## October 22, 2011

### DYNAMICS OF MACHINERY QUESTION BANK

ME2302 : DYNAMICS OF MACHINERY
DYNAMICS OF MACHINERY QUESTION BANK
ANNA UNIVERSITY QUESTION BANK

PART – A (2 Marks Questions)

1. Why is flywheel necessary in a punching press?
2. Define crank effort and crank pin effort.
3. Distinguish between the unbalanced force caused due to rotating and reciprocating masses.
4. State and explain the principle of superposition.
5. When the crank is at the inner dead center, in a horizontal reciprocating steam engine, then the velocity of the piston will be ______________(zero / minimum / maximum).
6. Define co-efficient of fluctuation in speed for a flywheel.
7. Find the work done per cycle for an engine whose torque curve is given by T = (25000 + 5000 sin 2θ – 10000 cos 2θ) Nm.
8. Why are the cranks of a locomotive, with two cylinders, placed at 90° to each other?
9. Sketch the Time Vs Displacement plot for under damped and over damped systems.
10. Define logarithmic decrement.
11. What type of motion is exhibited by a vibrating system when it is critically damped?
12. Define Dynamic magnifier.
13. The engine of an aeroplane rotates in clockwise direction when seen from the tail end and the aeroplane takes a turn to the left. What will be the effect of gyroscopic couple on the aeroplane?
14. When is a governor said to be ‘hunt’?
15. Define D’Alembert’s principle.
16. What is meant by balancing of rotating masses?
17. Define the term swaying couple.
18. What is meant by degrees of freedom in a vibrating system?
19. Define critical speed.
20. Define Magnification factor.
21. Explain the term ‘vibration isolation’.
22. Write a note on ‘Hunting of Governors’.
23. Write the expression for Gyroscopic Couple.
24. Define angular velocity of precession.
25. Why single cylinder needs large size flywheel?
26. Mention any two methods to avoid derailment of the locomotive.
27. Compare the magnitude and direction of the unbalanced forces in the case of rotating masses and reciprocating masses.
28. What is the angle between excitation frequency and actual frequency at resonance?
29. Give an expression for inertia and damping force.
30. What is the role of transmission ratio?
31. Give an application of critical damping.
32. Define the meaning of stability of a governor.
33. Which part of the automobile is subjected to the gyroscopic couple?

PART – B (16 Marks Questions)

1. The variation of crankshaft torque of a four cylinder petrol engine may be approximately represented by taking the torque as zero for crank angles 0° and 180° and as 260 Nm for crank angles 20° and 45°, the intermediate portions of the torque graph being straight lines. The cycle is being repeated in every half revolution. The average speed is 600 rpm. Supposing that the engine drives a machine requiring constant torque, determine the mass of the flywheel of radius of gyration 250 mm, which must be provided so that the total variation of speed shall be one percent. (AU, NOV 06)

2. A single cylinder vertical engine has a bore of 300 mm and a stroke of 400 mm. The connecting rod is 1 m long and the mass of the reciprocating parts is 140 kg. on the expansion stroke, with the crank at 30° from the top dead center, the gas pressure is 0.7 MPa. If the engine runs at 250 rpm, determine (i) net force acting on the piston (ii) resultant load on the gudgeon pin (iii) thrust on the cylinder walls, and (iv) the speed above which, other things remaining the same, the gudgeon pin load would be reversed in direction. (AU, NOV 06)

3. A shaft carries four rotating masses A, B, C and D which are completely balanced. The masses B, C and D are 50 kg, 80 kg and 70 kg respectively. The masses C and D make angles of 90° and 195° respectively with mass B in the same sense. The masses A, B, C and D are concentrated at radius 75 mm, 100 mm, 50 mm and 80 mm respectively. The plane of rotation of masses B and C are 250 mm apart. Determine (i) the magnitude of mass A and its angular position and (ii) the position planes A and D. (AU, NOV 06)

4. The cranks of a two cylinder, uncoupled inside cylinder locomotive are at right angles and are 325 mm long. The cylinders are 675 mm apart. The rotating mass per cylinders are 200 kg at crank pin and the mass of the reciprocating parts per cylinder is 240 kg. The wheel center lines are 1.5 m apart. The whole of the rotating and two thirds of the reciprocating masses are to be balanced and the balance masses are to be placed in the planes of the rotation of the driving wheels at a radius of 800 mm. Find (i) the magnitude and direction of the balancing masses. (ii) the magnitude of hammer blow (iii) variation in tractive force and (iv) maximum swaying couple at a crank speed of 240 rpm. (AU, NOV 06)

5. a) A spring mass system has spring stiffness of “k” N/m and a mass of “M” kg. It has the natural frequency of vibration as 12 Hz. An extra 2 kg mass is coupled to M and the natural frequency reduces by 2 Hz. Find the values of” k and “M”.
b) A stepped shaft of 0.05 m in diameter for the first 0.6 m length, 0.08 m diameter for the next 1.8 m and 0.03 m diameter for the remaining 0.25 m length. While the 0.05 m diameter end is fixed, the 0.03 m diameter end of the shaft carries a rotor of mass moment of inertia 14.7 kg-m2. If the modulus of elasticity of the shaft material is 0.83 x 1011 N/m2, find the natural frequency of torsional oscillations, neglecting the inertia effect of the shaft. (AU, NOV 06)

6. Between a solid mass of 10 kg and the floor are kept two slabs of isolators, natural rubber and felt, in series. The natural rubber slab has a stiffness of 3000 N/m and an equivalent viscous damping coefficient of 100 N.sec/m. The felt slab has a stiffness of 12000 N/m and equivalent viscous damping coefficient of 330 N.sec/m. Determine the undamped and the damped natural frequencies of the system in vertical direction, neglecting the mass of isolators. (AU, NOV 06)

7. A mass of 10 kg is suspended from one end of a helical spring, the other end being fixed. The stiffness of the spring is 10 N/mm. The viscous damping causes the amplitude to decrease to one tenth of the initial value in four complete oscillations. If a periodic force of 150 cos 50 t N is applied at the mass in the vertical direction, find the amplitude of the forced vibrations. What is its value at resonance? (AU, NOV 06)

8. 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. (AU, NOV 06)

9. A ship is propelled by a turbine rotor which has a mass of 5 tonnes and a speed of 2100 rpm. The rotor has a radius of gyration of 0.5 m and rotates in a clockwise direction when viewed from the stern. Find the gyroscopic effect in the following conditions. (i) the ship sails at a speed of 30 km/hr and steers to the left in curve having 60 m radius. (ii) the ship pitches 6° above and 6° below the horizontal position. The bow is descending with its maximum velocity. The motion due to pitching is simple harmonic and the periodic time is 20 seconds. (iii) the ship rolls at a certain instant it has an angular velocity of 0.03 rad/sec clockwise when viewed from stern.
(AU, NOV 06)

10. The length of the upper and lower arms of a porter governor are 200 mm and 250 mm respectively. Both the arms are pivoted on the axis of rotation. The central load is 150 N, the weight of each ball is 20 N and the friction on the sleeve together with the resistance of the operating gear is equivalent to a force of 30 N at the sleeve. If the limiting inclinations of the upper arms to the vertical are 30° and 40°, determine the range of speed of the governor.
(AU, NOV 06)

11. In a reciprocating engine mechanism, if the crank and the connecting rod are 300 mm and 1 m long respectively and the crank rotates at a constant speed of 200 rpm. Determine analytically,
(i) The crank angle at which the maximum velocity occurs and
(ii) Maximum velocity of the piston. (iii) Derive the equations. (AU, NOV 07)

12. 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. (AU, NOV 07)

13. (i) Four masses m1, m2, m3 and m4 attached to a rotating shaft on the same plane are 200 kg, 300 kg, 240 kg and 260 kg respectively. The corresponding radii of rotation are 0.2 m, 0.15 m, 0.25 m and 0.3 m respectively and the angles between successive masses are 45°, 75° and 135°. Find the position and magnitude of the balance mass required, if the radius of rotation is 0.2 m.
(ii) Explain with neat sketches, balancing of single revolving mass, by masses in two different planes in a rotating system. (AU, NOV 07)

14. A four cylinder vertical engine has cranks 150 mm long. The planes of rotation of the first, second and fourth cranks are 400 mm, 200 mm and 200 mm respectively from the third crank and their reciprocating masses are 50 kg, 60 kg and 50 kg respectively. Find the mass of the reciprocating parts for the third cylinder and the relative angular positions of the cranks in order that the engine may be in complete primary balance. (AU, NOV 07)

15. (i) A cantilever shaft 50 mm diameter and 300 mm long has a disc of mass 100 kg at its free end. The young’s modulus for the shaft material is 200 GN/m2. Determine the frequency of longitudinal and transverse vibrations of the shaft.
(ii) Explain with sketches different cases of damped vibrations. (AU, NOV 07)

16. A steel shaft 1.5 m long is 95 mm in diameter for the first 0.6 m of its length, 60 mm in diameter for the next 0.5 m of the length and 50 mm in diameter for the remaining 0.4 m of its length. The shaft carries two flywheels at two ends, the first having a mass of 900 kg and 0.85 m radius of gyration located at the 95 mm diameter end and the second having mass of 700 kg and 0.55 m radius of gyration located at the other end. Determine the location of the node and the natural frequency of free torsional vibration of the system. The modulus of rigidity of the shaft material may be taken as 80 GN/m2. (AU, NOV 07)

17. A mass of 10 kg is suspended from one end of a helical spring, the other end being fixed. The stiffness of the spring is 10 N/mm. The viscous damping causes the amplitude to decrease to one-tenth of the initial value in four complete oscillations. If a periodic force of 150 cos 50t N is applied at the mass in the vertical direction, find the amplitude of the forced vibrations. What is the value of resonance? (AU, NOV 07)

18. The mass of an electric motor is 120 kg and it runs at 1500 rpm. The armature mass is 35 kg and its CG lies 0.5 m from the axis of rotation. The motor is mounted on five springs of negligible damping so that the force transmitted is one-eleventh of the impressed force. Assume that the mass of the motor is equally distributed among the five springs. Determine: (i) Stiffness of each spring. (ii) Dynamic force transmitted to the base at the operating speed. (iii) Natural frequency of the system. (AU, NOV 07)

19. A porter governor has equal arms each 250 mm long and pivoted on the axis of rotation. Each ball has a mass of 5 kg and the mass of the central load on the sleeve is 25 kg. The radius of rotation of the ball is 150 mm when the3 governor begins to lift and 200 mm when the governor is at maximum speed. Find the minimum and maximum speeds and range of speed of the governor. (AU, NOV 07)

20. (i) Explain the effect of Gyroscopic couple on a Naval ship during pitching.
(ii) Explain the effect of Gyroscopic couple on a Aeroplane. (AU, NOV 07)

21. A vertical double acting steam engine develops 75 kW at 250 rpm. The maximum fluctuation of energy is 30 percent of the work done per stroke. The maximum and minimum speeds are not to vary more than 1 percent on either side of the mean speed. Find the mass of the flywheel required, if the radius of gyration is 0.6 m.

22. The length of crank and connecting rod of a vertical reciprocating engine are 300 mm and 1.5 m respectively. The crank is rotating at 200 rpm clockwise. Find analytically, (i) Acceleration of piston, (ii) velocity of piston and (iii) angular acceleration of the connecting rod when the crank has turned through 40 degree from the top dead center and the piston is moving downwards.

23. A two cylinder uncoupled locomotive has inside cylinders 0.6 m apart. The radius of each crank is 300 mm and are at right angles. The revolving mass per cylinder is 250 kg and the reciprocating mass per cylinder is 300 kg. The whole of the revolving and two-third of reciprocating masses are to be balanced and the balanced masses are placed, in the planes of rotation of the driving wheels, at a radius of 0.8 m. The driving wheels are 2 m in diameter and 1.5 m apart. If the speed of the engine is 80 km.p.h., find the hammer blow, maximum variation in tractive effort and maximum swaying couple.

24. A four cylinder engine has the two outer cranks at 120° to each other and their reciprocating masses are each 400 kg. The distance between the planes of rotation of adjacent cranks are 400 mm, 700 mm and 500 mm. Find the reciprocating mass and the relative angular position for each of the inner cranks, if the length of each crank is 350 mm, the length of each connecting rod 1.7 m and the engine speed 500 rpm.

25. A body of mass of 50 kg is supported by an elastic structure of stiffness 10 kN/m. The motion of the body is controlled by a dashpot such that the amplitude of vibration decreases to one –tenth of its original value after two complete cycles of vibration. Determine (i) the damping force at 1 m/s; (ii) the damping ratio; and (iii) the natural frequency of vibration.

26. Two parallel shafts A and B of diameters 50 mm and 70 mm respectively are connected by a pair of gear wheels, the speed of A being 4 times that of B. The mass moment of inertia of the flywheel is 3 kg-m2. Is mounted on shaft A at a distance of 0.9 m from the gears. The shaft B also carries a flywheel of mass moment of inertia 16 kg-m2 at a distance of 0.6 m from the gears. Neglecting the effect of the shaft and gear masses, calculate the fundamental frequency of free torsional oscillations and the positions of node. Assume modulus of rigidity as 84 GN/m2.

27. A mass of 500 kg is mounted on supports having a total stiffness of 100 kN/m and which provides viscous damping, the damping ratio being 0.4. The mass is constrained to move vertically and is subjected to a vertical disturbing force of the type F cos ωt. Determine the frequency at which resonance will occur and the maximum allowable value of F if the amplitude at resonance is restricted to 5 mm.

28. A machine of mass 75 kg is mounted on springs of stiffness 1200 kN/m and with an assumed damping factor of 0.2. A piston within the machine of mass 2 kg has a reciprocating motion with a stroke of 80 mm and a speed of 3000 cycles/min. Assuming the motion to be simple harmonic, Find (i) the amplitude of motion of the machine, (ii) its phase angle with respect to the existing force, (iii) the force transmitted to the foundation, and (iv) the phase angle of transmitted force with respect to the exciting force.

29. 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.

30. A disk with radius of gyration 60 mm and mass of 4 kg is mounted centrally on a horizontal axel of 80 mm length between the bearings. It spins about the axle at 800 rpm counter-clockwise when viewed from the right-hand side bearing. The axle precesses about vertical axis at 50 rpm in the clockwise direction when viewed from above. Determine the resultant reaction at each bearing due to the mass and gyroscopic effect.

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