Introduction:

Sometimes, two or more gears are made to mesh with each other to

transmit power from one shaft to another. Such a combination is

called gear train or train of toothed wheels. The nature of the train

used depends upon the velocity ratio required and the relative

position of the axes of shafts. A gear train may consist of spur, bevel

or spiral gears.

Types of Gear Trains:

Following are the different types of gear trains, depending upon the

arrangement of wheels:

1. Simple gear train,

2. Compound gear train,

3. Reverted gear train, and

4. Epicyclic gear train.

In the first three types of gear trains, the axes of the shafts over

which the gears are mounted are fixed relative to each other. But in

case of epicyclic gear trains, the axes of the shafts on which the gears

are mounted may move relative to a fixed axis.

When there is only one gear on each shaft, as shown in Fig. 13.1,

it is known as simple gear train. The gears are represented by their

pitch circles. When the distance between the two shafts is small, the

two gears 1 and 2 are made to mesh with each other to transmit

motion from one shaft to the other, as shown in Fig. 13.1 (a). Since

the gear 1 drives the gear 2, therefore gear 1 is called the driver and

the gear 2 is called the driven or follower. It may be noted that the

motion of the driven gear is opposite to the motion of driving gear.

The typical spur gears as shown in diagram. The direction of rotation

is reversed from one gear to another. It has no effect on the gear

ratio. The teeth on the gears must all be the same size so if gear A

advances one tooth, so does B and C.

A gear train is two or more gear working together by meshing their

teeth and turning each other in a system to generate power and

speed. It reduces speed and increases torque. To create large gear

ratio, gears are connected together to form gear trains. They often

consist of multiple gears in the train.

The most common of the gear train is the gear pair connecting

parallel shafts. The teeth of this type can be spur, helical or

herringbone. The angular velocity is simply the reverse of the tooth

ratio. Any combination of gear wheels employed to transmit motion

from one shaft to the other is called a gear train. The meshing of two

gears may be idealized as two smooth discs with their edges

touching and no slip between them. This ideal diameter is called the

Pitch Circle Diameter (PCD) of the gear.

Gear Terminology:

The following are the important dimensions and geometries

concerned with toothed gear:

Pitch Circle:

Pitch circle is the apparent circle that two gears can be taken like

smooth cylinders rolling without friction.

Addendum Circle:

Addendum circle is the outer most profile circle of a gear. Addendum

is the radial distance between the pitch circle and the addendum

circle.

Dedendum Circle:

Dedendum circle is the inner most profile circle. Dedendum is the

radial distance between the pitch circle and the dedendum circle.

Clearance:

Clearance is the radial distance from top of the tooth to the bottom

of the tooth space in the mating gear.

Backlash:

Backlash is the tangential space between teeth of mating gears at

pitch circles.

Full Depth:

Full depth is sum of the addendum and the dedendum.

Face Width:

Face width is length of tooth parallel to axes.

Diametral Pitch:

Diametral pitch (p) is the number of teeth per unit volume.

p = (Number of Teeth) / (Diameter of Pitch circle)

Module:

Module (m) is the inverse of diametral pitch.

m = 1/p

Circular Pitch:

Circular pitch is the space in pitch circle used by each teeth.

Gear Ratio:

Gear ratio is numbers of teeth of larger gear to smaller gear.

Pressure Line:

Pressure line is the common normal at the point of contact of mating

gears along which the driving tooth exerts force on the driven tooth.

Pressure Angle:

Pressure angle is the angle between the pressure line and common

tangent to pitch circles. It is also called angle of obliquity. High

pressure angle requires wider base and stronger teeth.

Pitch Angle:

Pitch angle is the angle captured by a tooth.

Pitch angle = 360/T

Contact Ratio:

Contact ratio is angle of angle of action and pitch angle.

Path of Approach:

Path of approach is the distance along the pressure line traveled by

the contact point from the point of engagement to the pitch point.

Path of Recess:

Path of recess is the distance traveled along the pressure line by the

contact point from the pitch point to the path of disengagement.

Path of Contact:

Patch of contact is the sum of path of approach and path of recess.

Arc of Approach:

Arc of approach is the distance traveled by a point on either pitch

circle of the two wheels from the point of engagement to the pitch.

Arc of Recess:

Arc of recess is the distance traveled by a point on either pitch circle

of the two wheels from the point to the point of disengagement.

Arc of Contact:

Arc of contact is the distance traveled by a point on either pitch circle

of the two wheels during the period of contact of a pair of teeth.

Angle of Action:

Angle of action is the angle turned by a gear during arc of contact.

COMPOUND GEAR TRAIN:

Theory

A compound gear is a number of gears fixed together. Consequently,

they rotate at the same speed.

The gears that make up a compound gear usually differ in size and

have a different number of teeth. This is useful if there is a need to

speed up or slow down the final output.

Compound gear trains have two or more pairs of gears in mesh, so

that they rotate together. This compound gear train has gears on

three shafts. The gear on the input shaft meshes with a larger gear

on a counter-shaft or cluster gear. The counter-shaft has a smaller

gear formed on it, in mesh with the output shaft gear. The motion of

the input is transferred through the large gear, along the counter-

shaft to the smaller gear, to the output. The output turns in the same

direction as the input, but at a reduced ratio, depending on the

relative sizes of the gears. Since two pairs of gears are involved, their

ratios are “compounded”, or multiplied together.

Diagram:

Working:

When there is more than one gear on a shaft, as shown in Fig. it is called a compound train of gear.

We have seen in previous section that the idle gears, in a simple train

of gears do not affect the speed ratio of the system. But these gears

are useful in bridging over the space between the driver and the

driven. But whenever the distance between the driver and the driven

or follower has to be bridged over by intermediate gears and at the

same time a great (or much less) speed ratio is required, then the

advantage of intermediate gears is intensified by providing

compound gears on intermediate shafts. In this case, each

intermediate shaft has two gears rigidly fixed to it so that they may

have the same speed. One of these two gears meshes with the driver

and the other with the driven or follower attached to the next shaft

as shown in Fig.

The input gear, with 12 teeth, drives its mating gear on the counter-

shaft, which has 24 teeth. This is a ratio of 2 to 1. This ratio of

DRIVEN over DRIVER at the Input - 2 to 1 - is then multiplied by the

Output ratio, which has a DRIVEN to DRIVER ratio of 3 to 1. This gives

a gear ratio of 6 to 1 between the input and the output, resulting in a

speed reduction and a corresponding increase in torque. Gear

reductions in the lower gears of manual transmissions can be

provided by compound gear trains.

Typical ratios are, 1st gear - 4.41 to 1 2nd gear - 2.63 to 1, and 3rd

gear - 1.61 to 1. Fourth gear is normally a ratio of 1 to 1. The input

and output shafts turn at the same speed. There is no torque

multiplication. A fifth gear is normally an overdrive ratio, typically

with a value of .87 to 1. Then the output shaft turns faster than the

input, but the output torque is reduced.

A further reduction is always provided by the final drive gears.

Their ratio is included when calculating overall gear reduction. The

overall gear ratio is the gearbox ratio multiplied by the final drive

ratio. A gearbox ratio of 3 to 1 with a final drive ratio of 4 to 1, gives

an overall ratio of 12 to 1. 12 revolutions of the crankshaft result in 1

turn of the driving road wheels. Assuming 100% efficiency, the

torque applied is 12 times the engine torque, although this is divided

equally between the driving wheels.

Calculation:

• For large velocities ratios, compound gear train arrangement is

preferred.

• The velocity of each tooth

• on A and B are the same so:

• A tA = B tB

C

D

A

B

DB

CA

C

DD

A

BBCA

C

DDC

A

BBA

C

D

D

C

A

B

B

A

tt

tt

tt

tt

Ttand

tt

ttand

tt

GR

tt

tt

OutNInNaswritten

bemayratiogearTheNSince

GRtt

tt

shaftsametheonareCandBgearSince

C

D

A

B

C

D

A

B

D

A

CB

:

2

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.

Applications:

- Any power plant that uses more than a single steam turbine as a

prime mover to transmit the power compound gear.

- They use a compound gear train to get everything going the same

way at the same time and at the same speed in ship for instance.

Content:

1. Introduction

2. Types of Gear Trains

3. Gear Terminology

4. COMPOUND GEAR TRAIN

a. Theory

b. Diagram

c. Working

d. Calculation

e. Advantages and Disadvantages

f. Application