Dynamics of Machines R 2017

1. Unit V
MECHANISM FOR CONTROL
DYNAMICS OF MACHINES
MECHANISM FOR CONTROL
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B.K.Parrthipan, M.E., M.B.A., (Ph.D).,
Assistant Professor / Mechanical Engineering
Kamaraj College of Engineering and Technology.

2. Governor
• Governor is a device which is used to regulate the mean speed
of an engine, when there are variations in the load.
• when the load on an engine increases, its speed decreases,
therefore it becomes necessary to increase the supply of
working fluid.working fluid.
• On the other hand, when the load on the engine decreases, its
speed increases and thus less working fluid is required.
• The governor automatically controls the supply of working
fluid to the engine with the varying load conditions and keeps
the mean speed within certain limits.
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3. The governors are broadly classified as
1. Centrifugal governors and
2. Inertia governors.
Governor - types
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4. Centrifugal Governor
In these governors, the change in centrifugal forces of the
rotating masses due to change in the speed of the engine is
utilized for movement of the governor sleeve. These governors
are commonly used because of simplicity in operation.
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5. Centrifugal Governor
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6. Gravity Controlled Centrifugal
Governors
In this type of governors there is gravity force due to weight
on the sleeve or weight of sleeve itself which controls
movement of the sleeve. These governors are comparatively
larger in size.larger in size.
(a) Watt governor
(b) Porter governor
(c) Proell governor
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7. Spring Controlled Centrifugal
Governors
In these governors, a helical spring or several springs are
utilized to control the movement of sleeve or balls. These
governors are comparatively smaller in size.
(a) Hartnell governor
(b) Wilson-Hartnell governor
(c) Hartung governor
(d) Pickering governor
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8. Terms used in Governors
• Height of a governor.
It is the 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 usually denoted by h.
• Equilibrium speed.• Equilibrium speed.
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.
• Mean equilibrium speed.
It is the speed at the mean position of the balls or the sleeve.
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9. Terms used in Governors
• Maximum and minimum equilibrium speeds.
The speeds at the maximum and minimum radius of rotation
of the balls, without tending to move either way are known as
maximum and minimum equilibrium speeds respectively.
• Sleeve lift.• Sleeve lift.
It is the vertical distance which the sleeve travels due to
change in equilibrium speed.
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10. Watt Governor
It is basically a conical pendulum with links attached to a
sleeve of negligible mass. The arms of the governor may be
connected to the spindle in the following three ways :
1. The pivot P, may be on the spindle axis as shown in Fig.(a).
2. The pivot P, may be offset from the spindle axis and the arms
when produced intersect at O, as shown in Fig.(b).
3. The pivot P, may be offset, but the arms cross the axis at O, as3. The pivot P, may be offset, but the arms cross the axis at O, as
shown in Fig.(c).
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11. Watt Governor
Let
m = Mass of the ball in kg,
w = Weight of the ball in newtons = m.g,
T = Tension in the arm in newtons,
ω = Angular velocity of the arm and ball about the spindle axis in
rad/s,rad/s,
r = Radius of the path of rotation of the ball
FC = Centrifugal force acting on the ball in newtons = m ω 2r
h = Height of the governor in metres.
It is assumed that the weight of the arms, links and the sleeve are
negligible as compared to the weight of the balls.
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12. Watt Governor
Now, the ball is in equilibrium under the action of
1. the centrifugal force (FC) acting on the ball,
2. the tension (T) in the arm, and
3. the weight (w) of the ball.
Taking moments about point O, we haveTaking moments about point O, we have
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13. Porter Governor
• The Porter governor is a modification of a Watt’s governor,
with central load attached to the sleeve as shown in Fig. (a).
• 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.required to enable the balls to rise to any predetermined level.
• Consider the forces acting on one-half of the governor as
shown in Fig. (b).
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14. Porter Governor
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Though there are several ways of determining the relation between
the height of the governor (h) and the speed of the balls (N), yet
the following two methods are important
1. Method of resolution of forces and
2. Instantaneous centre method.

15. Porter Governor
m = Mass of each ball in kg,
w = Weight of each ball in newtons = m.g,
M = Mass of the central load in kg,
and
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W = Weight of the central load in newtons = M.g,
r = Radius of rotation in metres,
h = Height of governor in metres ,
N = Speed of the balls in r.p.m .,
F = Frictional force
α= Angle of inclination of the arm (or upper link) to the
vertical, and
β = Angle of inclination of the link (or lower link) to the
vertical.

16. Proell Governor
• The Proell governor has the balls fixed at B and C
to the extension of the links DF and EG, as shown
in Fig. (a).
• The arms FP and GQ are pivoted at P and Q
respectively. Consider the equilibrium of therespectively. Consider the equilibrium of the
forces on one-half of the governor as shown in
Fig. (b).
• The instantaneous centre (I) lies on the
intersection of the line PF produced and the line
from D drawn perpendicular to the spindle axis.
The perpendicular BM is drawn on ID.
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17. Proell Governor
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18. Hartnell Governor
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19. Hartung Governor
• A spring controlled governor of the Hartung
type is shown in Fig. (a).
• In this type of governor, the vertical arms of
the bell crank levers are fitted with spring ballsthe 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.
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20. Hartung Governor
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S = Spring force,
FC = Centrifugal force,
M = Mass on the sleeve, and
x and y = Lengths of the vertical and horizontal arm of the bell
crank lever respectively.

21. Wilson-Hartnell Governor
• A Wilson-Hartnell governor is a governor in
which the balls are connected by a spring in
tension as shown in Fig.
• An auxiliary spring is attached to the sleeve
mechanism through a lever by means of which themechanism through a lever by means of which the
equilibrium speed for a given radius may be
adjusted.
• The main spring may be considered of two equal
parts each belonging to both the balls. The line
diagram of a Wilson- Hartnell governor is shown
in Fig.
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22. Wilson-Hartnell Governor
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23. Wilson-Hartnell Governor
P = Tension in the main spring or ball spring A,
S = Tension in the auxiliary spring B,
m = Mass of each ball,m = Mass of each ball,
M = Mass of sleeve,
Sb = Stiffness of each ball spring,
Sa = Stiffness of auxiliary spring,
FC = Centrifugal force of each ball, and
r = Radius of rotation of balls,
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24. Pickering Governor
• A Pickering governor is mostly used for driving gramophone. It
consists of three straight leaf springs arranged at equal angular
intervals round the spindle.
• Each spring carries a weight at the centre. The weights move
outwards and the springs bend as they rotate about the spindle axis
with increasing speed.with increasing speed.
• In Fig. (a), the governor is at rest. When the governor rotates, the
springs together with the weights are deflected as shown in Fig. (b).
The upper end of the spring is attached by a screw to hexagonal nut
fixed to the governor spindle.
• The lower end of the spring is attached to a sleeve which is free to
slide on the spindle. The spindle runs in a bearing at each end and is
driven through gearing by the motor. The sleeve can rise until it
reaches a stop, whose position is adjustable.
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25. Pickering Governor
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26. Pickering Governor
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m = Mass attached at the centre of the leaf spring,
a = Distance from the spindle axis to the centre of gravity of the mass,
when the governor is at rest,
ω = Angular speed of the governor spindle,
δ = Deflection of the centre of the leaf spring at angular speed , when
the governor is rotating

27. Characteristics of Governors
Sensitiveness
Sensitiveness is the ratio of the difference between the
maximum and minimum equilibrium speeds to the mean
equilibrium speed.
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28. Iso chronism
A governor is said to be isochronous if equilibrium speed is
constant for all the radii of rotation in the working range.
Hunting
A governor is said to be hunt if the speed of the engine
fluctuates continuously above and below the mean speed. This
Characteristics of Governors
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.
Stability
A governor is said to be stable when there is one radius of
rotation of the balls for each speed which is within the speed
range of the governor.
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29. Characteristics of Governors
Effort
The effort of a governor is the mean force exerted at the sleeve
for a given percentage change of speed. (or lift of the sleeve).
Power
The power of a governor is the work done at the sleeve for aThe power of a governor is the work done at the sleeve for a
given percentage change of speed. It is the product of the mean
value of the effort and the distance through which the sleeve
moves.
Power = Mean effort × lift of sleeve
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30. Controlling Force
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 the centrifugal reaction.
Controlling force, FC = mω2r
When the graph between the controlling force (FC) as ordinate
and radius of rotation of the balls (r) as abscissa is drawn, thenand radius of rotation of the balls (r) as abscissa is drawn, then
the graph obtained is known as controlling force diagram.
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31. Controlling Force Diagram for Spring-
Controlled Governors
The controlling force diagram for the
spring controlled governors is a straight
line.
1. The relation between the controlling1. The relation between the controlling
force (FC) and the radius of rotation (r) for
the stability of spring controlled
governors is given by the following
equation
FC = ar – b
where a and b are constants.
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32. Controlling Force Diagram for Spring-
Controlled Governors
2. The relation between the controlling
force and the radius of rotation, for an
isochronous governor is,
FC = a.rFC = a.r
3. A governor is said to be unstable and
the relation between the controlling force
and the radius of rotation is,
FC = a.r + b
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33. Gyroscope
• A gyroscope is a device for measuring or maintaining orientation,
based on the principles of angularmomentum.
• Mechanically, a gyroscope is a spinning wheel or disk in which the
axle is free to assume any orientation. Although this orientation
does not remain fixed, it changes in response to an external torque
much less and in a different direction than it would without the
large angular momentum associated with the disk's high rate of spinlarge angular momentum associated with the disk's high rate of spin
and moment of inertia.
• Since external torque is
minimized by mounting the
device in gimbals, its
orientation remains nearly
fixed, regardless of any
motion of the platform on
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34. PrecessionalAngularMotion
(Vectorial representation of angularmotion)
• Weknow that the angularaccelerationisthe rate of changeof
angularvelocity with respect totime.
• It isavector quantity and maybe represented by drawingavector
diagramwith the help of right handscrewrule.
• Consider a disc, asshown in Fig. (a), revolving or spinning about the axis OX
(known as axis of spin) in anticlockwise when seenfrom the front, with an
angularvelocity in aplane at right anglesto thepaper.
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35. • After ashort interval of time t,letthediscbespinningaboutthenewaxisofspin
OX’(atan angleδθ ) with anangular velocity (ω +δω).
• Usingthe right handscrewrule, initial angularvelocity of the discω isrepresented by
vector ox;and thefinalangular velocityofthedisc(ω +δω )is represented by vector ox’as
showninFig.(b).
• Thevectorxx’representsthechange ofangular velocity in time δt i.e.theangular acceleration
ofthedisc.Thismay beresolvedintotwocomponents,oneparallel to oxandtheother
perpendiculartoox.
5
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36. • where dθ/dtistheangularvelocityoftheaxis ofspinabouta certainaxis,
whichis perpendiculartothe plane in which the axis of spin is going to
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38. GyroscopicCouple
• Consideradiscspinning with anangular velocity ωrad/s about the axisofspin OX,
inanticlockwisedirectionwhenseenfromthefront,asshowninFig.
• SincetheplaneinwhichthediscisrotatingisparalleltotheplaneYOZthereforeit iscalled
planeofspinning.
The plane XOZ is a horizontal plane and the
axis of spin rotates in a plane parallel to the
horizontalplaneabout an axisOY.
Inotherwords,theaxis ofspin is said tobe
rotatingor processingabout an axisOY.
In otherwords,theaxisofspin is said tobe
rotatingabout an axisOY(whichis
perpendiculartoboththeaxes OX and OZ)at
an angular velocityωprad/s.
ThishorizontalplaneXOZis calledplaneof
precessionand OYis theaxis ofprecession.
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39. • Sincethe angular momentum isavector quantity, therefore itmaybe represented
by the vector OX,as shown inFig.
• TheaxisofspinOXisalsorotatinganticlockwisewhenseenfromthetopaboutthe axisOY.
• Lettheaxis OX isturnedintheplaneXOZthrougha smallangle δθ radianstothe position
OX',intimeδt seconds.Assumingtheangularvelocityωtobeconstant,the angularmomentum
willnowberepresentedbyvectorOX’.
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40. where ω = Angular velocity of precession of the axiswhere ωp= Angular velocity of precession of the axis
of spin or the speed of rotation of the axis of spin
about the axisof precessionOY.
In S.I.units, the units of CisN-mwhenIisin kg-m2.
Relationship between force
(F),torque (τ), momentum
(p), and angularmomentum
(L)vectors in arotating
system,r= Positionvector
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41. Effectof the Gyroscopic Couple on an
Aero-plane
• Thetop andfront view of anaero-plane areshown in Fig.
• Letengineorpropellerrotates in the clockwise direction whenseenfrom the rear or tail
end andthe aero-plane takesaturn to the left.
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42. Effectof the Gyroscopic Couple on an
Aero-plane
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43. Effectof the Gyroscopic Couple on an
Aero-plane
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44. • Thetop and front viewsof anavalship are shown in Fig. Thefore
end of the ship iscalled bow and therearend is known as sternor
aft.Thelefthandandrighthandsidesoftheship,when viewed from
the stern are called portand star-boardrespectively.
• Theeffect of gyroscopiccouple on the navalship will occur in the
Effectof the Gyroscopic Couple on a
Navel Ship
• Theeffect of gyroscopiccouple on the navalship will occur in the
following threecases:
1. Steering
2. Pitching, and
3. Rolling
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45. Effect of Gyroscopic Couple on a Naval
Ship during Steering
• Steering is the turning of a complete ship in a curve towards left or
right, while itmovesforward.
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46. Effectof Gyroscopic Couple on a Naval Ship
during Steering
S. No. View Point
Direction of
rotor direction
Turn Effect
1 Stern Clockwise Left Bow raised Stern depressed
2 Stern Clockwise Right Bow depressed Stern raised2 Stern Clockwise Right Bow depressed Stern raised
3 Stern Anticlockwise Left Bow depressed Stern raised
4 Stern Anticlockwise Right Bow raised Stern depressed
5 Bow Anticlockwise Left Bow raised Stern depressed
6 Bow Anticlockwise Right Bow depressed Stern raised
7 Bow Clockwise Left Bow depressed Stern raised
8 Bow Clockwise Right Bow raised Stern depressed
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47. Effectof Gyroscopic Couple on a Naval
Ship duringPitching
• Pitching is the movement of acomplete ship up
and down in avertical plane about transverse axis,
asshown in Fig.
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49. Effectof Gyroscopic Couple on a Naval Ship
duringPitching
S. No. Pitching View Point
Direction of
rotor direction
Effect
1 Upward Stern Clockwise Ship turn towards star board side
2 Upward Stern Anticlockwise Ship turn towards port side
3 Upward Bow Clockwise Ship turn towards port side
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3 Upward Bow Clockwise Ship turn towards port side
4 Upward Bow Anticlockwise Ship turn towards star board side
5 Downward Stern Clockwise Ship turn towards port side
6 Downward Stern Anticlockwise Ship turn towards star board side
7 Downward Bow Clockwise Ship turn towards star board side
8 Downward Bow Anticlockwise Ship turn towards port side

50. Effectof Gyroscopic Couple on a Naval
Ship duringRolling
• We know that, for the effect of gyroscopic couple to occur, the axis
of precessionshould alwaysbe perpendicular to the axisofspin.
• If, however, the axis of precession becomes parallel to the axis of
spin, there will be no effect of the gyroscopic couple acting on
the body of theship.the body of theship.
• In caseof rolling of aship, the axis of precession (i.e.longitudinal
axis)isalwaysparalleltothe axisof spin for all positions.
• Hence, there is no effect of the gyroscopic couple acting on the
body of aship during rolling.
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