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Question 15.32: In the epicyclic gear train shown in Fig.15.36, the compound...

In the epicyclic gear train shown in Fig.15.36, the compound wheels E and F rotate freely on shaft A which carries the planet carrier G. The planets B and C are compounded gears. The number of teeth on each gear are: z_{e}=30 ; z_{b}=20, z_{c}=18, z_{d}=68.
The shafts A and K rotate in the same direction at 250 rpm and 100 rpm respectively. Determine the speed of shaft J.

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Table 15.29 is used to find the speed of gears.

z_{f}=z_{c}+z_{d}-z_{b}=18+68-20=66 .

n_{a}=n_{g}= y =250 .

n_{e}=n_{h} \times 15 / 30=-100 \times 15 / 30=-50 .

x+y=-50 .

x=-300 .

n_{j}=n_{d}=y+297 x / 340=250+(297 / 340)(-300) .

= –12.06 rpm, i.e. 12.06 rpm cw.

Table 15.29
Revolutions of Operation
Gear D, 68 Gear B/C, 20, 18 Gear E/F, 30, 66 Arm, G
-z / z_{b} \times\left(-z_{c} / z_{d}\right)=

-(33 / 10) \times(-18 / 68)=297 / 340

 -z / z_{b}=-66 / 20

=-3.3

 +1 0 1. Arm fixed,+1 rev to E ccw
297x/340 -3.3x +x 0 2. Multiply by x
y + 297x/340 y-3.3x y+x y 3. Add y

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