Planetary Geartrain Speeds
The planetary geartrain has two inputs (the sun gear and carrier) and one output (the ring gear). (See Figure 8.41.) When viewed from the right-hand side, the hollow carrier shaft is driven at 3600 rpm clockwise, and the shaft for the sun gear turns at 2400 rpm counterclockwise. (a) Determine the speed and direction of the ring gear. (b) The carrier’s shaft is driven by an electric motor capable of reversing its direction. Repeat the calculation for the case in which it is instead driven at 3600 rpm counterclockwise. (c) For what speed and direction of the carrier’s shaft will the ring gear not rotate?
Approach
To fi nd the speed and direction of the appropriate gear in each operating condition, we apply Equations (8.24)
\omega _{s}+n\omega _{r} -(1+n)\omega_{c}=0 (8.24)
and (8.25),
n=\frac{N_{r}}{N_{s}} (8.25)
together with the sign convention shown in Figure 8.36. With clockwise rotations being positive, the known speeds in part (a) are \omega _{c} = 3600 rpm and \omega _{s} = - 2400 rpm. In part (b), when the carrier’s shaft reverses direction,\omega _{c} = - 3600 rpm.
