In an epicyclic gear train of the sun and planet type shown in Fig.15.33, the pitch circle diameter of the annular wheel A is to be nearly equal to 216 mm, and the module is 4 mm. When the annular wheel is stationary, the spider which carries three planet gears P of equal size, has to make one

Question

In an epicyclic gear train of the sun and planet type shown in Fig.15.33, the pitch circle diameter of the annular wheel A is to be nearly equal to 216 mm, and the module is 4 mm. When the annular wheel is stationary, the spider which carries three planet gears P of equal size, has to make one revolution for every five revolutions of the driving spindle carrying S gear. Determine the number of teeth on all the wheels and also the exact pitch circle diameter of A.

Accepted Answer

[latex] d_{a}=d_{s}+2 d [/latex].

[latex] 216=4\left(z_{s}+2 z_{p}\right) [/latex].

[latex] z_{s}+2 z_{p}=54 [/latex].

[latex] d_{a}=m z_{a}, z_{a}=\frac{216}{4}=54 [/latex] (1).

Table 15.27 is used to find the speed of gears.

x + y = 5.

[latex] y-\frac{x z_{s}}{z_{p}}=-1 [/latex].

Solving, we get

[latex] x\left(1+\frac{z_{s}}{z_{p}}\right)=6 [/latex] (2).

Also [latex] y-\frac{x z_{s}}{z_{a}}=0 [/latex].

Table 15.27
Revolutions of				Operation
A	P	S	Spider	Operation
[latex]\frac{-z_{s}}{z_{a}}[/latex]	[latex]\frac{-z_{s}}{z_{p}}[/latex]	+1	0	1. Spider fixed, +1rev to S ccw
[latex]\frac{-x z_{s}}{z a}[/latex]	[latex]\frac{-x z_{s}}{z_{p}}[/latex]	+x	0	2. Multiply by x
[latex]y-\frac{x z_{s}}{z_{a}}[/latex]	[latex]y-\frac{x z_{s}}{z_{p}}[/latex]	y+x	y	3. Add y

Thus [latex] x\left(1+\frac{z_{s}}{z_{a}}\right)=5 [/latex] (3).

Solving Eqs. (1), (2), and (3), we get

[latex] l_{c}-z_{s}=10, z_{p}=22, d_{a} 216 mm [/latex].

Question 15.29: In an epicyclic gear train of the sun and planet type shown ...

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