# B.TECH III Year I Semester (R09) Regular & Supplementary Examinations November 2012 DYNAMICS OF MACHINERY

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2 1 7. Derive the following expressions, for an uncoupled two cylinder locomotive engine: (a) Variation in tractive force. (b) Swaying couple and (c) Hammer blow. 8. (a) What are free damped and forced vibrations? Explain. (b) The following data are given for a vibratory system with viscous damping; Mass2.5 kg; spring constant=3 N/mm and the amplitude decreases to 0.25 of the initial value after five consecutive cycles. Determine the damping coefficient of the damper in the system. Page 2 of 2

4 2 7. (a) Explain why only a part of the unbalanced force due to reciprocating masses is balanced by revolving mass. (b) The axes of a three-cylinder air compressor are at 120 to one another and their connecting rods are coupled to a single crank. The length of each connecting rod is 240 mm and the stroke is 160 mm. The reciprocating parts have a mass of 2.4 kg per cylinder. Determine the primary and secondary force if the engine runs at 2000 rpm. 8. (a) Discuss the effect of inertia of a shaft on the free torsional vibrations. (b) Calculate the whirling speed of a shaft 20 mm diameter and 0.6 m long carrying mass of 1 kg at its mid-point. The density of the shaft material is 40 Mg/m 3, and ;young s modulus is 200 GN/m 2.Assume the shaft to be freely supported. Page 2 of 2

5 3 B.TECH III Year I Semester (R09) Regular & Supplementary Examinations November 2012 DYNAMICS OF MACHINERY (Mechanical Engineering) Time: 3 hours Max. Marks: 70 Answer any FIVE questions All questions carry equal marks 1. (a) Explain the special characteristics exhibited by the gyroscope when it is operating. (b) The rotor of a turbine installed in a boat with its axis along the longitudinal axis of the boat makes 1500 r.p.m. clockwise when viewed from the stern? The rotor has a mass of 750 kg and a radius of gyration of 300 mm. If at an instant the boat pitches in the longitudinal vertical plane so that the bow rises from the horizontal plane with an angular velocity of 1 rad/s, determine the torque acting on the boat and the direction in which it tends to turn the boat at the instant? 2. (a) State the laws of static and dynamic friction. (b) A conical pivot bearing supports a vertical shaft of 200 mm diameter. It is subjected to a load of 30 kn. The angle of the cone is 120 and the coefficient of friction is Find the power lost in friction when the speed is 140 r.p.m. assuming. (i) Uniform pressure and (ii) Uniform wear. 3. (a) Describe the working of a band and block brake with the help of a neat sketch. Deduce the relation for ratio of tight and slack side tensions. (b) A conical friction clutch is used to transmit 90 kw at 1500 r.p.m. The semi cone angle is 20 and the coefficient of friction is 0.2. If the mean diameter of the bearing surface is 375 mm and the intensity of normal pressure is not to exceed 0.25 n/mm 2, find the dimensions of the conical bearing surface and the axial load required. 4. (a) Define the terms coefficient of fluctuation of energy and coefficient of fluctuation of speed in the case of flywheels. (b) The turning moment diagram for a multi cylinder engine has been drawn to a scale of 1 mm =4500 N-m vertically and 1 mm=2.4 horzontally. The intercepted areas between output torque curve and mean resistance line take in order from one end are 342,23,245,303,115,232,227,164 mm 2, when the engine is running at 150 r.p.m. If the mass of the flywheel is 1000 kg and the total fluctuation of speed does not exceed 3% of the mean speed, find the minimum value of the radius of gyration. 5. (a) Define and explain the following terms relating to governors: (i) Stability and (ii) Hunting. (b) In a porter governor, the mass of the central load is 18 kg and the mass of each ball is 2 kg. The top arms are 250 mm while the bottom arms are each 300 mm long. The friction of the sleeve is 14 N. If the top arms make 45 with the axis of rotation in the equilibrium position. Find the range of speed of the governor in that position. 6. (a) What is meant by static and dynamic unbalance in machinery? How can the balancing be done? (b) Four masses A,B,C and D are attached to a shaft and revolve in the same plane. The masses are 12 kg,10 kg, 18 kg and 15 kg respectively and their radii of rotations are 40 mm, 50 mm, 60 mm and 30 mm the angular position of the masses B,C and D are 60 and 135 and 270 from the mass A. Find the magnitude and position of the balancing mass at a radius of 100 mm. Contd. in page 2 Page 1 of 2

6 3 7. The cylinder axes of a V-engine are at right angle to each other. The weight of each piston is 2 kg and of each connecting rod 2.8 kg the weight of the rotating parts like crank webs and the crank pin is 1.8 kg. The connecting rod is 400 mm long and its centre of mass is 100 mm from the crank pin centre. The stroke of the piston is 160 mm. Show that the engine can be balance d for the revolving and the primary force by a revolving counter mass. Also, find the magnitude and the position if its centre of mass from the crankshaft centre is 100 mm. What is the value of the resultant secondary force if the speed is 840 rpm? 8. (a) Deduce an expression for the natural frequency of free transverse vibrations for a beam fixed at both ends and carrying a uniformly distributed mass of m kg per unit length. (b) Explain the term logarithmic decrement, as applied to damped vibrations. Page 2 of 2

8 4 7. The following data refer to a two cylinder uncoupled locomotive: Rotating mass per cylinder = 280 kg Reciprocating mass per cylinder = 300 kg Distance between wheels = 1400 mm Distance between cylinder centres = 600 mm Diameter of treads of driving wheels = 1800 mm Crank radius = 300 mm Radius of centre of balance mass = 620 mm Locomotive speed = 90 Dead load on each wheel = 3.5 tonne. Determine (i) The balancing mass required in the planes of driving wheels if whole of the revolving and two-third of the reciprocating mass are to be balanced. (ii) The swaying couple. (iii) The variation in the attractive force. (iv) The maximum and minimum pressure on the rails. (v) The maximum speed of locomotive without lifting the wheels from the rails. 8. (a) Define, in short, free vibrations, forced vibrations and damped vibrations. (b) A shaft 1.5 m long, supported in flexible bearings at the ends carries two wheels each of 50 kg mass. One wheel is situated at the centre of the shaft and the other at a distance of 375 mm from the centre towards left. The shaft is hollow of external diameter 75 mm and internal diameter 40 mm. The density of the shaft material is 7700 kg/ m 3 and modulus of elasticity is 200 GN/m 2. Find the lowest whirling speed of the shaft, taking into account the mass of the shaft. Page 2 of 2

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