An epicyclic gear train as shown in Fig.15.34, has a sun wheel S of 30 teeth and two planet wheels P - P of 45 teeth. The planet wheels mesh with the internal teeth of a fixed annulus A. The driving shaft carrying the sun wheel transmits 4 kW at 360 rpm. The driven shaft is connected to an arm,

Question

An epicyclic gear train as shown in Fig.15.34, has a sun wheel S of 30 teeth and two planet wheels P - P of 45 teeth. The planet wheels mesh with the internal teeth of a fixed annulus A. The driving shaft carrying the sun wheel transmits 4 kW at 360 rpm. The driven shaft is connected to an arm, which carries the planet wheels. Determine the speed of the driven shaft and the torque transmitted, if the overall efficiency is 95%.

Accepted Answer

Given: [latex] z_{s}=30, z_{p}=45 [/latex].

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

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

[latex] z_{a}=30+90=120 [/latex].

Table 15.28 is used to find the speed of gears.

Table 15.28
Revolutions of				Operation
A	P	S	Arm	Operation
[latex]\frac{-z_{s}}{z_{a}}=\frac{-30}{120}[/latex]	[latex]\frac{-z_{s}}{z_{p}}=-\frac{30}{45}[/latex] [latex]=-\frac{1}{4}[/latex]	+1 [latex]=-\frac{2}{3}[/latex]	0	1. Arm fixed, +1 rev to S, ccw
[latex]\frac{-x}{4}[/latex]	[latex]-\frac{2 x}{3}[/latex]	+x	0	2. Multiply by x
[latex]y-\frac{x}{4}[/latex]	[latex]y-\frac{2 x}{3}[/latex]	y+x	y	3. Add y

A fixed: [latex]y-\frac{x}{4}=0[/latex].

y + x = 360.

x = 288 rpm, y = 72rpm
Speed of driven shaft = 72 rpm

Input torque, [latex]T_{1}=\frac{4 imes 10^{3} imes 60}{2 \pi imes 360}=106.1 Nm[/latex].

[latex]T_{1} n_{1}+T_{2} n_{2}=0[/latex].

[latex]T_{2}=-106.1 imes \frac{360}{72}=-530.5 Nm[/latex].

Question 15.30: An epicyclic gear train as shown in Fig.15.34, has a sun whe...

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