JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech II DYNAMICS OF MACHINERY Previous Question Paper (April/May - 2023 - R16)
Note: i) Question paper consists of Part A, Part B. ii) Part A is compulsory, which carries 25 marks. In Part A, Answer all questions. iii) In Part B, Answer any one question from each unit. Each question carries 10 marks and may have a, b as sub questions.
Part A
State the general expression for gyroscopic couple and mention the units of each term involved in it.
Answer
The general expression for the gyroscopic couple (C) acting on a rotating body is given by the product of the moment of inertia and the angular velocity of the body and the angular velocity of the axis of precession:
Where:
- C is the gyroscopic couple in Newton-meters (N-m).
- I is the mass moment of inertia of the disc in kilogram-meters squared (kg-m²).
- ω is the angular velocity of the disc in radians per second (rad/s).
- ωp is the angular velocity of precession of the axis of spin in radians per second (rad/s).
Explain the terms with the help of a neat sketch: bow, stern, star-board side, port side, pitching, rolling and steering.
Answer
In marine engineering, the orientation and movement of a ship are defined by the following terms:
- Bow: The forward-most part of the ship.
- Stern: The rear-most part of the ship.
- Starboard side: The right-hand side of the ship when facing forward.
- Port side: The left-hand side of the ship when facing forward.
- Pitching: The angular motion of the ship about the transverse axis, causing the bow and stern to rise and fall.
- Rolling: The angular motion of the ship about the longitudinal axis, causing the ship to oscillate from side to side.
- Steering: The process of controlling the direction of the ship, typically achieved by adjusting the rudder to create a turning moment.
A sketch would depict a ship's hull with an arrow pointing forward for the bow, backward for the stern, right for starboard, and left for port, with curved arrows indicating rotation around the longitudinal axis for rolling and the transverse axis for pitching.
Differentiate between the terms ‘fluctuation of energy’ and ‘fluctuation of speed’ as applied to flywheels.
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Draw and explain the turning moment diagram for a 4-stroke single cylinder internal combustion engine.
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Distinguish between boundary friction and fluid friction.
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Compare absorption and transmission type of dynamometers.
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List the various gravity-controlled and spring-controlled governors.
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Explain the principle of direct and reverse cranks as used in balancing.
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On what parameters the natural frequency of vibration depends.
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Explain the behavior of a whirling shaft below and above the critical speed.
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Part B
A uniform disc of diameter 250 mm and weighing 5 N is mounted at one end of an arm of length 0.5 m. The other end of the arm is free to rotate in a universal bearing. If the disc rotates about the arm with a speed of 240 rpm clock wise, looking from the front, with what speed will it precess about the vertical axis?
Answer
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An aeroplane makes a complete half circle of 75 m radius towards the left when flying at 200 km/h. The rotary engine and the propeller of the plane have a mass of 35 kg with radius of gyration of 0.25 m. The engine runs at 2400 rpm clock wise, when viewed from the rear. Find the gyroscopic couple on the plane and state its effect on it.
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A four-bar mechanism is subjected to a force of 5 kN at point E at an angle of 1200 with the plane of the fixed link AD. Calculate the input torque to link AB for the static equilibrium of the mechanism. The dimensions of the various links are AB = AD = 300 mm, BC = 450 mm, CD = 400 mm, CE = 150 mm.
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A single cylinder vertical engine has a bore of 300 mm, a stroke of 350 mm and a connecting rod of length 700 mm. The weight of the reciprocating parts is 125 kg. When the piston is at quarter-stroke from TDC and is moving downwards, the net pressure on it is 0.55 MPa. If the speed of the engine is 240 rpm, calculate the turning moment on the crankshaft. Also calculate Thrust in the connecting rod and thrust on the cylinder walls.
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Determine the maximum and minimum speed of a flywheel of mass 25 kg and radius of gyration of 100 mm when the fluctuation of energy is 50 N-m. The mean speed of the engine is 1000 rpm.
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Distinguish between the functions of a flywheel and governor.
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Draw and explain the working principle of internal expanding shoe brake. Derive an expression for total moment of the frictional force about the fulcrum.
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A torsion dynamometer is fitted on a turbine shaft to measure the angle of twist. It is observed that the shaft twists 1.5 degrees in a length of 5 metres at 500 rpm. The shaft is solid and has a diameter of 200 mm. If the modulus of rigidity of the shaft material is 85 GPa, find the power transmitted by the turbine.
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State the assumptions of ‘uniform pressure intensity’ and ‘uniform rate of wear’. What is the need for these two assumptions?
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A single plate clutch transmits 7 kW at 900 rpm. The axial pressure is limited to 0.07 MPa. The coefficient of friction is 0.25. Find mean radius and face width of the friction lining assuming the ratio of the mean radius to the face width as 4, and outer and inner radii of the clutch plate.
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In Hartnell governor, the lengths of ball and sleeve arms of a bell crank lever are 120 mm and 100 mm respectively. The distance of the fulcrum of the bell crank lever from the governor axis is 150 mm. Each governor ball has a mass of 4 kg. The governor runs at a mean speed of 300 rpm with the ball arms vertical and sleeve arms horizontal. For an increase of speed of 4%, the sleeve moves 10 mm upwards. Neglecting friction, determine: a) Minimum equilibrium speed if the total sleeve movement is limited to 20 mm, b) Spring stiffness, c) Sensitiveness of governor.
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A shaft carries four rotating masses A, B, C and D in this order along its axis. The masses are assumed to be concentrated A at a radius of 120 mm, B at 150 mm, C at 100 mm, and D at 180 mm. The masses at A, C and D are 10, 15 and 12 kg, respectively. The planes of rotation of A and B are 150 mm apart and of B and C are 200 mm apart. The angle between A and C is 90 degrees. If the shaft is in complete dynamic balance, determine: a) The angles between the radii of A, B and D, b) The distance between the planes of rotation of C and D, and c) The mass B.
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A 25 mm wide and 50 mm deep steel bar is freely supported at two points that are 1 m apart and carries a load of 100 kg midway between them. Determine the natural frequency of the transverse vibration, neglecting the weight of the bar. Also find the frequency of vibration if an additional load of 100 kg is distributed uniformly along the length of the shaft. Take E=200 GPa.
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In a spring mass vibrating system, the natural frequency of vibration is reduced to half the value when a second spring is added to the first spring in series. Determine the stiffness of the second spring in terms of that of the first spring.
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A three-mass torsional system is shown in figure. Determine the torsional stiffness of the shaft BC to make the first natural frequency 6 Hz. Then calculate the corresponding second natural frequency. G = 80 Pa.
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