# Ravigneaux Gear

Planetary gear with two sun gears and two planet gear sets

• Library:
• Simscape / Driveline / Gears

## Description

The Ravigneaux Gear block represents a planetary gear train with dual sun and planet gear sets. The two sun gears are centrally located and separated longitudinally along a common rotation axis. The smaller of these gears engages an inner planet gear set, which in turn engages an outer planet gear set. The outer planet gear set, whose length spans the distance between the two sun gears, engages both the larger sun gear and the ring gear.

A carrier holds the planet gear sets in place at different radii. The carrier, which rigidly connects to a drive shaft, can spin as a unit with respect to the sun and ring gears. Revolute joints, each located between a planet gear and the carrier, enable the gears to spin about their individual longitudinal axes.

The relative angular velocities of the sun, planet, and ring gears follow from the kinematic constraints between them. For more information, see Equations.

The block models the Ravigneaux gear as a structural component based on Sun-Planet, Planet-Planet, and Ring-Planet Simscape™ Driveline™ blocks. The figure shows the block diagram of this structural component.

To increase the fidelity of the gear model, you can specify properties such as gear inertia, meshing losses, and viscous losses. By default, gear inertia and viscous losses are assumed negligible. The block enables you to specify the inertias of the internal planet gears only. To model the inertias of the carrier, large sun, small sun, and ring gears, connect Simscape Inertia blocks to ports C, SL, SS, and R.

### 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

The Ravigneaux gear imposes four kinematic and four geometric constraints on the four connected axes and the two internal wheels (inner and outer planets):

`${r}_{Ci}{\omega }_{C}={r}_{SS}{\omega }_{SS}+{r}_{Pi}{\omega }_{Pi}$`
`${r}_{Ci}={r}_{SS}+{r}_{Pi}$`
`${r}_{Co}{\omega }_{C}={r}_{SL}{\omega }_{SL}+{r}_{Po}{\omega }_{Po}$`
`${r}_{Co}={r}_{SL}+{r}_{Po}$`
`$\left({r}_{Co}-{r}_{Ci}\right){\omega }_{C}={r}_{Pi}{\omega }_{Pi}+{r}_{Po}{\omega }_{Po}$`
`${r}_{Co}-{r}_{Ci}={r}_{Po}+{r}_{Pi}$`
`${r}_{R}\omega R={r}_{Co}{\omega }_{C}+{r}_{Po}{\omega }_{Po}$`
`${r}_{R}={r}_{Co}+{r}_{Po}$`

Where:

• rCi is radius of the inner carrier gear.

• ωC is angular velocity of the carrier gears.

• ωSS is angular velocity of the small sun gear.

• rPi is radius of the inner planet gear.

• ωPi is angular velocity of the inner planet gear.

• rCo is radius of the outer carrier gear.

• rSL is radius of the large sun gear.

• ωSL is angular velocity of the large sun gear.

• rPo is radius of the outer planet gear.

• ωPo is angular velocity of the outer planet gear.

• ωR is angular velocity of the ring gear.

The ring-to-sun ratios are:

`${g}_{RSS}={r}_{R}/{r}_{SS}={N}_{R}/{N}_{SS}$`

`${g}_{RSL}={r}_{R}/{r}_{SL}={N}_{R}/{N}_{SL}$`

Where:

• gRSS is the ring-to-small sun gear ratio.

• NR is the number of teeth in the ring gear.

• NSS is the number of teeth in the small sun gear.

• gRSS is the ring-to-large sun gear ratio.

• NSL is the number of teeth in the large sun gear.

In terms of these gear ratios, the key kinematic constraints are:

`$\left({g}_{RSS}-1\right){\omega }_{C}={g}_{RSS}{\omega }_{R}-{\omega }_{SS}$`

`$\left({g}_{RSL}-1\right){\omega }_{C}={g}_{RSL}{\omega }_{R}-{\omega }_{SL}$`

The six degrees of freedom reduce to two independent degrees of freedom. The gear pairs are (1,2) = (LS,P), (SS,P), (P,R), and (P,P).

### Warning

The gear ratio gRSS must be strictly greater than the gear ratio gRSL. The gear ratio gRSL must be strictly greater than one.

The torque transfers are:

`${g}_{RSS}{\tau }_{SS}+{\tau }_{R}-{\tau }_{loss}\left(SS,R\right)=0$`

`${g}_{RSL}{\tau }_{SL}+{\tau }_{R}-{\tau }_{loss}\left(SL,R\right)=0$`

Where:

• τSS is torque transfer for the small sun gear.

• τR is torque transfer for the ring gear.

• τloss(SS,R) is torque transfer loss between the small sun gear and the ring gear.

• τSL is torque transfer for the large sun gear.

• τloss(SL,R) is torque transfer loss between the large sun gear and the ring gear.

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.

## Limitations and Assumptions

• Gears are assumed rigid.

## Ports

### Conserving

expand all

Rotational conserving port associated with the planet gear carrier.

Rotational conserving port associated with the ring gear.

Rotational conserving port associated with the large sun gear.

Rotational conserving port associated with the small sun 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

expand all

### Main

Ratio gRLS of the ring gear wheel radius to the large sun gear wheel radius.

Ratio gRSS of the ring gear wheel radius to the small sun gear wheel radius. This gear ratio must be strictly greater than the ring-to-large sun gear ratio.

### 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.

Array of torque transfer efficiencies, [ηLS, ηSS, ηRP, ηPP], for large sun-planet, small sun-planet, ring-planet, and planet-planet gear wheel pair meshings, respectively. The array element 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 large sun gear to the sun planet gears, ηLSP. 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```.

Array of mechanical efficiencies, ratios of output power to input power, for the power flow from the small sun gear to the sun planet gears, ηSSP. 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```.

Array of mechanical efficiencies, ratios of output power to input power, for the power flow from the ring gear to the sun planet gears, ηRP. 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```.

Array of mechanical efficiencies, ratios of output power to input power, for the power flow from the small sun planet gears to the large sun planet gears, 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```.

Array of power thresholds above which the full efficiency factors apply. Enter the thresholds for the large sun gear, small sun gear, large sun planet gears, and small sun planet gears, all relative to the gear carrier, in this order. 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 Friction model is set to `Constant efficiency` or ```Temperature-dependent efficiency```.

### Viscous Losses

Array of viscous friction coefficients [μLS, μSS, μLSP, μSSP] for the large sun-carrier, small sun-carrier, large sun planet-carrier, and small sun planet-carrier gear motions, respectively.

### Inertia

Inertia model for the block:

• `Off` — Model gear inertia.

• `On` — Neglect gear inertia.

#### Dependencies

When this parameter is set to `On` exposes related parameters.

Moment of inertia of the combined planet gears. This value must be positive.

#### Dependencies

This parameter is exposed when the Inertia parameter is set to `On`.

Moment of inertia of the planet gear carrier. This value must be positive.

#### Dependencies

This parameter is exposed when the Inertia parameter is set to `On`.

Moment of inertia of the combined planet gears. This value must be positive.

#### Dependencies

This parameter is exposed when the Inertia parameter is set to `On`.

### 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`.

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.

#### Dependencies

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

expand all