Reg. No.
B.E. B.Tech. DEGREE EXAMINATION, MAY 2017
Fifth Semester
Mechanical Engineering
01UME501 DYNAMICS OF MACHINERY
(Regulation 2013)
Duration: Three hours Maximum: 100 Marks
Answer ALL Questions
PART A (10 x 2 20 Marks) 1. State and explain D Alemberts principle. 2. List few functions of flywheel. 3. What is hammer blow? 4. What is field balancing of rotors?
5. What is meant by vibration? 6. What is degree of freedom? 7. Define the term damping factor. 8. What is transmissibility ratio? 9. How to differentiate applied torque and reaction torque?
10. Define the term spin, precession and gyroscopic planes.
Question Paper Code: 31751
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PART B x 16 80 Marks)
11. A horizontal steam engine running at 120 rpm, has a bore of 250 mm and stroke of 400 mm. The connecting rod is 0.6 m and mass of the reciprocating parts is 60 kg. When the crank has turned through an angle of 45° from the inner dead centre, the steam pressure on the cover end side is 550 kN/m2 and that on the crank end side is 70 kN/m2. Considering the diameter of the piston rod equal to 50 mm, determine: turning moment on the crank shaft, thrust on the bearing and acceleration of the flywheel, if the power of the engine is 20 kW, mass of the flywheel 60 kg and radius of gyration 0.6 m.
Or
The turning moment diagram of a four stroke engine is assumed to be represented by four triangles, the areas of which the line of zero pressure are
Suction stroke 440 mm2
Compression stroke 1600 mm2
Expansion stroke 7200 mm2
Exhaust stroke 660 mm2
Each mm2 of area represents 3N.m of energy. If the resisting torque is uniform, determine the mass of the rim of a flywheel to keep the speed between 218 and 222rpm when the mean radius is to be 1.25m.
12. A shaft carries four masses C and D of magnitude 200 kg, 300 kg, 400 kg and 200 kg respectively and revolving at radii 80 mm, 70 mm, 60 mm and 80 mm in planes measured from A at 300 mm, 400 mm and 700 mm. The angles between the cranks measured anticlockwise are A to B B to C 70° and C to D 120°. The balancing masses are to be placed in planes X and Y. The distance between the planes A and X is 100 mm, between X and Y is 400 mm and between Y and D is 200 mm. If the balancing masses revolve at a radius of 100 mm, find their magnitudes and angular positions.
Or
The stroke of each piston of 6 cylinder 2 stroke inline engine is 320mm and the connecting rod is 800mm long. The cylinder centre lines are spaced at 500mm. the crack are at 60° apart and firing order is 145236. The reciprocating mass per cylinder is 100kg and the rotating parts are 50kg per crank. Determine the out of balance force and couples about the mid plane if the engine rotates at 200rpm.
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13. Derive the expression for various damping conditions in a free vibration.
The potential energy V of a linear spring-mass system is defined as 64x2 where x is the displacement in meters measured from the neutral equilibrium position. The kinetic energy T of the system is given by 8x2. Determine the differential equation of motion for the system and find the period of its oscillation. Neglect energy loss.
Or
A vertical shaft of 5 mm diameter is 200 mm long and is supported in long bearings at its ends. A disc of mass 50 kg is attached to the centre of the shaft. Neglecting any increase in stiffness due to the attachment of the disc to the shaft, find the critical speed of rotation and the maximum bending stress when the shaft is rotating at 75% of the critical speed. The centre of the disc is 0.25 mm from the geometric axis of the shaft. E 200 GN/m2.
14. A coil of spring stiffness 4 N/mm supports vertically a mass of 20 kg at the free end. The motion is resisted by the oil dashpot. It is found that the amplitude at the beginning of the fourth cycle is 0.8 times the amplitude of the previous vibration. Determine the damping force per unit velocity. Also find the ratio of the frequency of damped and undamped vibrations.
Or
A machine part of mass 2 kg vibrates in a viscous medium. Determine them damping coefficient when a harmonic exciting force of 25 N results in a resonant amplitude of 12.5 mm with a period of 0.2 s. If the system is excited by a harmonic force of frequency 4 Hz what will be the percentage increase in the amplitude of vibration when damper is removed as compared with that with damping.
15. A pair of locomotive driving wheels with the axle, have a moment of inertia of 180 kg-m2. The diameter of the wheel treads is 1.8 m and the distance between wheel centre is1.5 m. When the locomotive is travelling on a level track at 95km/h, defective ballasting causes one wheel to fall 6 mm and to rise again in a total time of 0.1s. If the displacement of the wheel takes place with simple harmonic motion, find: The gyroscopic couple set up, and The reaction between the wheel and rail due to this couple.
Or
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Find the angle of inclination with respect to the vertical of a two wheeler negotiating a turn. Given combined mass of the vehicle with its rider 250 kg moment of inertia of the engine flywheel 0.3 kg-m2 moment of inertia of each road wheel 1 kg-m2 speed of engine flywheel 5 times that of road wheels and in the same direction height of centre of gravity of rider with vehicle 0.6 m two wheeler speed 90 km/h wheel radius 300 mm radius of turn 50 m.