This document discusses the gyroscopic effect on bearings that support a spinning disc or wheel. It defines key terms like gyroscope, axis of spin, gyroscopic effect, precession, and axis of precession. It then describes how a disc mounted on a horizontal axle between two bearings will experience precession when it spins, and how this causes a gyroscopic couple reaction force on each bearing. Equations are provided showing how to calculate the resultant reaction forces on each bearing when considering both the weight-induced reactions and the gyroscopic couple reaction. In summary, it analyzes how a spinning disc's precession due to its own spin introduces gyroscopic forces that affect the bearing reactions.

1. Sanjivani Rural Education Society’s
Sanjivani College of Engineering, Kopargaon-423603
( An Autonomous Institute Affiliated to Savitribai Phule Pune University, Pune)
NAAC ‘A’ Grade Accredited, ISO 9001:2015 Certified
Subject :- Theory of Machines II
T.E. Mechanical (302043)
Unit 5 GYROSCOPE
5.2 Gyroscopic Efect on Bearing
By
Prof. K. N. Wakchaure(Asst Professor)
Department of Mechanical Engineering
Sanjivani College of Engineering
(An Autonomous Institute)
Kopargaon, Maharashtra
Email: wakchaurekiranmech@Sanjivani.org.in Mobile:- +91-7588025393

2. INTRODUCTION
• Gyroscope: It is a body which while spinning about an axis is free to move in other direction under the action of external
forces.
• Axis of spin: It is axis about which the body revolves.
• Gyroscopic effect: Consider a body spinning about an axis OX . If a couple represented by a vector OZ perpendicular to
OX is applied, then the body tries to precess about an axis OY, which is perpendicular to both OX and OZ. This combined
effect is called gyroscopic or precessional effect.
• The plane of spin, plane of precession, and plane of gyroscopic couple are mutually perpendicular.
• Precession: It means the rotation about the third axis OY, which is perpendicular to both the spin axis OX and the couple
axis OZ.
• Axis of precession: The third axis OY about which a body revolves and is perpendicular to both the spin axis OX and
couple axis OZ, is called the axis of precession.
• Mechanical gyroscope: It is a special mechanism generally employed for the control of angular motion of a body.
Gyroscope is an instrument, which appears as a device possessing intelligence. Gyroscopic effects can be used in several
applications for directional control, e.g. in Gyrocompass used on aeroplanes and ships and in inertia guidance control
system for missiles and space craft control.

3. Plane of Precession
Plane of
Spinning
Plane of Gyroscopic
couple
Axis of Spinning
AxisofPrecession
Plane of Precession
Plane of
Spinning
Plane of
Gyroscopic couple
INTRODUCTION

4. Axis of Spinning
AxisofPrecession

5. 𝑙1 𝑙2
𝑙
A B
• Consider a disc of mass m and radius of gyration K mounted centrally on a horizontal axle of length between the
bearings.
• Let the disc spin with angular speed 𝜔 counter-clockwise when viewed from the right-hand side bearing.
• The axle precesses about a vertical axis at 𝜔 𝑝 speed in the Anti clock-wise direction when viewed from above. T
Reaction on each wheel due to weight of Disc
By taking moment about A
𝑀 × 𝑔 × 𝑙1 − 𝑅 𝐵𝑊 × 𝑙 = 0 𝑅 𝐴𝑤 𝑅 𝐵𝑊
𝑀 × 𝑔
𝑅 𝐵𝑊 = 𝑀 × 𝑔 ×
𝑙1
𝑙
𝑅 𝐴𝑊 = 𝑀 × 𝑔 ×
𝑙2
𝑙
Reaction on bearing due to weight of Mass are 𝑅 𝐴𝑊 and 𝑅 𝐵𝑊
Reaction on bearing due to Gyroscopic couple is 𝑅 𝐺
EFFECT OF GYROSCOPIC COUPLE ON BEARINGS
EFFECT OF GYROSCOPIC COUPLE ON BEARINGS

6. Axis of Spinning
AxisofPrecession
𝑙1
𝑙2
𝑙
A B
𝑅 𝐴𝑤 𝑅 𝐵𝑊
Gyroscopic Couple 𝐶 = 𝐼 × 𝜔 × 𝜔 𝑃
Reaction due to co𝑢𝑝𝑙𝑒 𝐶 = 𝑅 𝐺 × 𝑙
Reaction on Ea𝑐ℎ 𝑏𝑒𝑎𝑟𝑖𝑛𝑔 𝑅 𝐺 =
𝐶
𝑙
EFFECT OF GYROSCOPIC COUPLE ON BEARINGS

7. 𝑙1
𝑙2
𝑙
A B
𝑅 𝐴𝑤 𝑅 𝐵𝑊
Gyroscopic Couple 𝐶 = 𝐼 × 𝜔 × 𝜔 𝑃
Gyroscopic Reaction on Ea𝑐ℎ 𝑏𝑒𝑎𝑟𝑖𝑛𝑔 𝑅 𝐺 =
𝐶
𝑙
𝑅 𝐺𝑅 𝐺
𝑅 𝐵𝑊 = 𝑀 × 𝑔 ×
𝑙1
𝑙
𝑅 𝐴𝑊 = 𝑀 × 𝑔 ×
𝑙2
𝑙
𝑅𝑒𝑠𝑢𝑙𝑡𝑎𝑛𝑡 𝑅𝑒𝑎𝑐𝑡𝑖𝑜𝑛 𝑎𝑡 𝐵𝑒𝑎𝑟𝑖𝑛𝑔 𝐴 𝑅 𝐴 = 𝑅 𝐴𝑊 + 𝑅 𝐺
𝑅𝑒𝑠𝑢𝑙𝑡𝑎𝑛𝑡 𝑅𝑒𝑎𝑐𝑡𝑖𝑜𝑛 𝑎𝑡 𝐵𝑒𝑎𝑟𝑖𝑛𝑔 𝐵 𝑅 𝐵 = 𝑅 𝐵𝑊 − 𝑅 𝐺
EFFECT OF GYROSCOPIC COUPLE ON BEARINGS

8. https://youtu.be/ty9QSiVC2g0

9. Axis of Spinning
AxisofGyroscopic
Couple
Gyroscopic EffectCondition
Observer: STERN End
Rotor: CCW
Pitching: DOWNWARD
AxisofReactive
GyroscopicCouple
Wheel will rotate in Anticlockwise direction
about vertical axis when viewed from top
Due to weight o the wheel, wheel
precesses in downward direction

10. Thank You….
10Subject :- Theory of Machines II