Sun-Planet

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

• Library:

• Simscape / Driveline / Gears / Planetary Subcomponents

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Description

The Sun-Planet gear block represents a set of carrier, planet, and sun gear wheels. The planet is connected to and rotates with respect to the carrier. The planet and sun corotate with a fixed gear ratio that you specify and in the same direction with respect to the carrier. A sun-planet and a ring-planet gear are basic elements of a planetary gear set. 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 settings, set the Friction parameter to Temperature-dependent efficiency.

Equations

Ideal Gear Constraints and Gear Ratios

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

$$r_{\text{C}}{\omega }_{\text{C}}=r_{\text{S}}{\omega }_{\text{S}}+r_{\text{P}}{\omega }_{\text{P}}$$

The planet-sun gear ratio is

$$g_{\text{PS}}=r_{\text{P}}/r_{\text{S}}=N_{\text{P}}/N_{\text{S}}$$

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

$${\omega }_{\text{S}}=–g_{\text{PS}}{\omega }_{\text{P}}+(\text{1 }+g_{\text{PS}}){\omega }_{\text{C}}$$

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:

$$g_{\text{PS}}{\tau }_{\text{S}}+{\tau }_{\text{P}}–{\tau }_{\text{loss}}=0$$

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

Nonideal Gear Constraints and Losses

In the nonideal case, τ_loss ≠ 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 (Simscape).

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

C — Planet gear carrier

rotational mechanical

Rotational conserving port associated with the planet gear carrier.

P — Planet gear

rotational mechanical

Rotational conserving port associated with the panet gear.

S — Sun gear

rotational mechanical

Rotational conserving port associated with the sun gear.

H — Heat flow

thermal

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

Main

Planet (P) to sun (S) teeth ratio (NP/NS) — Planet-to-sun gear ratio

2 (default) | scalar greater than 1

Ratio g_PS of the planet gear wheel radius to the sun gear wheel radius. This gear ratio must be strictly greater than 1.

Meshing Losses

Friction model — Friction model

No meshing losses - Suitable for HIL simulation (default) | Constant efficiency | Temperature-dependent efficiency

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.

Ordinary efficiency — Efficiency

0.98 (default) | scalar | 0 < η_SP ≤ 1

Torque transfer efficiency, η_SP, for sun-planet gear wheel pair meshings. The value 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.

Temperature — Temperature

[280, 300, 320] K (default) | array of increasing values

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.

Efficiency — Gear efficiency

[.95, .9, .85] (default) | array | 0 < η_SP ≤ 1

Array of mechanical efficiencies, ratios of output power to input power, for the power flow from the ring gear to the planet gear, η_RP. 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.

Sun-carrier power threshold — Power threshold

0.001 W (default) | scalar

Power threshold, p_th, 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

Sun-carrier viscous friction coefficient — Viscous friction

0 N*m/(rad/s) (default)

Viscous friction coefficient μ_S for the sun-carrier gear motion.

Thermal Port

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

Thermal mass — Thermal mass

50 J/K (default) | scalar

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.

More About

Hardware-in-the-Loop Simulation

For optimal simulation performance, in the Meshing Losses settings, set the Friction model parameter to the default value, No meshing losses - Suitable for HIL simulation.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.