Trains - Islamic University of Gazasite.iugaza.edu.ps/mhaiba/files/2013/09/CH13-Gear-Trains...13.2....

Chapter 13

Gear Trains

12/25/2015

Dr. Mohammad Suliman Abuhiba, PE1

4th Exam on Tuesday

15/12/2015

12/25/2015

Dr. Mohammad Suliman Abuhiba, PE

2

13.2. Types of Gear Trains

1. Simple gear train

2. Compound gear train

3. Reverted gear train

4. Epicyclic gear train: axes of shafts on which

gears are mounted move relative to a fixed axis

In first three types of gear trains, axes of shafts

over which gears are mounted are fixed relative

to each other

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13.3. Simple Gear Train

Simple gear train: only one gear on each shaft

Gears are represented by their pitch circles.

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N1 = Speed of gear 1(driver) in rpm

N2 = Speed of gear 2 (driven or follower) in rpm

T1 = Number of teeth on gear 1

T2 = Number of teeth on gear 2

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When number of intermediate gears are odd,

driver & driven rotate in same direction

If number of intermediate gears are even, motion

of driven will be in opposite direction of driver

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Consider a simple train of gears with one

intermediate gear

N1 = Speed of driver in rpm

N2 = Speed of intermediate gear in rpm

N3 = Speed of driven or follower in rpm

T1 = Number of teeth on driver,

T2 = Number of teeth on intermediate gear

T3 = Number of teeth on driven or follower

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Speed ratio & train value, in a simple train of

gears, is independent of size & number of

intermediate gears.

Intermediate gears are called idle gears

Idle gears are used to:

1. connect gears where a large center distance is

required

2. obtain desired direction of motion of driven gear

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13.4. Compound Gear Train

More than one gear on a shaft, Fig. 13.2.

Used Whenever:

distance between driver & driven has to be bridged

over by intermediate gears

a great speed ratio is required

Each intermediate shaft has two gears rigidly

fixed to it

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Usually for a speed reduction in excess of 7 to 1,

a simple train is not used and a compound train

or worm gearing is employed.

Gears which mesh must have same circular pitch

or module

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Example 13.1

The gearing of a machine tool is shown in Fig. 13.3.

The motor shaft is connected to gear A & rotates at

975 rpm. Gear wheels B, C, D and E are fixed to

parallel shafts rotating together. The final gear F is

fixed on output shaft. What is the speed of gear F ?

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Gear A B C D E F

No. of teeth 20 25 50 75 26 65

13.5. Center Distancex = Distance between centers of two shafts

N1 = Speed of driver

T1 = Number of teeth on driver

d1 = Pitch circle diameter of driver

N2 , T2 & d2 = Corresponding values for driven

pc = Circular pitch

Distance between centers of two shafts

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Example 13.2

Two parallel shafts, about 600 mm apart are to be

connected by spur gears. One shaft is to run at 360

rpm and the other at 120 rpm. Design the gears, if

the circular pitch is to be 25 mm.

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13.6. Reverted Gear Train

Reverted gear train: axes of

1st driver & last driven are

co-axial (Fig. 13.4)

motion of 1st gear & last

gear is like

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T1 = # of teeth on gear 1

r1 = Pitch circle radius of

gear 1

N1 = Speed of gear, rpm

T2, T3, T4 = Number of

teeth on respective gears

r2, r3, r4 = Pitch circle radii

of respective gears

N2, N3, N4 = Speed of

respective gears, rpm

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Circular pitch or module of all gears is assumed

to be same

number of teeth on each gear is directly

proportional to its circumference or radius.

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Example 13.3

The speed ratio of the

reverted gear train, Fig.

13.5, is to be 12. The

module pitch of gears A

& B is 3.125 mm and

of gears C & D is 2.5

mm. Calculate the

suitable numbers of

teeth for the gears. No

gear is to have less

than 24 teeth.

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13.7 Epicyclic Gear

Train

Axes of shafts, over

which gears are

mounted, move relative

to a fixed axis.

Useful for transmitting

high velocity ratios with

gears of moderate size

in a comparatively

lesser space.

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13.8. Velocity Ratios of Epicyclic

Gear Train

1. Tabular method

2. Algebraic method

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Gear Train - Tabular method

TA = Number of teeth

on gear A

TB = Number of teeth

on gear B

CCW = +ve

CW = -ve

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Gear Train - Tabular method

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No. Conditions of motion Revolutions of elements

Arm C Gear A Gear B

1 Arm C fixed-gear A

rotates through +1 rev

0 +1 -TA / TB

2 Arm C fixed-gear A

rotates through +x rev

0 +x -x TA / TB

3 Add + y revolutions to

all elements

+y +y +y

4 Total motion +y x+y y -x TA / TB


Gear Train - Algebraic method

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Example 13.4

In an epicyclic gear train, an arm carries two gears

A & B having 36 and 45 teeth respectively.

1. If the arm rotates at 150 rpm ccw about the

center of gear A which is fixed, determine the

speed of gear B.

2. If gear A instead of being fixed, makes 300 rpm

in the cw direction, what will be the speed of

gear B ?

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Example 13.5

In a reverted epicyclic gear train, arm A carries two gears B

and C and a compound gear D - E. Gear B meshes with

gear E and gear C meshes with gear D. The number of

teeth on gears B, C and D are 75, 30 and 90 respectively.

Find the speed and direction of gear C when gear B is fixed

and arm A makes 100 rpm cw.

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Example 13.6

An epicyclic gear consists of

three gears A, B and C. Gear

A has 72 internal teeth and

gear C has 32 external teeth.

Gear B meshes with both A

and C and is carried on an

arm EF which rotates about

the center of A at 18 rpm. If

gear A is fixed, determine the

speed of gears B & C.

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Example 13.7

How many revolutions does the

arm, to which pinions B & C are

attached, make:

1. When A makes one revolution

cw & D makes half a

revolution ccw

2. When A makes one revolution

cw & D is stationary

Number of teeth on gears A & D

are 40 & 90 respectively.

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Example 13.8In an epicyclic gear train, the internal

wheels A & B and compound wheels C

& D rotate independently about axis O.

Wheels E & F rotate on pins fixed to

arm G. E gears with A & C and F gears

with B & D. All wheels have the same

module and the number of teeth are:

TCv= 28; TD = 26; TE = TF = 18.

1. Find number of teeth on A & B

2. If arm G makes 100 rpm cw & A is

fixed, find speed of B

3. If arm G makes 100 rpm cw &

wheel A makes 10 rpm ccw; find

speed of wheel B.

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Example 13.9

In an epicyclic gear of the “sun &

planet” type shown, the pitch circle

diameter of the internally toothed ring

is to be 224 mm and the module 4

mm. When the ring D is stationary, the

spider A, which carries three planet

wheels C of equal size, is to make one

revolution in the same sense as the

sun wheel B for every five revolutions

of the driving spindle carrying the sun

wheel B. Determine suitable numbers

of teeth for all the wheels.

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Example 13.10

Two shafts A and B are co-axial. A gear C (50 teeth)

is rigidly mounted on shaft A. A compound gear D-E

gears with C and an internal gear G. D has 20 teeth

and gears with C. E has 35 teeth and gears with an

internal gear G. Gear G is fixed and is concentric

with the shaft axis. The compound gear D-E is

mounted on a pin which projects from an arm keyed

to the shaft B. Find the number of teeth on internal

gear G assuming that all gears have the same

module. If shaft A rotates at 110 rpm, find the speed

of shaft B.

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Example 13.1012/25/2015


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Trains - Islamic University of Gazasite.iugaza.edu.ps/mhaiba/files/2013/09/CH13-Gear-Trains...13.2....

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