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Planet-Planet

Planetary gear set of carrier, inner planet, and outer planet wheels with adjustable gear ratio and friction losses

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

Description

The Planet-Planet gear block represents a set of carrier, inner planet, and outer planet gear wheels. Both planetary gears are connected to and rotate with respect to the carrier. The planets corotate with a fixed gear ratio that you specify. For model details, see Equations.

Thermal Model

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 tab, set the Friction model parameter to ```Temperature-dependent efficiency```.

Equations

Ideal Gear Constraints and Gear Ratios

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

`${r}_{\text{C}}{\omega }_{\text{C}}={r}_{\text{Po}}{\omega }_{\text{Po}}+{r}_{\text{Pi}}{\omega }_{\text{Pi}}$`
`${r}_{\text{C}}={r}_{\text{Po}}+{r}_{\text{Pi}}$`

The outer planet-to-inner planet gear ratio is

`${g}_{\text{oi}}={r}_{\text{Po}}/{r}_{\text{Pi}}={N}_{\text{Po}}/{N}_{\text{Pi}}$`

Where N is the number of teeth on each gear. In terms of this ratio, the key kinematic constraint is

The three degrees of freedom reduce to two independent degrees of freedom. The gear pair is (1, 2) = (Pi,Po).

The torque transfer is

In the ideal case, there is no torque loss, that is τloss = 0.

Nonideal Gear Constraints and Losses

In the nonideal case, τloss ≠ 0. For more information, see Model Gears with Losses.

Variables

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.

Dependencies

Variable settings are exposed only when, in the Meshing Losses settings, the Friction model parameter is set to `Temperature-dependent efficiency`.

Limitations and Assumptions

• Gear inertia is assumed negligible.

• Gears are treated as rigid components.

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

Ports

Conserving

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Rotational conserving port associated with the planet gear carrier.

Rotational conserving port associated with the outer planet gear.

Rotational conserving port associated with the inner planet gear.

Thermal conserving port associated with heat flow. Heat flow affects gear temperature, and therefore, power transmission efficiency.

Dependencies

This port is exposed when, in the Meshing Losses settings, the Friction parameter is set to `Temperature-dependent efficiency`.

Exposing this port also exposes related parameters.

Parameters

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Main

Ratio goi of the outer planet gear radius wheel to the inner planet gear wheel radius. This gear ratio must be strictly positive.

Meshing Losses

Friction model for the block:

• `No meshing losses - Suitable for HIL simulation` — Gear meshing is ideal.

• `Constant efficiency` — Transfer of torque between gear wheel pairs is reduced by a constant efficiency, η, such that 0 < η ≤ 1.

• `Temperature-dependent efficiency` — Transfer of torque between gear wheel pairs is defined by table lookup based on the temperature.

Dependencies

If this parameter is set to:

• `Constant efficiency` — Related parameters are exposed.

• `Temperature-dependent meshing losses` — A thermal port and related parameters are exposed.

Torque transfer efficiency, ηPP, for the outer and inner planet gear wheel pair meshing. This values must be greater than `0` and less than or equal to `1`.

Dependencies

This parameter is exposed when the Friction model parameter is set to ```Constant efficiency```.

Array of temperatures used to construct a 1-D temperature-efficiency lookup table. The array values must increase from left to right.

Dependencies

This parameter is exposed when Friction model is set to `Temperature-dependent efficiency`.

Array of mechanical efficiencies, ratios of output power to input power, for the power flow from the outer planet gear to the inner planet gear, ηPP. The block uses the values to construct a 1-D temperature-efficiency lookup table.

Each array element values is the efficiency at the temperature of the corresponding element in the Temperature array. The number of elements in the Efficiency array must be the same as the number of elements in the Temperature array. The value of each Efficiency array element must be greater than `0` and less than or equal to `1`.

Dependencies

This parameter is exposed when the Friction model parameter is set to ```Temperature-dependent efficiency```.

Power threshold, pth, above which full efficiency is in effect. Below this values, a hyperbolic tangent function smooths the efficiency factor. For a model without thermal losses, the function lowers the efficiency losses to zero when no power is transmitted. For a model that considers thermal losses, the function smooths the efficiency factors between zero at rest and the values provided by the temperature-efficiency lookup tables at the power thresholds.

Dependencies

This parameter is exposed when the Friction model parameter is set to ```Constant efficiency``` or ```Temperature-dependent efficiency```.

Viscous Losses

Viscous friction coefficient μPi for the inner planet-carrier gear motion.

Thermal Port

These settings are exposed when, in the Meshing Losses settings, the Friction model parameter is set to `Temperature-dependent efficiency`.

Thermal energy required to change the component temperature by a single degree. The greater the thermal mass, the more resistant the component is to temperature change.

Dependencies

This parameter is exposed when, in the Meshing Losses settings, the Friction model parameter is set to `Temperature-dependent efficiency`.

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See Also

Simscape Blocks

Introduced in R2011a

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