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Exercises
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1. A key 2.5 cm width and 5 cm length is fastened thru a 3-in diameter shaft. The yield stress of the key is 70 MPa. If the factor of safety is 4, find the power delivered by the shaft at a speed of 380 rpm. a. 30 kW b. 25 kW c. 20 kW d. 35 kW 2. A keyed gear deliver a torque of 915 N-m thru its shaft of 64 mm outside diameter. If the key has thickness of 16 mm and width of 12 mm, find the length of the key. Assume the permissible stress values of 62 MPa for shear and 100 MPa for tension. a. 30.3 mm b. 38.4 mm c. 22.8 mm d. 42.1 mm 3. A 52 mm diameter shaft of SAE 1040 grade, cold rolled, having a yield point of 60 ksi and with a key having a dimension of 3/4 x 3/4 x 4.5 inches, has a factor of safety of 4.0, calculate the minimum yield point in the key based on shearing. a. 25.2 ksi b. 29.2 ksi c. 27.1 ksi d. 32.8 ksi 4. A 1.8 m pulley is fastened to a 130 mm shaft by means of a square key with 150 mm length. What force tangent to the pulley rim will crush the key if the bearing stress is 400 MPa. Assume key and shaft are of the same material. b. 75.3 kN c. 82.1 kN d. 64.3 kN 5. A one meter pulley is fastened to a 100 mm shaft by means of 30 mm square key and 180 mm length. What force tangent to the pulley rim will shear the key if the shearing stress is 220 MPa. a. 208.7 kN b. 189.3 kN c. 175.3 kN d. 118.8 kN 6. A 150 kN force is acting on a key that has a length five times its height. If the bearing stress of the key is 420 MPa, calculate the maximum height of the key. a. 18.3 mm b. 16.3 mm c. 15.8 mm d. 11.9 mm 7. A flat key is to be used in a 50 mm diameter shaft that will transmit 2.5 kN-m torque. If the bearing stress of the key is 450 MPa, compute for the cross sectional dimension of the flat key to be used using key length of 22 mm. a. 18 mm b. 17 mm c. 22 mm d. 20 mm 8. A rectangular key was used in a pulley connected to a line shaft that transmits 18 kW at 580 rpm. If the shearing stress of the key is 250 MPa, determine the force acting on key length, if the key width is one-fourth of shaft diameter and key length of one inch. a. 55.1 kN b. 64.3 kN c. 43.9 kN d. 60.2 kN 9. A 7/16-in height x 3.5-in length flat key is keyed to a 2.5-inch diameter shaft. Compute the torque developed in key if the bearing stress allowable is 28 ksi. a. 32981.9 in-lb b. 21031.7 in-lb c. 42111.8 in-lb d. 26796.9 in-lb 10. A rectangular key is used in a pulley connection to transmit 120 kW at 1300 rpm on a 55-mm shaft diameter. Determine the force required to remove the shaft from the hub if f=0.50. a. 32.0 kN b. 35.0 kN c. 38.0 kN d. 40.0 kN 11. An 80 mm diameter shafting of SAE 1040 grade, cold rolled, having a yield point of 55 ksi and 1/2 x 3/4 x 4 inches key. Compute the minimum yield point in the key in order to transmit the torque of the shaft. The factor of safety is 5. a. 75331.1 psi c. 96532.1 psi d. 65889.3 psi 12. A flat key is to be designed for 75 mm diameter shaft which will transmit a 200 kW power at 420 rpm. If the allowable shearing stress is 220 MPa and the key width is 18 mm, find the length of the key. a. 25.5 mm b. 28.3 mm c. 30.6 mm d. 35.6 mm 13. A 6-spline shaft (d=0.80D, b=0.25D, t=0.10D) to slide when under load has a compressive area of 2.5 in2 and shearing area of 3.5 in2. Find the minimum diameter of the shaft required if the hub length is 2.25-in. a. 1 in b. 2 in c. 3 in d. 0.5 in 14. A 1-1/2-in diameter, 4-spline shaft (d=0.85D, b=0.241D, t=0.075D) and permanent fit, has a permissible pressure of 900 psi. Find the shearing force in the spline, if the hub length is 2-in. a. 2602.8 lbs b. 2833.9 lbs c. 2239.1 lbs d. 2440.7 lbs 15. A 6-spline shaft (d=0.80D, b=0.25D, t=0.075D) and to slide when not under load has a diameter of 2.5-in and is used to transmit 120 HP at 1850 rpm. Find the compressive stress in the spline if the hub length is 18% of the shaft diameter. a. 6752.0 psi b. 7895.9 psi c. 8526.1 psi d. 5621.4 psi 16. A 2.0-in diameter, 10-spline shaft (d=0.91D, b=0.156D, t=0.045D) and permanent fit is used to transmit 120 kW power at 1800 rpm. Find the shearing stress of the spline if the hub length is 1-3/4-in. a. 2563.9 psi b. 3219.2 psi d. 2889.1 psi 17. A 1.8-in diameter, 8-spline shaft (d=0.90D, b=0.15D, t=0.05D) and permanent fit is used to transmit 100 kW power at 2000 rpm. Find the compressive force in the spline. a. 617.6 lbs b. 622.8 lbs c. 587.1 lbs d. 564.3 lbs 18. The transmission gears of an automobile are carried on a 2.5-in, 6-spline shaft (d=0.80D, w=0.25D, h=0.10D) to slide when under load. The hub length of each gear is 1-5/8-in. Determine the total horsepower transmitted at 3000 rpm, with 820 psi permissible pressure on the splines. a. 107 b. 120 c. 112 d. 98 19. A 1.75-in diameter, 4-spline shaft (d=0.85D, b=0.241D, t=0.10D) and permanent fit has a permissible pressure of 800 psi. Find the compressive force, if the hub length is 2.5-in. a. 1250 lbs b. 1400 lbs c. 1520 lbs d. 1626 lbs 20. A 6-spline shaft (d=0.85D, b=0.25D, t=0.075D) and to slide when not under load has a diameter of 2.8-in. Determine the overall power transmitted if the shearing force is 2300 lbs and shaft rotates at 2600 rpm. a. 583.4 hp b. 623.8 hp c. 677.5 hp d. 553.1 hp 21. An 1.50 diameter, 10-spline shaft (d=0.91D, b=0.156D, t=0.045D) and permanent fit has a compressive force of 2000 lbs. Find the total torque transmitted if the hub length is 1.75-in. a. 1642.1 in-lb b. 14325.0 in-lb c. 15021.9 in-lb d. 16742.4 in-lb 22. A 4-spline shaft (d=0.80D, b=0.25D, t=0.10D) and to slide when not under load has a diameter of 2.5-in. Calculate the shearing stress if the shearing force is 2400 lbs. The hub length is 2-in. a. 480 psi b. 550 psi c. 430 psi d. 523 psi 23. A 2-in diameter, 6-spline shaft (d=0.90D, b=0.25D, t=0.05D) and permanent fit has a compressive force of 2200 lbs. Calculate the compressive stress for a hub length of 1.50-in. a. 2530.8 psi b. 2653.1 psi c. 2444.4 psi d. 2312.1 psi Transmission gears of an automobile are carried on a 2.25-in, 10-spline shaft (d=0.81D, b=0.156, t=0.095D) and slide when under load. The hub length of each gear is 1-5/8-in. It transmits at 2800 rpm with 850 psi permissible pressure on the spline. Determine: 24. Area under compression in the spline a. 0.200 in2 b. 0.347 in2 c. 0.481in2 d. 0.520 in2 25. The compressive force per spline a. 265.1 lbs b. 278.3 lbs c. 287.1 lbs d. 295.3 lbs 26. Total torque transmitted a. 3106.1 in-lbs b. 3665.4 in-lbs c. 2865.3 in-lbs d. 2690.8 in-lbs 27. Total horsepower a. 110.6 hp b. 183.2 hp c. 196.2 hp d. 119.5 hp |
Keys
A rectangular key was used in a pulley connected to a lineshaft with a power of 125 kW at a speed of 900 rpm. If the shearing stress of the shaft is 40 N/mm2 and the key to be 22 N/mm2. Determine the length of the rectangular key if the width is one fourth of that of the shaft diameter.
SOLUTION:
Spline Shaft
A 10-in spur gear transmitting 105 hp at 360 rpm is to be fastened to a shaft made of SAE 1045 water quenched 197 BHN. It is a 6-splined shaft permanent fit. The gear is made of AISI 1022 as rolled. If the power transmitted wit heavy shock, determine the spline dimensions. SAE 1045 WQ 197 BHN: Sy = 60,000 psi / AISI 1022 as rolled: Sy = 52,000 psi. For 6-splined shaft permanent fit: b = 0.25D, t = 0.05D and d = 0.9D.
SOLUTION:
