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Filiz Ahmet,

A double reduction set of gearing is as shown in the above figure. Wheel A is the driver gear, wheels B and C fixed to the same shaft and wheel D is the final gear in the train. The number of teeth on each wheel is A=20, B=50, C=40, D=30 teeth.
a- Determine the velocity ratio of the gearing system.
b- Calculate the speed of rotation of wheel D when wheel A rotates at 1800 rev/min.
c- Calculate the torque of wheel D when the torque of A is 100 N.m and the efficiency of the gear train is 90%.

a- Velocity ratio = product of teeth of driven gears/ product of teeth on driver gears
i.e. velocity ratio (ig) = (nD nB / nC nA) = (30 x 50) / (20 x 40) = 1.875

b- ND = NA / ig = 1800 / 1.875 = 960 rev/min

c- TD = TA ig hg = 100 x 1.875 x 0.9 = 168.75 N.m

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