Machinery's Handbook, 31st Edition
CALCULATIONS FOR BELTS AND PULLEYS
2563
FLEXIBLE BELTS AND SHEAVES Flexible belt drives are used in industrial power transmission applications, especially when the speeds of the driver and driven shafts must be different or when shafts must be widely separated. The trend toward higher speed prime movers and the need to achieve a slower, useful driven speed are additional factors favoring the use of belts. Belts have numerous advantages over other means of power transmission; these advantages include overall economy, cleanliness, no need for lubrication, lower maintenance costs, easy in- stallation, dampening of shock loads, and the abilities to be used for clutching and vari able speed power transmission between widely spaced shafts. Calculations for Belts and Pulleys Belt speed plays an important role in the amount of load a friction drive system can trans mit. Higher speeds will require higher preloads (increased belt tension) to compensate for the higher centrifugal force. In positive drive (toothed belt) systems, higher speeds gener ate dynamic forces caused by unavoidable tolerance errors that may result in increased tooth or pin stresses and shorter belt life. Pulley Diameters and Drive Ratios.— Minimum pulley diameters determined by belt manufacturers are based on the minimum radius that a belt can wrap around a pulley with out stressing the load-carrying members. For positive drive systems, minimum pulley diameters are also determined by the minimum number of teeth that must be engaged with the sprocket to guarantee the operating load. Diameters of driving and driven pulleys determine the velocity ratio of the input rela- tive to the output shaft and are derived from the following formulas: for all belt systems, velocity ratio V = D pi / D po , and for positive (toothed) drive systems, velocity ratio V = N i / N o , where D pi is the pitch diameter of the driving pulley, D po is the pitch diameter of the driven pulley, N i is the number of teeth on the driving pulley, and N o is the num- ber of teeth on the driven pulley. For most drive systems, a velocity ratio of 8:1 is the largest that should be attempted with a single reduction drive, and 6:1 is a reasonable maximum. Wrap Angles and Center-to-Center Distances.— The radial distance for which the belt is in contact with the pulley surface, or the number of teeth in engagement for positive drive belts, is called the wrap angle. Belt and sprocket combinations should be chosen to ensure a wrap angle of about 120 ° around the smaller pulley. The wrap angle should not be less than 90 ° , especially with positive drive belts, because if too few teeth are in engagement, the belt may jump a tooth or pin and timing or synchronization may be lost. For flat belts, the minimum allowable center-to-center distance (CD) for any belt-and- sprocket combination should be chosen to ensure a minimum wrap angle around the smaller pulley. For high-velocity systems, a good rule of thumb is a minimum CD equal to the sum of the pitch diameter of the larger sprocket and one-half the pitch diameter of the smaller sprocket. This formula ensures a minimum wrap angle of approximately 120 ° , which is generally sufficient for friction drives and will ensure that positive drive belts do not jump teeth. Pulley Center Distances and Belt Lengths.— Maximum center distances of pulleys should be about 15 to 20 times the pitch diameter of the smaller pulley. Greater spacing requires tight control of the belt tension because a small amount of stretch will cause a large drop in tension. Constant belt tension can be obtained by application of an adjustable tensioning pulley applied to the slack side of the belt. Friction drive systems using flat belts require much more tension than positive drive belt systems. Belt length can be calculated from: L = 2 C + π ( D 2 + D 1 )/2 + ( D 2 − D 1 ) 2 /4 C for friction drives, and length L = 2 C + π ( D 2 + D 1 )/2 + ( D 2 + D 1 ) 2 /4 C for crossed belt friction belt drives, where C is the center distance, D 1 is the pitch diameter of the small pulley, and D 2
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