Chapter 3 _ Belts, Ropes and Chains _ Theory of Machines - Part 1

Theory Of Machines - Part 1 Recommend

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SECTION—A

Topics Chapter 1 : Basic Concepts of Chapter Machines Chapter 2 : Lower Pairs Chapter 3 : Belts, Ropes and Chapter Chains

Q. 3.1. (a) Write the names of different types of belt drives.

Chapter 4 : Cams Chapter 5 : Friction Devices

Ans.

Chapter 6 : Flywheels Chapter 7 : Governors Chapter 8 : Balancing

Q. 3.1. (b) With the help of sketch show a right angle for quarter turn drive? . Ans.

in this drive, the axes of the driving and driven shafts are non-intersecting non-intersecting but at righ angle to each other. In the drive shown in fig. 3.1, the driving pulley must rotate in anticlockwise direction. If the direction is reversed the belt will run off the pulleys.

Q 31 (c) With the help ii sketch show the angular drive intersecting drive’ Ans.

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This drive is used for shaft whose axes intersect when produced In this drive, two guide pulleys are used, one for the tight side of the belt and the other for the slack side if the direclion of rotation of dnvmg pulley is reversed, the belt will not run off the pulleys

Q 3 1 (d) What is the function of gravity idler’ Ans On account of constant use of belt, it gets permanently stretched This reduces the initial tension in the belt a nd increase’ the slip bet een the belt and pulley In that case slack slide of the belt is pressed by gravity pulley. The gravity pulley is m ounted on an arm and is free to rotate when the belt passes under it, as in fig 3.3.

Q. 3.1. (e) What is the function of idle pulley? Ans. Idle pulley is used to increase the angle of contract of belt wi th driven pulleys when the power is transmitted to two or more dri ys as in fig.3.4

Q. 3.1. (t) What is slip in a belt drive? Ans. Slip may be defined as the relativ e motion between pulley and belt The difference between the linear speed of pulley rim and belt is m easure of sIip Slip cap be avoided by. increasing the coefficient of friction or by increasing the angle of contact between pulley and belt

Q. 3.1. (g) What is crowning of pulley? Ans. Rim of a pulley is given camber on the surface. The camber is called crowning. Due ptumech.loremate.com/tom1/node/3

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to crowning, the belt will not slip off the pulley when it rotates because the belt has tendency to move to the farthest distance from the pulley axis due to centrifugal force,

and this is possible only if the belt is in the middle of the pulley.

Q. 3.1. (h) Define pitch as used in roller chain. Ans. It is the distance between the axes of

Q. 3.1. (i) Draw cross-section of a V-belt? Ans. The cross-sectioq of V-belt is shown in the Fig (i)

Q. 3.1. (k) What is the condition for the maximum power transmitted by a belt from one pulley to another? Ans. The centrifugal tension should be equal to one-third of the permi ssible tension in the belt.

SECTION—B

Q. 3.2. Explain the purpose of intermediate or counter shaft pulleys.

Axis of driving shaft, X2 : Axis of intermediate or counter shaft, X3 : Axis of driven shaft. ptumech.loremate.com/tom1/node/3

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(1) DrivIng pulley keyed to driving shaft. (2) and (3) = Intermediate pulleys keyed to counter shaft, (4) = Driven pulley key ed to driven shaft. Countershaft pulleys are usec!, where very high speed reduction is required. For ex ample, if speed of 9 : I is required, (1) The diameter of driven.will be very large and the angle of contact of belt on driving pulley will be ver y small due to which slip can take place. To avoid these two difficulties intermediate pulleys (2) and (3) are used. A speed reduction of 3 : 1 is obtained between (1) and (2)and between (3) and (4). Thus total speed reduction of 9:1 is obtained without using very big pulleys.

Q. 3.3. Explain the function of loose and fast pulleys? Ans.

In a factory or workshop where several machines are driven from a single driving shaft, shaft of each machine has two pulleys. One pulley which is keyed to the machine shaft is called fast pulley and the second pulley which has a bush in its hole and is free to rotate on the shaft of ma chine, is called loose pulley. When the belt is shifted to fast pulley, the power is transmitted to the machine. But when the machine is to be stopped without stopping the other machines, the belt is shifted to its loose pulley with the help of belt actuator. in that position in belt will rotate the loose pulley but the machine shaft will not rotate because the loose pulley is free tO rota te on it

Q. 3.4. Write a short note on belt materials. Ans. The desirable properties of the belt material are: (i) High coefficient of friction, (ii) Flexibility, (nz) Durability, (iv). Strength The materials for belts are divided into two groups (a) Leather, (b) Fabric There are two v arieties of leather oak tanned and chrome tanned In order to mak e a belt, the layers of the leather ar e connected together Belts are specified according to the number of layer s e g single-ply, double-ply or tripleply The fabric belts are m ade from canvas or cotton impregnated with rubber Leather belts have high coefficient of friction and high power transmitting capacity Canvas belts are cheaper, resistance to moisture and can operate at high speeds V-belts are made of fabrics and cords, which are moulded in rubber and covered with fabric

Q.3.5 Derive an expression for veldtity ratio in belt drive Ans Let d1 = diameter of driving pulley d2 diameter of driven pulley r p in of driving pulley = r p m of driven pulley s1 % = slip between driving pulley and belt s2% slip betweem belt and driven pulley ptumech.loremate.com/tom1/node/3

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The velocity of inner surface of belt is less than that of outer surface Therefore, velocity of middle surface is considered and for calculating that, the effective diameter of pulley is taken as (d + t) where tis the belt thickness.

Q. 3.6. A pulley 40 cm in diameter running at 300 r.p.m. is connected by a belt to another pulley at a distance of 4m and the second ptilley has to run at 220 r.p.m. the belt is 5 cm thick and 15 cm wide. Allowing a slip of 4% between belt and each pulley, determine the size of second pulley and total effective slip. Ans. Diameter of driving pulley, d1 40 (viii) I t has shock absorbing capacity. Disadvantages (i) Manufacturing of pulleys with groove i s comparatively complicated. (ii) High initial cost (iii) Very high speeds not possible due to centrifugal forces. (iv) Mismatch in lengths of multi-belts drive adversely affects its working and life. (v) Cannot be used when c/c distance is large (vi) Cannot be used with cone pulley for getting different speeds (vu) Cannot be used with loose and fast pulleys

Speed of driving pulley, n1 = 300 rpm Speed of driven pulley, n2 220 rpm

Q. 3.7. Explain creep as applied to a belt drive. Ans. When power is being transmitted, the tension T1 in tight side is greater than the ptumech.loremate.com/tom1/node/3

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tension T2 in slack side of belt. If we mark two points at a distance x apart on tight side the distance between these two points will become (x — &) when the points leaves the driving pulley . Thus there is relative motion of belt on the driving pulley in the direction opposite to direction of motion of rim. Similarly the le ngth (x — ox) which approaches the driven pulley become x after leav ing & thus there is relative motion of belt on driven pulley in direction of motion of its rim. The relative m otion of the belt on the pulley due to difference in tension in belt, is called creep. Velocity ratio considering creep is given as under.

Q. 3.8. Derive an expression for length of open belt. Ans.

Q. 3. 9. Device an expression for length of crossed belt. ptumech.loremate.com/tom1/node/3

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Ans.

Putting the values of a a nd cos a in eqn (z)

Q 3.10 if r1 is radius of bigger pulley, r2 is radius of smaller pulley and D is the c/c distance, what is the angle of contact in case of (z) open belt (n) crossed belt Ans. As seen from fig 3 7 for open belt Angle of contact on bigger pulley (it + 2cr) Angle of contact on smaller pulley = (it - 2cr)

Q. 3. 11. What is the function of cone pulley or stepped pulley? Ans. When the driven shaft is to be ptumech.loremate.com/tom1/node/3

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rotated at different speeds whereas the speed of driving shaft is constant, two cone pulleys are used. One cone pulley is ke yed to driving shaft and the second cone pulley is key ed to the driven shaft. When the belt is on steps (1) and (4), the speed of driven shaft is lowest. To increase the speed of driven shaft, the belt is shifted to steps (2) and(5). For furtl3,r increase in speed of driven shaj(Jh belt is shifted to steps (3) and ((7

Q. 3.12. Driven shaft is to be rotated at 80, 120 and 160 rpm from a driving shaft rotating at 240 rpm. The c/c distance between the shafts is 3 m. The diameter of smallest step of cone pulley is 25 cm. Determine the diameters of the remaining steps for open belt drive. Ans. Refer to Fig 3.9. Let the steps on driving cone pulley are (1), (2) and (3). and the steps on driven cone pulley are (4), (5) and (6). The speed of driven shaft will be minimum i.e . 80 rpm when belt is at the smallest step (d1 = 25 cm) of the driving cone. For steps (1) and (4)

Thus driving cone pulley diameters : 25 cm, 33.6 cm and 40.8 cm Driven cone pulley diamete rs: 75 cm, 67.2 cm and 81.6 cm.

Q. 3.13. Driven shaft is to be rotated at 100, 140 and 180 rpm from a driving shaft running at 220 rpm. The c/c distance is 3 m and the smallest, step diameter is 16 cm. Determine the diameter of other steps for crossed belt drive. Ans. Refer to fig 3.9. , ‘ The speed of driven shaft will be minimum. i.e:100 rpm when the belt is at steps (1) and (4) when the belt is on steps (1) & (4):


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Q. 3.14. What are the merits and demerits of V-belt drive? Ans V-belt drive has the following advantages and disadvantages Advantages: (i) V-belts are endless, i.e. no joint, therefore the drive is smooth and quiet in operation even a t high speeds. (ii) More power can be transmitted due to more te nsion ratio obtained for the same strength of belt, angle of contact and coefficient of friction. (iii) It is positive drive as slip is negligible due to wedge action. (iv) It can be used when the c/c distance between pulleys is smal l. This results in compact construction. They can be easily shielded with guards. (v) More than one belt can be used on pulley so more tra nsmission of power. (vi) Its wear and tear is less, resulting in longer life (vii) They perm it high speed-reduction even up to 7: 1.

Q. 3.15 What are the advantages and disadvantages of chain drive Ans Advantages (i) Effective transmission of power over considerable distances (ii) 1-ligh transmission efficiency (iii) Small size compared to belt drive (iv) As no initial tension is required therefore smaller load on shaft than in belt drive (v) Possibility of transmitting power to sever al shafts by one chain (vi) It is positive drive because there is no slip (viz) Can be used for short distances Disadvantages (z) Increase in chain pitch due to wear of the chain joints thus requiring the use of wear take-up devices (ii) Relatively high production cost. (iii) Noisy operations. (iv) Periodic velocity fluctuations ptumech.loremate.com/tom1/node/3

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(v) More complicated design (vi) Need for accurate mounting (vii) It requires more maintenance.


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This force tries to lift BC from the pulley. Due to this nsiOfl T is produced in AB and in CD. To balance F the portion AB and portion CD apply force Tc on BC at B & C respectively.


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i.e. for transmitting maximum. power, the centrifugal tension should be equal to onethird of the total tension in tight side. The velocity of belt for maxim umm. P, is given by:

Q. 3.20. What is centrifugal tension ? What is its effect on power transmission?

Here, T1 = total tension in tight side of belt. Its maxm. value can be equal to the permissible tension T

From (a) and (b), it is clear that the effect of Tc is to reduce the power capacity of a belt. Centrifugal Tension:


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Portion AB moves along circular path, therefore, centrifugal force Fc acts on it. Similarly F acts on portion CD of belt. Due to these forces on AB and CD, the tensile force Tc, called centrifugal tension is produced in the tight and slack side of belt. Q. 3.21. What is initial tension in belt? Ans. When a driving pulley and a driven pulley are connected with a belt, an initial tension is given to the belt when the pulleys are stationary. This tension is called initial tension T0. When the driving pulley starts rotating, the pulley pulls the belt from one side and delivers the bell on other side. Thus tension in one side increases to T1 and tension in other side decreases to T, Increase in length of belt on tight side = k (T1 — T0) where k is constant. Decrease in length of belt on slack side k (T0 - T2) But total length remains same, therefore,

Q. 3.22. Derive an expression for the ratio of driving tensions in the rope drive, assuming the angle of the groove of the pulley to be as 2. Ans The answer to this question is exactly similar to the answer to Q 3 17, except that the fig. 3.12 is to be re placed by Fig. 3.15 shown below.

Q. 3.23. A shaft rotating at 200 rpm drives another shaft at 300 rpm. and transmits 6 kW through a belt. The belt is 100 mm wide and 10mm thick. The distance between the shafts is 4 m. The smaller pulley is 0.5 m diameter. Calculate the stress in the belt, if it is an open belt. Take i = 0.3.


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Ratio of frictional tensions:

Q. 3.24. A shaft which rotates at constant speed of 160 rpm is connected by belting to a parallel shaft 72 cm apart which. has to run at 60, 80 and iUO rpm. The smallest pulley on drive shaft is 30cm. Determine the remaining diameters of the stepped pulleys for cross belt and open belt Ans.


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3. If the diametres are equal in case of open belt 0 = it radians. 4. If velocity of belt (or dia and speed of pulley) not given,

Q. 3.26. The mass of belt material is lg/cm3 and maxm. permissible tension is 21 bar. Determine the maxm. power that can be transmitted by 25 cm x 1.1 cm belt if the ratio of friction tension is 2.


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Q. 3.25. Determine the width of belt required to transmit 7.5 kW, mass of belt is 1gm/cm3, thickness is 10 mm speed is 15 ni/s. permissible stress is 14 bar and ratio of friction tensions is 2.2.


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Q. 3.28. In a rope drive the angle of lap is 140°, groove angle 45°, mass of rope 0.7kg/rn, coefficient of friction 0.25, pulley dia 160 m and power transmitted is 100kw. Determine’ the number of ropes and the initial tension. The speed of pulley is 200 rpm and belt can withstand 800 N.

Q. 3.29. How is slip in a belt drive different from creep Ans.


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Q. 3.30. A rope drive transmits 75 kW through a 150 cm diameter 45° grooved pulley rotating at 200 r.p.m. Co-efficient of friction between the ropes and pulley is 0.3 an4 angle of lap is 160°. Each rope has mass 0.6 kg/rn and can safely take a pull of 800 N. Taking centrifugal tension in account, determine: (i) the number of ropes required, (ii) initial rope tension.


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Chapter 3 _ Belts, Ropes and Chains _ Theory of Machines - Part 1

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