Main Content

Planetary gear set of carrier and beveled planet and sun wheels with adjustable gear ratio, assembly orientation, and friction losses

**Library:**Simscape / Driveline / Gears / Planetary Subcomponents

The Sun-Planet Bevel gear block represents a carrier and beveled planet and sun wheels. The planet is connected to and rotates with respect to the carrier. The planet and sun gears corotate with a fixed gear ratio. You control the direction of rotation by setting the assembly orientation left or right. For model details, see Equations.

You can model
the effects of heat flow and temperature change by enabling the optional thermal port. To enable
the port, set **Friction model** to ```
Temperature-dependent
efficiency
```

.

The Sun-Planet Bevel block imposes one kinematic and one geometric constraint on the three connected axes:

$${r}_{C}{\omega}_{C}={r}_{S}{\omega}_{S}\pm {r}_{P}{\omega}_{P}$$

$${r}_{C}={r}_{S}\pm {r}_{P}$$

where:

*r*is the radius of the carrier gear._{C}*ω*is the angular velocity of the carrier gear._{C}*r*is the radius of the sun gear._{S}*ω*is the angular velocity of the sun gear._{S}*r*is the radius of the planet gear._{P}*ω*is the angular velocity of the planet gear._{P}

The planet-sun gear ratio is defined as

$${g}_{PS}=\frac{{r}_{P}}{{r}_{S}}=\frac{{N}_{P}}{{N}_{S}},$$

where:

*g*is the planet-sun gear ratio. As $${r}_{P}>{r}_{S}$$, $${g}_{PS}>1$$._{PS}

*N*is the number of teeth in the planet gear._{P}*N*is the angular velocity of the sun gear._{S}

In terms of this ratio, the key kinematic constraint is:

$${\omega}_{S}={g}_{PS}{\omega}_{P}-{\omega}_{C}$$ for a left-oriented bevel assembly

$${\omega}_{S}={g}_{PS}{\omega}_{P}+{\omega}_{C}$$ for a right-oriented bevel assembly

The three degrees of freedom reduce to two independent degrees of freedom. The
gear pair is (1,2) = (*S*,*P*).

**Warning**

The planet-sun gear ratio, *g _{PS}*,
must be strictly greater than one.

The torque transfer is defined as

$${\tau}_{P}={\tau}_{loss}-{g}_{PS}{\tau}_{S},$$

where:

*τ*is the torque loss._{loss}*τ*is the torque for the sun gear._{s}*τ*is the torque for the planet gear._{p}

In the ideal case where there is no torque loss, *τ _{loss}* = 0. The resulting torque transfer equation is $${\tau}_{P}={g}_{PS}{\tau}_{S}$$.

In the nonideal case, *τ _{loss}* ≠ 0. For more information, see Model Gears with Losses.

Use the **Variables** settings to set the priority and initial target
values for the block variables before simulating. For more information, see Set Priority and Initial Target for Block Variables.

Gear inertia is assumed to be negligible.

Gears are treated as rigid components.

Coulomb friction slows down simulation. For more information, see Adjust Model Fidelity.