JNTU
JNTU B.Tech II DYNAMICS OF MACHINES Previous Question Paper (March - 2022 - R16)
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A flywheel having a mass of 20 kg and a radius of gyration of 300 mm is given a spin of 500 rpm about its axis which is horizontal. The flywheel is suspended at a point that is 250 mm from the plane of rotation of the flywheel? Find the rate of precession of the wheel.
Answer
Given: Mass m = 20 kg, radius of gyration k = 0.3 m, spin speed N = 500 rpm, distance of suspension x = 0.25 m.
First, calculate the moment of inertia (I) and angular velocity of spin (ω):
The torque due to gravity (T) acting on the flywheel is:
The gyroscopic torque is given by T = I × ω × ωp, where ωp is the angular velocity of precession. Setting the gyroscopic torque equal to the gravitational torque:
The rate of precession is 0.52 rad/s.
The moment of inertia of an aeroplane air screw is 20 kg m2 and the speed of rotation is 1000 rpm clockwise when viewed from the front. The speed of the flight is 200 km per hour. Find the gyroscopic reaction of the air screw the aeroplane when it makes a left-handed turn on a path of 150 m radius.
Answer
Given: I = 20 kg·m2, N = 1000 rpm, v = 200 km/h = 55.56 m/s, R = 150 m.
Calculate angular velocity of spin (ω) and angular velocity of precession (ωp):
The gyroscopic couple (C) is calculated as:
For a clockwise rotation viewed from the front, a left-handed turn results in a gyroscopic reaction that acts to pitch the nose of the aeroplane upwards.
Explain in what way the gyroscopic couple affects the motion of an aircraft while taking a turn.
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The turbine rotor of a sea vessel having a mass of 950 kg rotates at 1200 rpm clockwise when looking from the stern. The vessel pitches with an angular velocity of 1.2 rad/s. The radius of gyration of the hull is 300 mm. What will be the gyroscopic couple transmitted to the hull, when the bow rises?
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Classify dynamometers and explain function of transmission type dynamometer.
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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 friction clutch is required to transmit 34.5 kW at 2000 rpm. It is to be single plate disk type with both sides of the plate effective; the pressure is being applied axially by means of springs and limited to 70 kPa on the plate. If the outer diameter of the friction limit is 1.5 times the internal diameter, find the required dimensions d1 and d2 of the clutch ring and the total force exerted by the springs. Assume uniform wear condition (coefficient of friction=0.3).
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Explain the principle of working of an inertia governor with the help of neat sketches.
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Each arm of a Porter governor is 400 mm long. The upper arms are pivoted on the axis of the sleeve and the lower arms are attached to the sleeve at a distance of 40 mm from the axis. Each ball has a mass of 6 kg and the weight on the sleeve is 50 kg. Find the range of speed of the governor if the extreme radii of rotation of the balls are 260 mm and 300 mm.
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A certain machine requires a torque of (1500+200 sin θ) N-m to drive it where θ is the angle of rotation of the shaft. The machine is directly coupled to an engine which produces a torque of (1500+250 sin 2θ) N-m. The flywheel and other rotating parts attached to the engine has a mass of 300 kg at a radius of gyration of 200 mm. If the mean speed of the engine is 200 rpm, find:
Total fluctuation of speed
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Maximum and minimum angular accelerations of the flywheel.
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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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The measurements on a mechanical vibration system show that the mass is 10 kg and the springs can be combined to give an equivalent spring of stiffness 5.5 kg/cm. If the vibrating systems have a dashpot attached which exerts a force of 0.05 kg when the mass has a velocity of 10 mm/s. Find:
Critical damping coefficient
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Damping factor
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Logarithmic decrement and
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Ratio of two consecutive amplitudes.
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