gyroscopic unit2

8/11/2019 Gyroscopic unit2

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GYROSCOPEA gyroscope is a device for measuring or maintaining orientation, based

on the principles of conservation of angular momentum.

In essence, a mechanical gyroscope is a spinning wheel or disk whose

axle is free to take any orientation.

Gyroscopes are installed in ships in order to minimize the rolling and

pitching effects of waves. They are also used in aero planes, monorail

cars, gyrocompasses etc.

APPLICATIONS:

Applications of gyroscopes include navigation for the stabilization of

flying vehicles like radio-controlled helicopters. Due to their high

precision, gyroscopes are also used to maintain direction in tunnelmining. Gyroscopes are also used in Air & Land Vehicles, Ships,

Hovercrafts etc.


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GYROSCOPE


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GYROSCOPE


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GYROSCOPE


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GYROSCOPE


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GYROSCOPE

PRECESSIONAL ANGULAR MOTION:

The angular velocity of the axis of spin (i.e d/dt) is known as angular

velocity of precession and is denoted by P.

The axis, about which the axis of spin is to turn, is known as axis of

precession.

The angular motion of the axis of spin about the axis of precession is

known as precessional angular motion.

The Cause of Precession: Newtons1st Law of Motion.

Law of Conservation of Angular Momentum.


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GYROSCOPE

GYROSCOPE COUPLE

The couple I..p,in the direction of the vector (xxor ab) is the active

gyroscopic couple, which has to be applied over the disc when the axis

of spin is made to rotate with angular velocity P about the axis of

precession.

When the axis of spin itself moves with angular velocity P, the disc is

subjected to reactive couple whose magnitude is same but opposite indirection 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 reactive gyroscopic

couple.

The gyroscopic couple is usually applied through the bearings whichsupport the shaft.


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GYROSCOPEThe resisting couple/ reactive couple will act in the direction opposite to

that of the gyroscopic couple. This means that, whenever the axis of

spin changes its direction, a gyroscopic couple is applied to it through

the bearing which supports the spinning axis.


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GYROSCOPE


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GYROSCOPE


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GYROSCOPE


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GYROSCOPEPROPELLERrotates in CLOCKWISEdirection when seen from rear end and

Aeroplane turns towards LEFT


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GYROSCOPEThe reactive gyroscopic couple tends to dipthe tailand raisethe nose

of aeroplane.


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GYROSCOPEPROPELLERrotates in CLOCKWISEdirection when seen from rear end and

Aeroplane turns towards RIGHT


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GYROSCOPEThe reactive gyroscopic couple tends to raisethe tailand dipthe nose

of aeroplane.


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GYROSCOPEPROPELLER rotates in ANTICLOCKWISE direction when seen from rear

end and Aeroplane turns towards LEFT


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GYROSCOPEThe reactive gyroscopic couple tends to raisethe tail and dipthe nose of

aeroplane.


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end and Aeroplane turns towards RIGHT


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GYROSCOPEThe reactive gyroscopic couple tends to raisethe nose and dip the tail of

aeroplane.


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GYROSCOPEPROPELLER rotates in CLOCKWISE direction when seen from rear end

and Aeroplane is landing or nose move downwards

The reactive gyroscopic couple tends to turn the nose of aeroplane

toward right


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GYROSCOPEPROPELLER rotates in CLOCKWISE direction when seen from rear end

and Aeroplane is Takes off or nose move upwards


toward left


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end and Aeroplane is Takes off or nose move upwards


toward right


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end and Aeroplane is Landing or nose move downwards


toward left


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GYROSCOPEBasic principle of stabilization of gyroscope:


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In rolling, external couple is in transverse plane. So reaction couple

from gyroscope should also act in same plane. (i.e. along longitudinal

axis). So choice is there to choose spin axis either in the vertical or intransverse direction and accordingly for precession axis).

This depends upon practical constraint. Precession is given to

gyroscope manually (just like steering wheel).

GYROSCOPE


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Gyroscopic effect on Rolling of ship.

The axis of the rotor of a ship is

mounted along the longitudinal

axis of ship and therefore, there is

no precession of this axis. Thus, no

effect of gyroscopic couple on the

ship frame is formed when theship rolls

GYROSCOPE


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GYROSCOPEGyroscopic effect on Pitching of ship The pitching motion of a ship

generally occurs due to waves which can be approximated as sine wave.

During pitching, the ship moves up and down from the horizontal

position in vertical plane

BowIt is the fore end of shipSternIt is the rear end of ship

StarboardIt is the right hand side of the ship looking in the direction

of motion

Port It is the left hand side of the ship looking in the direction of

motion

GYROSCOPE


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GYROSCOPEGyroscopic effect on Pitching of ship

GYROSCOPE


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GYROSCOPEGyroscopic effect on Pitching of ship

GYROSCOPE


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GYROSCOPEGyroscopic effect on Steering of ship

Left turn with clockwise rotor

When ship takes a left turn and the rotor rotates in clockwise direction

viewed fromStern.

GYROSCOPE


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GYROSCOPE

Gyroscopic effect on Steering of ship

Right turn with clockwise rotor

When ship takes a Right turn and the rotor rotates in clockwisedirection viewed from Stern.

GYROSCOPE


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GYROSCOPE

Stability of Four Wheeled Vehicle negotiating a turn.

GYROSCOPE


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GYROSCOPE


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m = Mass of the vehicle (kg)

W = Weight of the vehicle (N) = m.g,

h = Height of the centre of gravity of the vehicle (m)

rW = Radius of the wheels (m)

R = Radius of track or curvature (m)

IW= Mass moment of inertia of each wheel (kg-m2)

IE= Mass moment of inertia of the rotating parts of the engine (kg-m2)

W= Angular velocity of the wheels (rad/s)

E = Angular velocity of the engine (rad/s)

G = Gear ratio = E/ W,

v = Linear velocity of the vehicle (m/s)= W rW,

x = Wheel track (m)b = Wheel base (m)

GYROSCOPE


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GYROSCOPE


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When the wheels and rotating parts of the engine rotate in the same

direction, then positive sign is used in the above equation. Otherwise

negative sign should be considered.

Assuming that the vehicle takes a left turn, the reaction gyroscopic

couple on the vehicle acts between outer and inner wheels.

GYROSCOPE


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G OSCO


This gyroscopic couple tends to press the outer wheels and lift the

innerwheels.

Due to the reactive gyroscopic couple, vertical reactions on the road surface

will be produced. The reaction will be vertically upwards on the outer wheels

and vertically downwards on the inner wheels.

GYROSCOPE


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GYROSCOPE


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Stability of Four Wheeled Vehicle negotiating a turn.Effect of Centrifugal Couple When a vehicle moves on a curved path, a

centrifugal force acts on the vehicle in outward direction through the

centre of gravity of the vehicle

This centrifugal couple tends to press the outer and lift the inner

GYROSCOPE


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Due to the centrifugal couple, vertical reactions on the road surface willbe produced. The reaction will be vertically upwards on the outer wheels

and vertically downwards on the inner wheels.

GYROSCOPE


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GYROSCOPE


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A little consideration will show that when the vehicle is running at high

speeds, PI may be zero or even negative. This will cause the inner

wheels to leave the ground thus tending to overturn the automobile. In

order to have the contact between the inner wheels and the ground,the sum of P/2 and Q/2 must be less than W/4.

GYROSCOPE


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A rear engine automobile is travelling along a track of 100 metres mean

radius. Each of the four road wheels has a moment of inertia of 2.5 kg-m2

and an effective diameter of 0.6 m. The rotating parts of the engine havea moment of inertia of 1.2 kg-m2. The engine axis is parallel to the rear

axle and the crankshaft rotates in the same sense as the road wheels. The

ratio of engine speed to back axle speed is 3 : 1. The automobile has a

mass of 1600 kg and has its centre of gravity 0.5 m above road level. The

width of the track of the vehicle is 1.5 m.

Determine the limiting speed of the vehicle around the curve for all four

wheels to maintain contact with the road surface. Assume that the road

surface is not cambered and centre of gravity of the automobile lies

centrally with respect to the four wheels.

GYROSCOPE


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GYROSCOPE


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Stability of Two Wheeled Vehicle

GYROSCOPE


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Let

m = Mass of the vehicle and its rider in kg,

W = Weight of the vehicle and its rider in newtons = m.g,h = Height of the centre of gravity of the vehicle and rider,

rW = Radius of the wheels,

R = Radius of track or curvature,

IW= Mass moment of inertia of each wheel,

IE= Mass moment of inertia of the rotating parts of the engine,

W = Angular velocity of the wheels,

E= Angular velocity of the engine rotating parts,

G = Gear ratio = E/ W,

v = Linear velocity of the vehicle = W

rW

,

= Angle of heel. It is inclination of the vehicle to the vertical

for equilibrium.

GYROSCOPE


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GYROSCOPE


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Stability of Two Wheeled Vehicle negotiating a turn

GYROSCOPE


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Stability of Two Wheeled Vehicle negotiating a turn

A motor cycle with its rider has a mass of 300 kg. The centre of gravity

of the machine and rider combined being 0.6 m above the ground with

machine in vertical position. Moment of inertia of each wheel is 0.525

kg m2 and the rolling diameter of 0.6 m. The engine rotates 6 times the

speed of the road wheels and in the same sense. The engine rotating

parts have a mass moment of inertia of 0.1686 kg m2. Find (i) the angle

of heel necessary if the vehicle is running at 60 km/hr round a curve of30 m (ii) If the road and tyre friction allow for the angle of heel not to

exceed 50o, what is the maximum road velocity of the motor cycle.

gyroscopic unit2

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