problems for practice

PROBLEMS FOR PRACTICE

On Flat Belt Drives

1. A prime mover runs at 400 rpm drives a generator at 600 rpm through a belt drive. The diameter of the pulley on the output shaft of the prime mover is 600 mm and thickness of belt is 5 mm. Determine the diameter of the generator pulley in the following cases:

(i) Neglecting thickness of belt.

(ii) Considering thickness of belt.

(iii) Considering thickness of belt and assuming a total slip of 3%.

[Ans. (i) 400 mm; (ii) 398.3 mm; (iii) 386.2 mm]

2. An engine, running at 1440 rpm drives a line shaft by means of a belt. The engine pulley is 500 mm diameter and the pulley on the line shaft being 800 mm. A 450 mm diameter pulley on the line shaft drives a 650 mm diameter pulley keyed to a dynamo shaft. Find the speed of the dynamo shafts when (i) there is no slip, and (ii) there is a slip of 2% at each drive. 

[Ans. (i) 623 rpm; (ii) 598 rpm]

3. The pulleys of two parallel shafts 8 m apart are 600 mm and 800 mm in diameters and are connected by a crossed belt. It is needed to change the direction of rotation of the driven shaft by adopting the open belt drive. Calculate the change in length of the belt. 

[Ans. Shorten the belt by 60 mm]

4. A pulley 1 m diameter is driven by a belt at 200 rpm. If the tensions on the tight and slack sides are 900N and 300N respectively, find the power transmitted. Neglect slip.

[Ans. 6.28 kW]

5. A shaft running at 160 rpm is to drive another shaft at 250 rpm and transmit 21 kW. The belt is 11.5 cm wide and 12 mm thick. The coefficient of friction between the belt and the pulley is 0.25. The distance between the shaft is 2.75 metres. The smaller pulley is 60 cm diameter. Determine the stress in (a) as open belt, (b) a cross belt, connecting the two pulleys. 

[Ans. (a) 21 × 105 N/m2, (b) 16.75 × 105 N/m2]

6. The following data relate to a flat belt drive: Power transmitted 18 kW; Pulley diameter 1.8 m; Angle of contact 175°; Speed of pulley 300 rpm; Coefficient of friction between belt and pulley surface is 0.30; Permissible stress for belt 300 N/cm2; Thickness of belt 8 mm; Density of the belt material 0.95 kg/m3. Determine the width of belt required taking centrifugal tension into account.

[Ans. 44 mm] 

7. A leather belt 125 mm wide and 6 mm thick, transmits power from a pulley with the angle of lap 150° and μ = 0.3. If the mass of 1 m3 of leather is 1 Mg and the stress in the belt is not to exceed 2.75 MPa, find the maximum power that can be transmitted and the corresponding speed of the belt. 

[Ans. 30.28 m/s; 22.66 kW]

8. An open belt running over two pulleys 240 mm and 600 mm diameter connects two parallel shafts 3 m apart and transmits 3.73 kW from the smaller pulley that rotates at 300 rpm and the safe working tension is 98 N/cm width. Take μ = 0.3. Determine: μ (i) minimum width of belt, (ii) initial tension in belt, and (iii) length of belt required. 

[ Ans. (i) 167 mm; (ii) 1149 N; (iii) 7332 mm]

9. Two parallel shafts whose centre lines are 4.8 m apart, are connected to open belt drive. The diameter of the larger pulley is 1.5 m and that of smaller pulley 1 m. The initial tension in the belt when it is stationary is 3 kN. The mass of the belt is 1.5 kg/m length. The coefficient of friction between the belt and the pulley is 0.3. Taking centrifugal tension into account, calculate the power transmitted, when the smaller pulley rotates at 400 rpm. 

[A.U., Apr/May 2011] 

[Hint: Refer Example 8.11] 

[Ans. 42.1 kN]

10. An open flat belt drive connects two parallel shafts 1.2 m apart. The driving and the driven shafts rotate at 350 rpm and 140 rpm respectively and the driven pulley is 400 mm in diameter. The belt is 5 mm thick and 80 mm wide. Coefficient of friction between belt and pulley is 0.3 and maximum permissible tension in the belting is 140 N/cm2. Determine: (a) diameter of the driving pulley, (b) maximuch power that can be transmitted by the belting, and (c) required belt tension.

[Ans. (a) 160 mm; (b) 462 W; (c) 395.89 N]

11. A flat belt, 8 mm thick and 100 mm long wide transmits power between two pulleys running at 1600 m/min. The mass of the belt is 0.9 kg/m length. The angle of lap in the smaller pulley is 165° and the coefficient of friction between the belt and pulley is 0.3. If the maximum permissible stress in the belt is 2 MN/m2. Find the maximum power transmitted and initial tension in the belt.

[Hint: Refer Example 8.10]

[A.U., Nov/Dec 2006] 

[Ans. 14.83 kW; 1002 N]

12. In an open belt drive, the linear velocity of the belt is 3 m/s. The angle of lap on the smaller pulley is 166°, the coefficient of friction is 0.3 and the power transmitted is 3 kW. Determine the effect of power transmission in the following cases:

(i) Initial tension in the belt is increased by 10%

(ii) Initial tension in the belt is decreased by 10%

(iii) Angle of lap is increased by 10% by the use of an idler pulley, for the same speed and the tension on tight side.

(iv) Coefficient of friction is increased by 10% by suitable dressing to the friction surface of the belt.

[Ans. (i) % increase in power = 10%; (ii) % decrease in power = 10%; (iii) % increase in power = 6.23%; (iv) % increase in power = 8.85%]

On V-Belt Drives 

13. A belt drive consists of two V-belts in parallel, on grooved pulleys of the same size. The angle of groove is 30°. The cross-sectional area of each belt is 750 mm2 and μ = 0.12. The density of the belt material is 1.2 Mg/m3 and maximum safe stress in the material is 7 MPa. Calculate the power that can be transmitted between pulleys 300 mm diameter rotating at 1500 rpm. Find also the shaft speed in rpm at which the power transmitted would be a maximum. 

[Ans. 171.67 kW; 2807 rpm]

14. An engine of 25 kW, has a speed of 650 rpm. It has to drive an electric generator at 1500 rpm by means of V-belts. Diameter of pulley on the engine is 600 mm and the centre to centre distance between the shafts is 3 metre. Groove angle of the pulley is 30° and the coefficient of friction is 0.25. If the maximum safe strength of the belt is 500 N, determine the number of V-belts required for the drive. Neglecting the belt thickness, and assuming the open drive. 

[Ans. 3 belts]

15. A compressor is driven by a 1400 rpm motor by means of a flat belt of thickness 20 mm and width 250 mm. The motor pulley is 315 mm diameter and the compressor pulley is 1250 mm. The shaft centre distance is 1200 mm and an idler is used to make the angle of lap on the smaller pulley 210° and on larger pulley 280°: Coefficient of friction is 0.25 on the smaller pulley and 0.3 on the larger pulley. The maximum allowable belt stress is 2.1 N/mm2 and the belt weighs 1 × 105 N/mm. Determine the power of the drive.

To eliminate idler pulley, the smaller pulley is changed with V-groove pulley with groove angle of 34°. μ= 0.3. Larger pulley and other data remaining the same, what μ shall be the power transmitted. 

[Ans. 107.82 kW; 124.59 kW]

On Rope Drives

16. A rope drive transmits 600 kW from a pulley of effective diameter 3.75 m which runs at a speed of 90 rpm. The angle of lap is 160°, the groove angle 45°, the coefficient of friction 0.28, mass of the rope 1.35 kg/m and the allowable tension in each rope is 2.27 KN. Find the smallest number of ropes that will be required. 

[Ans. 22 ropes] 

17. A rope drive transmits 74 kW through a 1.5 m diameter, 45° grooved pulley rotating at 200 rpm. μ = 0.3 and the angle of lap is 160°. Each rope has a mass of 0.06 kg/m and can safely take a pull of 800 N. Taking centrifugal tension into account determine: (i) the number of ropes required for the drive, and (ii) initial rope tension. 

[Ans. (i) 7; (ii) 451.38 N]

18. A pulley used to transmit power by means of ropes has a diameter of 3.6 metres and has grooves of 45° angle. The angle of contact is 170° and the coefficient of friction between the ropes and the groove sides is 0.28. The maximum possible tension in the ropes is 941.8 N and the weight of the rope is 1472 N per metre length. What is the speed of pulley in rpm and the power transmitted if the condition of maximum power prevails. 

[Ans. 76.7 rpm; 120.6 kW]