JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech II DYNAMICS OF MACHINES Previous Question Paper (July/August - 2021 - R16)
Answer any Five Questions. All Questions Carry Equal Marks.
Main
A ship is propelled by a turbine rotor having a mass of 6 tonnes and a speed of 2400 rpm. The direction of rotation of the rotor is clockwise when viewed from the stern. The radius of gyration of the rotor is 450 mm. Determine the gyroscopic effect when the:
Ship steers to the left in a curve of 60 m radius at a speed of 18 knots (1 knot = 1860 m/h)
Answer
Given: Mass m = 6000 kg, Speed N = 2400 rpm, Radius of gyration k = 0.45 m, Radius of curve R = 60 m, Ship speed v = 18 knots = 18 × (1860/3600) = 9.3 m/s. Angular velocity of rotor ω = (2π × 2400) / 60 = 251.33 rad/s. Moment of inertia I = mk2 = 6000 × (0.45)2 = 1215 kg·m2. Angular velocity of precession ωp = v / R = 9.3 / 60 = 0.155 rad/s. Gyroscopic couple C = Iωωp = 1215 × 251.33 × 0.155 = 47350 N·m. Since the rotor rotates clockwise and the ship steers left, the gyroscopic effect causes the bow to rise and the stern to lower.
Ship pitches 7.5 degrees above and 7.5 degrees below the normal position and the bow is descending with its maximum velocity; the pitching motion is simple harmonic with a periodic time of 18 seconds
Answer
Pitching angle θ = φ sin(ωpt), where φ = 7.5° = 7.5 × (π/180) = 0.1309 rad. Time period T = 18 s, so angular velocity of precession ωp = 2π / T = 2π / 18 = 0.349 rad/s. Maximum angular velocity of pitching ωp,max = φ × ωp = 0.1309 × 0.349 = 0.0457 rad/s. Gyroscopic couple C = Iωωp,max = 1215 × 251.33 × 0.0457 = 13955 N·m. When the bow is descending, the gyroscopic effect acts to turn the ship towards the starboard (right) side.
Ship rolls and at the instant, its angular velocity is 0.035 rad/s counter clockwise when viewed from the stern. Also, find the maximum angular acceleration during pitching.
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What is the effect of the gyroscopic couple on the stability of a four wheeler while negotiating a curve? In what way does this effect along with that of the centrifugal force limit the speed of the vehicle?
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How do the effects of gyroscopic couple and of centrifugal force make the rider of a two-wheeler tilt on one side? Derive a relation for the limiting speed of the vehicle.
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A simple band brake is operated by a lever of length 500 mm. The brake drum has a diameter of 500 mm and the brake band embraces 5/8th of the circumference. One end of the band is attached to the fulcrum of the lever while the other end is attached to a pin on the lever 100 mm from the fulcrum. If the effort applied to the end of the lever is 2 kN and the coefficient of friction is 0.25, find the maximum braking torque on the drum.
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Derive the expression for the torque transmitting capacity of a single plate clutch by considering uniform pressure.
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A punching machine is required to punch 2 cm diameter holes in 1.5 cm thick plates having ultimate shear stress of 320 N/sq.mm. If 30 holes are to be punched per minute and if punching operation requires 1/10th of a second, find moment of inertia of a suitable flywheel in order that the speed lies between 141 and 159 rpm.
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Define the term coefficient of fluctuation energy and deduce it.
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A spring loaded governor of a Hartnell type has arms of equal length. When the sleeve is in the mid-position, the masses rotate in a circle of diameter 150 mm (the ball arms are vertical in the mid-position). Neglecting friction, the equilibrium speed for this position is 360 rpm, the maximum sleeve movement is 30 mm and the maximum variation of speed taking account of friction is ±6% of the mid-position speed. The mass of the sleeve is 5kg and friction may be considered equivalent to 35 N at the sleeve. Assume that the power of the governor is sufficient to overcome the friction by 1% change of speed either way at mid position. Neglecting obliquity effect of arms, determine:
The value of each rotating mass
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The spring stiffness in N/mm
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The initial compression of the spring.
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A 2-cylinder uncoupled locomotive with cranks at 90° has a crank radius of 32.4 cm. The distance between centers of driving wheel is 150 cm. The pitch of cylinders is 60 cm. The diameter of treads of driving wheel is 180 cm. The radius of center of gravity of balance weights is 65 cm. The pressure due to dead load on each wheel is 4 tonnes. The weight of reciprocating and rotating parts per cylinder are 330 kg and 300 kg respectively. The speed of locomotive is 60 kmph. Find:
The balancing weights both in magnitude and position required to be placed in the planes of driving wheels to balance whole of the revolving and 2/3 of reciprocating masses.
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Swaying couple.
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The variation of tractive force.
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Explain the method of finding the counter masses in two planes to balance the dynamic unbalance of rotating masses.
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A circular disc mounted on a shaft carries three attached masses of 4 kg, 3 kg and 2.5 kg at radial distances of 75 mm, 85 mm and 50 mm and at the angular positions of 45°, 135° and 240° respectively. The angular positions are measured counter clockwise from the reference line along the x-axis. Determine the amount of the counter mass at a radial distance of 75 mm required for the static balance.
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Distinguish between longitudinal, transverse and torsional vibrations along with examples.
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Discuss the effect of damping on vibratory system. What is meant by under damping, over damping and critical damping? Explain.
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