1 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) Write a short note on gyroscope. (b) An aeroplane runs at 600 km/h. The rotor of the engine weighs 4000 N with radius of gyration of 1 metre. The speed of rotor is 3000 r.p.m. in anticlockwise direction when seen from rear side of the aeroplane. If the plane takes a loop upwards in a curve of 100 metres radius, find (1). Gyroscopic couple developed: and. (2) Effect of reaction gyroscopic couple developed on the body of aeroplane. 2. (a) What is meant by the expression friction circle? Deduce an expression for the radius of friction circle in terms of the radius of the journal and the angle of friction. (b) An effort of 1500 N is required to just move a certain body up an inclined plane of angle 12, force acting parallel to the plane. If the angle of inclination is increased to 15, then the effort required is 1720 N. Find the weight of the body and the coefficient of friction. 3. (a) What is a clutch? Make a sketch of a single-plate clutch and describe it s working. (b) A cone clutch is to transmit 7.5 kw at 900 r.p.m. The cone has a face angle of 12. The width of the face is half of the mean radius and the normal pressure between the contact faces is not to exceed 0.09 N/mm 2. Assuming uniform wear and the coefficient of friction between contact faces as 0.2. Find the main dimensions of the clutch and the axial force required to engine the clutch. 4. (a) Draw the turning moment diagram of a single cylinder double acting steam engine. (b) The crank of a three-cylinder single-acting engine are set equally at 120 the engine speed is 540 rpm. The turning-moment diagram for each cylinder is a triangle for the power stroke with a maximum torque of 100.m at 60 after dead-centre of the corresponding crank. On the return stroke, the torque is sensibly zero. Determine (a) The power developed. (b) The coefficient of fluctuation of speed if the flywheel has a mass of 7.5 kg with a radius of gyration of 65 mm. (c) The coefficient of fluctuation of energy. (d) The maximum angular acceleration of the flywheel. 5. A proell governor has equal arms of length 300 mm. The upper and lower ends of the arms are pivoted on the axis of the governor. The extension arms of the lower links are each 80 mm long and parallel to the axis when the radii of rotation of the balls are 150 mm and 200 mm. The mass of each ball is 10 kg and the mass of the central load is 100 kg. Determine the range of speed of the governor. 6. (a) Two masses in different planes are necessary to rectify the dynamic unbalance comment. (b) A shaft with 3 metres span between two bearings carries two masses of 10 kg and 20 kg acting at the extremities of the arms 0.45 m and 0.6 m long respectively. The planes in which these masses rotate are 1.2 m and 2.4 m respectively from the left end bearing supporting the shaft. The angle between the arms is 60. The speed of rotation of the shaft is 200 rpm if the masses are balanced by two counter masses rotating with the shaft acting at radii of 0.3 m and placed at 0.3 m from each bearing centers. Estimate the magnitude of the two balance masses and their orientation with respect to the X axis, i.e mass of 10 kg. Page 1 of 2 Contd. in page 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
2 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 application of gyroscopic principles to aircrafts. (b) The mass of the motor cycle along with the rider is 180 kg. The height of the centre of gravity of total mass is 60 cm above the ground when it moves straight. Each wheel has diameter equal to 70 cm and polar mass moment of inertia of each wheel is 2 kgm 2. The engine rotates at a speed 5 times the road wheel and engine rotating parts have polar mass moment of inertia equal to 0.2 kgm 2. Determine the angle of heel required if motor cycle negotiates a curve of radius 100 m at a speed of 108 km/hr. 2. (a) A truncated conical pivot of cone angle ϕ rotating at speed N supports a load W. The smallest and largest diameter of the pivot over the contact area are d and D respectively. Assuming uniform wear, derive the expression for the frictional torque. (b) A 150 mm diameter valve against which a steam pressure of 2 MM/m 2 is acting is closed by means of a square threaded screw 50 mm in external diameter with 6 mm pitch. If the coefficient of friction is 0.12: Find the torque required to turn the handle. 3 (a) What is a brake? What is the difference between a brake and a clutch? (b) A Single dry plate clutch transmits 7.5 kw at 900 r.p.m. The axial pressure is limited to 0.07 M/mm 2. If the coefficient of friction is 0.25, find (1) Mean radius and face width of the friction lining assuming the ratio of the mean radius to the face width as 4 and 2. (2) Outer and inner radii of the clutch plate. 4. (a) Explain the terms fluctuation of energy and fluctuation of speed as applied to flywheels. (b) A vertical double action steam engine develops 75 kw at 250 r.p.m. The maximum fluctuation of energy is 30 per cent of the work done per stroke. The maximum and minimum speeds are not to vary more than I per cent on either side of the mean speed. Find the mass of flywheel required. If the radius of gyration is 0.6 m. 5. (a) Define and explain the following terms relating to governors: (i) Sensitiveness and (ii) Isochronisms. (b) The arms of a porter governor are 300 mm long. The upper arms are pivoted on the axis of rotation and the lower arms are attached to the sleeve at a distance of 35 mm from the axis of rotation. The load on the sleeve is 54 kg and the mass of each ball is 7 kg determine the equilibrium speed when the radius of the balls is 225 mm. What will be the range of speed for this position if the frictional resistance to the motion of the sleeve are equivalent to a force of 30 N? 6. (a) Define and explain the term balancing of rotating masses what will be the harm if the rotating parts of a high speed engine are not properly balanced? (b) A shaft carries five masses A,B,C,D and E which revolve at the same radius in planes which are equidistant from one another. The magnitude of the masses in planes A, C and D are 50 kg, 40 kg and 80 kg respectively. The angle between A and C is 90 and that between C and D is 135. Determine the magnitude of the masses in planes B and E and their positions to put the shaft in complete rotating balance. Page 1 of 2 Contd. in page 2
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
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 0.025. 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
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
4 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) A four wheel trolley car of total mass 2000 kg running on rails of 1 m gauge, rounds a curve of 25 m radius at 40 km/h. The track is banked at 10. The wheels have an external diameter of 0.6 m and each pair of an axle has a mass of 200 kg. The radius of gyration for each pair is 250 mm. The height of C.G. of the car above the wheel base is 0.95 m, allowing for centrifugal force and gyroscopic couple action; determine the pressure on each rail. 2. (a) What is meant by the expression friction circle? Deduce an expression for the radius of friction circle in terms of radius of the journal and angle of friction. (b) A conical pivot bearing supports a vertical shaft of 200 mm diameter. It is subjected to a load 30 kn. The angle of the cone is 120 and the coefficient of friction is 0.025. Find the power lost in friction when the speed is 140 r.p.m. assuming? (i) Uniform pressure and (ii) Uniform wear. 3. (a) Explain function of absorption type dynamometer. (b) A car moving on a level road at a speed km/h has a wheel base 2.8 meters, distance of C.G. from ground level 600 mm, and the distance of C.G. from rear wheels 1.2 meters. Find the distance travelled by the car before coming to rest when brakes are applied. (i) To the rear wheels. (ii) (iii) To the front wheels and To all the four wheels. The coefficient of friction between the tyres and the road may be taken as 0.6. 4. (a) What is meant by piston effort and crank effort? (b) The turning moment diagram for a four stroke gas engine may be assumed for simplicity to be represented by four triangles, the areas of which from the line of zero pressure are as follows: Expansion stoke=3550 mm 2 : exhaust stroke=500 mm 2 : suction stroke=350 mm 2 : and compression stroke=1400 mm 2. Each mm 2 represent 3 N-m. Assuming the resting moment to be uniform. Find the mass of the rim of a flywheel required to keep the mean speed 200 r.p.m with ±2%. The mean radius of the rim may be taken as 0.75 m. Also determine the crank positions for the maximum and minimum speeds. 5. (a) What are the effects of friction and of adding a central weight to the sleeve of a watt governor? (b) A loaded governor of the porter type has equal arms and links each 250 mm long. The mass of each ball is 2 kg and the central mass is 12 kg. When the ball radius is 150 mm, the valve is fully open and when the radius is 185 mm, the valve is closed? Find the maximum speed and the range of speed. If the maximum speed is to be increased 20% by an addition of mass to the central load. Find what additional mass is required? 6. (a) Discuss how a single revolving mass is balanced by two masses revolving in different planes. (b) Four masses A,B.C and D revolve at equal radii and are equally spaced along a shaft. The mass B is 7 kg and the radii of C and D make angles of 90 and 240 respectively with the radius of B. Find the magnitude of the masses A. C and D and the angular position of A so that the system may be completely balanced. Contd. in page 2 Page 1 of 2
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