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Exercises
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1. A coupling whose bolt circle diameter is 70 cm contains 6 bolts. The torsional shearing stress of 90 mm diameter shaft is 50 MPa and for the bolt is 40 MPa. The compressive stress of the bolt is 75 MPa. Determine the flange thickness of the coupling. a. 3.2 mm b. 6.5 mm c. 2.2 mm d. 4.4 mm 2. An 80-mm diameter shaft is transmitting 320 kW at 620 rpm. A solid coupling has six, 18 mm diameter bolts. Calculate the required bolt circle of the coupling based on the average shearing stress of 40 MPa in the bolts. a. 155 mm b. 190 mm d. 182 mm 3. A flange coupling with bolt circle diameter of 260 mm uses 8 bolts, 25 mm diameter. The torque transmitted is 18 kN-m and compressive stress of bolt is 18 MPa. Calculate the required flange thickness. a. 32.1 mm b. 38.5 mm c. 41.8 mm d. 28.7 mm 4. The total force of 130 kN is required for the flange coupling that has 6 bolts and a shearing stress of 38 MPa for the bolt. Compute the required bolt diameter. a. 18.3 mm b. 16.2 mm c. 26.9 mm d. 30.1 mm 5. A turbine is connected to a generator by means of a flange coupling that has a bolt circle diameter of 520 mm. The generator output is 50 MW, 3600 rpm and 85% efficiency. If there are 18 bolts, determine the force acting on each bolt. a. 28.8 kN b. 35.1 kN c. 33.3 kN d. 35.8 kN 6. A flange coupling having 200 mm bolt circle and 20 mm thickness uses 8 bolts of 16 mm diameter to connect two shafts. It is use to transmit 80 kW at 200 rpm. Find the factor of safety in bearing if the yield point in compression is 450 MPa. a. 18 b. 20 c. 16 d. 14 7. An engine of a motor vehicle with a wheel diameter of 700 mm develops 60 kW at 1800 rpm. Determine the axial force on the clutch, in kN. Outside and inside diameters of the clutch are 250 mm and 220 mm, respectively. There are 4 mating pairs of mating surfaces with f = 0.28. b. 3.22 kN c. 4.01 kN d. 1.99 kN 8. The larger diameter and face of the disk of a multiple disk clutch are 225 mm and 20 mm respectively. The load applied to the spring of the clutch axially is 1500 N. Assuming that there are 8 pairs of friction 0.18 and turning 800 rpm. Find the power transmitted by the clutch using uniform pressure method. a. 11.7 kW b. 12.7 kW c. 13.7 kW d. 14.7 kW 9. A block clutch has four wooden shoes each contacting with 80 degrees of the inside of a 13-in drum. The coefficient of friction is 0.40 and the maximum contact pressure is not to exceed 40 psi. This clutch is to transmit 20 hp at 280 rpm. Determine the required width of the shoes. a. 3.2 in b. 4.3 in c. 2.0 in d. 1.3 in 10. An engine developing 50 HP at 1200 rpm is fitted with a cone clutch built into the flywheel. The cone has a face angle of 12 degrees and maximum diameter of 15 in. The coefficient of friction is 0.30. The normal pressure on the clutch face is not to exceed 13 psi. Determine the face width required. a. 5 in b. 4 in c. 3 in d. 2 in 11. Using uniform wear, find the power capacity of a single disc clutch with an outside diameter of 180 mm and inside diameter of 110 mm, rotating at 1100 rpm (f=0.30). The axial operating force is 900 N. a. 4.2 kW b. 3.5 kW c. 5.1 kW d. 2.3 kW 12. Determine the power capacity of uniform wear cone clutch having a major diameter of 280 mm, minor diameter of 210 mm, length of contact of 120 mm, f =0.28, speed of 850 rpm and has an operating force of 600 N. a. 6.32 kW b. 5.77 kW c. 4.56 kW d. 7.88 kW 13. Find the cone angle of a clutch having a major diameter of 280 mm and minor diameter of 220 mm and length of contact of 260 mm. a. 4.2 deg b. 6.6 deg c. 7.5 deg d. 8.2 deg 14. Find the power capacity and the cone angle of a cone clutch under uniform pressure having 220 mm major diameter, 180 mm minor diameter, length of contact of 120 mm, 880 rpm, f=0.35, and allowable pressure of 80 kPa. a. 12.5 kW & 6.3o b. 16.3 kW & 8.0o c. 19.5 kW & 9.6o d. 25.3 kw & 5.0o 15. Determine the power capacity of a cone clutch with mean diameter of 260 mm if the conical elements inclined at 8.5 degrees and axial force of 500 N. The rotational force of driver is 220 rpm and the friction is 0.25. a. 3.5 kW b. 2.5 kW c. 4.5 kW d. 5.5 kW 16. A simple disc clutch has an outside diameter of 220 mm and inside diameter of 110 mm. The friction is 0.30 and the applied load is 1300 N. Calculate the torque transmitted using uniform wear. a. 22.6 J b. 33.4 J c. 45.2 J d. 38.1 J 17. The angle of contact of a band clutch is 260 degrees. The cross-section of the band is 1/16-in x 2-in. The design stress for the band material is 8500 psi. If the drum is 15 inches in diameter and rotates at 360 rpm, find the power capacity of the clutch if f=0.35. a. 30.0 hp b. 36.2 hp c. 48.3 hp d. 39.6 hp 18. A band clutch has an angle of contact of 260 degrees on a 16-in diameter drum. The rotational speed of the drum is 260 rpm and the clutch transmits 10 HP. The band is 1/16-in thick and has a design stress of 4800 psi. How wide should the band be? Use f=0.35. a. 2.8 in b. 4.1 in c. 1.3 in d. 3.3 in 19. A cone clutch has cone elements at an angle of 13 degrees. The clutch transmits 20 HP at speed of 1000 rpm. The mean diameter of the conical friction section is 15” and the coefficient of friction is 0.20. Find the axial force needed to engage the clutch. a. 230 lbs b. 210 lbs d. 240 lbs 20. A disc clutch has 6 pairs of contacting friction surfaces. The frictional radius is 2.5-in and the coefficient of friction is 0.28. An axial force is 120 lbs acts on the clutch. The shaft speed is 380 rpm. What is the power transmitted by the clutch? a. 6 hp b. 5 hp c. 4 hp d. 3 hp 21. A clutch has an outside diameter of 9-in and inside diameter of 4-in. An axial force of 600 lb is used to hold the two parts together. If friction is 0.30, how much torque can the clutch handle? a. 614 in-lb b. 622 in-lb c. 600 in-lb d. 631 in-lb 22. How much torque can a cone clutch transmit if the angle of the conical elements is 12 degrees? The mean diameter of conical sections is 180 mm and an axial force of 500 N is applied. Consider a coefficient of friction of 0.40. a. 86.6 J b. 72.3 J c. 90.1 J d. 63.3 J 23. A cone clutch has an angle of 10 degrees and coefficient of friction of 0.40. Compute the axial force required if the capacity of the clutch is 12 kW and 520 rpm. The mean diameter of the active conical sections is 310 mm. Use uniform wear method. a. 617.2 N b. 632.1 N c. 655.4 N d. 677 N 24. Determine the force with which the brake shoe of a diesel electric train must be pressed against the wheel to absorb 220,000 ft-lb of energy in 18 seconds if the mean velocity of wheel relative to the brake shoe is 40 fps and the coefficient of friction is 0.30. a. 1018.5 lbs b. 1221.8 lbs c. 2256.7 lbs d. 1432.9 lbs 25. A simple band brake has 80 cm drum with coefficient of friction of 0.28 and arc of contact of 250 degrees. The drum sustains a load of 820 kg and rotates at 280 rpm. Determine the power absorbed by the band. a. 82.3 kW b. 94.3 kW c. 64.2 KW d. 58.1 kW 26. A band brake is used to fasten to a 900 mm drum with tight side 4 times the slack side of force. The torque transmitted is 3 kN-m and a steel band with a maximum tensile stress of 70 MPa and 3 mm thick will be used. What should be its width, in mm? a. 38.1 mm b. 42.3 mm c. 54.1 mm d. 30.5 mm 27. A band brake is installed on a drum rotating at 260 rpm and a diameter of 880 mm. The angle of contact is 1.5 rad and one end of the brake band is fastened to a fixed pin while the other end to the brake arm 160 mm from the fixed pin. The coefficient of friction is 0.30 and the straight brake arm is 1100 mm long and is placed perpendicular to the diameter bisecting the angle of contact. Find the minimum force, in N applied at the end of the brake arm necessary to stop the drum if 70 kW is being absorbed. a. 255.8 N b. 243.9 N c. 273.1 N d. 231.9 N 28. A band brake has an angle of contact of 250 degrees and is to sustain a torque of 12,000 in-lbs. The band bears against a cast iron drum of 15-in diameter. The coefficient of friction is 0.35. Find the tension at the tight side. a. 1021.9 lbs b.1122.7 lbs c. 1866.0 lbs d. 1521.5 lbs 29. The ratio of band tension in a band brake is 5. If angle of contact is 260 degrees, determine the coefficient of friction. a. 0.44 b. 0.21 c. 0.56 d. 0.35 30. A band brake has a straight brake arm of 1.8 m and is placed perpendicular to the diameter bisecting the angle of contact of 270 degrees which is 200 mm from the end of the slack side. If 220 N force is applied at the other end downward of brake arm, determine the tension at slack side. a. 6.6 kN b. 5.3 kN c. 3.8 kN d. 2.8 kN 31. A steel band has a maximum tensile stress of 60 MPa and thickness of 5 mm. If the tension in the tight side is 8 kN, what width of band should be used? a. 20.5 mm b. 18.2 mm c. 26.7 mmd. 29.8 mm 32. On a brake drum the difference in tension between the slack side and the tight side is 8 kN. If the ratio in the band tension is 4, determine the tension in the tight side. a. 12.7 kN b. 10.7 kN c. 18.5 kN d. 15.8 kN 33. In a brake, the tension on tight side is thrice the slack side. If coefficient of friction is 0.30, determine the angle of contact of the band. a. 210 deg b. 222 deg c. 256 degd. 238 deg 34. A brake has a difference in band tension of 5 kN. The drum diameter is 1.5 meter and rotating at 280 rpm. Calculate the power needed to drive the drum. a. 220 kW b. 189 kW c. 253 kW d. 158 kW |
Flange Coupling
A plane flange coupling for a 75 mm diameter shaft has the following dimensions: bore, 75 mm; hub diameter, 135 mm; hub length, 95 mm; flange diameter, 255 mm; flange thickness, 25 mm; bolt diameter, 20 mm; bolt circle diameter, 210 mm; number of bolts, 6 and key size, 20 mm square. Shaft material: Sy = 406,680 kPa; flange material: Sy = 350,000 kPa; bolt and key material: Sy = 455,000 kPa. Using a factor of safety of 3 based on yield strength. Calculate the safe power that can be transmitted at 100 rpm.
SOLUTION:
Clutch
The large diameter and face of the disc of a multiple disc clutch are 255 mm and 25 mm, respectively. The helical compression spring used to engage the clutch has 9.50 active coils of 10 mm steel wire. The outer coil diameter is 80 mm. The free length of the spring is 185 mm. When in place with the clutch engaged. Its length is 130 mm. Assuming 10 pairs of contact surface and the motor runs at 1,200 rpm and coefficient of friction on the contact surface as 0.15, find: (a) The axial force available for the clutch (b) kW power that the clutch can transmit. Let the spring modulus G = 80 GPa.
Solution:
