NapurStudents - TGPCET · b) A, B, C and D are four masses carried by a rotating shaft at radii 110...

NKT/KS/17/7399/7425 1 P.T.O

B.E. Sixth Semester (Mechanical Engineering / Power Engineering) (C.B.S.) Dynamics of Machines

P. Pages : 4 NKT/KS/17/7399/7425

Time : Three Hours Max. Marks : 80

_____________________________________________________________________

Notes : 1. All questions carry marks as indicated.

2. Solve Question 1 OR Questions No. 2.






8. Due credit will be given to neatness and adequate dimensions.

9. Assume suitable data whenever necessary.

10. Illustrate your answers whenever necessary with the help of neat sketches.

11. Use of non programmable calculator is permitted.

1. a) Discuss the effect of reactive Gyroscopic couple on aircraft.

4

b) The mass of a turbine rotor of a ship is 10 tonnes and has a radius of gyration 0.8 m. It

rotates at 1600 rpm clockwise when looking from stern. Determine gyroscopic effect in -

i) If the ship travelling at 120 kmph steers to left in a curve of 80 m radius.

ii) If the ship is pitching and the bow is descending with the maximum velocity. The

pitch is SHM, the periodic time being 20 seconds, and total angular movement

between the extreme positions is 10°.

iii) If the ship is rolling and at a certain instant has an angular velocity of 0.04 rad/sec

clockwise when looking from stern.

9

OR

2. a) Explain Gyroscopic analysis of Gyrocrusher.

4

b) A four wheeled trolley car of total mass 2000 kg running on rails of 1.6 m gauge, rounds a

curve of 30 m radius at 54 kmph. The track is banked at 8°. The wheels have an external

diameter of 0.7 m and each pair the axle has a mass of 200 kg. The radius of gyration for

each pair is 0.3 m. The height of centre of gravity of car above the wheel base is 1 m.

Determine, allowing for centrifugal force and gyroscopic couple actions, the pressure on

each rail.

9

3. a) Discuss various methods of force analysis.

5

b) In a cam mechanism following are the specification. Cam speed is 1500 rpm, follower

stroke is 50 mm, cam angles for outstroke and return stroke are 130° and 100° respectively.

Follower is moving with uniform acceleration and retardation with acceleration equal to

retardation during outstroke and during return stroke. Mass of the follower is 4 kg.

Determine the necessary spring stiffness so as to ensure the contact of the follower and cam

throughout the cycle of motion of the mechanism.

8

OR

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4. For the mechanism shown find the forces acting at each joint and the external torque that

must be applied to link 2.

O2A = 50 mm,

O2O4 = 325 mm

AB = 425 mm

O4B = 200 mm

O4G4 = 100 mm

M4 = 3 kg. IG4 = 0.059 kg m2, 4 = 240 rad/s2 clockwise.

AG4 = 677 m/s2 < 250°

O2

45º

A

B

G4250º

AG44

O4

13

5. The firing order of a four cylinder vertical four stroke inline engine 1-3-4-2. The piston

stroke is 120 mm. The distance between cylinder centerlines are 100 mm each. The

reciprocating masses per cylinder is 2 kg and the Engine speed is 2000 rpm. Determine

the out of balance primary and secondary forces and couples in the engine taking a plane

midway between the cylinder 2 & 3 as the reference plane. Is it possible to balance the

engine completely with proper firing order ? Comment.

14

OR

6. a) Discuss static and dynamic balancing machine.

4

b) A, B, C and D are four masses carried by a rotating shaft at radii 110mm, 140 mm and 175

mm & 150 mm respectively. The planes in which the masses rotate are spaced at 400 mm

apart and the magnitude of the masses B, C and D are 10 kg, 6 kg and 3 kg respectively.

Find the required mass 'A' and the relative angular setting of the four masses so that the

shaft will be in complete dynamic balance.

10

7. a) Discuss the operation of flywheel in punching machines with neat sketch & also state its

different equations.

6

b) A punching machine has a capacity of producing 30 holes of 20 mm diameter per minute in

a steel plate of 16 mm thickness. The material of plate has ultimate of shear strength of 360

N/mm2. The actual punching operation lasts for a period of 36° rotation of the crank shaft.

This crank shaft is powered by a flywheel through a reduction gear having a ratio of 1:8

mech = 80%.

Speed fluctuation = 10%

Mean dia. Of flywheel = 0.75 m

Determine :

i) Power required

ii) Fluctuation of energy

iii) Cross section of rim if no width to thickness ratio is 1.3.

8

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8. a) Explain Hartnell governor in detail & derive the expression for stiffness of spring.

7

b) The mass of each ball of a proell governor is 3 kg & the weight on the sleeve is 20 kg. Each

arm is 220 mm long & the pivots of the upper & the lower arms are 20 mm from the axis.

For the mid position of the sleeve, the extension links of the lower arms are vertical, the

height of the governor is 180 mm & the speed is 150 rpm. Determine the lengths of the

extension links.

7

9. a) Determine the natural frequency of the spring mass pulley system as shown in figure.

r

M

m

kx

7

b) A circular disk of mass 2 kg and diameter 0.2 m is attached to lower end of an elastic vertical

shaft of brass material for which modulus of rigidity, 216 m/N104.4C and the

diameter, d = 5 mm and length, L = 1m. Calculate the natural frequency of torsional

pendulum.

6

OR

10. a) A spring mass system consists of a spring of stiffness 350 N/m. The mass is 0.35 kg The

mass is displaced 20 mm beyond the equilibrium position and released. The damping

coefficient is 14 N-s/m Determine -

i) Critical damping coefficient

ii) Damped natural frequency

iii) Logarithmic decrement.

8

b) Explain vibration isolation and critical speed of shaft in brief.

5

11. a) If two masses 'm' are displaced as shown in figure by linear distance X1 and X2 such that

x2 > x1, when attached to three springs of same stiffness 'K'. Determine two natural

frequencies and equation of motion.

k

m

m

x1

x2

k

k

8

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b) Explain FFT analyser in short.

OR

5

12. a) A centrifugal pump rotating at 400 rpm is driven by an electric motor at 1200 rpm through

a single stage reduction gearing. The moments of inertia of the pump impeller and the

motor are 1500 kg m2 and 450 kg m2 respectively. The lengths of the pump shaft and

motor shaft are 500 mm and 200 mm and their diameters are 100 mm and 50 mm

respectively. Neglecting the inertia of the gears, find the frequency of torsional

oscillations of the system G = 85 GN/m2.

10

b) Explain vibration absorber.

3

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KNT/KW/16/7399/7425 1 P.T.O

B.E. Sixth Semester (Mechanical Engineering / Power Engineering) (C.B.S.) Dynamics of Machines

P. Pages : 3 KNT/KW/16/7399/7425


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1. a) Discuss the effect of reactive Gyroscopic couple on aircraft.

4

b) The mass of a turbine rotor of a ship is 10 tonnes and has a radius of gyration 0.8 m. It

rotates at 1600 rpm clockwise when looking from stern. Determine the gyroscopic effect

in-

1) If the ship travelling at 120 kmph steers to left in a curve of 80 m radius.

2) If the ship is pitching and the bow is descending with the maximum velocity.

The pitch is SHM, the periodic time being 20 seconds, and total angular

movement between the extreme positions is 10º.

3) If the ship is rolling and at a certain instant has an angular velocity of 0.04

rad/sec clockwise when looking from stern.

9

OR

2. a) Explain Gyroscopic analysis of Gyrocrusher.

4

b) A four-wheeled trolley car of total mass 2000 kg running on rails of 1.6 m gauge, rounds a

curve of 30 m radius at 54 kmph. The track is banked at 8º. The wheels have an external

diameter of 0.7 m and each pair with axle has a mass of 200 kg. The radius of gyration for

each pair is 0.3 m. The height of center of gravity of car above the wheel base is 1m.

Determine, allowing for centrifugal force and gyroscopic couple actions, the pressure on

each rail.

9

3. a) Discuss various methods of force analysis.

5

b) In a cam mechanism following are the specification.

Cam speed is 1500 rpm, follower stroke is 50 mm, Cam angles for outstroke and return

stroke are 130º and 100º respectively. Follower is moving with uniform acceleration and

retardation with acceleration equal to retardation during outstroke and with SHM during

return stroke. Mass of the follower is 4 kg.

Determine the necessary spring stiffness so as to ensure the contact of the follower and

cam throughout the cycle of motion of the mechanism.

8

OR

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4. For the mechanism shown find the forces acting at each joint and the external torque that

must be applied to link 2

º250s/m677A

,clockwises/rad240,kgm059.0I

,kg3M,mm100GO,mm200BO

,mm425AB,mm325OO,mm50AO

24G

24

24G

4444

422

.

O2

A

B

250o

4

4GA

O4

G4

45o

α

13

5. The firing order of a four cylinder vertical four stroke inline engine is 1-3-4-2. The piston

stroke is 120 mm The distance between cylinder centrelines are 100 mm each. The

reciprocating masses per cylinder is 2kg and the engine speed is 2000 rpm. Determine the

out of balance primary and secondary forces and couples in the engine taking a plane

midway between the cylinder 2 & 3 as the reference plane.

12

Is if possible to balance the engine completely with proper firing order? Comment.

2

6. a) Discuss static and dynamic balancing machines.

4

b) A, B, C and D are four masses carried by a rotating shaft at radii 110 mm, 140 mm, and 175

mm & 150 mm respectively. The planes in which the masses rotate are spaced at 400 mm

apart and the magnitude of the masses B,C and D are 10 kg, 6 kg and 3 kg respectively.

Find the required mass 'A' and the relative angular settings of the four masses so that the

shaft will be in complete dynamic balance.

10

7. a) Discuss operation of flywheel in punching machines with neat sketch & also state its

different equations.

7

b) A punching press is driven by a constant torque electric motor. The press is provided with

a flywheel that rotates at maximum speed of 225 r.p.m. The radius of gyration of the

flywheel is 0.5 m. The press punches 720 holes per hour; each punching operation takes 2

seconds and requires 15 KN-m of energy. Find the power of the motor and the minimum

mass of the flywheel if speed of the same is not to fall below 200 r.p.m.

7

OR

8. a) Explain Hartnell governor in detail and derive the expression for stiffness of the spring.

6

b) In a Wilson-Hartnell type of governor, the mass of each ball is 5 kg. The lengths of the

ball arm and the sleeve arm of each bell-crank lever are 100 mm and 80 mm respectively.

The stiffness of each of the two springs attached directly to the balls is 0.4 N/mm. The

lever for the auxiliary spring is pivoted at its midpoint. When the radius of rotation is 100

mm, the equilibrium speed is 200 rpm. If the sleeve is lifted by 8 mm for an increase in

speed by 6%, find the required stiffness of the auxiliary spring.

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9. a) Determine the undamped natural frequency of small oscillations of the system shown in the

figure. The uniform disc of mass 'm' has two springs attached to it as shown in the figure.

Assume that the disc rolls without slipping.

A

O

B

rK

2K

7

b) A circular disk of mass 2 kg and diameter 0.2 m is attached to lower end of an elastic vertical

shaft of brass material for which modulus of rigidity, 216 m/N104.4C and the diameter,

d = 5 mm and length, L = 1m. Calculate the natural frequency of torsional pendulum.

6

OR

10. a) A steel shaft, 10 cm diameter supported by bearings, 1.2 m apart carries two pulleys

weighing 300 N and 800 N are placed 0.25 m and 0.65 m from left hand bearing

respectively. Determine the critical speed of the shaft. (Take E = 2 107 N/cm2).

7

b) Explain vibration isolation and critical speed of the shaft in brief.

6

11. a) If two masses 'm' are displaced as shown in figure by linear distance x1 and x2 such that

x2 > x1, when attached to three springs of same stiffness 'K', determine two natural

frequencies and equation of motion.

m

m

K

x1

x2

K

K

7

b) Explain FFT analyser in short.

6

OR

12. a) A centrifugal pump rotating at 500 rpm is driven by an electric motor at 1500 rpm through

a single stage reduction gearing. The moment of inertia of pump impeller and motor are

1400 kg. m2 and 400 kg. m2 respectively. The lengths of the pump shaft and motor shaft

are 500 mm and 250 mm and their dimeters are 100 mm and 50 mm respectively. Find the

frequency of torsional vibration of the system.

Take, G = 84 GN/m2.

Neglect inertia of gears.

9

b) Explain vibration Absorber.

4

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Special Thanks to Abhijith Alolickal

NJR/KS/18/4538/4564 1 P.T.O

B.E. (Mechanical Engineering / Power Engineering) Sixth Semester (C.B.S.) Dynamics of Machines

P. Pages : 4 NJR/KS/18/4538/4564


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1. a) Explain with neat sketch how the gyroscopic couple exerts on the bearings of a rotor if the

rotor is rotating about the shaft in clockwise direction if viewed from the left side. Show

when the axis is precened in (a) clockwise (b) anticlockwise

l

w

Fig. 1 (a)

4

b) The wheel of a motor cycle and the engine parts have a moment of inertia 2.5 kgm2/0.15

kgm2 and respectively. The axis of rotation of the engine Crank shaft is parallel to that of

the road wheels. If the gear ratio is 5 : 1 and the diameter of the road wheels 0.65 m, find

the magnitude and direction of the gyroscopic couple when the motor cycle rounds a curve

of 30 m radius at 16 m/s.

OR

9

2. a) An aeroplane makes a complete half circle of radius 50 m towards left, when flying at

200km / hr . The rotary engine and the propeller of the plane has a mass of 400 kg with

radius of gyration 300 mm. The engine runs at 24000 rpm clockwise, when viewed from

the rear. Find the gyroscopic couple on the aircraft and state its effect on it. What will be

the effect, if the aeroplane turns to its right instead of the left.

8

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b) The turbine rotor of a ship weighs 5000 kg. It has a radius of gyration 0.75 m. The rotor

rotates at 1800 rpm clockwise when seen from rear. Determine the gyroscopic effects set

up. When the ship travelling at 80 km/hr, steers to left in a curve of 100 m radius.

5

3. For the given angular velocity of link 2, Find the forces acting at each joint and the

external torque that must be applied to link 2.

B

67.2º

O4

A

W2

355ºG3

O2 45ºAG3

2 2 4 4 3 3O A 50mm, O O 325mm, AB 425mm, BO 200mm, AG BG ,− − − − =

23 3M 1.2kg IG 0.0066 Nms= = , 2 2

3 36500rad / s (clockwise), AG 951m / s L3550 = =

14

4. A cam and follower mechanism causes the mass to move to the right a distance of 25 mm

with harmonic motion in 150º of cam rotation, dwell for 30º, then return to the starting

position in 180º of cam rotation also with harmonic motion. The spring is assembled with

22 - N preload and it has a rate of 4.4kN / m . The follower mass is 17.5 g. Compute the

cam speed in revolutions per minute at which jump would begin. Also show the lift off point

on the diagram drawn without calculation.

14

5. a) What are different types of governors? Give practical applications. What are new

technological changes in latest governors?

5

b) A porter governor has all four arms 25 cm long. The upper arms are attached on the axis of

rotation and the lower arms are attached to the sleeve at a distance of 3 cm from the axis.

The mass of each ball is 5 kg and mass of sleeve 50 kg. The extreme radii of rotation are 15

cm and 20 cm. Determine the range of speed of governor.

OR

8

6. a) Explain with neat sketch how flywheel works in mechanical presses.

4

b) In a turning moment diagram, the areas above and below the mean torque line taken in order

are 395, 785, 140, 440, 1060 and 370 2mm , having scales of 1 mm = 5 Nm and 1 mm =

10º a long Y and X axis respectively. Find mass of flywheel at a radius of gyration 150 mm

and maximum fluctuation of speed is limited to 1.5% of mean speed which is 1800 rpm.

9

7. a) What is difference between static balancing and dynamic balancing.

2

b) A shaft carries four masses in parallel planes A, B, C and D in order, along a shaft. The

masses at B and C weigh 18 kg and 12.5 kg respectively and each has an eccentricity of 6

cm. The masses at A and D have an eccentricity of 8 cm. The angle between the masses at

B and C is 100º and that between the masses at B and A is 190º (both angles measured in

12

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the same sense) The axial distance between the planes A and B is 10 cm and between B and

C 20 cm. If the shaft is in complete dynamic balance,

determine :

i) the weight of the masses at A & D.

ii) the distance between the planes C & D.

iii) the angular position of the mass at D.

OR

8. The firing order in a six cylinder four stroke inline engine is 1 - 4 - 2 - 6 - 35. The piston

stroke is 12 cm and length of each connecting rod is 25 cm. The pitch distance between

cylinder centre lines are 8 cm, 16 cm, 12 cm, 16 cm, 8 cm respectively. The reciprocating

mass per cylinder is 0.62 kg and the engine runs at 2800 rpm. Determine the out of balance

primary and secondary force and couples on the engine taking a plane midway between

cylinder 3 and 4 as a reference plane.

14

9. a) For a spring mass system in horizontal position determine the equation of motion using

energy method also derive relation for natural frequency.

4

b) Answer the following questions.

i) State the parameters corresponding to m, c, k and x for a torsional system.

ii) What effect does a decrease in stiffness of the system have an the natural period.

iii) Why is it important to find the natural frequency of a vibrating system.

6

c) Explain with neat sketch how a vibrator in a mobile phone works.

OR

3

10. a) How can you find the natural frequency of a system by measuring its static deflection? An

industrial press is mounted on a rubber pad to isolate it from its foundation. If the rubber

pad is compressed 5 mm by the self - weight of the press, find the natural frequency of the

system.

4

b) The free vibration response of an electric motor of weight 500 N mounted on a foundation

is shown in fig. 10 (b). Identify the following :

i) the nature of damping provided by foundation.

ii) the spring constant and damping coefficient of the foundation, and

iii) undamped and damped natural frequencies of the electric motor.

0.1 0.2 0.30.5 1

2

48 x(t)mm

0

t sec

0.60.4

Fig.10 (b)

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11. Find the natural frequencies of the system shown in fig. 11 with 1 2 1m m, m 2m, k k= = =

and 2k 2k= . Determine the response of the system when k 1000N / m, m 20kg= = , and

the initial values of the displacements of the masses 1m and 2m are 1 and 1− respectively.

m1

m2

k1

k2

x1(t)

x2(t)

Fig. (11)

OR

13

12. a) Two rotors A & B are attached to the ends of a shaft 50 cm long. Weight of the rotor A is

300 N and it's radius of gyration is 30 cm and the corresponding values of B are 500 N and

45 cm respectively. The shaft is 7 cm in diameter for the first 25 cm; 12 cm diameter for

the next 10 cm and 10 cm diameter for the remaining length. The modulus of rigidity of the

shaft material is 11 28 10 N / m .

Find :

i) the position of the node and

ii) the frequency of torsional vibration.

7cm 12cm 10cm

A B

25cm 10cm 15cm

Fig. 12 (a)

10

b) Write short note on any one.

i) FFT Analyser.

ii) Vibration Absorber.

*************

3

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