Sun-Planet

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

Library

Simscape / Driveline / Gears / Planetary Subcomponents

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 Sun-Planet Gear Model.

Thermal Modeling

You can model the effects of heat flow and temperature change through an optional thermal conserving port. By default, the thermal port is hidden. To expose the thermal port, right-click the block in your model and, from the context menu, select Simscape > Block choices. Select a variant that includes a thermal port. Specify the associated thermal parameters for the component.

Sun-Planet Gear Model

Ideal Gear Constraints and Gear Ratios

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

r_Cω_C = r_Sω_S + r_Pω_P , r_C = r_P + r_S .

The planet-sun gear ratio g_PS = r_P/r_S = N_P/N_S. N is the number of teeth on each gear. In terms of this ratio, the key kinematic constraint is:

ω_S = –g_PSω_P + (1 + g_PS)ω_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_PSτ_S + τ_P – τ_loss = 0 ,

with τ_loss = 0 in the ideal case.

Nonideal Gear Constraints and Losses

In the nonideal case, $${\tau }_{loss}\ne 0$$. See Model Gears with Losses.

Limitations

• Gear inertia is assumed negligible.

• Gears are treated as rigid components.

• Coulomb friction slows down simulation. See Adjust Model Fidelity.

Ports

Port	Description
C	Rotational conserving port representing the planet carrier
P	Rotational conserving port representing the planet gear
S	Rotational conserving port representing the sun gear
H	Thermal conserving port for thermal modeling

Parameters

Main

Ring (R) to sun (S) teeth ratio (NP/NS)

Ratio g_RS of the ring gear wheel radius to the sun gear wheel radius. This gear ratio must be strictly greater than 1. The default value is 2.

Meshing Losses

Parameters for meshing losses vary with the block variant chosen—one with a thermal port for thermal modeling and one without it.

 Without Thermal Port

Friction model

Select how to implement friction losses from nonideal meshing of gear teeth. The default is No meshing losses.

• 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 satisfying 0 < η ≤ 1. If you select this option, the panel changes from its default.

   Constant Efficiency

  Ordinary efficiency

  Torque transfer efficiency η_SP for sun-planet gear wheel pair meshing.

  Sun-carrier power threshold

  Power threshold above which the full efficiency factor is in effect. Below this value, a hyperbolic tangent function smooths the efficiency factor, lowering the efficiency losses to zero when no power is transmitted. The default value is 0.001 W.

 With Thermal Port

Temperature

Array of temperatures used to construct a 1-D temperature-efficiency lookup table. The array values must increase left to right. The temperature array must be the same size as the Efficiency array. The default array is [280 300 320] K.

Efficiency

Array of component efficiencies used to construct a 1-D temperature-efficiency lookup table. The array values are the efficiencies at the temperatures in the Temperature array. The two arrays must be the same size. The default array is [0.95 0.9 0.85].

Sun-carrier power threshold

Power threshold above which the full efficiency factor is in effect. A hyperbolic tangent function smooths the efficiency factor between zero at rest and the value provided by the temperature-efficiency lookup table at the power threshold. The default value is 0.001 W.

Viscous Losses

Sun-carrier viscous friction coefficient

Viscous friction coefficient μ_S for the sun-carrier gear motion. The default is 0.

From the drop-down list, choose units. The default is newton-meters/(radians/second) (N*m/(rad/s)).

Thermal Port

Thermal mass

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. The default value is 50 J/K.

Initial temperature

Component temperature at the start of simulation. The initial temperature alters the component efficiency according to an efficiency vector that you specify, affecting the starting meshing or friction losses. The default value is 300 K.

Real-Time Simulation

Hardware-in-the-Loop Simulation

For optimal simulation performance, use the Meshing Losses > Friction model parameter default setting, No meshing losses - Suitable for HIL simulation.

Extended Capabilities

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