A belt is a flexible power transmission element that seats tightly on a set of pulleys or sheaves. When the belt is used for speed reduction, the typical case, the smaller sheave is mounted on the high-speed shaft, such as the shaft of an electric motor. The larger sheave is mounted on the driven machine. The belt is designed to ride around the two sheaves without slipping. The belt is installed by placing it around the two sheaves while the center distance between them is reduced. Then the sheaves are moved apart, placing the belt in a rather high initial tension. When the belt is transmitting power, friction causes the belt to grip the driving sheave, increasing the tension in one side, called the "tight side," of the drive. The tensile force in the belt exerts a tangential force on the driven sheave, and thus a torque is applied to the driven shaft. The opposite side of the belt is still under tension, but at a smaller value. Thus, it is called the "slack side." The most widely used type of belt, particularly in industrial drives and vehicular applications, is the V-belt drive. The V-shape causes the belt to wedge tightly into the groove, increasing friction and allowing high torques to be transmitted before slipping occurs. Most belts have high-strength cords positioned at the pitch diameter of the belt cross section to increase the tensile strength of the belt. The cords, made from natural fibers, synthetic strands, or steel, are embedded in a firm rubber compound to provide the flexibility needed to allow the belt to pass around the sheave. Often an outer fabric cover is added to give the belt good durability. The data given in this program are for the narrow-section belts: 3V, 5V and 8V. The pulley, with a circumferential groove carrying the belt, is called a sheave (usually pronounced "shiv"). The size of a sheave is indicated by its pitch diameter, slightly smaller than the outside diameter of the sheave. The speed ratio between the driving and the driven sheaves is inversely proportional to the ratio of the sheave pitch diameters. This follows from the observation that there is no slipping (under normal loads). Thus, the linear speed of the pitch line of both sheaves is the same as and equal to the belt speed, vb. Then Since R1 = D1/2 and R2 =D2/2, then The angular velocity ratio is The relationships between pitch length, L, center distance, C, and the sheave diameters are Where: B = 4L - 6.28(D2 - D1) The angle of contact of the belt on each sheave is These angles are important because commercially available belts are rated with an assumed contact angle of 180°. This will occur only if the drive ratio is 1 (no speed change). The angle of contact on the smaller of the two sheaves will always be less than 180°, requiring a lower power rating. Note: the angle of wrap on the smaller sheave should be greater then 120°. The length of the span between the two sheaves, over which the belt is unsupported, is This is important for two reasons: You can check the proper belt tension by measuring the amount of force required to deflect the belt at the middle of the span by a given amount. Also, the tendency for the belt to vibrate or whip is dependent on this length. The contributors to the stress in the belt are as follows: The tensile force in the belt, maximum on the tight side of the belt. The bending of the belt around the sheaves, maximum as the tight side of the belt bends around the smaller sheave. Centrifugal forces created as the belt moves around the sheaves. The maximum total stress occurs where the belt enters the smaller sheave, and the bending stress is a major part. Thus, there are recommended minimum sheave diameters for standard belts. Using smaller sheaves drastically reduces belt life. The design value of the ratio of the tight side tension to the slack side tension is 5.0 for V-belt drives. The actual value may range as high as 10.0. The factors involved in se