The H. P. transmitted by an iron wire cable is found by where the letters have the same significance as in the formulas for rope drives. A steel cable will transmit double the above amount. The breaking strain for iron cables is 40,000 pounds per square inch of cross section area, and for steel cables 80,000 pounds. A factor of safety of 10 is generally allowed for rope and cable transmission. A factor of safety is the number which expresses the ratio of the ultimate strength of a body to the working load. The weights of wire cables per foot in length are as follows: 1. What is the weight of a in. dia. cable at 1.2 lbs. per ft. 837 ft. long, and what H. P. can be transmitted at 100 R. P. M. over 12 ft. dia. sheaves? 2. What is the difference in H. P. of problem 1 when figured by the formula and by ft.-lbs. of work? 3. What is the weight of a in. iron cable 700 ft. long, and what H. P. can be transmitted over 10 ft. dia. sheaves at 80 R. P. M.? 4. What H. P. can be transmitted by a 1 in. cable at 95 R. P. M. over a 12 ft. dia. sheave? 5. The length of a 13 in. iron cable is 800 ft. and it weighs 2 lbs. per ft. Find the F. P. M. required to transmit 200 H. P. 6. Find the dia. of sheave at 125 R. P. M. and length of a in. steel cable to transmit 90 H. P. and be inside the safe limit. CHAIN TRANSMISSION One form of chain used for hoisting machinery is made of round wire links as short as possible for strength. Let d=diameter of wire, then the length of link inside=2.5 d; width of link inside=1.5 d. The following table gives sizes of wire for hoists: Another form of chain used for giving a positive motion between two shafts by means of sprocket wheels, is the flat link and block chain; here the strain on the chain is limited by the shearing stress on the pivots. ред x. Ꭹ PD Fig.44. The sprockets should not have less than 7 teeth; the larger the sprocket the less will be the strain on chain and consequently less wear on the pivots of the rivets. The formula for sizes of sprockets is as follows: N= number of teeth in sprocket, Adistance between centers of rivets in link, B = distance between centers of rivets in block, for 1 inch pitch of chain b is usually .325 inch when A= .6 inch and B= .4 inch. The bottom diameter of sprocket wheel is the important dimension, therefore size b must be taken accurately. Then OD=PD+b and Bottom diameter = PD-b. PROBLEMS 1. What is the dia. of an 8 tooth sprocket wheel with a 1 in. pi. chain? 2. What is the OD and bottom dia. of a 20 tooth sprocket with 1 in. pi. chain? 3. What are the distances A, B, and dia. of b, for a 1 in. pi. chain, when proportionally the same as for 1 in. pitch? 4. What are the OD and PD for a 20 tooth sprocket, with 1 in. pi. chain? 5. Find the diameters for a 24 tooth sprocket for a 11⁄2 in. pi. chain. 6. Find A, B, and b, for 12 in. pi. when proportionally the same as for a 1 in. pi. chain. 7. Find the diameters for a 28 tooth sprocket with a 12 in. pi. chain. 8. What are the PD and OD for a sprocket of 28 teeth and 1 in. pi. chain? 9. Find the bottom dia. for a sprocket of 30 teeth and 1 in. pi. chain. SHAFTING The H. P. which a line shaft can impart to connected machinery is limited by the strength of the material of which it is made. The principal strain is in the twisting of the round bar when the pulleys are made to revolve carrying driving belts to the various machines. The twisting of the shaft is called its torsional strain, and the formula which determines the amount of torsion which a shaft will safely stand is where d=the diameter of shaft in inches, w= the pull of the belt in pounds, r=the radius of the pulley in feet, C=the constant for breaking moment which is found by experiment for cold rolled steel to be 660 pounds. 10 is the factor of safety. Then the above formula may be written PROBLEMS 1. Find values for H and N by transposing the formula for d, given above. 2. A 4 in. dia. shaft runs 150 R. P. M. What is the safe load in H. P. to put on the shaft? 3. Find the H. P. that can be transmitted by a shaft 21⁄2 in. dia. at 200 R. P. M. 4. What H. P. can be transmitted by a 5 in. dia. shaft running at 275 R. P. M.? 5. What dia. shaft will be required to transmit 500 H. P. running at 150 R. P. M.? 6. What dia. of shaft will be required to transmit 250 H. P. running at 74 R. P. M.? 7. How fast should a shaft revolve that is to transmit 1,000 H. P. and is 12 in. diameter? 8. What is the dia. of a shaft that is to transmit 150 H. P. at 150 R. P. M.? 9. Find the R. P. M. of a 5 in. shaft to transmit 300 H.P. 10. Find the dia. of a shaft to transmit 12 H. P. at 500 R. P. M. 11. Find the dia. of a shaft to transmit 400 H. P. at 200 R. P. M. 12. What dia. of shaft will be required to transmit 1,000 H. P. at 36 R. P. M.? 13. What dia. of shaft will be required to transmit 200 H. P. at 180 R. P. M.? 14. Find the H. P. transmitted by an 8 in. dia. shaft at 115 R. P. M. |