Trains - site.iugaza.edu.pssite.iugaza.edu.ps/mhaiba/files/2013/09/CH13-Gear-Trains.pdf · Example...

Chapter 13

Gear Trains

11/23/2013

Dr. Mohammad Suliman Abuhiba, PE 1

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 the

gears are mounted may move relative to a fixed

axis.

In the first three types of gear trains, axes of

shafts over which the gears are mounted are

fixed relative to each other

11/23/2013

Dr. Mohammad Suliman Abuhiba, PE

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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 the number of intermediate gears are odd,

the driver & driven rotate in the same direction

If number of intermediate gears are even, the

motion of the driven will be in the opposite

direction of the 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

The 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

Compound train of gears: more than one gear on a shaft,

Fig. 13.2.

Used Whenever distance between driver & driven has to

be bridged over by intermediate gears and at the same

time 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 the 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. Design of Spur Gears x = Distance between centers of two shafts

N1 = Speed of the driver

T1 = Number of teeth on the driver

d1 = Pitch circle diameter of the 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 1 in

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 in 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 the shafts, over

which the gears are

mounted, may move

relative to a fixed axis.

Epicyclic gear trains are

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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Step

No.

Conditions of motion Revolutions of elements

Arm C Gear A Gear B

1 Arm fixed-gear A rotates through +1 rev 0 +1 -TA / TB

2 Arm 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

2. Algebraic method

Example 13.4

In an epicyclic gear train, an arm carries two gears A and B

having 36 and 45 teeth respectively. If the arm rotates at

150 rpm in the ccw direction about the center of gear A

which is fixed, determine the speed of gear B.

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 clockwise.

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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 the pinions B and C

are attached, make:

1. when A makes one revolution

cw and D makes half a

revolution ccw

2. when A makes one revolution

cw and D is stationary

The number of teeth on gears A &

D are 40 and 90 respectively.

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Example 13.8 In an epicyclic gear train, the internal

wheels A and B and compound wheels

C and D rotate independently about

axis O. The wheels E and F rotate on

pins fixed to the arm G. E gears with A

& C and F gears with B & D. All the

wheels have the same module and the

number of teeth are: TC= 28; TD= 26;

TE= TF= 18.

1. Find the number of teeth on A & B

2. If arm G makes 100 rpm cw and A

is fixed, find the speed of B

3. If arm G makes 100 rpm. Cw and

wheel A makes 10 rpm ccw; find the

speed of wheel B.

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Example 13.9

In an epicyclic gear of the ‘sun and

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 13.10 11/23/2013


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Evaluation Quiz

Quiz will be held on

Wednesday 20/11/2013

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