Choose a rubber belt to transmit 15 hp (11.2 kW) from a 7-in (17.8-cm) diameter pulley driven by a shunt-wound dc motor. The pulley speed is 1300 r/min, and the belt drives an electric generator. The arrangement of the drive is such that the arc of contact of the belt on the pulley is 220°.
Calculation Procedure:
The belt service factor allows for the typical conditions met in the use of a belt with a given driver and driven machine or device. Table 3 lists typical service factors Sf used by the B. F.
TABLE 3 Service Factor S
Squirrel-cage ac motor |
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Application |
Normal torque, line start |
High torque |
Wound rotor ac motor (slip ring) |
Single- phase capacitor motor |
Dc shunt- wound motor |
Diesel engine, four or more cylinders, above 700 r/min |
|
Agitators Compressors Belt conveyors (ore, coal, sand) Screw conveyors Crushing machinery Fans, centrifugal Fans, propeller Generators and excitors Line shafts Machine tools Pumps, centrifugal Pumps, reciprocating |
1.0-1.2 1.2-1.4 ······ ······ ······ 1.2 1.4 1.2 1.4 1.0-1.2 1.2 1.2-1.4 |
1.2-1.4 ······ 1.4 1.8 1.6 ······ 2.0 ······ ······ ······ 1.4 ······ |
1.2 1.4 ······ ······ 1.6 1.4 1.6 ······ 1.4 1.2-1.4 1.4 1.4-1.6 |
1.2 ·· ·· ·· ·· ·· ·· 1.4 1.0 1.2 ·· |
1.2 1.2 1.6 ······ 1.4 1.6 1.2 1.4 1.0-1.2 1.2 ······ |
1.2 1.4-1.6 1.4 1.6 2.0 1.6 1.8-2.0 |
Goodrich Company. Entering Table 3 at the type of driver, a shunt-wound dc motor, and projecting downward to the driven machine, an electric generator, shows that Sf = 1.2.
A rubber belt can contact a pulley in a range from about 140 to 220°. Since the hp capacity ratings for belts are based on an arc of contact of 180°, a correction factor must be applied for other arcs of contact.
Table 4 lists the arc-of-contact correction factor Cc. Thus, for an arc of contact of 220°, Cc = 1.12.
The belt speed is S = p RD, where S = belt speed, ft/min; R = pulley rpm; D = pulley diameter, ft. For this pulley, S = p(1300)(7/12) = 2380 ft/min (12.1 m/s).
Table 5 lists minimum recommended pulley diameters, belt material, and number of plies for various belt speeds. Choose the pulley diameter and number of plies for the next higher belt speed when the computed belt speed falls between two tabulated values. Thus, for a belt speed of 2380 ft/min (12.1 m/s), use a 7-in (17.8-cm) diameter pulley as listed under 2500 ft/min (12.7 m/s). The corresponding material specifications are found in the left-hand column and are four plies, 32-oz (0.9-kg) fabric.
Enter Table 6 at 32 oz (0.9 kg) four-ply material specifications, and project horizontally to the belt speed. This occurs between the tabulated speeds of 2000 and 2500 ft/min (10.2 and 12.7 m/s). Interpolating, we find [(2500 - 2380)/(2500 - 2000)](4.4 - 3.6) = 0.192. Hence, the power rating of the belt hpbi is 4.400 - 0.192 = 4.208 hp/in (1.2 kW/cm) of width.
TABLE 4 Arc of Contact Factor K-Rubber Belts
Arc of contact, ° |
140 |
160 |
180 |
200 |
220 |
Factor K |
0.82 |
0.93 |
1.00 |
1.06 |
1.12 |
TABLE 5 Minimum Pulley Diameters in (cm) -Rubber Belts of 32-oz (0.9
kg) Hard Fabric
Belt speed, ft/min (m/s) |
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Ply |
2000 (149.4) |
2500 (186.4) |
3000 (223.7) |
4000 (298.3) |
3 4 5 6 7 8 9 10 |
4 (10.2) 5 (12.7) 8 (20.3) 11 (27.9) 15 (38.1) 18 (45.7) 22 (55.9) 26 (66.0) |
4 (10.2) 6 (15.2) 8 (20.3) 11 (27.9) 15 (38.1) 19 (48.3) 23 (58.4) 27 (68.6) |
4 (10.2) 6 (15.2) 9 (22.9) 12 (30.5) 16 (40.6) 20 (50.8) 24 (61.0) 28 (71.1) |
4 (10.2) 7 (17.8) 10 (25.4) 13 (33.0) 17 (43.2) 21 (53.3) 25 (63.5) 29 (73.7) |
The required belt width W = hpSf/(hpbiCc), or W = (15)(1.2)/[(4.208)(1.12)] = 3.82 in (9.7 cm). Use a 4-in (10.2-cm) wide belt.
Related Calculations: Use this procedure for rubber-belt drives of all types. For additional service factors, consult the engineering data published by B. F. Goodrich Company, The Goodyear Tire and Rubber Company, United States Rubber Company, etc.