Answer to Question #200277 in Mechanical Engineering for Muhammad Idrees

Question

In an epicyclic gear train of the ‘sun and planet type’ as shown in Fig. 13.41, the pitch circle diameter of the internally toothed ring D is to be 216 mm and the module 4 mm. When the ring D is stationary, the spider A, which carries three planet wheels C of equal size, is to make one revolution in the same sense as the sun wheel B for every five revolutions of the driving spindle carrying the sunwheel B.

Determine suitable number of teeth for all the wheels and the exact diameter of pitch circle of the ring.

Answer 1

When the sun wheel makes +5 revolutions the spindle make +1 revolution

Therefore, $x+y=5 \implies x=-y+5 \implies 5-y=5-1 \implies x=4$

$y-x*\frac{T_B}{T_D}=0 \implies 2-4*\frac{T_B}{T_D}=0 \implies T_D=4T_B$

$T_D=\frac{d_D}{m}=\frac{216}{4}=56$ But the standard is 56.

So, $T_B=\frac{T_D}{4}=\frac{56}{4}=14$

Assuming the pitch of all the gears to be the same

$d_D=d_B+2d_C$

Since the number of the teeth is proportional to their pitch circle diameters

$T_D=T_B+2T_C \implies 14+2T_C=56 \implies T_C=\frac{56-14}{2}=21$

Exact pitch circle diameters

$d _D =d_B +2d_C=mT_B+2mT_C= 4(14+2*21)=224 mm ​$