Planetary gear train with two meshed planet gear sets

**Library:**Simscape / Driveline / Gears

This block represents a planetary gear train with two meshed planet gear sets between the sun gear and the ring gear. A single carrier holds the two planet gear sets at different radii from the sun gear centerline, while allowing the individual gears to rotate with respect to each other. The gear model includes power losses due to friction between meshing gear teeth and viscous damping of the spinning gear shafts.

Structurally, the double-pinion planetary gear resembles a Ravigneaux gear without its second, large, sun gear. The inner planet gears mesh with the sun gear and the outer planet gears mesh with the ring gear. Because it contains two planet gear sets, the double-pinion planetary gear reverses the relative rotation directions of the ring and sun gears.

The teeth ratio of a meshed gear pair fixes the relative angular velocities of the two gears in that pair. The parameter settings provide two parameters to set the ring-sun and outer planet-inner planet gear teeth ratios. A geometric constraint fixes the remaining teeth ratios—ring-outer planet and inner planet-sun. This geometric constraint requires that the ring gear radius equal the sum of the sun gear radius with the inner and outer planet gear diameters:

$${r}_{r}={r}_{s}+2\cdot {r}_{pi}+2\cdot {r}_{po},$$

where:

*r*is the ring gear radius_{r}*r*is the sun gear radius_{s}*r*is the inner planet gear radius_{pi}*r*is the outer planet gear radius_{po}

In terms of the ring-sun and outer planet-inner planet teeth ratios, the ring-outer planet teeth ratio is

$$\frac{{r}_{r}}{{r}_{po}}=2\cdot \frac{\frac{{r}_{r}}{{r}_{s}}}{\left(\frac{{r}_{r}}{{r}_{s}}-1\right)}\cdot \frac{\left(\frac{{r}_{po}}{{r}_{pi}}+1\right)}{\frac{{r}_{po}}{{r}_{pi}}},$$

The inner planet-sun teeth ratio is

$$\frac{{r}_{pi}}{{r}_{s}}=\frac{\left(\frac{{r}_{r}}{{r}_{s}}-1\right)}{2\left(\frac{{r}_{po}}{{r}_{pi}}+1\right)},$$

The block is a composite component. It contains three underlying blocks—Ring-Planet, Planet-Planet, and Sun-Planet—connected as shown in the figure. Each block connects to a separate drive shaft through a rotational conserving port.

You can model
the effects of heat flow and temperature change by exposing an optional thermal port. To expose
the port, in the **Meshing Losses** settings, set the
**Friction** parameter to ```
Temperature-dependent
efficiency
```

.