Question

Common Data Questions:
A planetary gear train has four gears and one carrier. Angular velocities of the gears are ${\omega }_1,{\omega }_2,{\omega }_3,\text{and}{\omega }_4$, respectively. The carrier rotates with angular velocity ${\omega }_5$

For ${\omega }_1=60$ rpm clockwise (cw) when viewed from the left, what is the angular velocity of the carrier and its direction so that Gear 4 rotates in conuterclockwise (ccw) direction at twice the angular velocity of Gear 1 when viewed from the left?

• A. 130 rpm, cw
• B. 223 rpm, ccw
• C. 256 rpm, cw
• D. 156 rpm, ccw

Answer 1

The correct option is D 156 rpm, ccw

Given:
$N_1+y=+60$ ...(i) $[{\omega }_4=60]$

Also
$\frac{N_1}{6}+y=-2(N_1+y)$

$[{\omega }_4=2{\omega }_1]$

$\therefore \frac{N_1}{6}+y=-2N_1-2y$

$\frac{N_1}{6}+2N_1=-3y$

$\frac{13N_1}{6}=-3y$

$N_1=(60-y)$ from equation (i)

$\frac{13}{6}[60-y]-3y$

$780-13y=-18y$

$780=-18y+13y$

$780=-5y$

$y=-\frac{780}{5}=-156\text{rpm}$

Negative sign represents counter clockwise direction.