# 132 the gear 1 is the driving gear mounted on shaft a

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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.

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