Gear train

1. Title of the Course: Dynamics of Machines
Course Code: UMCH0503
Unit 1:---Gear Trains
Types of Gear trains- Simple, Compound, Reverted, Epicyclic gear train,
Tabular method for finding the speeds of elements in epicyclic gear train,
Differential gear box. Equivalent mass and Moment of Inertia applied to
gear trains.
Unit 2:---Gyroscope
Gyroscopic couple, Spinning and Precessional motion, Gyroscopic couple
and its effect on – i) Aero plane ii) Ship iii) Four-Wheeler iv) Two –
Wheeler.
Unit 3:---Static and Dynamic force analysis
Velocity and acceleration of slider crank mechanism by analytical method,
Inertia force and torque, D’Alembert’s principle, Dynamically equivalent
system, force analysis of reciprocating engine mechanism.

2. Unit 4:--- Balancing and Flywheel
Static and Dynamic balancing of rotary and reciprocating masses. Primary
and Secondary forces and couples. Direct and Reverse cranks. Balancing of
Single cylinder, Multi cylinder-Inline Engines. Function of flywheel and
Study of turning moment diagram.
Unit 5:---Free Vibrations (SDOF)
Basic concepts and definitions, vibration measuring parameters-
Displacement, Velocity and acceleration, Free and forced vibrations,
Equivalent Springs. Types of damping. Free vibrations with and without
damping (Rectilinear, Torsional & Transverse), degree of damping.
Logarithmic decrement, equivalent viscous damping, Coulomb damping .
Unit 6:---Forced Vibrations (SDOF)
Forced vibrations with viscous damping, magnification factor, frequency
response curves, vibration isolation and transmissibility, forced vibrations
due to support excitation. Critical speed of shafts.

3. Textbooks
• Ratan S.S, “Theory of Machines”, Tata McGraw
Hill, New Delhi, 3rd Edition, 2011
• Sadhu Singh,“Theory of Machines”, Pearson
Education, 2nd Edition, 2009
• H. G. Phakatkar,“Theory of Machines I”,
Edition 2009.Nirali Publication,5th Edition
2009.
• Mechanical Vibrations by Grover G.K.,
Nemchand Publications

4. Lab Work
• Experiment No.1:- Experiment on Torque Measurement in Epicyclic Gear Train.
• Experiment No. 2:- Experiment on Gyroscope.
• Experiment No. 3:- Determination of M.I. using Bifilar and Trifilar suspension system.
• Experiment No. 4:- Determination of M.I. of connecting rod by Compound pendulum method.
• Experiment No. 5:- Experiment on Balancing of rotary masses (Static and Dynamic).
• Experiment No. 6:- Experiment on equivalent spring mass system.
• Experiment No.7:-Determination of logarithmic decrement for single DOF damped system
• Experiment No. 8:- Experiment on study of forced vibration characteristics
• Experiment No. 9:- Experiment on Whirling of Shaft
• Experiment No. 10:- Study and experiment on Vibration measuring Instrument
• Experiment No.11:- Industrial visit based on above syllabus.

5. Revision of gear
• Types of Gears
Spur Gear, Helical Gear, Bevel Gear, Worm
and worm wheel, rack and pinion
Gear Terms -
Z = Number of teeth, d= Pitch circle diameter (PCD)
Module (m) = d/z,
Circular Pitch ( Pc) = Π d/z = Π m
velocity ratio = speed of follower/ speed of driver

6. Gear Train
• When two or more gears are made to mesh
with each other to transmit power from one
shaft to another such combination is
called gear trains.
• We have generally 4-types of gear trains, and
those are:
• Simple Gear Train
• Compound Gear Trains
• Reverted gear Trains
• Epicyclic Gear Trains

7. Simple Gear Trains
• When there is only one gear fitted on each
shaft, then this type of gearing system named
Simple gear trains.

8. Velocity Ratio

9. Idler gears
• It may be noted that when the number of
intermediate gear is odd the motion of both
the driver gear and driven gear have the same
direction of motion, but when the number of
driver gear and driven gear even then we see
the opposite direction of motion between
driver and driven gears.

10. Idler Gears are used
- To connect gears where a large center
distance is required
- to obtain desired direction of motion of the
driven gear ( CW or CCW)
- to obtain high speed ratio

11. Compound Gear Trains
• When we need higher speed ration or a much
lower speed ratio then we need to use
compound gear trains.
• In this case, each intermediate shaft has two-
gears rigidly fixed to it.
• Due to both the gears fitted on the same
shaft, we can see the same speed in both the
gears.

13. Advantages of Compound gear train
• A much larger speed reduction from the first
shaft to the last shaft can be obtained with
small gear.
• If a simple gear trains used to give a large
speed reduction, the last gear has to be very
large.

14. • Reverted gear Trains:
• In the case of the reverted gear train, the
driver and the last gear are Co-axial.
• This type of arrangement is used in clocks and
in simple lathe where back gears are used to
give a slow speed to the chuck.

16. Problem
• A compound gear train of 4 gears has
following teeth, gear A = 36, B = 50, C = 24 and
D = 54. Gear B and C are on same shaft and
rotate together. If gear A transmits 4.5 Kw at
200 rpm and gear train has 80% efficiency,
what is torque on output shaft?

17. SOLUTION
• GIVEN :
• ZA = 36, ZB = 50, ZC = 24, ZD = 54,
• B and C Compound, NB = NC
• Power at A = 4.5 Kw = 4500 watts
• NA = 200 rpm
•
• ND ZA ZC
• ---- = -------------
• NA ZB ZD
•
• 36 x 24
• ND = ------------------- x 200 = 64 rpm
• 50 x 54
•
• Output Power = PD = 0.8 x 4500 = 3600 watts
• 2 Π ND TD
• PD = ---------------
• 60
•
• 2 Π x 64 x TD
• 3600 = ----------------------------
• 60
•
• Torque at D (TD )= 537 N-M

18. Epicyclic Gear Trains
• When axis of one gear move relative to other
then the gear train is known as Epicyclic Gear
Train
• The epicyclic gear train is useful for
transmitting high-velocity ratio with a gear of
moderate size and in less space.