Anna University, Chennai Nov/Dec 2012 Examinations
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Dynamics of Machinery ME2302
V Sem MECH
Unit I-V
1.     The turning moment diagram for a petrol engine is drawn to a scale of 1mm to 6N-9-9m and the horizontal scale of 1mm to 1˚.The turning moment repeat itself after every half revolution of  the engine. The area above and below the mean torque line are 305, 710, 50,350,980and 275mm2. The mass of rotating parts is 40kg at a radius of gyration of 140mm.Clculate the coefficient of fluctuation of speed if the mean speed is 1500rpm.
2.     For reciprocating engine, derive the expression for (i)Velocity and acceleration of the piston      (ii)Angular velocity and angular acceleration of the connecting rod
3.     The radius of gyration of a fly wheel is 1meter and fluctuation of speed is not to exceed 1% of the mean speed of the flywheel. If the mass of the flywheel is 3340kg and the steam develops 150KW at 135rpm, then find, 1.Maximum fluctuation of energy   2. Coefficient of fluctuation of energy
4.     A machine supported symmetrically on four springs has a mass of 80 kg. The mass of the reciprocating parts is 2.2 kg which move through a vertical stroke of 100 mm with simple harmonic motion. Neglecting damping, determine the combined stiffness of the spring so that the force transmitted to foundation is 1/20th of the impresses force. The machine crank shaft rotates at 800 rpm.If under working conditions, the damping reduces the amplitudes of successive vibrations by 30%, find (i) the force transmitted to the foundation at resonance and (ii) the amplitude of vibration at resonance.
5.     A four cylinder vertical engine has cranks 150mm long. The plane of rotation of the first, second and fourth cranks are 400mm,200mm and 200mm respectively from that of the third crank and their reciprocating masses are 50kg,60kg and 50kg respectively. Find the mass of the reciprocating parts for the third cylinder and relative angular position of the cranks in order that the engine may be in complete balance
6.     Derive the following expression of effects of partial balancing in two cylinder locomotive  engine (i) Variation of tractive force  (ii) Swaying couple (iii) Hammer blow
7.      A, B, C and D are four masses carried by a rotating shaft at radii 100mm,125mm,200mm and 150mm respectively. The planes in which the masses revolve are spaced 600mm apart and the masses of B,C and D are 10kg,5kg and 4kgrespectively.Find the required mass A and relative angular setting of the four masses so that the shaft be in complete balance
8.     A vertical double acting steam engine has a cylinder 300 mm diameter and 450 mm stroke and runs at 200 rpm. The reciprocating parts has a mass of 225 kg and the piston rod is 50 mm diameter. The connecting rod is 1.2 m long. When the crank has turned through 125° from the top dead center the steam pressure above the piston is 30 kN/m2 and below the piston is 1.5 kN/m2. Calculate
(i)                Crank-pin effort and
(ii)              The effective turning moment on the crank shaft
9.     Derive an expression for the natural frequency of the free longitudinal vibration by
(i)                (i)Equilibrium method  (ii) Energy method    (iii)Rayleigh’s method
10.Determine equation of motion when a liquid column vibrating in a ‘U’tube by
(i)                Newton’s method  (ii) Energy method and hence find its natural frequency
11. The barrel of a large gun recoils against a spring on firing. At the end of the firing, a dashpot is engaged that allows the barrel to return to its original position in minimum time without oscillation. Gun barrel mass is 400kg  and initial velocity of recoils 1m.Determine spring stuffiness and critical damping coefficient of dashpot.
12.Explain the sketches different cases of damped vibrations.
13. A mass of 10kg is suspended from one end of a helical spring, the other end being fixed. The stiffness of the  spring is10N/mm.The viscous damping causes the amplitude to decreases to one-tenth of the initial value in four  complete oscillations. If a periodic force of 150cos50t N is applied at the mass in the vertical direction .Find the amplitude of the forced vibrations? What is its value of resonance?
14.A harmonic exiting force of 25N is acting on a machine part which is having a mass of 2Kg and vibrating in
viscous medium. The exciting force causes resonant amplitude of 12.5mm with a period of 0.2sec
15. An industrial machine weighting 445kg is supported on a spring with a statical deflection of 0.5cm.If the
machine has rotating imbalance of 25kg-cm.Determine the force transmitted at 1200rpm and the dynamic
amplitude at the speed.
16.Explain the effect of Gyroscopic couple on a Naval ship during pitching.
17. The length of the upper and lower arms of a porter governor are 200mm and 250mm respectively. Both the arms are pivoted on the axis of rotation. The central load is 150N, the weight of the each ball is 20N and the friction of the sleeve together with the resistance of the operating gear is equivalent to a force of 30N at the sleeve. If the limiting inclinations of the upper arms to the vertical are 30˚ and 40˚ taking friction in to account. Find the range of speed of the governor
18.Calclate the minimum speed of a proell governor, which has equal arms each of 200mm and are provided on the axis of rotation. The mass of each ball is 4kg and the central mass on the sleeve is 20kg.The extension arms of the lower links are each 60mm long and parallel to the axis when the minimum radius of the ball is 100mm.of load.
19.The rotor of a turbine yatch rotates at 1200rpm clockwise when viewed from stern. The rotor has a mass of 750 kg and radius of gyration of 250mm.Find the maximum gyroscopic couple transmitted to the hull when yacht pitches with a maximum angular velocity of 1 rad/s.What is the effect of this couple?
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