337513(37)
B.E (Fifth Semester) Examination,
Apr.-May., 2008
(Mechanical Branch)
DYNAMICS OF MACHINES
Time allowed : FOUR Hours
Maximum Marks : 80
Minimum Pass Marks : 28
Note :- Attempt all questions. All questions carry equal marks. Attempt the question as per internal choices. Assume suitable data wherever necessary.
1. Part (a) and (b) are compulsory. Attempt any one from part (c) and (d).
(a) What is function of a governer? How does it differ from that of flywheel ? 2
(b) Define the following terms related to governer.
(i) Stability
(ii) Sensitiveness
(iii) Isochronism
(iv) Hunting 4
(c) All the arms of a porter governer are 178 mm long and are hinged at a distance of 38 mm from the axis of rotation . The mass of each ball is 1.15 and the mass of the sleeve is 20 kg . The governer sleeve begin to rise at 280 rpm when the links are at an angle of 30 to the vertical. Assuming the friction force to be constant , determine the minimum and maximum speed of rotation when the inclination of the arm to the vertical is 45. 10
(d) In a spring loaded Hartnell type governer the extreme radii of rotation of the balls are 80 mm and 120 mm. The ball arm and the sleeve arm of the bell crank lever are equal in length . The mass of each ball is 2 kg of the speed at the two extreme point are 400 and 420 rpm. Find :
(i) the initial compression of the central spring.
(ii) the spring constant .
2. Part (a) is compulsory. Attempt any one from part (b) and (c).
(a) Explain the difference between static and dynamic balancing. 2
(b) A shaft carries four masses A,B,C and D of magnitude 200 kg, 300 kg, 400kg, and 200 kg respectively and revolving at radii 80 mm , 70 mm, 60 mm and 80 mmm in planer measured from A at 300 mm, 400 mm and 700 mm. The angles between the cranks measured anticlockwise are A to B 45 , B to C 70 , and C to D 120 . The balancing masses are to be placed in places X and Y . The distance between the planes A and X is 100 mm, between X any Y is 400 mm , and between Y and D is 200mm. If the balancing masses revolve at a radius of 100 mm, find their magnitudes and angular positions . 14
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(c) The cranks of a two cylinder uncoupled outside cylinder locomotive are at right angles and are 300 mm long . The distance between the centre lines of the cylinder is 1.8 . The wheels centre lines are 1.4 m apart . The rotation mass per cylinder is 350 kg and the mass of the riciprocating parts per cylinder is 285 kg . The whole of the rotating and two third of the reciprocating masses are to be balanced in the plane of the driving wheels at a radius of 800 mm, then find :
(i) the magnitude and angular positions of balance mass
(ii) The maximum speed of the locomotive in km/hr. without lifting the wheels from the rails if the dead load on each driving wheel is 28000 m and dia of the driving wheel is 1.89 m and
(iii) Sawying couple at the maximum speed . 14
3. Part (a) is compulsory. Attempt any two from part (b) , (c) and (d).
(a) Explain the gyroscopic effect on aircrafts. 2
(b) A uniform disc of 15 cm diameter and mass 5 kg mounted centrally on bearing which maintains its axel in a horizontal plane is shown in fig. Speed of spin is 1000rpm , while the uniform precessional speed is 60 rpm about the vertical. If the distance between the bearing is 10 cm , find the resultant reaction at each bearing due to weifgt and gyroscopic effect. 7
(c) A motor cycle with rider has a mass of 250 kg . The centre of gravity of the motor cycle and the rider falls 60 cm above the ground when running straigth in vertical position. Each road wheel diameter is 60 cm with polar mass moment of inertia of 1 kg cm2. The engine rotates 6 times faster than the wheels in the same direction and the rotating parts of the engine have a mass moment of inertia of 0.175 jgm2 . Determine the angle of inclination of the motocycle or the angle of heat required if it is speeding at 80 km/hr. and rounding a curve of radius 50m. 7
(d) The mass of turbine rotor of a ship is 3500 kg . It has a radius of gyration of 45 cm and a speed of 3000 rpm clockwise when looking from the stem . Estimate the gyroscopoc couple and its effect upon the ship under following two conditions :
(i) When the seep is steering to the left in curve of 100m radius at a speed of 36 km/hr .
(ii) When the ship is pitching in simple harmonic motion, the bow falling with maximum velocity. THe period of pitching is 49 sec and the toral angular displacement between extreme positions of pitching is 12 degrees. 7
4. Part (a) is compulsory. Attempt any one from part (b) and (c) .
(a) What do you mean by over-damped, under damped and critical damped system? 2
(b) A shaft of length 1.25 m is 75 mm in diameter for the first 275 mm of its length , 125 mm in diameter for next 500mm length, 87.5 mm in dia for next 375 mm and 175 mm in dia for remaining 100 mm length . The shaft carries two rotor at two ends . The mass moment of inertia of first and second rotor is 75 kg m2 and 50 kg m2 respectively . Find the frequency of natural Torsional vibration of the system. Take modulus of Rigidity of material as 800 N/m2 . 14
(c) A machine of mass 10 kg is supported on springs and dashpots. THe total stiffness pf the spring is 5 N/mm and total damping is 0.075 m/mmls. The system is initially at rest and a velocity of 100 mm/s is imparted to the mass. Determine :
(i) the displacement and velocity of mass as a function of time .
(ii) the displacement and velocity after one second.
5 . Part (a) is compulsory. Attempt any two from part (b) , (c) and (d).
(a) Draw turning moment diagram of a four strokes cylcle internal combustion engine. 2
(b) A certain machine require a torque of (5000 + 500 sin0) N-m t0o drive it , where 0 is the angle of rotation of shaft measured from certain datum . The machine is directly coupled to an engine which produces a torque of (5000 + 600 sin20) N-m . The fly wheel and the other rotating parts attached to the engine has a mass of 500 kg at a radius of gyration of 0.4 m. If the mean speed is 150 rpm, find (i) the fluctuation of energy , (ii) the total percentage fluctuation of speed , (iii) the maximum and minimum angular accelaeration of fly wheel and coressponding shaft position . 7
(c) A puching press is required to punch 40 mm diameter holes in a plate of 15 mm thickness at the rate of 30 holes 1 min . It requires 6 N-m of energy per mm2 of sheared area . If the punching takes 1/10 of a second and the rpm of the flywheel varies from 160 to 140 determinethe mass of the flywheel having radius of gyration of 1 metre . 7
(d) Deduce an expression for the inertia force in reciprocating parts , neglecting the weight of the connection rod . 7
