Define free , forced and damped vibrations

1. When the loaded sleeve moves up and down along the spindle, the frictional force acts on it in a direction OPPOSITE to that of motion of sleeve.

2. What is a Hartnell governor?

i. A Hartnell governor is a spring loaded governor. It consists of two bell crank levers pivoted at the points O, O to 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.

3. What is a Hartung governor?

i. In this type of governor, the vertical arms of the bell crank levers are fitted with spring balls which compress against the frame of the governor when the rollers at the horizontal arm press against the sleeve. It is a spring controlled governor.

4. What is a Wilson-Hartnell governor?

i. A Wilson-Hartnell governor is a governor in which the balls are connected by a spring in tension. An auxiliary spring is attached to the sleeve mechanism through a lever by means of which the equilibrium speed for a given radius may be adjusted.

5. What is a pickering governor?

i. A pickering governor consists of three straight leaf springs arranged at equal angular intervals round the spindle. Each spring carries a weight at the center. The weight moves outwards and the spring bend as they rotate about the spindle axis with increasing speed. It is mostly used for driving gramophone.

6. Define sensitiveness of governors?

i. It is defined as the ratio of difference between the maximum and minimum equilibrium speeds to the mean equilibrium speed.

7. Define stability of governors?

i. A governor is said to be stable, when for every speed within the working range, there is a definite configuration (ie) there is only one radius of rotation of the governor balls at which the governor is in equilibrium. For a stable governor, if the equilibrium speed increases, the radius of the governor balls must also increase.

8. A governor is said to be unstable if the radius of the rotation DECREASES as the speed INCREASES.

9. Define isochronous governors.

i. A governor is said to be isochronous, when the equilibrium speed is constant, for all radii of rotation of the balls within the working range, neglecting friction. The isochronisms is the state of infinite sensitivity.

10. Define Hunting of a governor?

i. 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.

11. Define effort of a governor?

i. The effort of a governor is the mean force exerted at the sleeve for a given percentage change of speed.

12. Define power of a governor?

i. The power of a governor is the work done at the sleeve for a given percentage change of speed.

ii. Power = Mean effort * lift of sleeve.

13. Write down the expression for governor effort and power of a porter governor?

i. Governor effort = [ 2m/(1+q) + M ] C * g

ii. Governor power = 4C^2/1+2C [m + M/2 + 1+q] g *h

14. Where C is the % change of speed.

15. What is a controlling force diagram?

i. 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.

16. Define Controlling force.

i. 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.w^2 r

17. What is co-efficient of Insensitiveness?

i. 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.

The ratio N-N/N is called co-efficient of insensitiveness of governor.

18. When the sleeve of a porter governor moves upwards, the governor speed INCREASES

19. A Hartnell governor is a SPRING LOADED GOVERNOR.

20. PICKERING GOVERNOR is used to drive a gramophone.

21. In a Hartnell governor if a spring of greater stiffness is used, then the governor will be LESS SENSITIVE.

22. Name any four spring loaded governors?

Hartnell governor.

Hartung governor.

Wilson Hartnell governor.

Pickering governor.

23. What is viscous damping?

i. When the frictional resistance (damping) to the motion of the body is directly propotional to the speed of the movement, it is called viscous damping.

24. Define Simple Harmonic Motion.

i. A periodic motion of a particle whose acceleration is always directly towards the mean position and is propotional to its distance from the mean position, is known as S.H.M

25. What is amplitude?

i. The maximum displacement of a vibrating body from the mean position.

26. Define particle motion, time period and frequency.

i. A motion which repeats itself after equal intervals of time is known as periodic motion.

ii. Time taken to complete one cycle is called time period Tp.

27. What is Resonance?

i. Resonance occurs when the frequency of the external force equal to the natural frequency of vibration of the system.The amplitude of vibration at resonance becomes excessive.

28. Define Damping.

i. It is the resistance to the motion of vibrating body.

29. Explain about degree of freedom?

i. A system has n degree of freedom, if it needs n independent variables to specify completely the configuration of the system at any instant.

30. Define single degree of freedom.

i. A mass supported by a spring and constrained to move in one direction without rotation is a single degree of freedom system.

31. EXAMPLE:

Simple pendulum oscillating in one plane.A crank slider mechanism, since only the crank angle is sufficient to define the system completely.

32. Define period of vibration or time period?

i. The time period after which the motion repeats itself is time period .It is expressed in seconds (S).

33. Define a cycle?

i. Motion completed during one time period.

34. What is frequency?

i. The number of cycles described in one second.Unit : Hz (hertz)

35. What are the types of vibratory motion?

i. Free or natural vibrations.

ii. Forced vibrations

iii. Damped vibrations.

1. Define gyroscopic acceleration

If the angular velocity of the disc changes the direction but remains constant in magnitude, then angular acceleration of the disc is given by

c = * d/dt = * P

36. The angular acceleration c is known as gyroscopic acceleration.

2. What is reactive gyroscopic couple?

37. When the axis of spin itself moves with angular velocity P the disc 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.

3. What are the applications of gyroscopic couple?

38. The gyroscopic couple is usually applied through the bearings which support the shaft.

39. The gyroscopic principle is used in an instrument or toy known as gyroscopic.

40. They are installed in ships in order to minimize the rolling and pitching effects of waves.

41. They are used in aero planes, monorails cars, gyrocompasses etc.

4. Write down the expressions for gyroscopic couple acting on the aero plane

42. C = I * * P

43. Where I= mass moment of inertia.

44. = angular velocity of the engine

45. P = angular velocity of the precession = V/R rad/sec.

5. When the engine or propeller rotates in anticlockwise direction when viewed from the rear or tail end and aero plane takes a left turn, then the effect of reactive gyroscopic couple will be

46. Ans: to dip the nose and raise the tail of the aero plane.

6. The front end of the ship is called __________ and the rear end is known as _________

47. Ans: bow, (stern or aft).

7. The left hand and the right hand sides of the ship when viewed from the stern is called ________ and _______

48. Ans: port and starboard.

8. What are the different types of motions of a naval ship, while considering gyroscopic couple?

49. Steering.

50. Pitching.

51. Rolling.

9. Define steering.

52. Steering is the turning of a complete ship in a curve towards left or right while it moves forward.

10. Define pitching.

53. Pitching is the movement of a complete ship up and down in a vertical plane about transverse axis. The pitching of the ship is assumed to take place with SHM i.e. the motion of the axis of spin about transverse axis is simple harmonic.

11. Write down the expressions for maximum angular velocity of precession and maximum gyroscopic couple.

54. Pmax = * 1 = * ( 2 / tp )

55. Cmax = I* * Pmax 12. The maximum gyroscopic couple tends to shear the ________during pitching.

56. Ans: holding down bolts.

13. The angular acceleration during pitching is given by_______

57. Ans: = d / dt = - (1 ) sin 1 t

14. The angular acceleration is maximum if _________

58. Ans: sin 1 t = 1

15. Maximum angular acceleration during pitching is __________

59. Ans: max = - (1 )

16. Write the effect of gyroscopic couple during rolling of a ship.

60. In case of rolling of a ship, the axis of precession is parallel to the axis of spin for all positions. Hence there is no effect of the gyroscopic couple acting on the body of the ship.

17. What is the condition for the effect of gyroscopic couple to occur?

61. The axis of precession should always be perpendicular to the axis of spin.

18. What is the effect of centrifugal force acting on a four wheel drive?

62. Since the vehicle moves along a curved path, centrifugal force will act outwardly at the centre of gravity of the vehicle. The effort of this centrifugal force is to overturn the vehicle.

63. Fc = mV / R

19. Define angle of heel.

64. It is the inclination of the vehicle to the vertical for equilibrium.

20. What is balancing couple?

65. Balancing couple = m.g.h sin

66. The balancing couple acts in clockwise direction when seen from the front of the vehicle.

21. A disc is spinning with an angular velocity rad/sec about the axis of spin. The couple applied to disc causing precession will be __________

67. Ans: I. . P

22. The engine of an aero plane rotates in clockwise direction when seen from the tail end and the aero plane takes a turn to left. The effect of gyroscopic couple on the aero plane will be _________

68. Ans: to raise the nose and dip the tail.

23. A motor car moving at a certain speed takes a left turn in a curved path. If the engine rotates in the same direction as that of wheels due to centrifugal force _________

69. Ans: the reaction on the outer wheels increases and on the inner wheel decreases.

24. Define kinematics of machines.

70. It is that branch of theory of machines which deals with the relative motion between various parts of the machines.

25. Define dynamics of machines.

71. It is that branch of theory of machines which deals with forces and their effects while acting upon the machine parts in motion.

26. Define kinetics.

72. It is that branch of theory of machines which deals with the inertia forces which arise from the combined effect of the mass and motion of the machine parts.

27. Define statics.

73. It is that part of theory of machines which deals with the force and their effects while the machine parts are at rest.

28. The three vectors in a gyroscopic which are mutually perpendicular are _________, __________ and _________.

74. Ans: axis of precession, axis of spin and axis of reactive gyroscopic couple.

29. There will be no effect of gyroscopic couple acting on the body of a ship due to rolling. Why

75. Since the axis of the precession becomes parallel to the axis of spin, there will be no effect of the gyroscopic couple acting on the body of the ship, during rolling.

76. Governor

1. What is the function of the governor?

77. The function of the governor is to regulate the mean speed of an engine, when there are variations in the load (eg) when the load on the engine increases, its speed decreases, therefore it becomes necessary to increase the supply of fuel. It is done by governor automatically.

2. What are the types of governors?

78. Centrifugal governor

79. Inertia governor.

3. What are centrifugal governors?

80. 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.

4. When the balls rotate at uniform speed, controlling force is equal to the _______ and they _________

81. Ans: centrifugal force, balance each other.

5. Define height of a governor.

82. It is a vertical distance from the centre of the ball to a point where the axes of the arms

83. ((Or) arms produced) intersect on the spindle axis. It is denoted by `h.

6. Define equilibrium speed.

84. 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 downwards.

7. Define mean equilibrium speed.

85. It is the speed at the mean position of the balls or the sleeve.

8. Define maximum and minimum equilibrium speeds.

86. The speed at the maximum and minimum radius of rotation of the balls, without tending to move either way are known as maximum and minimum speeds.

9. What is sleeve lift?

87. It is the vertical distance which the sleeve travels due o change in equilibrium speed.

10. Write down the expression for finding the height of a watt governor.

88. h= 895 / N metres.

89. Where h ( height of the governor

90. N( Speed in r.p.m.

11. What is a porter governor?

91. The porter governor is a modification of a watts governor, with central load attached to the sleeve. The load moves up and down the central spindle. This additional

92. Define free, forced and damped vibrations?

93. Forced vibrations: when a body vibrates under the influence of external force, the body is said to be under forced vibrations

94. Free vibrations: the body is said to be under free vibrations, when no external force acts on the body, after providing an initial displacement.

95. Damped vibrations: when there is a reduction in amplitude over every cycle of vibration, the motion is said to be damped vibrations.

96. What are the types of free vibrations?

97. Longitudinal vibrations

98. Transverse vibrations

99. Torsional vibrations

100. Explain longitudinal transverse and torsional vibrations?

101. Longitudinal vibrations: When the particles of a shaft moves parallel to axis of the shaft, then vibrations are called longitudinal vibrations.

102. Transverse vibrations: When the particles of the shaft move perpendicular to axis of the shaft, then the vibrations are known as transverse vibrations.

103. Torsional vibrations: When the particles of the shaft move in a circle about the axis of the shaft, then the vibrations are known as torsional vibrations.

104. What are the methods for finding out natural frequency of free longitudinal vibrations?

105. Equilibrium method

106. Energy method

107. Rayleighs method

108. Explain Energy method?

1. In this method, summation of kinetic energy (K.E) and potential energy (P.E) must be a quantity, which is same at all, times.

ii. d/dt (K.E+P.E) = 0

109. Explain Rayleighs method?

i. In this method, the maximum kinetic energy at mean position is equal to the max. Potential energy (strain energy) at extreme position.

110. Give the formula for natural frequency of free longitudinal and transverse vibrations?

i. F n = 0.4985 / (( ---- Static deflection

111. What is the effect of constraints inertia in longitudinal and transverse vibrations?

In longitudinal vibrationsi. Natural frequency, fn = 1/ 2( ((s)/(m+m /3)

112. Where m--- mass of the disc ,

113. m --- mass of constraint(shaft)

s --- stiffness

114. In transverse vibrations

1. Natural Frequency, fn = 1/2( (s/(m+33mc /140)

115. Name the methods employed in determining the natural frequency of free vibrations for a shaft subjected to number of point loads.

Energy method

Dunkerleys method

116. Give the formula for Dunkerlys method.

117. Fn= 0.4985/ (((1+(2+(3++(s/1.27)

Where (1,(2, (3 are the static deflections due to point loads at W1, W2 , W3 and W ; (s = static deflection due to uniformly distributed load

118. Define whirling speed or critical speed of a shaft?

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.

119. Give the formula for finding out the whirling speed?

120. Nc = 0.4985/(( r.p.s also ( Nc / N)2 =1+ e/y

121. N = critical speed or whirling speed in r.p.s N = speed of shaft in r.p.s

122. ( = static deflection in m e = eccentricity in m

123. y = additional deflection in m

124. what are the types of damping

over damping -----> (c/2m)2 >s/m ;under damping ----> s/m>(c/2m)2critical damping ------> (c/2m)2 =s/m

where c = damping coefficient m= mass of spring and s = stiffness of spring

125. Define damping factor or damping ratio.

i. The ratio of actual damping coefficient to critical damping coefficient is known as damping factor

126. It is equal to C/Cc127. Define logarithmic decrement.

It is defined as the natural logarithm of the amplitude reduction factor. The amplitude reduction factor is ratio of any 2 successive amplitudes on same side of the mean position.

128. How frequency of under damped forced vibrations are determined?

129. Differential equation method

130. Graphical method

131. Define magnification factor or dynamic magnifier?

132. D = xmax/ x0 .It is the ratio of maximum displacement x of the forced vibration to deflection (x0 ) due to the static force F.

133. What is isolation factor transmissibility ratio?

134. The ratio of force transmitted (FT ) to the force applied (F) is known as isolation factor.

135. Give the formula for natural frequency of free torsional vibrations?

136. fn = 1 / 2( ((q/I)

137. where q torsional stiffness Imass moment of inertia

138. what is the effect of inertia of constraint torsional vibrations?

139. Fn = 1/2( ((q/(I+Ic/3)

I----mass moment of inertia

140. q--- torsional stiffness

141. Ic ---- total mass moment of inertia of constant shaft

142. Define node.

143. The point or section of the shift whose amplitude of torsional vibration is zero is known as node.

144. What are free torsional vibrations of two-rotor system?

i. When two rotors A and B are rotating on two extreme ends of a shaft in opposite direction,

fnA = fnB145. In this system, torsional vibrations occurs only when the two rotors A and B move in opposite directions

146. What are the conditions of two-rotor system?

147. FnA = fnB148. (b) l = lA + lB149. Where lA ---- distance of node from rotor A

lB ----- distance of node from rotor B

150. fnA , fnB ---- frequency of torsional vibrations for rotor A and B

151. What are free torsional vibrations of three-rotor system?

152. Here the two rotors rotate in one direction and the third rotor rotates in opposite direction with the same frequency.

153. What are the conditions to be satisfied by equivalent system?

154. The kinetic energy of equivalent system must be equal to kinetic energy of original system

155. The strain energy of equivalent system must be equal to strain energy of original system.

156. At a nodded point in a shaft, the amplitude of torsional vibration is zero

157. A shaft carrying two-rotor s at its ends will have one node

158. When a body is subjected to transverse vibrations, the stress induced will be tensile stress

159. What are the factors affecting critical speed of a shaft?

160. Diameter of disc

161. Span of shaft

162. Eccentricity

163. If the roots of equation of motion for a vibrating system are real, then the system will be over damped

164. In vibration isolation system, if w/wn < (2 ,then for all values of damping factor, the transmissibility will be greater than unity

165. In under damped vibration system, if x and x are successive values of amplitude on same side of mean position, then logarithmic decrement is ( = ln (x1/x2)