chapter 3 _ belts, ropes and chains _ theory of machines - part 1

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Theory Of Machines - Part 1

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Chapter 1 : Basic Concepts of

Machines

Chapter 2 : Lower Pairs

Chapter 3 : Belts, Ropes and

Chains

Chapter 4 : Cams

Chapter 5 : Friction Devices

Chapter 6 : Flywheels

Chapter 7 : Governors

Chapter 8 : Balancing

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Chapter 3 : Belts, Ropes and Chains

SECTIONA

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

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 but at righangle to each other. In the drive shown in fig. 3.1, the driving pulley must rotate in anticlockwise direction. Ifthe 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.


This drive is used for shaft whose axes intersect when producedIn this drive, two guide pulleys are used, one for the tight side of the belt and the other forthe slack sideif 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 theinitial tension in the belt and increase the slip bet een the belt and pulley In that case slackslide of the belt is pressed by gravity pulley. The gravity pulley is mounted on an arm andis 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 with driven pulleys whenthe 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 relative motion between pulley and belt The differencebetween the linear speed of pulley rim and belt is measure of sIip Slip cap be avoided by.increasing the coefficient of friction or by increasing the angle of contact between pulleyand 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


to crowning, the belt will not slip off the pulley when it rotates because the belt hastendency 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 beltfrom one pulley to another? Ans. The centrifugal tension should be equal to one-third of the permissible tension in thebelt.

SECTIONB

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.


(1) DrivIng pulley keyed to driving shaft. (2) and (3) = Intermediate pulleys keyed tocounter shaft, (4) = Driven pulley keyed to driven shaft. Countershaft pulleys are usec!, where very high speed reduction is required. For example,if speed of 9 : I is required,(1) The diameter of driven.will be very large and the angle of contact of belt on drivingpulley will be very small due to which slip can take place. To avoid these two difficultiesintermediate 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 withoutusing 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 pulleywhich has a bush in its hole and is free to rotate on the shaft of machine, is called loosepulley.When the belt is shifted to fast pulley, the power is transmitted to the machine. But whenthe machine is to be stopped without stopping the other machines, the belt is shifted to itsloose pulley with the help of belt actuator. in that position in belt will rotate the loosepulley but the machine shaft will not rotate because the loose pulley is free tO rotate 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) FabricThere are two varieties of leather oak tanned and chrome tannedIn order to make a belt, the layers of the leather are connected together Belts arespecified according to the number of layers e g single-ply, double-ply or tripleplyThe fabric belts are made from canvas or cotton impregnated with rubberLeather belts have high coefficient of friction and high power transmitting capacity Canvasbelts are cheaper, resistance to moisture and can operate at high speedsV-belts are made of fabrics and cords, which are moulded in rubber and covered withfabric

Q.3.5 Derive an expression for veldtity ratio in belt drive Ans Let d1 = diameter of driving pulleyd2 diameter of driven pulleyr p in of driving pulley= r p m of driven pulleys1 % = slip between driving pulley and belts2% slip betweem belt and driven pulley


The velocity of inner surface of belt is less than that of outer surface Therefore, velocity ofmiddle surface is considered and for calculating that, the effective diameter of pulley istaken 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 toanother 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 andeach pulley, determine the size of second pulley and total effective slip. Ans. Diameter of driving pulley, d1 40 (viii) It has shock absorbing capacity. Disadvantages(i) Manufacturing of pulleys with groove is 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 rpmSpeed 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


tension T2 in slack side of belt.If we mark two points at a distance x apart on tight side the distance between these twopoints will become (x &) when the points leaves the driving pulley . Thus there isrelative motion of belt on the driving pulley in the direction opposite to direction ofmotion of rim.Similarly the length (x ox) which approaches the driven pulley become x after leaving& thus there is relative motion of belt on driven pulley in direction of motion of its rim.The relative motion of the belt on the pulley due to difference in tension in belt, is calledcreep.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.


Ans.

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

Q 3.10 if r1 is radius of bigger pulley, r2 is radius of smaller pulley and D is thec/c distance, what is the angle of contact in case of (z) open belt (n) crossedbelt 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


rotated at different speeds whereas the speed of driving shaft is constant, twocone pulleys are used. One cone pulley is keyed to driving shaft and thesecond cone pulley is keyed 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 drivingshaft rotating at 240 rpm. The c/c distance between the shafts is 3 m. Thediameter of smallest step of cone pulley is 25 cm. Determine the diameters ofthe 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 cmDriven cone pulley diameters: 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 drivingshaft running at 220 rpm. The c/c distance is 3 m and the smallest, stepdiameter is 16 cm. Determine the diameter of other steps for crossed beltdrive. 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):


Q. 3.14. What are the merits and demerits of V-belt drive? Ans V-belt drive has the following advantages and disadvantagesAdvantages:(i) V-belts are endless, i.e. no joint, therefore the drive is smooth and quiet inoperation even at high speeds.(ii) More power can be transmitted due to more tension ratio obtained for the samestrength 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 small. This results in compactconstruction. They can be easily shielded with guards.(v) More than one belt can be used on pulley so more transmission of power.(vi) Its wear and tear is less, resulting in longer life(vii) They permit high speed-reduction even up to 7: 1.

Q. 3.15 What are the advantages and disadvantages of chain drive AnsAdvantages(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 beltdrive(v) Possibility of transmitting power to several shafts by one chain(vi) It is positive drive because there is no slip(viz) Can be used for short distancesDisadvantages(z) Increase in chain pitch due to wear of the chain joints thus requiring the use of weartake-up devices(ii) Relatively high production cost.(iii) Noisy operations.(iv) Periodic velocity fluctuations


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


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


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

Q. 3.20. What is centrifugal tension ? What is its effect on powertransmission?

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

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


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 tensileforce 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 initialtension is given to the belt when the pulleys are stationary. This tension is called initialtension T0.When the driving pulley starts rotating, the pulley pulls the belt from one side anddelivers the bell on other side. Thus tension in one side increases to T1 and tension inother 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 ropedrive, 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 thatthe fig. 3.12 is to be replaced by Fig. 3.15 shown below.

Q. 3.23. A shaft rotating at 200 rpm drives another shaft at 300 rpm. andtransmits 6 kW through a belt. The belt is 100 mm wide and 10mm thick. Thedistance 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.


Ratio of frictional tensions:

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


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 tensionis 21 bar. Determine the maxm. power that can be transmitted by 25 cm x1.1 cm belt if the ratio of friction tension is 2.


Q. 3.25. Determine the width of belt required to transmit 7.5 kW, mass ofbelt is 1gm/cm3, thickness is 10 mm speed is 15 ni/s. permissible stress is14 bar and ratio of friction tensions is 2.2.


Q. 3.28. In a rope drive the angle of lap is 140, groove angle 45, mass ofrope 0.7kg/rn, coefficient of friction 0.25, pulley dia 160 m and powertransmitted 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.


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

chapter 3 _ belts, ropes and chains _ theory of machines - part 1

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