Unformatted text preview: shaft A , gears 2 and 3 are compound gears which are mounted on shaft B . The gears 4 and 5 are also
compound gears which are mounted on shaft C and the gear 6 is the driven gear mounted on shaft D.
Let
N 1 = Speed of driving gear 1,
T 1 = Number of teeth on driving gear 1,
N 2 ,N 3 ..., N 6 = Speed of respective gears in r.p.m., and
T 2 ,T 3..., T 6 = Number of teeth on respective gears.
Since gear 1 is in mesh with gear 2, therefore its speed ratio is N1 T2
=
N2 T1
Similarly, for gears 3 and 4, speed ratio is ...(i) N3 T4
=
N4 T3
and for gears 5 and 6, speed ratio is ...(ii) N5 T6
=
N6 T5 ...(iii) The speed ratio of compound gear train is obtained by multiplying the equations (i), (ii) and (iii),
∴
* N1 N3 N5 T2 T4 T6
×
×
=
×
×
N 2 N 4 N 6 T1 T3 T5 or *N 1 N6 = T2 × T4 × T6
T1 × T3 × T5 Since gears 2 and 3 are mounted on one shaft B , therefore N 2 = N 3. Similarly gears 4 and 5 are mounted on
shaft C, therefore N 4 = N 5. 432 l Theory of Machines
Speed of the first driver
Speed of the last driven or follower
Product of the number of teeth on the drivens
=
Product of the number of teeth on the drivers i.e. Speed ratio = Speed of the last driven or follower
Speed of the first driver
Product of the number of teeth on the drivers
=
Product of the number of teeth on the drivens
The advantage of a compound train over a simple gear train is that a much larger speed
reduction from the first shaft to the last shaft can be obtained with small gears. If a simple gear train
is used to give a large speed reduction, the last gear has to be very large. 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.
Train value = and Note: The gears which mesh must have the same circular pitch or module. Thus gears 1 and 2 must have the
same module as they mesh together. Similarly gears 3 and 4, and gears
5 and 6 must have the same module. Example 13.1. The gearing of a machine tool is shown
in Fig. 13.3....
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This note was uploaded on 02/13/2014 for the course MIE 301 taught by Professor Celghorn during the Fall '08 term at University of Toronto.
 Fall '08
 CELGHORN

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