt traveling as denoted by the arrows. The center line of the belt is in the plane of rotation of A on the side on which it advances to A. Now, if the position of the pulleys is changed, the same rule applies. It is evident, therefore, that the belt motion must occur in the one direction only and shafts at any angle one to another may have motion

Fig. 3 communicated from one to the other by a similar belt connection, providing a line at right angles to the axis of one forms also a right angle with the axis of the other.

The axes of shafts may be set at any angle to the plane of rotation, provided that the axle line of pulley A at right angles to the imaginary line C, which is at right angles to the axis of the shaft of pulley A, and the side of the driving pulley which delivers the belt is in line with the center line of the driven pulley.

Fig. 4

It sometimes occurs that these provisions cannot be carried out, and in those cases pulleys to guide the direction of the motion of the belts must be employed. Thus, in Fig. 5, an arrangement of guide or mule pulleys is shown which are placed at the intersection of the middle planes of pulleys A and B. The dotted

Fig 5 line TR shows the intersection of the two planes. The axes of the mule pulleys are made to coincide with this line, in which case the belts will have the suitable directions and can be run in both directions.

An arrangement of guide pulleys by which two pulleys not in the same plane are connected, is shown in

Fig. 6. As will be noticed, the arc of contact of the smaller pulley A is increased by the use of the two-idlers C and D, and the belt may be run in either direction. From the foregoing it can be seen that belts can run in any direction, providing pulleys are placed in proper positions.

It often happens when new belts are required, the width necessary to transmit a certain horse power must be known. This can be determined by the following formula:

W=800 H / S where W= width of belt in inches, H = horse-power to be transmitted and S = speed of belt in feet per minute. If the width is given and it is required to find the number of horse-power the belt is capable of transmitting, the formula becomes

H=WS / 800

Suppose, for example, a belt is 8 in. wide and its speed is 2000 ft. per minute, then H = (8 x 2000) % 800 = 20 horse power. This rule is used when both pulleys are of the same diameter. When two pulleys are used of different diameters, multiply the length of the belt in contact on the smaller pulley by 360 and divide the product by the circumference of the pulley. The

Fig. 6 quotient will be the arc of contact. After the arc of contact is found, subtract it from 180 and multiply the remainder by 3. This last result is to be added to 800 and the sum used when computing the power of the belt. The following article shows how the arc of contact is used when computing the power of the belt. Suppose the small pulley to be 24 in. in diameter and the length of contact 30 in., then (30 x 360 ÷ (24÷3 3.1416) = 143 degrees. Then (180-143) x 3 = 111 and 800 + 111 =911, which is the sum to be used in the horse-power formula. Suppose under those conditions an 8-in. belt is used which runs 2500 ft. per minute, then according to the formula (2500 x 8)5÷911 = 21.9 horse-power.

In all the above cases, a single belt was implied in the calculations. When a double belt is used it will transmit 1 1/2 times the power of a single belt, and in order to find the width of a double belt, multiply the width of a single belt by 2/8. For instance, if it requires a single belt 15 in. in diameter to transmit a certain horse-power, it will only require a 2/3 x 15 = 10-inch double belt to do the same work.-"The Practical Engineer."