DYNAMICS OF MACHINERY

Transcription

1 ME 6505 UNIT I DYNAMICS OF MACHINERY FORCE ANALYSIS PART A 1 MARK 1. Piston and cylinder of a reciprocating steam engine forms a a. turning pair b. rolling pair c. sliding pair d. spherical pair 2. A ball and a socket joint form a a. turning pair b. rolling pair c. sliding pair d. spherical pair 3. The function of an element is to a. transmit motion b. to serve as a support c. to guide other elements d. all of the above e. none of the above 4. In simple harmonic motion, acceleration is proportional to a. displacement b. velocity c. square of displacement d. square of velocity e. none of the above 5. The frequency of vibration will be equal to(v=3m/sec, a=30 cm) a. 2 vib/sec b. 1.8 vib/sec c vib/sec d. 1.3 vib/sec 6. Bifilar suspension is an experimental method of determining a. periodic time b. moment of inertia c. centre of gravity d. centre of percussion 7. A disc is rotating about an axis with an angular velocity and the axis of rotation is changing its position. The change in direction of plane of rotation of the disc is called a. rotational motion b. processional motion c. rectilinear motion d. none of the above 8. The rate at which the axis of rotation changes its position is known as a. angular velocity b. angular velocity of precession c. linear velocity d. sliding velocity 9. The gyroscopic acceleration depends upon a. instantaneous value of ω c. both a and b b. the rate at which the axis of spin changes its speed d. none of the above 10. The tangential component of acceleration of slider will be(angular velocity 5 rad/sec, vel 1.5 m/sec, angular accln 2 rad/sec 2, acceleration 0.5 m/sec 2 ) a. 16m/sec b. 11m/sec 2 c. 8.5m/sec 2 d. zero 11. The normal component of acceleration of slider will be(angular velocity 5 rad/sec, vel 1.5 m/sec, angular accln 2 rad/sec 2, acceleration 0.5 m/sec 2 ) a m/sec 2 b. 13 m/sec 2 c. -12m/sec 2 d. -10m/sec The total acceleration of slider will be a. 10m/sec 2 b. 20m/sec 2 c. 25m/sec 2 d. 30m/sec The gyroscopic acceleration will be(2100 rpm, 40m at speed of 72km/hr) a. 100 rad/sec 2 b. 105 rad/sec 2 c. 110 rad/sec 2 d. 120 rad/sec The product of moment of inertia and angular velocity is known as a. kinetic energy b. angular momentum c. angular torque d. none of the above 15. A machine is said to be self-locking if efficiency of the machine is a. more than 50% b. equal to 50% c. less than 50% d. equal to 100% 16. The equivalent coefficient of friction for V-threads is a. equal to actual coefficient of friction b. less than actual coefficient of friction c. greater than actual coefficient of friction d. none of the above

2 17. If the screw is self- locking, then the value of helix angle will be equal to approximately(60, 0 15) a. 8 b. 12 c. 10 d In case of flat pivot bearing, the rubbing velocity is a. maximum at the centre of contact area b. zero at the centre and maximum at the outer radius c. uniform throughout the contact area d. zero at the outer radius 19. The rate of wearing in case of flat pivot bearing is a. inversely proportional to the rubbing velocity b. inversely proportional to the pressure intensity c. directly proportional to the rubbing velocity d. directly proportional to the pressure intensity e. both c and d 20. The frictional torque, transmitted in case of flat pivot bearing for uniform wear, is equal to a. µwr b. 2/3 µwr c. 1/3 µwr d. ½ µwr ANSWERS Q.No Ans. c d d a c b b b c a Q.No Ans. c b c b c c c b e d PART B 2 MARKS 21. Write about D Alembert s principle. [Bharathiya r Univ. Nov 97, Au Dec-11] According to Newton s Law Resultant force =ma The above equation can be written as F-ma=0 -ma is known as inertia force D Alembert s principle states that the resulta nt force Acting on a body together with the reversed effective force (or inertia force),are in equilibrium 22. Define coefficient of fluctuation of speed[ms U. Nov 97] N1 N2 = max. Fluctuation speed N1+N = mean speed 2 The ratio of maximum fluctuation of speed to the mean speed is known as coefficient of fluctuation speed.

3 23. Define principle of superposition. [MU, April 2000] The principle of super position states that for linear system the individual responses to several disturbances of driving functions can be superposed in each other to obtain the total response of the system. 24. Define inertia force. [MKU, Oct 97, Au May-11] The inertia force is an imaginary force, which when cuts upon a rigid body, brings it in equilibrium position. This is equal to the accelerating force in same magnitude but F = -ma Where m mass of the body a - linear acceleration of the body. 25. Define inertial torque [Bharathiyar Univ. Nov 97] The moment of a force about a point is known as torque. The moment of couple about any arbitrary point is the same and is equal to magnitude of one of the two equal, parallel and opposite force and the perpendicular distance between them. The resultant of a couple is zero. 26. What is meant by turning moment diagram? Turning moment diagram (crank effort diagram) ia the graphical representation of the turning moment (or) crank effort (or) torque for various positions of the crank. It is also called T-ө diagram. Work done = Turning moment x angle turned. 27. Define equivalent masses? [MU, April 2000] It is defined as a group of bodies considered rigidly connected together, which will be given the same acceleration as the rigid body, when acted upon by the same forces. 28. What is free body diagram? A free body diagram is a sketch of the body isolated from rest of the machine and surroundings. It includes the known magnitudes and direction as well as other related information. 29. Define coefficient of fluctuation of energy (C E ) It is defined as the ratio of maximum fluctuation of energy to the work done per cycle. c e = co-efficient of fluctuation energy = E = maximum energy fluctuation of energy E work done/cycle 30. Define static equilibrium, dynamic equilibrium. [MS U. Nov 97] Static equilibrium: A system is said to be in static equilibrium, if all the velocities are zero if no motion takes place. Dynamic equilibrium: A system is said be in dynamic equilibrium if all the velocities do exist but remain constant but no acceleration may imply. PART C 16 MARKS 31. For reciprocating engine, derive the expression for (i) Velocity and acceleration of the piston (ii)angular velocity and angular acceleration of the connecting rod 32. In a reciprocating engine mechanism, if the crank and connecting rod are 300mm and 1m long respectively and the crank rotates at a constant speed of 200r.p.m.Determine analytically, 1. The crank angle at which the maximum velocity occurs and 2. Maximum velocity of piston. 3. Derive the relevant equations. [MU, April 2000] 43

4 33. (i) Deduce the expression for the inertia force in the reciprocating force neglecting the weight of the connecting rod. [MKU, Oct 97][AU,bDEC-12] (ii)a vertical petrol engine with cylinder of 150mm diameter and 200mm strokes has a connecting rod of 350mm long. The mass is 1.6kg and the engine speed is 1800 rpm. On the expansion stroke with crank angle 30 from TDC, the gas pressure is 750KPa. Determine the net thrust on the piston. 34. (i) Define coefficient of fluctuation of speed and coefficient of fluctuation of energy. (ii)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 35. The length of crank and connecting rod of a horizontal reciprocating engine are 100mm and 500mm respectively. The crank is rotating at 400rpm.When the crank has turned 30 from the IDC, find analytically1.velocity of piston 2.Acceleration of piston 3. Angular velocity of connecting rod 4. Angular acceleration of connecting rod. 36. The length and connecting rod of a horizontal reciprocating engine are 200mm and 1meter respectively. The crank is rotating at 400rpm.When the crank has turned 30 from the inner dead center, the difference of pressure between cover end and piston rod is 0.4 N/mm2. If the mass of the reciprocating parts is 100Kg and a cylinder bore is 0.4meters.Calculate (i)inertia force (ii) Force on piston (iii) Piston effort (iv) Thrust on the side of the cylinder walls (v) Thrust in the connecting rod (vi) Crank effort. 37. A horizontal gas engine running at 210rpm has a bore of 220mm and a stroke of 440mm.The connecting rod is 924mm long the reciprocating parts weight 20kg.When the crank has turned through an angle of 30 from IDC, the gas pressure on the cover and the crank sides are 500KN/m 2 and 60KN/m 2 respectively. Diameter of the piston rod is 40mm.Determine,1. Turning moment on the crank shaft 2.Thrust on bearing 3. Acceleration of the flywheel which has a mass of 8kg and radius of gyration of 600mm while the power of the engine is 22KW. [MU, April 2000] 38. A single cylinder vertical engine has a bore of 300mm and a stroke of 400mm.The connecting rod is 1000mm long. The mass of the reciprocating parts is 140kg.On the expansion stroke with the crank at 30 from the top dead cente r, the gas pressure is 0.7MPa.If it runs at 250rpm, determine; 1. Net force acting on the piston 2.resultant load on the gudgeon pin 3. Thrust on cylinder walls 4. The speed above which other things remaining same, gudgeon pin loads would be reversed in direction. 39. A vertical double acting steam engine has a cylinder 300mm diameter and 450mm stroke and runs at 200rpm.The reciprocating parts has a mass of 225kg and the piston rod is 50mm diameter. The connecting rod is 1.2m long. When the crank has turned 125 from IDC the steam pressure above the piston is 30KN/m2.calculate, (i)crank-pin effort [MS U. Nov 97] (ii)the effective turning moment on the crank shaft. [MS U. Nov 97] 40. 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 momen t 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.Calculate the coefficient of fluctuation of speed if the mean speed is 1500rpm.

5 41. The torque delivered by a two stroke engine is represented by T= ( sin2_-500cos2_) N-m where _ is the angle turned by the crank from the IDC. The engine speed is 250rpm.The mass of the flywheel is 400kg and radius of gyration 400mm.Determine, (i)the power developed (ii)the total percentage fluctuation of speed (iii)the angular acceleration of flywheel when the crank has rotated through an angle of 60 from the IDC. (iv) the maximum angular acceleration and retardation of the flywheel. [Au May-11] 42. A single cylinder horizontal steam engine has a stroke of 0.7 m and a connecting rod 1.8m long. The mass of reciprocating parts is 520kg and that of the connecting rod is 230kg. Centre of gravity of the connecting rod is 0.8m from crank pin and the moment of inertia about an axis through the centre of gravity perpendicular to the plane of motion is 100kg-m 2. For an engine speed of 90rpm and a crank position of 45 from the IDC, determine the torque on the crankshaft due to the inertia of these parts. [Au Dec-11] UNIT-II BALANCING PART A 1 MARK 43. The ratio of frictional torque transmitted for uniform pressure to the frictional torque for uniform wear incase of flat pivot, is equal to a. 1/3 b. 2/3 c. 1 d. 4/3 44. The value of limiting bearing pressure on a collar is about a. 1 kgf/cm 2 b. 5 kgf/cm 2 c. 10 kgf/cm 2 d. 15 kgf/cm The frictional torque for uniform wear, will be equal to(d=20cm,420rpm, µ=0.09) a kgf-m b. 15 kgf-m c kgf-m d. 20 kgf-m 46. The horse power lost in overcoming friction at the bearing, will be equal to a. 6.6 h.p b. 8.8 h.p c.4.4 h.p d. 2.2 h.p 47. The horse power transmitted by the friction between the surface, will be equal to a. 6.6 h.p b. 8.8 h.p c. 4.4 h.p d. 2.2 h.p 48. For uniform pressure the ratio of the frictional torque for a flat collar bearing to the frictional torque for a conical collar bearing is equal to a b. 1 c. sinθ d. cosθ 49. For uniform wear, the ratio of the frictional torque for a flat collar bearing to the frictional torque for a conical collar bearing, is equal to a b. 1 c. sinθ d. cosθ 50. The frictional torque transmitted by a conical collar bearing is a. less than that of flat collar bearing b. equal to that of flat collar bearing c. more than that of flat collar bearing d. none of the above 51. The horse power lost in friction would be equal to(d=40cm &20cm,420rpm) a b c d Friction clutch is a. Disc clutch b. cone clutch c. centrifugal clutch d. plate clutch e. all of the above f. none of the above 53. Friction circle in case of journal bearing is a. The circle of the journal b. the circle to which resultant force F is tangent c. the circle which is having radius equal to half of the radius of the journal d. the circle which is having radius equal to µ* R e. both b and d f. none of the above

6 54. The radius of friction circle increases a. with increase of load b. with increase of radius of journal c. with increase of speed d. with increase of co. efficient of sliding friction e. all of the above f. b and d only 55. The maximum efficiency of a screw jack is a function of a. helix angle b. angle of friction c. load lifted d. effort 56. The angular velocities of the two pulleys, connected either by an open belt or a crossed belt, are a. directly proportional to their diameters b. inversely proportional to their diameters c. proportional to the square of their diameters d. proportional to the square root of their diameters. 57. The effect of slip on velocity of the belt is to a. increase the velocity ratio b. decrease the velocity ratio c. keep the velocity ratio constant d. none of the above 58. The tension caused by centrifugal force on the belts a. increases power transmission b. decreases power transmission c. does not affect power transmission d. none of the above. 59. When maximum horse power is transmitted by a belt, the centrifugal tension in the belt is a. half the maximum tension allowed in the belt b. one-third the maximum tension allowed in the belt c. two-third the maximum tension allowed in the belt d. one-fourth the maximum tension allowed in the belt. 60. Creep in belt drive is due to a. weak material of the belt b. weak material of the pulley c. uneven extension and contractions d. none of the above 61. Crowning of pulley is done a. to avoid the slipping of the belt b. to make them more study c. to enable pulley rigidly fixed to the shaft d. to make pulley look more pleasant in appearance. 62. The shafts are connected by a cross belt, then the length of the belt would be(d=5mts, d=40cm,30cm) a. 1000cm b cm c cm d. 1120cm ANSWERS Q.No Ans. d b a b a c c c b e Q.No Ans. e f b b b b b a c a

7 PART B 2 MARKS 63. What is meant of by balancing? [MS U. Nov 97] When mass m attached to a rotati ng shaft, it produces Centrifugal force Fc=m ω2 r. this force will bend the shaft And create vibrations on it. To counteract the effect of this Centrifugal force, new mass is introduced which will develop Centrifugal force Fc1=m1w2r1 and this force Fc1 will cancel(balance) the unbalanced force Fc2. This process of introducing new mass to counter act the effect of centrifugal force of existing mass is called balancing of rotating masses. 64. What is Static balancing? [MU, April 2000, Au Dec-11, AU DEC-12] For static balancing of shaft, the net dynamic force acting on the shaft is made is zero. 65. What is dynamic balancing? [MKU, Oct 97, Au Dec -11, AU DEC-12 ] For dynamic balancing of shaft the net dynamic force acting on the shaft is made the net couple due to dynamic forces acting on the shaft is made zero. 66. What is complete balancing? [MS U. Nov 97] The dynamic balancing is also called complete Balancing. In dynamic balancing, both the resultant force and Couples are made to zero. 67. Define variation in attractive effort? The resultant unbalanced force due to the two cylinders, along the line of stroke, is known as variation in tractive effort. 68. What is partial balancing of reciprocating masses? [Au May-11] The primary unbalanced force is acting along the line Of stroke before balancing. While balancing, this force acts Along the perpendicular to the line of stroke. So complete Balancing of the force is not possible. As a compromise a Fraction of reciprocating masses are balanced. This is known As partial balancing of reciprocating masses. 69. Define swaying couple. [MKU, Oct 97] The unbalanced forces along the line of stroke for the Two cylinders form a couple about the centre axis between the Two cylinders. This couple creates swaying effect about the Vertical axis and it tends to sway the engine alternately in Clockwise and anticlockwise directions. This couple is known as swaying couple. 70. Define Hammer blow. [MU, April 2000, AU DEC-12] The maximum amount of unbalanced force along the Perpendicular to the line of stroke is known as Hammer blow Hammer blow= B ω 2 b Where B= balancing mass at radius b. 71. List out the classification of locomotives. (i). inside cylinder locomotives (ii). Outside cylinder locomotives. 72. What is of rotating masses? [MS U. Nov 97] When a masses is fixed to a rotating shaft, some amount of centrifugal force is exerted, which makes the shaft to bend and hence producing unwanted vibrations. The effect of centrifugal force can be prevented by attaching a another mass radially opposite, in such a manner it balances the effect of a force of the disturbing mass. The process of providing a balancing mass to the disturbing mass is called as balancing of rotating mass. 73. What are the different types of balancing of rotating masses. 1. Balancing of a single rotating mass by a single mass rotating in the same plane. 2. Balancing of a single rotating mass by two masses rotating in different planes. 3. Balancing of different masses rotating in the same plane. 4. Balancing of different masses rotating in different masses in different planes.

8 PART C 16 MARKS 74. A shaft is rotating at a uniform angular speed. Four masses M1, M2, and M3and M4 of magnitudes 300kg, 450kg, 360kg, 390kg respectively are attached rigidly to the shaft. The masses are rotating in the same plane. The corresponding radii of rotation are 200mm, 150mm, 250mm and 300mm respectively. The angle made by these masses with horizontal are 0, 45, 120 and 255 respectively. Find (i) the magnitude of balancing mass (ii) the position of balancing mass if its radius of rotation is 200mm. 75. Four masses M1, M2, M3, and M4 are 200kg, 300kg, 240kg and 260kg respectively. The corresponding radii of rotation are 0.2m, 0.15m, 0.25m and 0.3m respectively and the angle between successive masses45, 75, and135.find the position and magnitude of balance mass required if its radius of rotation is 0.25m. [MS Univ. Nov 97] 76. The data for three rotating masses are given below:- M1=4kg r1=75mm θ1=45 M2=3kg r2=85mm θ2=135 M3=2.5kg r3=50mm θ3=240 Determine the amount of counter mass at a radial distance of 65mm required for their static balance [MKU, Oct 97, Au Dec-11] 77. Four masses A, B, C, and D are completely balanced masses C and D makes angles of 90 and 195 respectively with B in the same sense. The rotating masses have the following properties: ma=25kg ra=150mm mb=40kg rb=200mm mc=35kg rc=100mm rd=180mm Planes B and C are 250mm apart. Determine (i) the mass A and its angular position (ii) the position of planes A and D. 78. 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. [AU, DEC-12] 79. Four masses A, B, C and D revolves at equal radii and equally spaced along a shaft. The mass B is 7kg and the radii of C and D make angle s of 90 and 240 respectively with the radius of B. Find the magnitude of masses A,C and D and angular position of A. So that the system may be completely balanced. [MU, April 2000] 80. A shaft caries four rotating masses A, B, C and D which are completely balanced. The masses B, C and Dare 50kg, 80kg and 70kg respectively. The masses C and D make angles of 90 and 195 respectively with mass B in the same s ense. The masses A,B,C and D are concentrated at radius 75mm,100mm,50mm and 90mmrespectively.The plane of rotation of masses B and C are 250mm apart. Determine (i) the magnitude of mass A and its angular position(ii) the position of planes A and D. 81. 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. [MS U. Nov 97] 82. A four cylinder vertical engine has cranks 300mm long. The plane of rotation of the first, third and fourth cranks are 750mm,1050mm and 1650mm respectively from that of the second crank and their reciprocating masses are 10kg,400kg and 250kg respectively. Find the mass of

9 the reciprocating parts for the second cylinder and relative angular position of the cranks in order that the engine may be in complete balance. 83. 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 [MU, April 2000] UNIT-III FREE VIBRATION PART A 1 MARK 84. Piston, piston rod and cross head of a steam engine constitute (a) one link (b) two link (c) three link (d) do not conform to the concept of a link 85. Connecting rod, big and small and brasses, caps and bolts constitute (a) one link (b) two link (c) three link (d) four link 86. Crank. Connecting rod, cylinder and piston of a steam engine constitute (a) one link (b) two link (c) three link (d) four link 87. Pick the odd one out (a) cam and follower (b) belt, rope and chain drive (c) ram guides in a shaper (d) ball and roller bearings 88. Two elements that permit relative motion which is completely constrained or successfully constrained constitute a (a) closed pair (b) lower pair (c) kinematic pair (d) mechanism 89. The number of link in a pantograph is (a) 3 (b) 4 (c) 5 (d) Type writer constitutes a (a) machine (b) mechanism (c) structure (d) inversion 91. Cam and follower mechanism constitutes a kinematic pair of type (a) lower and open (b) higher and open (c) lower and closed (d) higher and closed 92. A ball and socket joint constitutes a spherical pair having (a) no degree of freedom (b) one degree of freedom (c) two degrees of freedom (d) three degrees of freedom 93. The number of link l and the number of pairs p in a kinematic chain conform to the relation (a) i=p- 4 (b) i = 2p - 4 (c) i = 2p + 1 (d) i = 2 (p-1) 94. If the number of links in a mechanism is 6 the number of pairs would be (a) 4 (b) 5 (c) 6 (d) Is it possible to have a kinematic chain with 5 link and 5 joint? (a) no (b) yes (c) marginal case (d) data insufficient to make any prediction 96. A slider crank chain consists for a kinematic chain having plance motion is give by the equation (a) 1.3 (b) 2,2 (c) 3,1 (d) 4,0 (e) 0,4 97. The number of inversions of a double slider crank chain are (a) 2 (b) 3 (c) 4 (d) Mid -point of the floting link of elliptical trammel traces a (a) circle (b) parabola (c) ellipse (d) straight line 99. A Hook's joint is used to connect (a) two parallel shafts (b) two intersection shaft (c) two non-parallel intersecting shaft (d) two non-parallel, non intersecting shafts

10 100. A universal joint is an examble of (a) lower pair (b) higher pair (c) rolling pair (d) sliding pair 101. A four bar mechanism has instantaneous centres of rotation (a) 2 (b) 4 (c) 6 (d) The numberof link and instantaneous centres in a reciprocating engine mechanism are respectively (a) 4,4 (b) 4,3 (c) 4,6 (d) A mechanism has 7 links which are all binary except one which is ternary. the number of instantaneous centres of rotation will be (a) 14 (b) 21 (c) 28 (d) 42 ANSWERS Q.No Ans. a a d c c b b b b d Q.No Ans. b a c b c c a c c c PART B 2 MARKS 104. What is viscous damping? [MU, April 2000] [AU, DEC-12] When the frictional resistance (Damping) to the motion of the body is directly proportional to the speed of the movement, it is called viscous damping Define whirling (or) critical speed of a shaft? [MKU, Oct 97][AU, DEC-12] The speed at which the shaft runs so that the additional deflection Of shaft from the axis of rotation becomes infinite, is known as critical Or whirling speed Define periodic motion? A motion which repeats itself after equal intervals of time is known as periodic motion What is Resonance? [Bharathiyar Univ. Nov 97] Resonance occurs when the frequency of the external force Is equal to the natural frequency of vibrations of the system. The Amplitude of vibration at resonance becomes excessive Define Damping.[ AU, DEC-12] It is the resistance to the motion of vibrating body Define free and damped vibrations[mku, Oct 97] Free vibrations: The body is said to be under Free Vibrations, when no external force acts on the body, after Providing an initial displacement. Damped vibrations: when there is a reduction in amplitude Over every cycle of vibration, the motion is said to be Damped Vibrations 110. Explain Longitudinal Transverse and Torsional vibrations? [MU, April 2000] Longitudinal vibrations: when the particles of shaft moves parallel to axis of the shaft, then vibrations are called longitudional Vibrations.Transverse vibrations; when the particles of shaft move perpendicular To the axis of the shaft,then the vibrations are known as transverse Vibrations.Torsional vibrations:when particles of theshaft moves in a circle About the axis of the shaft,then the vibrations are known as Torsional vibrations. 50

11 111. Explain Energy method. [MS U. Nov 97] In this method, summation of kinetic energy (K.E) and potential energy (PE) must be a constant quantity which is same at all times. d/dt (K.E+P.E)= Explain Rayleigh s method? In this method, the maximum kinetic energy at mean Position is equal to the max. potential Energy (stain Energy)at Extreme position Define node? [MS U. Nov 97] The point (or) section of the shaft whose amplitude of torsional Vibration is zero, is known as node What are free torsional vibrations of three rotor system? Here the two rotors rotate in one direction and the third rotor rotates In opposite direction with the same frequency What are free Torsional vibrations of two rotor system? [MKU, Oct 97] When two rotors A and B are rotating on two extreme ends of a shaft in opposite direction, (a) FnA= ƒnb (b) l=ia+ib where la distance of node from rotor A 1B distance of node from rotor B ƒna, ƒnb frquency of torsional vibrations for rotor A and B 116. Write the governing differential equation of the system.[au Jun-11] d 2 x/dt 2 + c/m. dx/dt + s/m.x =0 PART C 16 MARKS 117. Derive an expression for the natural frequency of the free longitudinal vibration by (i) Equilibrium method (ii) Energy method (iii) Rayleigh s method 118. In a single degree of damped vibration system a suspended mass of 8kg makes 30 oscillations in 18 seconds. The amplitude decreases in 18 seconds. The amplitude decreases to 0.25 of the initial value after 5 oscillations. Determine (i) the spring stiffness (ii) logarithmic decrement (iii) damping factor (iv) Damping coefficient. [Au Dec-11][AU, DEC-12] 119. 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. (16) 120. (i)deduce the expression for the free longitudinal vibration in terms of spring stiffness, its inertia effect and suspended mass. [MU, April 2000] (ii)a spring mass system has spring stiffness s N/ m and has a mass of m kg.it has the natural frequency of vibration as 12Hz.An extra 2kg mass is coupled to m and natural frequency reduces by 2Hz.Find the value of s and m Avibrating system consists of a mass of 8kg,spring of stiffness 5.6N/m and dashpot of damping coefficient of 40N/m/s.Find,(i)Critical damping coefficient (ii) the damping factor (iii)the natural frequency of damped vibration (iv)the logarithmic decrement(v)the ratio of two consecutive amplitude (vi)the number of cycle after which the original amplitude is reduced to 20 percent. [MU, April 2000] 122. An instrument vibrates with a frequency of 1Hz when there is no damping. When the damping is provided, the frequency of damped vibration was observed to be 0.9Hz.

12 Find, (i) damping factor (ii) logarithmic decrement Find the equation of notion for the spring mass-dashpot system for the cases when (i) ζ= 2 (ii) ζ= 1 and (iii) ζ= 0.3. The mass m is displaced by a distance of 30 mm and released [MS U. Nov 97] 124. Between a solid mass of 0kg and the floor are kept two slabs of isolates, natural rubber and felt, in series. The natural rubber slab has a stiffness of 3000N/m and equivalent viscous damping coefficient of 100 N-sec/m. The felt has a stiffness of 12000N/m and equivalent viscous damping coefficient of 330Nsec/m. Determine undammed and the damped natural frequencies of the system in vertical direction. [Bharathiyar Univ. Nov 97] 125. (i) A cantilever shaft 50mm diameter and 300mm long has a disc of mass 100kg at its free end. The young s modulus for the shaft material is 200GN/m2.SDetermine the frequency of longitudinal and transverse vibration of the shaft. (ii) Explain the sketches different cases of damped vibrations 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 A steel shaft 100mm in diameter is loaded and support in shaft bearing 0.4m apart. The shaft carries three loads: first mass 12kg at the centre, second mass 10kg at a distance 0.12m from the left bearing and third mass of 7kg at a distance 0.09m from the right bearing. Find the value of the critical speed by using Dunker ley s method. E=2X10 11 N/m Write short notes on a. vibration isolation and transmissibility b. whirling of rotating shafts. [Au May-11] UNIT IV FORCED VIBRATION PART A 1 MARK 129. Instantaneous centre of rotation of a piston in a internal combustion engine lies at (a) centre of crank pin (b) centre of piston pin (c) centre of crankshaft bearing (d) infinity 130. Crankshaft rotating in the journal bearing of an engine forms a (a) screw pair (b) turning pair (c) spherical pair (d) rolling pair 131. The coriolis component of acceleration (a) leads the sliding velocity vector by 180 (b) rotates the sliding velocity vector about its origin along the direction of velocity (c) is directed along the sliding the velocity vector (d) is directed along the tangential acceleration The direction of coriolis component of acceleration is the direction (a) at right angles to that of relative angular velocity vector (b) relative to velocity vector for two coincident point rotated by180 in the direction of angular velocity of rotation of link (c) of relative velocity vector for two coincident point rotated by 90 in the direction of angular velocity of rotation of link (d) of relative velocity vector for two coincident point in the direction exactly opposite to that of angular velocity.

13 133. Coriolis component of acceleration exists whenever a point moves along a path that hqs (a) tangential acceleration (b) centripetal acceleration (c) linear motion (d) rotational motion 134. Instantaneous centre of rotation of a piston in an internal combustion engine lies at (a) centre of crank pin (b) centre of piston pin (c) centre of crankshaft bearing (d) infinity 135. A four bar mechanism has instantaneous centres of rotation (a) 2 (b) 4 (c) 6 (d) The number of links and instantaneous centres in areciprocating engine mechanism respectively (a) 4.4 (b) 4.3 (c) 4. 6 ( d) A mechanism has 7 links which are all binary except one which is tertiary and the number of instantaneous centres of rotation will be (a) 14 (b) 21 (c) 28 (d) Consider a point on a link connecting double slider crank chain.it would trace (a) a circular path (b) an elliptical path(c) a straight line path ( d) a parabolic path 139. Kline 's construction is mainly used to determine (a) displacement of piston (b) linear velocity and acceleration of piston (c) angular velocity of connecting rod ( (d) angular acceleration of link 140. Klien 's construction is applicable when the crank has (a) sloe rotational speed (b) uniform angular velocity (c) uniform angular acceleration (d) cyclic variations in velocity and acceleration A pulley 300 mm in diameter drives a pulley 1500mm in diameter by means of a belt 20mm thick. if the drive pulley turns 200 revolutions per minute,the speed of the driven pulley would be closer (a) 42rpm (b) 92 rpm (c) 435rpm (d) 950 rpm 142. Identify the wrong statement (a) slip is a measure of the difference between the linea speed of the rim of the pulley and the belt on it (b) belt slipping reduces the velocity ratio of the system (c) slippage is a self correcting evil (d) for the same percentage of slip at both the drive and driven pulleys,the velocity ratio remains unaffected 143. With whipping of open belt system (a) velocity ratio is increased (b) belt slipping gets enhanced (c) power transmitted remains unaffected (d) life of the belt is shortened 144. Creep in a belt occurs due to (a) weak material of the belt (b) weak material of the pulley (c) improper crowning (d) uneven contraction and extension of the belt The mid section of flat pulleys is slightly raised to (a) reduce tensionin the belt (b) increase the angle of contact (c) avoid lateral slip of the belt (d) save the pulley from any damage from the belt joints

14 146. The crowning height of the pulleys is (a) smaller for wider and larger belts at high speed (b) smaller for narrow and larger belts at slow speed (c) greater for wider and larger belt at high speed (d) independent of the belt width and speed of pulleys 147. An idler pulley is used (a) for frequent stoppage of motion (b) to maintain requisite tension in the belt (c) to change the direction of motion of the belt (d) to run only during non-load periods 148. The ratio between tension on the tight and slack side of the belt cannot be increased by (a) placing the pulleys closer (b) increasing the belt speed (c) dressing the belt material to increase the coefficient of friction between the belt and pulley material [d] employing crossed belt drive instead of open belt drive ANSWERS Q.No Ans. d b b c d d c c c b Q.No Ans. b b a d d d c a b b PART B 2 MARKS 149. Define Logarithmic decrement? [MS U. Nov 97] It is defined as the natural logarithm of the amplitude reduction Factor. The amplitude reduction factor is radio of any 2 successive amplitudes on Same side of the mean positions Define Damping Factor (or) Damping Ratio. [Bharathiyar Univ. Nov 97] The ratio of actual damping co-efficient to critical damping Coefficient is known as damping factor=c/cc 151. What is Isolation factor or Transmissibility ratio?[au Dec-11, AU,DEC-12] The ratio of the force transmitted (FT) to the force applied (F) is known as transmissibility ratio (or) Isolation factor What is excitation of support? [MKU, Oct 97] This type of excitation can occur in the locomotives or vehicles. The wheels of the vehicles act as the base or support for the entire system. As the wheels move vertically up and down along the road surface, forms a motion/excitation to the system How frequency of under damped forced vibrations is determined? (a) Differential equation method. (b) Graphical method Define simple Harmonic motion[mku, Oct 97] A periodic motion of a particle whose acceleration is always Directed towards the mean position and ism proportional to its distance From the mean position, is known as SHM 155. What is amplitude? [MU, April 2000] The maximum displacement of a vibrating body from the mean position.

15 156. Define magnification factor. [MS U. Nov 97] D = X max X0 It is the ratio of maximum displacement X max of the forced vibration to deflection X 0 due to the static force F Define transmissibility. In case of forced vibration, transmissibility is defined as the ratio of force transmitted to the foundation to the impressed force upon the system What are requirement for an isolator? [MU, April 2000] i) There should be no rigid connection between the unit and the base. i)the isolators should remain together in case the damping material s fails What is meant by harmonic forcing?[au Dec-11] It refers to a spring mass system with viscous damping, excited by a sinusoidal harmonic force. F=F 0 sinωt 160. State natural frequency of torsional vibration of a simple system.[au May-11] F n =1/2 CJ/Il PART C 16 MARKS 161.A mass of 50kg is supported by an elastic structure of total stiffness 20KN/m.The damping ratio of the system is 0.2.A simple harmonic disturbing force acts on the mass and at any time t seconds, the force is 60sin10t newtons. Find amplitude of the vibration and phase angle caused by the damping. [MS U. Nov 97] 162. A mass of 50kg is supported by an elastic structure of total stiffness 20KN/m.The damping ratio ofthe system is 0.25.A simple harmonic disturbing force acts on the mass and at any time t seconds, the force is 75cos12t newtons. Find amplitude of the vibration and phase angle caused by the damping. [Bharathiyar Univ. Nov 97] 163. 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? 164. 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. [MS U. Nov 97] 165. A body having a mass of 15kg is suspended from a spring which deflects 12mm under the weight of the mass. Determine the frequency of the free vibrations. What is the viscous damping force needed to make the motion a periodic at a speed of 1mm/s?If, when damped to this extend a disturbing force having a maximum value of 100N and vibrating at 6Hz is made to act on the body, determine the amplitude of the ultimate motion. [MU, April 2000] 166. A single cylinder vertical petrol engine of total mass of 200kg is mounted upon a steel chassis frame. The vertical static deflection of the frame is 2.4mm due to the weight of the engine.the mass of the reciprocating parts is 18kg and stroke of piston 160mm with S.H.M. If dashpot of damping coefficient of 1N/mm/s used to damped the vibrations, calculate al steady

16 state (i)amplitude of vibrations at 500rpm engine speed.(ii)the speed of the driving shaft at which resonance will occurs. [MKU, Oct 97] 167. A vertical single stage air compressor having a mass of 500kg is mounted on spring having stiffness of 1.96X10 5 N/m and dashpot with damping factor of 0.2m.The rotating parts are completely balanced and the equivalent reciprocating parts weight 20kg.The stroke is 0.2m.Determine the dynamic amplitude of vertical motion of the excitation force if the compressor is operate at 200rpm A machine 100kg has a 20kg rotor with 0.5mm eccentricity. The mounting spring have s=85x103. The operating speed is 600rpm and the unit is constrained to move vertically. Find (i) Dynamic amplitude of machine (ii) the force transmitted to the support. 169.A single cylinder engine has an out of balance force of 500N at an engine speed of 30rpm.The total mass of engine is 150kg and its carried on a set of total stiffness 300N/cm. (i) Find the amplitude of steady motion of the mass and maximum oscillating force transmitted to the foundation. [MKU, Oct 97] (ii)if a viscous damping is interposed between the mass and the foundation the damping force 1000N at 1m/s of velocity, find the amplitude of force damped oscillation of the mass and its angle of lag with disturbing force. ` 170. 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 The mass of an electric motor is 120kg and it runs at 1500rpm.The armature mass is 35kg and its centre gravity lies 0.5mm from 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) the stiffness of the spring (ii) the dynamic force transmitted to the base at the operating speed. (iii) Natural frequency of system. [MU, April 2000] 172. Find the stiffness of each spring when a refrigerator unit having a mass of 30kg is to be support by three springs. The force transmitted to the supporting structure is only 10% of the impressed force. The refrigerator unit operates at 420rpm. [MS U. Nov 97] 173. A 100kg machine is mounted on a spring stiffness N/m and damping factor 0.3. A 3kg piston within the machine has a reciprocating motion with a stroke of 100 mm and a speed of 1500 rpm, thus producing a harmonic force. Determine the amplitude of vibration of the machine and the force transmitted to the foundation.[au dec-11] 174. Describe the principle of undamped dynamic vibration absorber with suitable illustrations.[au May-11] UNIT V MECHANISMS FOR CONTROL PART A 1 MARK 175. The power transmitted by belt drive is designed on the basis of (a) angle of lap on the smaller pulley (b) angle of lap on the large pulley (c) average angle of lap of two pulleys (d) angle of lap of the driver pulley whether smaller or larger

17 176. The average tension on the tight and slack side of a flat belt drive system are 70k.g.f and 40 k.g.f respectively.if linear velocity of the belt is 5 m/s,the power transmitted by system would be about (a) 2 HP (b) 2.6HP (c) 3.3HP (d) 4.7 HP 177. For identical conditions of belt speed pulley, diameters centre distance and material of pulley and belt crossed belt drive transmit (a) more,more (b) more less (c) less less ( d) less more 178. The centrifugal tension in the flat belt drive system increases (a) in direct proportion to mass per unit length of the belt (b) in direct proportion to belt thickness (c) in direct proportion to square of belt speed (d) Exponentially with maximum permissible tension in the belt 179. The centrifugal tension in belts (a) increases power transmission (b) decreases power transmission (c) may increase or decrease power transmitted depending upon tension on slack and tight side of the belt system (d) does not affect the power transmitted 180. In belt drives the centrifugal tension (a) reduces the speed of driven wheel (b) reduces friction between the belt and pulley rim (c) reduces the driving power (d) reduces the lengthening of belt under tension 181. For maximum power transmitted by belt drive the centrifugal tension is equal to (a) half the effective tensionon the side of the belt drive (b) one -third of effective tension on the tight side of the belt drive (c) two-third of effective tensionon the tight side of the belt drives (d) three -fourth of effective tension on the tight side ofthe belt drive 182. For same power transmission v-belt are but as compared to flat belts: (a) narrow.thicker (b) thicker, narrow (c) wider, thinner (d) thinner wider 183. Which of the following is not a common section of v-belts? (a) a (b) c (c) e (d) f 184. Fan belt is automobiles is (a) a3-layer flat belt (b) a5-layer flat belt (c) B-section v-belt (d) E-section V-belt 185. A, P, I, V system is used for (a) fluctuating loads (b) suppressing torsional vibrations (c) infinitely variable speed drives (d) low torque drives 186. For constant velocity ratio positive drive with large distance between drive and driven shaft,one would use (a) flat belt drive (b) v-belt drive (c) chain drive (d) gear drive 187. Spot the odd one out (a) hartnell governor (b) hartung governor (c) proell governor (d) wils hartnell governor 188. Which one of the following is a spring controlled centrifugal governor? (a) pickering governor (b) porter governor ( c) proell governor (d) watt governor

18 189. The quality of a governor is judged by its (a) stability (b) sensitivity (c) effort (d) power 190. Which of the following provides a smooth and positive drive (a) rope drive (b) v- belt drive (c) chain drive (d) gear drive 191. Axial thrust is minimum in case of (a) spur gear (b) double helical gear (c) bevel gear (d) mintre gears 192. A rack is a gear of infinite (a) pitch (b) module (c) diameter (d) number of teeth 193. The cam size depends upon (a) pitch circle (b) base circle (c) the cam circle enclosing the cam profile (d) operation speed of the cam (e) prime circle 194. The reference point on the follower for the purpose of tracing the cam profile is (a) trace point (b) pitch point (c) cam centre (d) base point ANSWERS Q.No Ans. a a a a d c a a d c Q.No Ans. c c c a d d b c b a PART B 2 MARKS 195. What is the function of the governor? [MS U. Nov 97] The function of the governor is to regulate the mean speed of an engine, When there are variations in the load (e.g) when the load on the engine increases Its speed decreases, therefore it becomes necessary to increase the supply to The supply of fuel. It is done by governor automatically What are centrifugal governors? The centrifugal governors are based on the balancing of centrifugal force On the rotating balls by an equal and opposite radial force known as the Controlling force. It consists of two balls of equal weight, which are attached to the arms Define height of a governor. [Bharathiyar Univ. Nov 97] It is a vertical distance from the centre of the ball to a point where The axes of the arms ((or) arms produced) intersect on the spindle Axis. It is denoted by. h 198. Define equilibrium speed. [MKU, Oct 97] It is the speed at which the governor balls, arms etc., are in complete Equilibrium and the sleeve does not tend to move upwards or downloads

19 199. What is a porter governor? [MU, April 2000] The porter governor is a modification of a watt s governor, With central load attached to the sleeve. The load moves up and down the Central spindle. This additional downward force increases the speed of Revolution required to enable the balls to rise to any predetermined level What is a hartnell governor? A hartnell governor is a spring loaded governor. It consists Of the frame. The frame is attached to the governor spindle and therefore Rotates with it. Each lever carries a ball at the end of the vertical arm OB and a roller at the end of the horizontal arm OR Define sensitiveness of governors? It is defined as the radio of difference between the maximum and minimum equilibrium speeds to the mean equilibrium speed N1 minimum equilibrium speed N2 maximum equilibrium speed N1+N2 N= sensitiveness of the governor=n2-n1 2(N2-N1) = N N1+N2 2(ω2- ω1) = ω1+ ω Define Hunting of a governor? [AU,DEC-12] A governor is said to be hunt if the speed of the engine fluctuates continuously above and below the mean speed. This is caused by a too Sensitive governor which changes the fuel supply by a large amount when a Small change in the speed of rotation takes place Define effort of a governor. The effort of a governor is the mean force exerted at the sleeve For a given percentage change of speed Define power of governor. The power of a governor is the work done at the sleeve for a given Percentage change of speed Define power of governor. [MKU, Oct 97] The power of a governor is the work done at the sleeve for a given percentage change of speed. Power=Mean effort*lift of sleeve 206. What is a controlling force diagram? When the graph between the controlling force (Fc) as Ordinate and radius of rotation of the balls(r) as abscissa is drawn Then the graph obtained is known as controlling force diagram Define controlling force. When a body rotates in a circular path, there is an Inward radial force or centripetal force acting on it. In case of a governor running at a steady speed, the inward force acting on the Rotating balls is known as controlling force. It is equal and opposite To centrifugal reaction. Fc=m. ω2r

20 208. What is co-efficient of Insensitiveness? Generally we have assumed the governor to be frictionless. In Actual practice there is always friction in the joints and operating mechanism of the governor. Since the frictional force always acts in the opposite direction To that of motion, therefore when the speed of rotation decreases, the friction Prevents the downward movement of the sleeve and the radial inward Movement of the balls. N -N The ratio is called co-efficient of insensitiveness N of governor What is centripetal acceleration and its magnitude? [MS U. Nov 97] The acceleration of a particle at any instant moving Along a circular path in a direction normal to the tangent at That instant and directed towards the center of the circular Path is called centripetal acceleration An= ω 2r Total acceleration a= (at)2+(an)2. Where an= normal acceleration and at=tangential acceleration 210. What is active force? [Bharathiyar Univ. Nov 97] When a body moves along a curved path with a uniform Linear velocity, a force in the direction of centripetal acceleration Has to be applied externally over the body, so that it moves along The required path. This external force is known as active force What is Reactive Force? [MU, April 2000] When a body itself is moving with uniform linear velocity Along a circular path, it is subjected to the centrifugal force radially Outwards. This centrifugal force is called reactive force Define gyroscopic acceleration. If the angular velocity of the disc changes the direction but Remains constant in magnitude, than angular acceleration of the Disk is given by Άc= ω *dө ---= w.wp dt 213. What is reactive gyroscopic couple? [AU. May 2004] When the axis of spin itself moves with angular velocity Wp the disk is subjected to reactive couple. This reactive couple to which the disc is subjected, when the axis Of spin rotates about the axis of precession is known as Reactive gyroscopic couple What is balancing couple? Balancing couple = m.g.h sinө The balancing couple acts in clockwise direction when seen From the front of the vehicle How governors are classified?[au May-11] 1. centrifugal governors (a) Pendulum type: Example: Watt governor (b)gravity controlled type: Example: porter and proell governors (c) Spring controlled type: Example: Hartnell and Hartung governors. 2. Inertia governors What is gyroscopes? [Au May-11] Whenever a rotating body changes its axis of rotation, a couple is applied on the rotating body(shaft). This couple is known as gyroscopes.