Gyroscopic effect on bearings

I
ACKNOWLEDGMENT
This acknowledges our sincere thanks to our project guide Prof.S.C.Fargade,
who helped us in selecting the project topic, understanding the subject; whose valuable
guidance and continuous encouragement throughout this work made it possible to
complete this project work well in advance.
We would also like to thank to team of “work shop of our college” for their direct
and indirect help without which we would not be able to complete this project.
We also wish to express our deep sense of gratitude to Dr. G. J. Vikhe Patil,
Principal, Amrutvahini College of Engineering, Sangamner. Prof. A. K. Mishra, HOD.
(Mechanical Engg.).
We are also thankful to other staff members of our esteemed college, Amrutvahini
College of Engineering, Sangamner for their special attention and suggestions towards the
project, and also thankful to our friends whose valuable guidance to us.
Akansha Jha
Gayatri Bihani
Rana Shah
Vikas Sinare

II
TABLE OF CONTENT
SR.
NO.
CONTENT
PAGE
NO.
List of Figures IV
List of Tables VI
Abstract VII
1. INTRODUCTION 1
2. LITERATURE SURVEY 4
2.1 History 4
2.2 Review of Papers 5
2.2.1 Angular motion
2.2.2 Gyroscopic couple
2.2.3 Direction of spin vector precession vector an
couple /torque vector with precession
5
6
8
3. WORKING OF GYROSCOPE 12
4. GYROSCOPIC EFFECT 15
4.1 Precessional angular motion 15
4.2
4.3
4.4
4.5
4.6
Concept of gyroscopic couple 18
Active and Reactive gyroscopic couple 19
Direction of active and Reactive gyroscopic couple 20
Controlled gyroscope 21
Gyroscopic effect on ship 22
4.6.1 Ship terminology 22
4.6.2 Gyroscopic effect on steering of ship 23
4.6.3 Gyroscopic effect on pitching of ship 24
4.7
4.8
4.9
Inertial navigation system
Aircraft Instrument
Other application
26
27
28
5. PROJECT STUDY ON GYROSCOPE 29
5.1 Component required 29
5.2 Component details 29
5.3 Experimental explanation 34

III
5.4 Working of experiment 35
6. OBSERVATION AND CALCULATION 37
6.1 Observation Table 37
6.2 Calculations 38
7. Result Table and Graph 47
7.1 Result Table 47
7.2 Graph 48
9. Conclusion 49
REFERENCES 50

IV
LIST OF FIGURES
FIG.NO. TITLE PAGE NO.
Fig. 1.1 Gyroscope Mechanism 01
Fig. 2.1 Gyroscope Apparatus 02
Fig. 2.2
Gyroscope invented by Léon
Foucault, and built by Dumoulin-
Froment
04
Fig. 2.3 Spinning body 06
Fig. 2.4 Gyroscopic Couple 07
Fig. 2.5
Direction of Spin vector, Precession
vector and Couple/Torque vector
08
Fig. 2.6
and 2.7
Direction of active and reactive
gyroscopic couple/ torque vector
09
Fig. 2.8
and 2.9
Direction of active and reactive
gyroscopic couple/ torque vector
10
Fig. 3.1 Working of gyroscope 12
Fig. 3.2 Gyroscope model 13
Fig. 4.1 Precessional angular motion 16
Fig. 4.2
Active and reactive gyroscopic
couple
19
Fig. 4.3 Right hand thumb rule 21
Fig. 4.4 Terms used in ships 22
Fig. 4.5 Effect of gyroscope on ships 23
Fig. 4.6
Gyroscopic effect on pitching of
ship
25
Fig. 5.1 Rotor system 29
Fig. 5.2 Dimmerstat 30
Fig. 5.3 Digital weighing gauge 31
Fig. 5.4 Bearing and bearing housing 32
Fig. 5.5 Gear motor 33
Fig 5.6 Gear motor with plate 33
Fig 5.7 Reaction acting on system 34

V
Fig 5.8 Project working 35
Fig 5.9 Working model 36

VI
LIST OF TABLES
TABLE
NO.
TITLE
PAGE
NO.
6.1 Observation Table 37
7.1 Result Table 38

VII
ABSTRACT
This Project involves an experimental model wherein we are finding the reactions
produced on the two bearings (located one at each side) due to the gyroscopic effect, first
experimentally and then theoretically using simple principle of gyroscope. For calculating
the reactions produced, we have to prepare the model with two regulators for varying the
speed of motors, one for the spinning rotor speed and the second for the rotation in
precession plane. According to sense of rotation and speed of rotor and precession the
reactive and active gyroscopic couple acts on the bearing, thus load on the bearing at time
of precession is more in one and less on the other side of the bearing and also the same
principle in opposite sense use for the precession i.e. for the turning in case of aeroplane
and ship.
Rotating machines such as steam or gas turbines, turbo-generators, internal
combustion engines, motors, and disc drives can develop inertia effects that can be
analyzed to improve the design and decrease the possibility of failure. Thus, different
readings obtained will allow us to design the bearing according to the convenience and
application.

Gyroscopic Effect on Bearing Reaction
1
1. INTRODUCTION
‘Gyre’ is a Greek word, meaning ‘circular motion’ and Gyration means the whirling
motion. A gyroscope is a spatial mechanism which is generally employed for the study of
precessional motion of a rotary body. Gyroscope finds applications in gyrocompass, used in
aircraft, naval ship, control system of missiles and space shuttle. The gyroscopic effect is also
felt on the automotive vehicles while negotiating a turn. A gyroscope consists of a rotor
mounted in the inner gimbal. The inner gimbal is mounted in the outer gimbal which itself is
mounted on a fixed frame as shown in Fig.1. When the rotor spins about X-axis with angular
velocity ω rad/s and the inner gimbal precesses (rotates) about Y-axis, the spatial mechanism
is forced to turn about Z-axis other than its own axis of rotation, and the gyroscopic effect is
thus setup. The resistance to this motion is called gyroscopic effect. [1]
Current trends in rotating equipment design focus on increased speeds, which
increase operational problems caused by vibration. At higher rotational speeds, the inertia
effects of rotating parts must be consistently represented to accurately predict rotor behavior.
Inertia effects in rotating structures are usually caused by gyroscopic moment introduced by
the precise motions of the vibrating rotor as it spins. As spin velocity increases, the
gyroscopic moment acting on the rotor becomes critical. Not accounting for inertia effects at
the design level can lead to bearing and support structure damage. It is also important to
consider bearing stiffness, support structure flexibility, and damping characteristics to
understand the stability of a vibrating rotor. [2]
Fig. 1.1 Gyroscope Mechanism

2
2. LITERATURE SURVEY
The axle of the spinning wheel defines the spin axis. The rotor is journal to spin about
an axis, which is always perpendicular to the axis of the inner gimbal. So the rotor possesses
three degrees of rotational freedom and its axis possesses two. The wheel responds to a force
applied about the input axis by a reaction force about the output axis. A simple gyroscope
apparatus is shown in fig 2.1
Fig 2.1 Gyroscope Apparatus
The behaviour of a gyroscope can be most easily appreciated by consideration of the
front wheel of a bicycle. If the wheel is leaned away from the vertical so that the top of the
wheel moves to the left, the forward rim of the wheel also turns to the left. In other words,
rotation on one axis of the turning wheel produces rotation of the third axis.
A gyroscope flywheel will roll or resist about the output axis depending upon whether
the output gimbals are of a free or fixed configuration. Examples of some free-output-gimbal
devices would be the attitude reference gyroscopes used to sense or measure the pitch, roll
and yaw attitude angles in a spacecraft or aircraft. The centre of gravity of the rotor can be in
a fixed position. The rotor simultaneously spins about one axis and is capable of oscillating
about the two other axes, and, thus, except for its inherent resistance due to rotor spin, it is
free to turn in any direction about the fixed point.

3
Some gyroscopes have mechanical equivalents substituted for one or more of the
elements. For example, the spinning rotor may be suspended in a fluid, instead of being
pivotally mounted in gimbals. A control moment gyroscope (CMG) is an example of a fixed-
output-gimbal device that is used on spacecraft to hold or maintain a desired attitude angle or
pointing direction using the gyroscopic resistance force.
In some special cases, the outer gimbal (or its equivalent) may be omitted so that the
rotor has only two degrees of freedom. In other cases, the centre of gravity of the rotor may
be offset from the axis of oscillation, and, thus, the centre of gravity of the rotor and the
centre of suspension of the rotor may not coincide .[3]
2.1 HISTORY[3]
Essentially, a gyroscope is a top, a self-balancing spinning toy, put to instrumental
use. Tops were invented in many different civilizations, including classical Greece, Rome,
Indus and China, and the Māori culture a thousand years later. Most of these, though using
the same conservation of angular momentum as a gyro, were not utilized as instruments.
The first known use of such a top as an instrument came in 1743, when John Serson
invented the "Whirling speculum" (or Serson's Speculum), a spinning top that was used as a
level, to locate the horizon in foggy or misty conditions. The instrument used more like an
actual gyroscope was made by German Johann Bohnenberger, who first wrote about it in
1817. At first he called it the "Machine". Bohnenberger's machine was based on a rotating
massive sphere.[6]
In 1832, American Walter R. Johnson developed a similar device that was
based on a rotating disk. The French mathematician Pierre-Simon Laplace, working at the
École Polytechnique in Paris, recommended the machine for use as a teaching aid, and thus it
came to the attention of Léon Foucault shown in Fig 2.2. In 1852, Foucault used it in an
experiment involving the rotation of the Earth. It was Foucault who gave the device its
modern name, in an experiment to see (Greek skopeein, to see) the Earth's rotation (Greek
gyros, circle or rotation), which was visible in the 8 to 10 minutes before friction slowed the
spinning rotor.

4
Fig 2.2 Gyroscope invented by Léon Foucault, and built by Dumoulin-Froment, 1852.
Above Photo is taken at National Conservatory of Arts and Crafts museum, Paris. In
the 1860s, the advent of electric motors made it possible for a gyroscope to spin indefinitely;
this led to the first prototype heading indicators and, quite more complicated devices, first
gyrocompasses. The first functional gyrocompass was patented in 1904 by German inventor
Hermann Anschütz-Kaempfe. The American Elmer Sperry followed with his own design
later that year, and other nations soon realized the military importance of the invention in an
age in which naval prowess was the most significant measure of military power and created
their own gyroscope industries. The Sperry Gyroscope Company quickly expanded to
provide aircraft and naval stabilizers as well, and other gyroscope developers followed suit.

5
In 1917, the Chandler Company of Indianapolis, created the "Chandler gyroscope"
with a pull string and pedestal. Chandler continued to produce the toy until the company was
purchased by TEDCO Inc. in 1982. The chandler toy is still produced by TEDCO today.
In the first several decades of the 20th century, other inventors attempted
(unsuccessfully) to use gyroscopes as the basis for early black box navigational systems by
creating a stable platform from which accurate acceleration measurements could be
performed (in order to bypass the need for star sightings to calculate position). Similar
principles were later employed in the development of inertial guidance systems for ballistic
missiles.
During World War II, the gyroscope became the prime component for aircraft and
anti-aircraft gun sights. After the war, the race to miniaturize gyroscopes for guided missiles
and weapons navigation systems resulted in the development and manufacturing of so called
midget gyroscopes that weighed less than 3 ounces (85 g) and had a diameter of
approximately 1 inch (2.5 cm). Some of these miniaturize gyroscopes could reach a speed of
24,000 revolutions per minute in less than 10 seconds.
3-axis MEMS-based gyroscopes are also being used in portable electronic devices
such as Apple's current generation of iPad, iPhone and iPod touch. This adds to the 3-axis
acceleration sensing ability available on previous generations of devices. Together these
sensors provide 6 component motion sensing; acceleration for X, Y, and Z movement, and
gyroscopes for measuring the extent and rate of rotation in space (roll, pitch and yaw).
2.2 REVIEW OF PAPERS[1]
2.2.1 ANGULAR MOTION
A rigid body, (Fig.2.3) spinning at a constant angular velocity ω rad/s about a spin
axis through the mass centre. The angular momentum ‘H’ of the spinning body is represented
by a vector whose magnitude is ‘Iω’. I represent the mass amount of inertia of the rotor about
the axis of spin.
‘.’ H= I ω

6
The direction of the angular momentum can be found from the right hand screw rule
or the right hand thumb rule. Accordingly, if the fingers of the right hand are bent in the
direction of rotation of rotor, then the thumb indicates the direction of momentum.
Fig.2.3 spinning body
2.2.2 GYROSCOPIC COUPLE
Consider a rotary body of mass m having radius of gyration k mounted on the shaft
supported at two bearings. Let the rotor spins (rotates) about X-axis with constant angular
velocity ω rad/s. The X-axis is, therefore, called spin axis, Y-axis, precession axis and Z-axis,
the couple or torque axis (Fig.2.4). The angular momentum of the rotating mass is given by,
H = mk2
× ω = I ω
Now, suppose the shaft axis (X-axis) precesses through a small angle δθ about Y-axis
in the plane XOZ, then the angular momentum varies from H to H + δH, where δH is the
change in the angular momentum, represented by vector ab. For the small value of angle of
rotation 5˚,

7
Fig 2.4 Gyroscopic Couple
We can write,
ܾܽ෢ = ‫ ܽ݋‬ෞ × δθ
δH = H × δθ
= Iω δθ
However, the rate of change of angular momentum is:
C =
ୢୌ
ୢ୲
=limஔ୲→଴ሺ
୍ன ஔ஘
ஔ୲
ሻ
= Iω
ୢ஘
ୢ୲
C = Iω.ωp
Where, C = gyroscopic couple (N-m)
ω= angular velocity of rotary body (rad/s)
ωp = angular velocity of precession (rad/s)

8
2.2.3 DIRECTION OF SPIN VECTOR, PRECESSION VECTOR AN COUPLE /
TORQUE VECTOR WITH FORCED PRECESSION
To determine the direction of spin, precession and torque/couple vector, right hand
screw rule or right hand rule is used. The fingers represent the rotation of the disc and the
thumb shows the direction of the spin, precession and torque vector (Fig.2.5). The method of
determining the direction of couple/torque vector is as follows.
Fig.2.5 Direction of Spin vector, Precession vector and Couple/Torque vector
Case (i):
Consider a rotor rotating in anticlockwise direction when seen from the right (Fig.2.6 and
Fig. 2.7), and to precess the spin axis about precession axis in clockwise and anticlockwise
direction when seen from top. Then, to determine the active/reactive gyroscopic couple
vector, the following procedure is used.

9
Fig. 2.6 Direction of active and reactive gyroscopic couple/torque vector in clockwise
Fig. 2.7 Direction of active and reactive gyroscopic couple/torque vector in
anticlockwise
Turn the spin vector through 900 in the direction of precession on the XOZ plane. The turned
spin vector will then correspond to the direction of active gyroscopic couple/torque vector.
The reactive gyroscopic couple/torque vector is taken opposite to active gyro vector direction

10
Case (ii):
Fig. 2.8 Direction of active and reactive gyroscopic couple/torque vector
Fig. 2.9 Direction of active and reactive gyroscopic couple/torque vector

11
Consider a rotor rotating in clockwise direction when seen from the right (Fig.2.8 and
Fig. 2.9), and to precess the spin axis about precession axis in clockwise and anticlockwise
direction when seen from top. Then, to determine the active/reactive gyroscopic couple
vector,
1) Turn the spin vector through 900 in the direction of precession on the XOZ plane
2) The turned spin vector will then correspond to the direction of active gyroscopic
couple/torque vector
3) The reactive gyroscopic couple/torque vector is taken opposite to active gyro vector
direction
4) The 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.
5)Please note that, for analyzing the gyroscopic effect of the body, always reactive
gyroscopic couple is considered.[1]

12
3. WORKING OF GYROSCOPE [4]
Why a gyroscope should resist being turned in any direction perpendicular to its axis.
Instead of a complete rim, four point masses, A, B, C, D, represent the areas of the rim that
are most important in visualizing how a gyro works. The bottom axis is held stationary but
can pivot in all directions. When a tilting force is applied to the top axis, point A is sent in an
upward direction and C goes in a downward direction.. Since this gyro is rotating in a
clockwise direction, point A will be where point B was when the gyro has rotated 90 degrees.
The same goes for point C and D. Point A is still traveling in the upward direction when it is
at the 90 degrees position in Fig 3.1, and point C will be traveling in the downward direction.
Fig. 3.1 Working of gyroscope
The combined motion of A and C cause the axis to rotate in the "precession plane" to
the right. This is called precession. A gyro's axis will move at a right angle to a rotating
motion. In this case to the right, if the gyro were rotating counterclockwise, the axis would
move in the precession plane to the left. If in the clockwise example the tilting force was a
pull instead of a push, the precession would be to the left. When the gyro has rotated another
90 degrees, point C is where point A was when the tilting force was first applied. The
downward motion of point C is now countered by the tilting force and the axis does not
rotate in the "tilting force" plane. The more the tilting force pushes the axis, the more the rim
on the other side pushes the axis back when the rim revolves around 180 degrees.

13
Actually, the axis will rotate in the tilting force plane in this example. The axis will
rotate because some of the energy in the upward and downward motion of A and C is used up
in causing the axis to rotate in the precession plane. Then when points A and C finally make
it around to the opposite sides, the tilting force (being constant) is more than the upward and
downward counter acting forces. The property of precession of a gyroscope is used to keep
monorail trains straight up and down as it turns corners. A hydraulic cylinder pushes or pulls,
as needed, on one axis of a heavy gyro. Sometimes precession is unwanted so two counter
rotating gyros on the same axis are used. Also a gimbal can be used.
The property of precession represents a natural movement for rotating bodies, where
the rotating body doesn’t have a confined axis in any plane. A more interesting example of
gyroscopic effect is when the axis is confined in one plane by a gimbal. Gyroscopes, when
gimbaled, only resist a tilting change in their axis. The axis does move a certain amount with
a given force.
Fig. 3.2 Gyroscope model

14
A quick explanation of how a gimbaled gyro functions Fig. 3.2 shows a simplified
gyro that is gimbaled in a plane perpendicular to the tilting force. As the rim rotates through
the gimbaled plane all the energy transferred to the rim by the tilting force is mechanically
stopped. The rim then rotates back into the tilting force plane where it will be accelerated
once more. Each time the rim is accelerated the axis moves in an arc in the tilting force plane.
There is no change in the RPM of the rim around the axis. The gyro is a device that causes a
smooth transition of momentum from one plane to another plane, where the two planes
intersect along the axis.

15
4. GYROSCOPIC EFFECT[5]
Whenever a body is rotating or spinning in a plane (plane YZ) about an axis (axis
OX) and its axis of rotation or spin is made to precess in an another perpendicular plane
(plane XZ), as shown in Fig. 4.1, the couple is induced on the rotating or spinning body
across the axis of rotation or spin in a third mutually perpendicular plane (plane XY).
Conversely, whenever a body is rotating in a plane (plane YZ) about an axis (axis OX) and a
couple is applied on the rotating body across the axis of rotation or spin in an another
perpendicular plane (plane XY), the rotating or spinning body starts processing in a third
mutually perpendicular plane (plane XZ). The above stated effects are known as gyroscopic
effects.
The two things are necessary for existence of gyroscopic effect
1) Rotating body
2) Force or couple trying to change the orientation of axis of rotation of a rotating body.
4.1PRECESSIONAL ANGULAR MOTION
Consider a disc spinning about an axis OX with an angular speed ‘ω’ as shown in Fig.
4.2(a). After a short interval of time ‘dt’, let the disc is spinning with an angular velocity (ω +
δω) about the new axis of spin ‘OX’ at an angle δθ with an axis OX. Using the right hand
rule, the initial angular velocity of disc ‘ω’ is represented by ox’, as shown in fig 4.2(b). The
vector xx’ represents the change of angular velocity in time δt. This change in angular
velocity can be resolved into two components one : parallel to ox and another perpendicular
to ox.
Correspondingly there are two components of angular acceleration of the disc
1) Component of angular acceleration along ox (αt )
2) Component of angular acceleration perpendicular to ox (αc )
1. Component of angular acceleration along ox is,
αt = limஔ୲→଴(
୶ୟ
ஔ୲
) = limஔ୲→଴(
୭୶ᇲ ୡ୭ୱ ஔ஘ି୭୶
ஔ୲
)
αt = limஔ୲→଴(
(னା ஔன ) ୡ୭ୱ ஔ஘ିன
ஔ୲
) =limஔ୲→଴(
ன ୡ୭ୱ ஔ஘ା ஔன ୡ୭ୱ ஔ஘ ିன
ஔ୲
)

16
Since δθ is very small, cos δθ ≅ 1, hence we get,
αt ൌ lim
ஔ୲→଴
ሺ
ω ൅ δω െ ω
δt
ሻ ൌ lim
ஔ୲→଴
ሺ
δω
δt
ሻ
αtൌ ሺ
δω
ఋ௧
)
2. Component of angular acceleration perpendicular to ox (αc )
αc = limஔ୲→଴ሺ
ୟ୶ᇱ
ஔ୲
ሻ = limஔ୲→଴ሺ
୭୶ᇲ ୱ୧୬ ஔ஘
ஔ୲
ሻ
αc = limஔ୲→଴ሺ
ሺனା ஔன ሻ ୱ୧୬ ஔ஘ିன
ஔ୲
ሻ =limஔ୲→଴ሺ
ன ୱ୧୬ ஔ஘ା ஔன ୱ୧୬ ஔ஘ ିன
ஔ୲
ሻ
Since δθ is very small, sin δθ ≅ δθ, hence we get,
αc ൌ lim
ஔ୲→଴
ሺ
ω δθ
δt
ሻ ൌ lim
ஔ୲→଴
ሺ
δθ
δt
ሻ
αc ൌ ω ωp
ωp =
ஔ஘
ஔ୲
= rate of precession of spin axis
= angular velocity of precession (or precessional angular velocity)
The precession of spin axis takes place in a plane XOX’ and about perpendicular axis passing
through O
Fig 4.1 Precessional angular motion

17
3. Total Angular Acceleration (α)
The total angular acceleration of the disc is given by,
α = αt + →αc
α = (
δω
ఋ௧
) + → ω
ஔ஘
ஔ୲
α = (
ஔன
ஔ୲
) + → ω ωp
Thus, the angular acceleration of the disc ‘ω’ is the vector sum of:
I. αt = (
ஔன
ஔ୲
) : Representing the change in magnitude of the angular velocity of disc ‘ω’
with respect to time.
II. αc = ω ωp : Representing the change in direction of the axis of spin with respect to
time.
Special cases of angular acceleration of disc:
I. Case : Direction of axis of spin is fixed:
In this case, ωp
ୢ஘
ୢ୲
= 0 i.e αc = 0
Hence, total angular acceleration of the disc is given by,
α = (
ୢன
ୢ୲
)
II. Magnitude of angular velocity of disc is constant:
In this case,
ୢன
ୢ୲
= 0 i.e αt = 0
Hence, total angular acceleration of the disc is given by,
α = ω (
ୢ஘
ୢ୲
)
α = ω . ωp

18
4.2 CONCEPT OF GYROSCOPIC COUPLE
Consider a disc spinning (rotating) with an angular velocity ‘ω’ about spin axis OX in an
anticlockwise direction, as shown in fig. 4.2. The plane in which the disc is spinning i.e plane
YOZ is called as plane of spin. The axis of spin is precessing in a horizontal plane XOZ
about an axis OY with an angular velocity ‘ωp’. The horizontal plane XOZ is called as plane
of precession and axis OY is called as precession axis.
Let, I = Mass moment of inertia of the disc about OX, kg-m2
ω = angular velocity of the disc, rad/s
ωp = angular velocity of precession of spin, rad/s
The initial position of the spin axis is OX. Let the spin axis OX is turned through a small
angle ‘δθ’ in time ‘δt’ in the horizontal plane XOZ about the precession axis OY.
1. Initial Angular Momentum of Disc
When the initial position of the spin axis is OX, the magnitude of angular momentum of
disc is Iω. As the angular momentum is a vector quantity, using right hand rule it is
represented by ox, as shown in fig. 4.2.
2. Final angular momentum of disc:
After time ‘δt’ when the final position of the spin axis is OX’, magnitude of angular
momentum of disc remains same i.e. I ω. Using right hand rule, it is represented by ox’, as
shown in fig. 4.2.
1. Change in angular momentum of Disc:
Change in angular momentum = ox’ – ox
= xx’ =ox’ δθ
= I ω δθ

19
1. Gyroscopic couple on disc:
Rate of change of angular momentum = I ω
ஔ஘
ஔ୲
This rate of change of angular momentum will result due to application of couple to a
disc. Therefore, the couple applied to the disc for causing precession is given by,
C = lim
ஔ୲→଴
I ωሺ
ஔ஘
ஔ୲
ሻ = ൌ I ωሺ
ୢ஘
ୢ୲
ሻ
C = I ω ωp
The couple is given by equation known as gyroscopic couple.
4.3 ACTIVE AND REACTIVE GYROSCOPIC COUPLES
Fig. 4.2 Active and reactive gyroscopic couple

20
1. Active Gyroscopic Couple:
i) The couple of magnitude C= I ω ωp which acts in the direction of xx’, represents the rate
of change of angular momentum.
ii) This couple which must be applied to the disc across the axis of spin to cause it to precess
in the horizontal plane about the axis of precession, is called the active gyroscopic couple.
iii) The vector xx’ lies in a plane XOZ (plane of precession). In case of small δθ, xx’ is
perpendicular to the vertical plane XOY. Therefore, the gyroscopic couple causing change in
angular momentum will be a plane XOY.
iv) Therefore the plane XOY is called the plane of gyroscopic couple and the axis OZ is
called the axis of gyroscopic couple or gyroscopic axis.
v) In short, the active gyroscopic couple is the couple applied to the disc across the axis of
spin so as to cause its precession.
2. Reactive Gyroscopic Couple:
i)When the axis of spin precess itself or is made to precess with angular velocity ‘ωp’, the
shaft on which the disc is mounted applies reactive gyroscopic couple through support
bearings, to the frame. Fig 4.3
ii) The magnitude of the reactive gyroscopic couple is same as that of the active gyroscopic
couple but direction is opposite.
4.4 DIRECTIONS OF ACTIVE AND REACTIVE GYROSCOPIC COUPLES
The right hand rule is used in deciding the directions of spin vector, precession vector and
gyroscopic couple vector
1) Curl the fingers of the right hand such that, the direction of curling fingers indicates the
direction of spin; the the thumb will indicate
direction of precession; then the thumb will indicate the direction of precession vector.
direction of active gyroscopic couple vector as shown in Fig 4.4

21
4.5 CONTROLLED GYROSCOPES
Controlled gyroscopes fall into three categories:
i. The north-seeking gyroscope is used in marine applications. In the settling (or normal)
position the spin axis is kept horizontal and in the plane of a meridian.
ii. The directional gyroscope is used in aircraft and is sometimes called a self-leveling free
gyroscope corrected for drift. With its spin axis horizontal it has directional properties but
does not automatically seek the meridian.
iii. The gyro-vertical has its spin axis vertical and is used to detect and measure angles of roll
and pitch.
These types of three-frame gyroscopes are called displacement gyroscopes because they can
measure angular displacements between the framework in which they are mounted and a
fixed direction-the rotor axis.
Fig 4.3 Right hand thumb rule

22
4.6 GYROSCOPIC EFFECT ON SHIP[1]
Gyroscope is used for stabilization and directional control of a ship sailing in the rough
sea. A ship, while navigating in the rough sea, may experience the following three different
types of motion:
(i) Steering: The turning of ship in a curve while moving forward
(ii) Pitching: The movement of the ship up and down from horizontal position in a vertical
plane about transverse axis
(iii)Rolling: Sideway motion of the ship about longitudinal axis.
For stabilization of a ship against any of the above motion, the major requirement is
that the gyroscope shall be made to precess in such a way that reaction couple exerted by the
rotor opposes the disturbing couple which may act on the frame.
4.6.1 SHIP TERMINOLOGY
(i) Bow – It is the fore end of ship
(ii) Stern – It is the rear end of ship
(iii) Starboard – It is the right hand side of the ship looking in the direction of motion
(iv) Port – It is the left hand side of the ship looking in the direction of motion
Consider a gyro-rotor mounted on the ship along longitudinal axis (X-axis) as shown
in Fig.10 and rotate in clockwise direction when viewed from rear end of the ship. The
angular speed of the rotor is ω rad/s. The direction of angular momentum vector ‫ܽ݋‬ෞ, based
on direction of rotation of rotor, is decided using right hand thumb rule as discussed earlier.
The gyroscopic effect during the three types of motion of ship is discussed.
Fig 4.4 Terms used in ship

23
4.6.2 GYROSCOPIC EFFECT ON STEERING OF SHIP
(i) Left turn with clockwise rotor
When ship takes a left turn and the rotor rotates in clockwise direction viewed from
stern, the gyroscopic couple act on the ship is analyzed in the following way. fig 4.6
Fig: 4.5 Effect of gyroscope on ship
Note that, always reactive gyroscopic couple is considered for analysis. From the above
analysis (Fig.4.6), the couple acts over the ship between stern and bow. This reaction couple
tends to raise the front end (bow) and lower the rear end (stern) of the ship.

24
(ii) Right turn with clockwise rotor
When ship takes a right turn and the rotor rotates in clockwise direction viewed from stern,
the gyroscopic couple acts on the ship is analyzed. Again, the couple acts in vertical plane,
means between stern and bow. Now the reaction couple tends to lower the bow of the ship
and raise the stern.
(iii) Left turn with anticlockwise rotor
When ship takes a left turn and the rotor rotates in anticlockwise direction viewed from stern,
the gyroscopic couple act on the ship is analyzed in the following way. The couple acts over
the ship is between stern and bow. This reaction couple tends to press or dip the front end
(bow) and raise the rear end (stern) of the ship.
(iv) Right turn with anticlockwise rotor
When ship takes a right turn and the rotor rotates in anticlockwise direction viewed from
stern, the gyroscopic couple act on the ship is according to. Now, the reaction couple tends to
raise the bow of the ship and dip the stern.
4.6.3 GYROSCOPIC 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.
Let θ = angular displacement of spin axis from its mean equilibrium position
A = amplitude of swing
A = angle in degree ×
ଶ஠
ଷ଺଴˚
And ωo = angular velocity of simple harmonic motion =
ଶ஠
୲୧୫ୣ ୮ୣ୰୧୭ୢ
The angular motion of the rotor is given as
θ =A sin ωot
ωp =
ௗఏ
ௗ௧

25
ωp =
ௗ
ௗ௧
(A sin ωot)
ωp =A ωo cos(ωot)
The angular velocity of precess will be maximum when cos(ωot) =1
ωpmax = A. ωo
ωpmax = A
ଶ஠
୲
Thus the gyroscopic couple, C = I. ω. ωp
Consider a rotor mounted along the longitudinal axis and rotates in clockwise direction when
seen from the rear end of the ship. The direction of momentum for this condition is shown by
vector ox. When the ship moves up the horizontal position in vertical plane by an angle θ
from the axis of spin, the rotor axis (X-axis) processes about Z axis in XY-plane and for this
case Z-axis becomes precession axis. The gyroscopic couple acts in anticlockwise direction
about Y-axis and the reaction couple acts in opposite direction, i.e. in clockwise direction,
which tends to move towards right side. However, when the ship pitches down the axis of
spin, the direction of reaction couple is reversed and the ship turns towards left side (Fig.
4.7).
Fig:4.6 GYROSCOPIC EFFECT ON PITCHING OF SHIP

26
4.7 INERTIAL NAVIGATION SYSTEMS[6]
Neither position nor velocity can be sensed directly by an inertial system. Acceleration
(change in velocity), however, can be detected by an accelerometer and this can be used to
determine the position of a ship, aircraft, or space vehicle.
Basically this navigational system comprises three components: the platform, the
gyroscopic frame and the computer. The accelerometers, mounted with their input axes
mutually at right angles, are carried on a platform. Two accelerometers measure acceleration
in the horizontal plane - the requirement for surface navigation.
For space navigation an additional accelerometer measures acceleration in the vertical
plane. Each of the acceleration signals can be converted into distance travelled by
determining, firstly, the total change in velocity which, added to the known initial velocity,
gives the vehicle velocity; and second, the total change in position that, added to the known
initial position, yields the present vehicle position.
The gyroscope frame is responsible for the stabilization off the platform. Three rate
gyroscopes are fitted in the frame with their input axes mutually perpendicular. Two of the
gyroscopes provide the horizontal alignment of the platform - an essential requirement to
eliminate the influence of accelerations due to gravity - while the third is responsible for the
north-south alignment. Pitch, roll and yaw are detected by the three gyroscope input axes.
The gimbal deflection of each of the gyroscopes is converted into a signal voltage that,
when amplified, drives a servomotor via a gear train to rotate the frame back to its original
position. The gyroscope frame also detects tilting and drifting due to the Earth’s rotational
movement. If the platform is to be kept horizontal and north-south stabilized, torque signals
must be applied to the roll and pitch servomotors to offset the precssion caused by the tilting,
as well as to the azimuth servomotor to eliminate the precession caused by drifting.
The rate gyroscopes are not spring-restrained. Instead, flotation gyroscopes in which
the precession is opposed by the viscous drag of a liquid are employed. The opposing torque
is therefore proportional to the precession rate, instead of the precession displacement, as in a
spring-restrained gyroscope.
The computer performs the necessary calculations. Specifically, it applies certain
corrections to the acceleration, integrates acceleration to velocity and velocity to distance,

27
computes latitude and longitude, and converts geocentric latitudes into geographical
latitudes.
If the inertial system is used for inertial guidance in space navigation, then the
computer also compares the vehicles position with the destination or target position to
provide steering commands and compares the vehicles velocity (both direction and
magnitude) with the programmed velocity vector to provide rocket steering and engine cut-
off commands.
4.8AIRCRAFT INSTRUMENTS[7]
The three primary gyroscopic instruments fitted to the flight panel are a rate-of-turn
indicator, a directional gyroscope, and an artificial horizon. Such gyroscopes may be driven
by electric motors or by air jets. The directional gyroscope forms a standard reference for the
pilot and navigator. It is a three-frame gyroscope with its spin axis in the horizontal plane. As
soon as tilt develops, a switch is closed between the gyroscope housing and the vertical
gimbal ring and a motor introduces a torque in the horizontal plane that causes the gyroscope
to precess back towards the horizontal.
The artificial horizon displays the rolling and pitching motion of the aircraft. It consists
basically of a three-framed gyroscope with its spin axis vertical and automatic correction
devices to counteract the apparent motion of the spin axis around the celestial pole and any
other random precessions.
4.9OTHER APPLICATIONS[7]
The gyroscope principle has been utilised in many other applications, such as the
gyrocompass, gyropilot, and in non-rotating gyroscope devices.
A compensated magnetic compass, free from external accelerations, indicates magnetic
north, which varies from true north from place to place on the Earth's surface. A
gyrocompass however, when properly adjusted, can be made to indicate true north.
The marine gyrocompass is a three-frame gyroscope with its spin axis horizontal. To
achieve the north-seeking and actual location (or meridian settling) properties of a gyroscope,
use is made of the tilting effect of the spin axis when it is not pointing true north. As soon as
tilt develops, a pendulum type device introduces torques that precesses the spin axis towards
the meridian, causing it to describe a spiral with an ever-decreasing radius.

28
When stabilized the spin axis is maintained in the meridian plane by a precession equal
but opposite to the drift at the particular latitude. When there is no tilting effect the marine
gyrocompass will lose its directional properties and become useless. This is the case at the
poles and also when a vehicle moves due west with a speed equal to the surface speed of the

29
5. PROJECT STUDY ON GYROSCOPE
5.1 COMPONENT REQUIRED
1) Base Table For Mounting The Assembly
2) Plywood Plate With Frame
3) Nuts And Bolts For Fixing The Component
4) A.C. Motor With Worm Gear Reduction Box
5) Bi-shaft A.C/D.C. Motor
6) Rotor
7) Dimmerstat
8) Digital Weighing Gauge
9) Bearings And Bearings Housing
10) Supporting Metal Strip
11) Procircle
5.2 COMPOMENTS DETAIL
1. Rotor system:
It consists of AC/DC bi-shaft motor [50W, 230V, 9500 rpm, Single Phase] and two
rotors having diameter 137 mm and weight 580 gm are mounted on both sides of motor shaft.
It is supported by a U clamp to restrict swing of motor.
Fig 5.1 Rotor System

30
2. Dimmer Stat:
It is an auto transformer which is generally connected to supply which provide us step
up /step down output depending on the terminal to which input is connected. Normally there
are two ways to operate a Dimmerstat:-
i. The output voltage can be varied from 0 to full supply voltage.
ii. Voltage from 0 to 12 % higher than supply voltage
The basic Dimmerstat is meant for operation from a nominal input voltage of 240V
1ph AC and can give output voltage anywhere between 0 to 240V or 0 to 270V AC by
simple transformer action. Two such Dimmerstats connected electrically and become suitable
for operation from a nominal input voltage of 415V 3Ph AC and can give output anywhere
between 0 to 270V. The dimmerstat used for driving the motor which runs the frame in
precessional axis requires a larger voltage than that of the one required for running the rotor
in spinning axis. Fig 5.2
Fig 5.2 Dimmerstat
3. Digital weighing Gauge:
An electronic measuring device that uses fiber optics to detect and transmit its
position to a digital or computer readout for display, it will calculate weight in Kg, ounces
and pounds depending on the settings. They come in various sizes depending on what you’re
weighting. spring balances or spring scales measure force or weight by balancing the force

31
due to gravity against the force on a spring, whereas a balance or pair of scales using a
balance beam compares masses by balancing the force of gravity (weight) due to the mass of
an object against the force due to gravity (weight) of a known mass. Either type of balance or
scales can be calibrated to read in units of force (weight) such as Newtons, or in units of
mass such as kilograms.
Fig 5.3 Digital weighing gauge
3. Bearing:
It is a machine element that constrains relative motion between moving parts to only the
desired motion. It allows one part to bear (i.e., to support) another, i.e., shaft on each side of
the motor is supported by the frame through the hooks. Bearings vary greatly over the size
and directions of forces that they can support. Forces can be predominately radial, axial
(thrust bearings) or bending moments perpendicular to the main axis. Different bearing types
have different operating speed limits. Speed is typically specified as maximum relative
surface speeds, often specified ft/s or m/s. Rotational bearings typically describe performance

32
in terms of the product DN where D is the diameter (often in mm) of the bearing and N is the
rotation rate in revolutions per minute. Generally there is considerable speed range overlap
between bearing types. Plain bearings typically handle only lower speeds, rolling element
bearings are faster, followed by fluid bearings and finally magnetic bearings which are
limited ultimately by centripetal force overcoming material strength.
We have used Roller bearing in which rolling element bearing life is determined by
load, temperature, maintenance, lubrication, material defects, contamination, handling,
installation and other factors. These factors can all have a significant effect on bearing life.
For example, the service life of bearings in one application was extended dramatically by
changing how the bearings were stored before installation and use, as vibrations during
storage caused lubricant failure even when the only load on the bearing was its own weight;
the resulting damage is often false brinelling. Bearing life is statistical: several samples of a
given bearing will often exhibit a bell curve of service life, with a few samples showing
significantly better or worse life. Bearing life varies because microscopic structure and
contamination vary greatly even where macroscopically they seem identical.
Fig 5.4 Bearing and bearing housing

33
5. Reduction Gear Box:
A reduction gear box is use to reduce the speed of main motor to our desire speed.
Here we use a 50:1 reduction ratio gear box by which we obtain a output speed of 28 RPM.
This also helps us for right angle power transmission.
Fig: 5.5 Gear Motor
6. Steel Plate to Rotate the Rotor System:
This plate is fitted with the gear box shaft which rotates with upper system resting on the
plate as per the input speed to the motor. To measure the RPM of the plate a procircle is
attached at the lower side of the plate by which degree of rotation is measured manually.
Fig: 5.6 Gear Motor with Plate

34
5.3 EXPERIMENTAL EXPLANATION:
The assembly consists of a motor having 1440 RPM coupled with worm gear reduction
box (1:50) through which motor power is transmitted 90˚ vertically. A circular plate is
mounted on the shaft in a horizontal plane with a procircle on it to calculate the angular
displacement. The plate is drilled with two holes symmetrically through which it is attached
to a wooden plate using bolts. So, when the metal plate rotates, wooden plate rotates with the
same RPM. The ends of the wooden plates are fixed onto a rectangular frame which has two
hooks to hang the digital weight gauge. A dual shaft motor having specification 50 W, max
speed 9500 rpm which is controlled by a dimmerstat to take the reading at various speed. On
the middle of both the shafts, rotors are welded and at its end, it is supported by the bearings.
The bearing housing has hooks to fit into the hook of digital weight gauge as shown in Fig
5.7 and Fig 5.8.
Fig 5.7 Reactions acting on the system

35
Fig 5.8 Project working
5.4. WORKING:
The bi-shaft motor is regulated at different speeds through a dimmerstat which runs the
shaft, rotor and bearing assembly. At the static condition, the reaction at bearing A and B is
displayed and will be equal on the sides. The rotor rotates on spinning axis. The motor and
rotor system which is hanged onto the frame rotates on a precession plane with precession
velocity ωp.
When rotor rotates in spinning axis, which sets up inertia in the system which is I*ω,
where, I = mk2
k = radius of gyration of rotor R/2
When rotor system rotates in precession plane, the gyroscopic effect is observed when
system takes turn in precession plane. When both motor rotates in anticlockwise direction,
using right hand thumb rule the active gyroscopic couple acts on the left side bearing and
opposite to that the reactive gyroscopic couple is acting. Due to this couple the variation in
digital weighing gauge is observed so that left side bearing is having less reaction than the
right side. This reaction depends upon the inertia of rotor and both the motor speed. This

36
reading is experimental reading and for the theoretical reaction, the gyroscopic couple is
calculated by I ω ωp.
By using, D’Alemberts principle we calculate the theoretical reaction on bearing and
compare the both result experimentally and theoretically.
Fig: 5.9 working model

37
6. OBSERVATIONS AND CALCULATIONS
6.1. OBSERVATION TABLE
1) Mass of rotor =0.58 kg
2) Diameter of rotor =137 mm
3) Distance between the bearings = 240 mm
Table 6.1: Observation Table
Sr
no.
Angular
velocity of
rotor
Angular
velocity of
precision
Reactive
Couple act
due the rotor
in Nm
Deflection
Reaction
on bearing
in kg after
precession
A
Deflection
Reaction on
bearing in kg
after precession
B
1 240 28.8 0.20585 0.08 -0.08
2 375 28.8 0.322 0.12 -0.12
3 568 28.8 0.488 0.20 -0.20
4 198 26.2 0.1548 0.06 -0.06
5 413 26.2 0.323 0.12 -0.12
6 601 26.2 0.466 0.18 -0.18
7 235 22.5 0.157 0.06 -0.06
8 387 22.5 0.313 0.12 -0.12
9 515 22.5 0.345 0.13 -0.13
10 195 20.0 0.116 0.04 -0.04
11 471 20.0 0.2811 0.11 -0.11
12 668 20.0 0.3978 0.15 -0.15
13 208 17.5 0.1086 0.04 -0.04
14 458 17.5 0.239 0.10 -0.10
15 695 17.5 0.362 0.14 -0.14

38
6.2. CALCULATIONS:
Inertia of rotor:
Radius of gyration of rotor: K = r/√2
Inertia of rotor = m‫ܭ‬ଶ
For two rotor multiplied by 2
= 2*0.58*(
଴.ଵଷ଻
ଶ
)2
= 2.7215*10ିଷ
kg m2
1. Calculation for 1st
reading
N=240 rpm Np=28.8 rpm
ω=25.13 rad/sec ωp=3.01rad/sec
C=I.ω. ωp
C=2.7215*10ିଷ
.*25.13*3.01
=0.20585N-m
Now drawing free body diagram for bearing rotor system
Ra =reaction at bearing at A in N
Rb=reaction at bearing at B in N

39
By using
D Alembert’s principal without precision,
ΣFy = 0
Ra +Rb=32.56 N
Taking moment at A
ΣM at A=0
5.68*0.025+21.18*0.12+5.68*0.215-Rb=0
Rb =16.28 N
Also Ra=16.28 N
As the motor made to precess, hence reactive gyroscopic couple applied by the disc to
bearings.
Taking moment at A
Ra*0.24 - 5.68*0.215 - 21.18*0.12 - 5.68*0.025 – C = 0
Ra*0.24 - 5.68*0.215 - 21.18*0.12 - 5.68*0.025 - 0.20585 = 0
Ra = 17.13N
Taking moment at B
Rb*0.24 - 5.68*0.215 - 21.18*0.12 - 5.68*0.025 + C = 0
Rb*0.24 - 5.68*0.215 - 21.18*0.12 - 5.68*0.025 + 0.20585 = 0
Ra = 15.43 N
This is the theoretical reaction on the bearings,

40
Practically its value due to gyroscopic couple is 0.08 kg addition on bearing A and
load on bearing B is reduces by 0.08 kg i.e. active gyroscopic couple and reactive gyroscopic
couple is equal and opposite. By using right hand thumb rule.
At bearing A, 0.08 kg addition i.e. at “A” total reaction is
Ra=16.28+0.08*9.81
Ra=17.06N
At bearing B, 0.08 kg addition i.e. at B total reaction is
Ra=16.28-0.08*9.81
Ra=15.49N
Actual reading is less than the theoretical reading so it is due to frictional resistance.
Calculation for another reading
.ω=43.25 rad/sec ωp=2.7436rad/sec
C=I.߱. ߱‫݌‬
C=2.7215*10ିଷ
.*43.25*2.7436
=0.323N-m

41
By using
Rb =16.28N
Also Ra=16.28N
bearing.
Taking moment at A
Ra *0.24-5.68*0.215-21.18*0.12-5.68*0.025-C=0
Ra *0.24-5.68*0.215-21.18*0.12-5.68*0.025-0.313=0
Ra=17.57N

42
Taking moment at B
Rb *0.24-5.68*0.215-21.18*0.12-5.68*0.025+C=0
Rb *0.24-5.68*0.215-21.18*0.12-5.68*0.025+0.313=0
Ra=14.98N
Practically its value due to gyroscopic couple is 0.12 kg addition on bearing A and load on
bearing B is reduces by 0.12kg i.e active gyroscopic couple and reactive gyroscopic couple
are equal and opposite. By using right hand thumb rule.
At bearing A, 0.12 kg addition i.e at A total reaction is
Ra=16.28+0.12*9.81
Ra=17.457N
At bearing B, 0.12 kg addition i.e at B total reaction is
Ra=16.28-0.12*9.81
Ra=15.1N
2. Calculation for another reading
N=668 rpm Np=20 rpm

43
C=I. ω. ω௣
C=2.7215*10ିଷ
*69.95*2.09
=0.3978N-m
By using
Rb =16.28N
Also Ra=16.28N
bearing.
Taking moment at A
Ra *0.24-5.68*0.215-21.18*0.12-5.68*0.025-C=0
Ra *0.24-5.68*0.215-21.18*0.12-5.68*0.025-0.3978=0
Ra=17.92N

44
Taking moment at B
Rb*0.24-5.68*0.215-21.18*0.12-5.68*0.025+C=0
Rb*0.24-5.68*0.215-21.18*0.12-5.68*0.025+0.3978=0
Ra=14.63N
Practically its value due to gyroscopic couple is 0.15 kg addition on bearing A and
load on bearing B is reduces by 0.15 kg. i.e. active gyroscopic couple and reactive
gyroscopic couple are equal and opposite. By using right hand thumb rule.
At bearing A, 0.15 kg addition i.e. at “A” total reaction is
Ra=16.28+0.15*9.81
Ra=17.75N
At bearing “B”, 0.15 kg addition i.e. at “B” total reaction is
Ra=16.28-0.15*9.81
Ra=14.8N
3. Calculation for another reading
C=I.ω. ωp
C=2.7215*10ିଷ
*72.78*1.83
0.397Nm

45
=0.362N-m
By using
Rb =16.28N
Also Ra=16.28N
bearing.
Taking moment at A
Ra*0.24 - 5.68*0.215 - 21.18*0.12 - 5.68*0.025 – C = 0
Ra*0.24 - 5.68*0.215 - 21.18*0.12 - 5.68*0.025 - 0.362 = 0
Ra = 17.77N

46
Taking moment at B
Rb *0.24-5.68*0.215-21.18*0.12-5.68*0.025+ C = 0
Rb *0.24-5.68*0.215-21.18*0.12-5.68*0.025+0.362 = 0
Ra=14.78N
Practically its value due to gyroscopic couple is 0.14 kg addition on bearing A and load on
bearing B is reduces by 0.14kg i.e active gyroscopic couple and reactive gyroscopic couple
are equal and opposite. By using right hand thumb rule.
At bearing A, 0.14 kg addition i.e at A total reaction is
Ra=16.28+0.14*9.81
Ra=17.65N
At bearing B, 0.15 kg addition i.e at B total reaction is
Ra=16.28-0.14*9.81
Ra=14.90N
0.362Nm

47
7. RESULT TABLE AND GRAPH
7.1 Result Table
Sr
no.
Speed of
rotor in rpm
Speed of
precision
in rpm
Reactive
Couple
act due
the rotor
in Nm
Theoretical
Reaction
on bearing
A
Practical
Reaction
on
bearing
A
Theoretical
Reaction
on bearing
B
Practical
Reaction on
bearing
B
1 240 28.8 0.20585 17.12 17.06 15.43 15.49
2 375 28.8 0.322 17.61 17.45 14.94 15.10
3 568 28.8 0.488 18.303 18.303 18.24 14.31
4 198 26.2 0.1548 16.915 16.86 15.645 15.69
5 413 26.2 0.323 17.615 17.45 14.944 15.10
6 601 26.2 0.466 18.21 18.04 14.348 14.514
7 235 22.5 0.157 16.924 16.868 15.63 15.69
8 387 22.5 0.313 17.574 17.45 14.98 15.10
9 515 22.5 0.345 17.7075 17.55 14.85 15.00
10 195 20.0 0.116 16.75 16.67 15.806 15.8876
11 471 20.0 0.2811 17.441 17.35 15.11 15.20
12 668 20.0 0.3978 17.927 17.75 14.6325 14.8085
13 208 17.5 0.1086 16.72 16.67 15.8375 15.887
14 458 17.5 0.239 17.265 17.261 15.29 15.30
15 695 17.5 0.362 17.778 17.65 14.78 14..906

48
7.2. Graph

49
8. CONCLUSION
As it is very important to know about the various loads acting on bearing at the design
phase so our experimental model will help to determine one of those load.
In this experiment we studied what is gyroscope, its history, how it works and what is
its principle and rule to determine the gyroscopic couple, also types of couple i.e. active and
reactive gyroscopic couple. `
This experimental model is useful to determine the gyroscopic effect on bearing
reaction. This gyroscopic effect is due to the gyroscopic couple, active gyroscopic couple
acts on bearing causes to reduce the reaction on the bearing on the other hand reactive
gyroscopic couple acts on the other bearing which increases the load on the bearing. So this
load is depends on the distance between the bearings , inertia of the rotor i.e. mass and the
diameter of the rotating part, angular velocity of rotating body as well as angular velocity of
precession .
This concept is useful in selection of bearing during particular application where extra
load due to gyroscopic effect occurs on any system.

50
REFERENCES
1.] S.S.Rathan(2009),Theory of Machines, Tata MC Graw Hill Education Pvt.ltd, New Delhi.
3rd edition, 2009, Page No. 480.
2.] Lalanne M and Ferraris G, “Rotor dynamics prediction in engineering”, publishing by
John Wiley & Sons Ltd, England, 2nd edition, 1998, Page 7234, Paper No. -9.
3.] http://en.wikipedia.org/wiki/Gyroscope
4.] Sharma,C.S, Kamalesh Purohit(2006),Theory of Mechanisms and Machines, Prentice-
Hall of India Pvt. Ltd. New Delhi, 2nd edition, 2006, Page 4356, Paper No. -5
5] Theory of machines ,by R.S.Khurmi and Gupta ,
6.] http://en.wikipedia.org/wiki/Inertial_navigation_system
7.] http://ed-thelen.org/Gyro-hcmut.html

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