Page 418 - Thomson, William Tyrrell-Theory of Vibration with Applications-Taylor _ Francis (2010)

Sec. 12.11 Branched Systems 405

( 1 )
(a)
*-1 1
1 1 1
1 1 IB 1
1 n
1 I4 r

; K, i. 1 1 /<2 \R : ^<3
I 1 "1------
1 1 1/1 1
1
1 1 1 1
1
1 1 1 1 J
^0 1 1 1
0 1 1 1
2 Figure 12.11-3. Branched system
(b) and reduced system.

Figure 12.11-4.

Figure 12.11-4 shows the free-body diagram of the two gears. With F/j shown
as positive torque, the torque exerted on gear A by gear B is negative as shown. The
torque balanee on gear A is then

7"/^ _ 'T' L 1 Y' R
^A\ ~~ ^A\ ^ ^ B\ (a)

Using Eq. (12.8-4) and noting that = 0, we have for shaft B
i f co^n^J^ \ 1
(».] (b)
1‘ «-^4 ) n " K ,
1
1 “ ,
Beeause obtain
- I 1 oL\ = - e (c)
(d)
By eliminating 0^4,
^ R _ (e)

1 — 0) 4