Unit - 5

ME 2302

DEPARTMENT OF MECHANICAL ENGINEERING

G.SARAVANANASSISTANT PROFESSORDEPARTMENT OF AERONAUTICAL

DYNAMICS OF MACHINERY

GOVERNORS A N D GYROSCOPES

UNIT – 5 MECHANISMS OF CONTROL

Governors

The first governor was designed by James Watt in 1788

A Governor is a feedback device on a machine or engine that is used to provide automatic control, as of speed, pressure, or temperature, when there are variation in load.

CLASSIFICATION OF GOVERNORS

Governors

Centrifugal governors Inertia governors

pendulum type loaded type

watt governor

gravity controlled spring controlled

Porter proell Hartnell hartung wilson pickering

governor governor governor governor hartnell governor

governor

CENTRIFUGAL GOVERNORS

A Centrifugal Governor (also known as Watt or fly-ball governor) is a specific type of governor, that controls the speed of an engine, by regulating the fuel admitted.

In the centrifugal type governors, rotation of the crank shaft is taken to a vertical spindle through suitable gears.

CENTRIFUGAL GOVERNORS

It consists of two balls of equal mass, which are attached to the arms. these balls are know as governor balls or fly balls.

The upper arms are keyed to the spindle and the lower arms which are known as links are connected to sleeve.

The sleeve surrounds the spindle and rotate as well as slide over the spindle. One end of a bell–crank lever is attached to the sleeve and the other end to a rod which actuates the fuel supply valve.

IMAGE: CENTRIFUGAL GOVERNOR

Principle of working

The centrifugal governors are based on the balancing of centrifugal force on the rotating balls by an equal and opposite radial force.

When the load on the engine decreases, the engine and governor speed increases.

This increases the centrifugal force acting on the balls and the balls move radially outwards. Therefore the sleeve rises upward.

Principle of working

This upward movement of the sleeve reduce the supply of the working fluid and hence the speed is decreased.

Similarly, when the load increases, the speed of the engine and governor decreases, this decreases the centrifugal force on the balls. hence the balls move inwards and sleeve moves downwards.

The downward movement of the sleeve increases the supply of the working fluid and hence the is increased.

CENTRIFUGAL GOVERNOR

Centrifugal force

FC=m.ω2.r

where,

m- Mass of the fly balls

ω- Angular speed of the governor

r- Radius of rotation.

APPLICATIONS OF THE CENTRIFUGAL GOVERNOR

Governors are seen on steam engines, internal combustion engines and variously fueled turbines.

They are used in: Automobiles to restrict/maintain

engine RPM, total speed Governors protect engine from

excessive rotational speed Used in some high performance

cars to limit vehicle speed. Used in a spring-loaded record

player, and telephone dials to limit the speed.

Inertia governors

In inertia governor, the balls are so arranged that the inertia force caused by an angular acceleration or retardation of the shaft tend their positions.

This governor is more sensitive than the centrifugal ,but it becomes very difficult to completely balance the resolving parts

Watts governor(simple conical governor)

It is the simplest form of centrifugal governor.

Depending upon the position of the upper arms, it has three types

a) pinned arm.

b) open-arm.

c) cross-arm

WATT GOVERNOR

Fc*h=W*r= m.g.r

h=g/ω2 ω=2πN/60 and

g=9.81m/s2 h=895/N2

where,

r-radius of rotation in m

h-height of the governor in m

Fc-centrifugal force acting on the balls

W-weight of each ball in Newton's

FREE BODY DIAGRAM

GRAVITY CONTROLLED

PORTER GOVERNOR The porter

governor is the modification of a watts governor, which central load attached to the sleeve. This modification leads to larger centrifugal force

i.e, higher speed are needed to bring the fly balls to the same radius

PORTER GOVERNOR

h=(m+(M(1+q)/2)/2*895/N2

h=(m+M)/m*895/N2 (q= tanβ/ tanα =1)

FC=m.ω2.r

tan α=r/h

EFFECT OF FRICTION GOVERNORh=(m.g+[(M.g±F)/2](1+q)) /2*895/N2

h=(m.g+[(M.g±F)/2]) /2*895/N2 when q=1

FREE BODY DIAGRAM

PROELL GOVERNOR

The porter governor is knows as proell governor if the two balls are mounted on the extension of the link

this governor can be analyzed in the same way as the porter governor by locating instantaneous centre.

PROELL GOVERNOR

Fc=BM/EM[m.g*(IM/BM)+M.g/2[(IM/BM)+MC/BM]

N2=BM/EM[(m+M/2(1+q))/m]*895/N2

SPRING LOADED GOVERNOR

HARTNELL GOVERNER In this type of governor, the balls are controlled

by a spring. The spring is fitted in compression so that a

force is applied to the sleeve . Two bell-crank levers, each carrying a mass at

one end and roller at the other end, are pivoted to a pair of arm which rotate with the spindle.


Hartnell governor working When speed increases, balls

move outward compelling the sleeve to slide on the spindle upwards against force.

If the speed decreases, the

sleeve moves downwards. The spring force is adjusted with the help of a nut

The movement of the sleeve

is communicated to the throttle of the engine.


HARTNELL GOVERNOR

The various forces acting on left-half of the governor

1.centrifugal force ,

Fc= m.ω2.r, acting at ball a radially outwards

2.weight of the ball,

w=mg, acting downwards

3.Force[(M.g+S)/2]acting downwards at B

1.spring forces s1 and s1

M.g+S=2(a/b)FC

At minimum radius r1= M.g+S1=2(a/b)FC1

At maximum radiusr2= M.g+S2=2(a/b)FC2


Where,FC1= m.ω1

2.r1- and FC2= m.ω22.r2-

(r2-r1)/a=x/bSleeve lift x = (b/a)(r2-r1)

r1= r-(x/2)(a/b)

r2=r+(x/2)(a/b)stiffness, s=(S2-S1)/Xinitial compression of spring(δ)initial compression of spring,δ=(S1-0)/s=S1/s


HARTUNG GOVERNOR A spring controlled of the

hartung type consists of a frame which is keyed to the governor shaft.

The horizontal arms are connected to the sleeve and the vertical arms to the spring.

When speed increases the spring is under compression.

FC*a=S.a+(M.g)/2*b


WILSON-HARTNELL GOVERNOR

In this governor the bell-crank levers are pivoted at the end of two arms which rotate with the spindle.

The vertical arms of the bell crank lever support the balls and horizontal arms are attached to the sleeve through rollers

The two balls are connected by two main spring. When speed increases the ball move outward and the sleeve moves upward causing tension in both the springs.


Equivalent stiffness of the auxiliary spring

S=sa(b/a) 2

4sb + (sa/2)( y/x * b/a) 2 = (Fc2 – Fc1)/(r2 – r1)

Where, s - Tension in the auxiliary spring in Newton's, sb - stiffness of main spring in N/m,

sa - stiffness of auxiliary spring in N/m,

r - Radius of rotation of balls in meters, Fc - centrifugal force of each ball in Newton's


PICKERING GOVERNOR

Pickering governor is commonly used in clock and gramophane mechanisms, for speed adjustment.

It consists of central spindle and three straight leaf springs symmetrically

placed around it.

Each of the spring has a weight in the form of a disc attached to it at the centre.

Top end of the spring are rigidly fixed to the hexagonal nut and the lower end are connected with the sleeve suitable by means of screws.

When the speed increases ,the weight move outwards causing with bending in the springs

The controlling force against lift of the sleeve is provided by the leaf spring


PICKERING GOVERNOR

The central load (W) W = Fc = m ω2 (a + δ)

Maximum deflection of leaf spring δ = (W * L3)/(192*E*I)

The empirical relation between the sleeve lift and the deflection λ = ( 2.4*δ2 )/LWhere, ω – Angular velocity of the governor spindle in rad /s, δ – Deflection of the centre of the leaf spring at angular velocity λ - lift of the sleeve corresponding to the deflection in meters L – distance between the fixed ends of the spring in meters

GYROSCOPE

GYROSCOPE

INTRODUCTION Whenever a rotating body changes its

axis of rotation, a couple(torque) is applied on the rotating body. this couple is known as gyroscopic couple. The couple is applied on the bearing which support the rotating shaft. The reaction of couple will be equal and opposite on each bearing. the couple makes a change in the direction of angular velocity, but it does not change in magnitude of angular velocity.

GYROSCOPE

GYROSCOPIC ACCELERATION A body rotating in a plane about a

fixed axis is subjected to the angular acceleration. But whenever a rotating body changes its axis of rotation, the body will be subjected to both the angular acceleration and another acceleration which is called gyroscopic acceleration.

Gyroscopic acceleration(αc)=ω. ωp

Angular velocity(ωp)=dѳ/dt

GYROSCOPE

Notes1.The axis about which the axis of spin is to turn is

known as axis of precession.2.The angular motion of the axis of spin about the axis

of precession is known as precessional angular motion.

3.If the angular velocity of the disc remains constant at all position of the axis of spin, then dѳ/dt=0 and αc=0

4.If the angular velocity of the disc changes the direction, but remains constant on magnitude, then angular acceleration of disc is

αc =ω.dѳ/dt=ω.ωp

GYROSCOPIC COUPLE(TORQUE)

CONFIGURATION ox is known as the axis of spin oy is known as the axis precession. oz is known as the axis gyroscopic couple .Since the plane in which the disc is rotating is

parallel to the plane yoz, therefore plane yoz is called the plane of spinning.

The axis of spin is said to be rotating or processing about an axis oy at an angular velocity ωp rad/sec.This horizontal plane xoz is called the plane of precession .

The plane xoy is known as plane of couple.

GYROSCOPIC COUPLE

GYROSCOPIC COUPLE

DERIVATION change in angular momentum=ox’ - ox = xx’

xx’ =ox. δѳ=I.ω. δѳ Rate of change of angular momentum xx’ / δt= I.ω. δѳ/ δt = I.ω. dѳ/ δt Rate of change of angular momentum is known as

gyroscopic couple so we can write c = I.ω. dѳ/ δt = I. ω.ωp

Where, ox-Initial angular momentum, ox’-angular momentum after time δt, xx’-change in angular momentum in time δt

GYROSCOPE

The couple obtained about is that which is required to cause the axis of spin to precess in the horizontal plane is known as the active gyroscopic couple or the active couple

When the axis of spin itself moves with angular velocity ω,the disc is subjected to a reactive couple whose magnitude is same but in the direction to that of active couple. This reactive couple to which the disc is subjected when the axis of spin rotates about the axis of precession is known as reacting gyroscopic couple

GYROSCOPIC EFFECT IN AIRPLANES

s.no View point Direction of propeller rotation

turn effect

1 Rear end clockwise left Nose raised , tail depressed

2 Rear end Anti clockwise right Nose depressed , tail raised

3 Rear end Anti clockwise left Nose depressed , tail raised

4 Rear end Anti clockwise right Nose raised , tail depressed

5 Front end Anti clockwise left Nose depressed , tail raised

6 Front end Anti clockwise right Nose depressed , tail raised

7 Front end clockwise Left Nose depressed , tail raised

GYROSCOPIC EFFECT IN AIRPLANES

TERMS USED IN SHIPS

GYROSCOPIC EFFECT IN SHIPS

Sl,no View point Direction of rotor rotation

Turn effect

1 stern clockwise left Bow raised, stern depressed

2 stern clockwise right Bow depressed, stern raised

3 stern Anti clockwise left Bow depressed, stern raised

4 stern Anti clockwise right Bow raised, stern depressed

5 bow Anti clockwise left Bow raised, stern depressed

6 bow Anti clockwise right Bow depressed, stern raised

7 bow clockwise left Bow raised, stern depressed

GYROSCOPIC EFFECT IN SHIPS

TYPES OF MOVEMENTS

The sea ship may have the following three movements

1.Steering –it is the turning in a curve either to the right or to the left hand side while the ship moves forward

2.pitching-it is the upward or downward angular movement of the ship in a vertical plane, about its transverse axis ,from the horizontal position

3.rolling-it is the sideway motion of the ship about its longitudinal axis

STBILITY OF AUTOMOBILE

STABILITY OF FOUR WHEEL AUTOMOBILE

incase of stability, it is essential that no wheel is supposed to be lifted of the ground while the vehicle takes a turn. The condition is fulfilled as long as the vertical reaction of the ground on any of wheels is positive (upwards).the centre of gravity (G) of the vehicle lies vertically above the road surface.

STABILITY

1.REACTION DUE TO WEIGHT OF THE VEHICLE

The weight of the vehicle (W) is equally distributed over four wheels which will act downwards. The equal and opposite reaction will be offered by the road surface to the wheel in the upward direction.

weight on each wheel =W/4=m.g /4(downward) reaction of ground wheel=m.g/4(upwards)

GYROSCOPE

2.REACTION DUE TO GYROSCOPIC COUPLE Due to the rotating wheels and the rotating parts of engine of the

vehicle, taking turn, the vehicle will be subjected to gyroscopic couple.The angular velocity of precession, ωp=v/R

c= cW ± cE

cW =4.I.ω. ωp cE =I.G.ω. ωp

c=ωW. ωp (4IW ± G.IE)

Where, cW=gyroscopic couple due to four wheels

cE =gyroscopic couple due to rotating parts of the engine

Vertical reaction at each of the outer or inner wheels, P/2=C/2X

GYROSCOPE

3.REACTION DUE TO CENTRIFUGAL EFFECT As the vehicle moves on a curved path, a centrifugal

force also acts on the vehicle in the outward direction at the center of the gravity of the vehicle.

centrifugal force(Fc)= m.v 2/R

co=Fc *h= (m.v 2/R)*h

co=overturning couple,

Let the magnitude of the two inner or outer wheels be ‘Q’. Q.x=co or Q=co/x = (m.v 2/R)*(h/x)

The vertical reaction of outer and inner wheels, Q/2= (m.v 2/R)*(h/2x)

GYROSCOPE

4.TOTAL REACTION

Total vertical reaction of outer wheels, Ro=(W/4)+(P/2)+(Q/2)

Total vertical reaction of inner wheels, Ri=(W/4)-(P/2)-(Q/2)

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Unit - 5