Gear Trains

1
Example 5
In a reduction gear shown in Figure, there is an
epicyclic train consisting of a sun wheel A on
the input shaft, a planet wheel B carried on an
arm K on the output shaft and an annular gear C.
Dr.T.V.Govindaraju,SSEC
2
Example 5
The latter can be held fixed, or can be connected
directly to the input shaft through the spur gear
drive DEFGH. Find the speed ratio from input to
output for the two cases (i) with EFG engaged.
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3
Example 5
For case (ii) determine also the torque
transmitted between A and D and between F G,
based on an input torque of 100 N-m. Take module
2 for all teeth.
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4
Example 5
Number of teeth on A D F G 40 Number of
teeth on C 80 H 100 E 30 B 20.
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5
Example 5-Continued
Solution The train EFG is not part of the
epicyclic train and must be therefore be treated
separately. Consider, train Z, K, H, C, B, A and
D
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Example 5-Continued
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Example 5-Continued
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Example 5-Continued
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Example 5-Continued

• When C is fixed
• m n 0
• ? n - m

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Example 5-Continued
(ii) When train EFG is engaged
Number of teeth on A F D G 40 Number of
teeth on C 80 H 100 E 30 B 20.
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Example 5-Continued
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Example 5-Continued


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Example 5-Continued
Input torque on A and D
100 N-m ?Resisting torque on Z TZ 100 ?
15 1500 N-m - in the opposite
direction of rotation


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Example 5-Continued
Force on the axis B

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Example 5-Continued
Let TC Torque exerted on C and G
Force between the teeth C and B

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Example 5-Continued
Since no angular acceleration of B, the force
between the teeth on A and B is also

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Example 5-Continued
both these forces being opposite to FB ? for
equilibrium of B

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Example 5-Continued
Torque on A

(D m x t)
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Example 5-Continued
Torque applied by G to H

(D m x t)
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20
Example 5-Algebraic Method
Consider, train Z, K, H, C, B, A and D
When C is fixed

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Example 5-Algebraic Method

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Example 5-Continued
(ii) When train EFG is engaged
Number of teeth on A F D G 40 Number of
teeth on C 80 H 100 E 30 B 20.
End of 5
Dr.T.V.Govindaraju,SSEC
23
Example 6
Figure shows a compound epicyclic gear train,
gears S1 and S2 being rigidly attached to the
shaft Q. If the shaft P rotates at 1000 rpm
clockwise, while the annular A2 is driven in
counter clockwise direction at 500 rpm, determine
the speed and direction of rotation of shaft Q.

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24
Example 6
The number of teeth in the wheels are S1 24
S2 40 A1 100 A2 120.

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Example 6-Continued
Solution Consider the gear train P, P1, A1 and
S1

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Example 6-Continued
If A1 is fixed n m0 gives n - m

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Example 6-Continued
OR

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Example 6-Continued
Now consider whole gear train

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Example 6-Continued
Now consider whole gear train

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Example 6-Continued
Now consider whole gear train

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Example 6-Continued
Now consider whole gear train

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Example 6-Continued
When P makes 1000 rpm 1000 (1)
and A2 makes 500 rpm n m -500 (2)
from (1) and (2)
? NQ n 3 m 449 (3 ? -949) 3296 rpm
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33
Example 7
The gear train shown in figure is used in an
indexing mechanism of a milling machine. The
drive is from gear wheels A and B to the bevel
gear wheel D through the gear train. The
following table gives the number of teeth on each
gear.
Dr.T.V.Govindaraju,SSEC
34
Example 7-Continued
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Example 7-Continued
How many revolutions does D makes for one
revolution of A under the following
situations (i) If A and B are having the same
speed and same direction (ii) If A and B are
having the same speed and opposite
direction (iii) If A is making 72 rpm and B is
at rest (iv) If A is making 72 rpm and B 36 rpm
in the same direction
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Example 7-Continued
Solution Gear D is external to the epicyclic
train and thus C and D constitute an simple gear
train.
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Example 7-Continued
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Example 7-Continued
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Example 7-Continued
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Example 7-Continued
For one revolution of A n m 1 (1) For A and
B for same speed and direction
n m n m (2) From (1) and
(2) n 1 and m 0
? If C or arm makes one revolution, then
revolution made by D is given by
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41
Example 7-Continued
(ii) A and B same speed, opposite direction
(n m) - (n
m) (3) n 0 m 1 ? When C is fixed and A
makes one revolution, D does not make any
revolution.
(iii) A is making 72 rpm (n m) 72 B
at rest (n m) 0 ? n m 36 rpm ? C
makes 36 rpm and D makes
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42
Example 7-Continued
(iv) A is making 72 rpm and B making 36 rpm
(n m) 72 rpm and (n m) 36 rpm
(n (n m)) 72 ? n 54 ? D makes
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