Planetary Gear Set

Purpose

Ideal planetary gear set

Library

Mechanical / Rotational / Components

Description

This component models a planetary gear set with a sun gear, planet gears connected via a carrier, and a ring gear. The component is divided into two subcomponents: a ring-planet gear subsystem and a sun-planet gear subsystem, as shown in Fig. 284.

Fig. 284 Planetary gear set system diagram

The planetary gear set has three external shafts: ring gear shaft (R), sun gear shaft (S), and carrier shaft (C). The relation between the angular speeds of the gears and carrier are described by the following equations:

\[\begin{split}\mathrm{N}_\mathrm{s} \omega_\mathrm{s} + \mathrm{N}_\mathrm{p} \omega_\mathrm{p} - (\mathrm{N}_\mathrm{s} + \mathrm{N}_\mathrm{p}) \omega_\mathrm{c} &= 0 \\ \mathrm{N}_\mathrm{r} \omega_\mathrm{r} + \mathrm{N}_\mathrm{p} \omega_\mathrm{p} - (\mathrm{N}_\mathrm{r} + \mathrm{N}_\mathrm{p}) \omega_\mathrm{c} &= 0\end{split}\]

where \(\mathrm{N}_\mathrm{r}\), \(\mathrm{N}_\mathrm{s}\), and \(\mathrm{N}_\mathrm{p}\) correspond to the number of teeth on the ring, sun, and each planet gear respectively, and \(\omega_\mathrm{r}\), \(\omega_\mathrm{s}\), \(\omega_\mathrm{p}\), and \(\omega_\mathrm{c}\) correspond to the angular speed of the ring gear, sun gear, planet gears, and carrier respectively.

These equations can further be simplified to:

\[\mathrm{N}_\mathrm{s} \omega_\mathrm{s} + \mathrm{N}_\mathrm{r} \omega_\mathrm{r} = (\mathrm{N}_\mathrm{s} + \mathrm{N}_\mathrm{r}) \omega_\mathrm{c}\]

The model includes an internal lumped moment of inertia representing the planet gears (which is set to zero by default). The moments of inertia of the ring and sun gears and the carrier can be modeled by connecting an Inertia to the corresponding shaft.

Parameters

Main

Number of sun teeth

Number of teeth on the sun gear.

Number of planet teeth

Number of teeth on each planet gear.

Number of ring teeth

Number of teeth on the ring gear.

Planet gear

Moment of inertia of planet gear

Combined planet gear inertia \(J\) in \((\mathrm{Nms}^2)\).

Initial speed of panet gear

Initial angular speed of each planet gear \(\omega_\mathrm{p}\) in \((\frac{\mathrm{rad}}{\mathrm{s}})\).

Probe Signals

Sun gear speed

Angular speed of sun gear \(\omega_\mathrm{s}\) in \((\frac{\mathrm{rad}}{\mathrm{s}})\).

Planet gear speed

Angular speed of each planet gear \(\omega_\mathrm{p}\) in \((\frac{\mathrm{rad}}{\mathrm{s}})\).

Carrier

Angular speed of carrier \(\omega_\mathrm{c}\) in \((\frac{\mathrm{rad}}{\mathrm{s}})\).

Ring gear speed

Angular speed of ring gear \(\omega_\mathrm{r}\) in \((\frac{\mathrm{rad}}{\mathrm{s}})\).