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JNTU B.Tech II DYNAMICS OF MACHINES Previous Question Paper (November/December - 2020 - R16)
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A flywheel of mass 10 kg and radius of gyration 200 mm is spinning about its axis, which is horizontal and is suspended at a point distant 150 mm from the plane of rotation of the flywheel. Determine the angular velocity of precession of the flywheel. The spin speed of flywheel is 900 rpm.
Answer
Given: Mass (m) = 10 kg, Radius of gyration (k) = 0.2 m, Distance (l) = 0.15 m, Spin speed (N) = 900 rpm.
First, calculate the angular velocity of the flywheel (ω):
Calculate the mass moment of inertia (I):
The gyroscopic couple (C) exerted by the weight of the flywheel is:
The gyroscopic couple is also defined as C = I × ω × ωp, where ωp is the angular velocity of precession. Rearranging for ωp:
Discuss the Static force analysis of Four-Bar mechanism under the action of:
i) One known force and ii) Two known forces.
Answer
Static force analysis of a four-bar mechanism involves determining the forces required to maintain equilibrium without considering inertia forces. The analysis typically utilizes the principle of virtual work or the method of superposition.
i) One known force: When a single known force acts on a link, the equilibrium of the entire mechanism is maintained by an input torque applied to the crank. By drawing the free body diagram of each link, we apply the condition that the sum of moments about the fixed pivots must be zero. The force is transmitted through the joints, and the required input torque is calculated by equating the power input to the power output (or using the method of moments about the instant centers).
ii) Two known forces: When two forces act on the mechanism, the superposition principle is applied. The effect of each force is analyzed independently by assuming the other is zero, and the resulting torques or forces are algebraically summed. Alternatively, the resultant force on each link is determined by considering the equilibrium of forces and moments simultaneously across all links, often resulting in a system of linear equations that are solved to find the unknown reaction forces at the pins and the required balancing torque.
Refer to Figure 1 of a Four-Bar mechanism given below:
Explain the Dynamic force analysis of the mechanism. The magnitude of ω2 is assumed to be known and constant. The points G2, G3 and G4 denote the centers of mass of the links 2, 3 and 4 respectively. It is required to determine the torque which the crankshaft at O2 exerts on the crank (link 2) to give the desired motion.
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A multi-disc clutch has 5 plates having four pairs of active friction surfaces. If the intensity of pressure is not to exceed 127 kN/m2, find the power in kW transmitted at 500 rpm, if the outer and inner radii of friction surfaces are 1.25 mm and 75 mm respectively. Assume uniform wear and take coefficient of friction as 0.3.
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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 2° in a length of 5 m at 600 rpm. The shaft is solid and has a diameter of 250 mm. If the modulus of rigidity is 84 GPa, find the power transmitted by the turbine.
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Prove that in the case of Proell governor, for a given value of m, M and h, the angular speed is less than that of Porter governor, where m = mass of each ball, M = mass of central load, and h = height of governor.
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A flywheel is used to give up 20 kJ of energy in reducing its speed from 105 rpm to 101 rpm. Determine its kinetic energy at 150 rpm.
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Draw and explain the Turning moment-Crank angle (T – θ) diagram for a multi-cylinder engine. And, from this diagram, deduce the concepts of Maximum fluctuation of energy, Coefficient of Fluctuation of Energy, Maximum Fluctuation of Speed, and Coefficient of Fluctuation of Speed.
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Referring to Figure 2, the particulars are:
wa = 890 N, ra = 22.9 cm, wb = 1335 N, rb = 17.8 cm
wc = 1068 N, rc = 25.4 cm, wd = 1157 N, rd = 30.5 cm
Find out the magnitudes of balancing masses required in planes L and M, and their angular locations with respect to mass wa.
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Explain the phenomenon of the whirling of shafts.
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A 1.2 m long shaft has a diameter of 45 mm for half the length, and 60 mm diameter for the remaining length. One end of the shaft is fixed, and the other end carries a rotor of mass 200 kg with a radius of gyration of 45 mm. Find the frequency of free torsional vibrations of the shaft. Neglect the inertia of the shaft, and take G = 84 GN/m2.
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