Ravigneaux Gear

Planetary gear with two sun gears and two planet gear sets

• 

Libraries:
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 the Sun-Planet, Planet-Planet, and Ring-Planet Simscape™ Driveline™ blocks. The figure shows the equivalent 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 to be negligible. The block enables you to specify the inertias of the internal planet gears. 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 enabling the optional thermal port. To enable the port, set Friction model to Temperature-dependent efficiency.

Equations

Ideal Gear Constraints and Gear Ratios

The Ravigneaux Gear block imposes four kinematic and four geometric constraints on the four connected axes and the two internal wheels (the inner and outer planet gears):

$$r_{Ci}{\omega }_C=r_{SS}{\omega }_{SS}+r_{Pi}{\omega }_{Pi}$$

$$r_{Ci}=r_{SS}+r_{Pi}$$

$$r_{Co}{\omega }_C=r_{SL}{\omega }_{SL}+r_{Po}{\omega }_{Po}$$

$$r_{Co}=r_{SL}+r_{Po}$$

$$\left(r_{Co}-r_{Ci}\right){\omega }_C=r_{Pi}{\omega }_{Pi}+r_{Po}{\omega }_{Po}$$

$$r_{Co}-r_{Ci}=r_{Po}+r_{Pi}$$

$$r_R{\omega }_R=r_{Co}{\omega }_C+r_{Po}{\omega }_{Po}$$

$$r_R=r_{Co}+r_{Po}$$

where:

• r_Ci is the radius of the inner carrier gear.

• ω_C is the angular velocity of the carrier gears.

• r_SS is the radius of the small sun gear.

• ω_SS is the angular velocity of the small sun gear.

• r_Pi is the radius of the inner planet gear.

• ω_Pi is the angular velocity of the inner planet gear.

• r_Co is the radius of the outer carrier gear.

• r_SL is the radius of the large sun gear.

• ω_SL is the angular velocity of the large sun gear.

• r_Po is the radius of the outer planet gear.

• ω_Po is the angular velocity of the outer planet gear.

• ω_R is the 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:

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

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

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

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

• N_SL 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 g_RSS must be strictly greater than the gear ratio g_RSL. The gear ratio g_RSL 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:

• τ_SS is the torque transfer for the small sun gear.

• τ_R is the torque transfer for the ring gear.

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

• τ_SL is the torque transfer for the large sun gear.

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

In the ideal case where there is no torque loss, τ_loss = 0.

Nonideal Gear Constraints and Losses

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

Assumptions and Limitations

• The gears are assumed to be rigid.

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

Ports

Conserving

C — Planet gear carrier

rotational mechanical

Rotational mechanical conserving port associated with the planet gear carrier.

R — Ring gear

rotational mechanical

Rotational mechanical conserving port associated with the ring gear.

SL — Large sun gear

rotational mechanical

Rotational mechanical conserving port associated with the large sun gear.

SS — Small sun gear

rotational mechanical

Rotational mechanical conserving port associated with the small sun gear.

H — Heat flow

thermal

Thermal conserving port associated with heat flow. Heat flow affects the power transmission efficiency by altering the gear temperatures.

Dependencies

To enable this port, set Friction model to Temperature-dependent efficiency.

Parameters

Main

Ring (R) to large sun (SL) teeth ratio (NR/NSL) — Ring to large sun gear rotation ratio

2 (default) | positive scalar

Ratio g_RLS of the ring gear to sun gear rotations as defined by the number of ring gear teeth divided by the number of large sun gear teeth.

Ring (R) to small sun (SS) teeth ratio (NR/NSS) — Ring to small sun gear rotation ratio

3 (default) | positive scalar greater than (NR/NSL)

Ratio, g_RSS, of the ring gear wheel to small sun gear rotations as defined by the number of ring gear teeth divided by the number of small sun gear teeth. This gear ratio must be strictly greater than Ring (R) to large sun (SL) teeth ratio (NR/NSL).

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 the gear wheel pairs is reduced by a constant efficiency, η, such that 0 < η ≤ 1.

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

Large sun-planet, small sun-planet, ring-planet and planet-planet ordinary efficiencies — Torque transfer efficiencies

[.98, .98, .98, .99] (default) | vector

Vector of torque transfer efficiencies, [η_LS, η_SS, η_RP, η_PP], for large sun-planet, small sun-planet, ring-planet, and planet-planet gear wheel pair meshings, respectively. The vector elements must be in the range (0,1].

Dependencies

To enable this parameter, set Friction model to Constant efficiency.

Temperature — Temperature

[280, 300, 320] K (default) | vector

Vector of temperatures used to construct a 1-D temperature-efficiency lookup table. The vector elements must increase from left to right.

Dependencies

To enable this parameter, set Friction model to Temperature-dependent efficiency.

Large sun-planet efficiency — Torque transfer efficiency from the large sun gears to the planet gears

[.95, .9, .85] (default) | vector

Vector of output-to-input power ratios that describe the power flow from the large sun gear to the planet gears, η_LSP. The block uses the values to construct a 1-D temperature-efficiency lookup table.

Each element is an efficiency that relates to a temperature in the Temperature vector. The length of the vector must be equal to the length of the Temperature vector. Each element in the vector must be in the range (0,1].

Dependencies

To enable this parameter, set Friction model to Temperature-dependent efficiency.

Small sun-planet efficiency — Torque transfer efficiency from the small sun gears to the planet gears

[.95, .9, .85] (default) | vector

Vector of output-to-input power ratios that describe the power flow from the small sun gears to the planet gears, η_SSP. The block uses the values to construct a 1-D temperature-efficiency lookup table.

Each element is an efficiency that relates to a temperature in the Temperature vector. The length of the vector must be equal to the length of the Temperature vector. Each element in the vector must be in the range (0,1].

Dependencies

To enable this parameter, set Friction model to Temperature-dependent efficiency.

Ring-planet efficiency — Torque transfer efficiency from the ring gear to the planet gears

[.95, .9, .85] (default) | vector

Vector of output-to-input power ratios that describe the power flow from the ring gear to the planet gears, η_RP. The block uses the values to construct a 1-D temperature-efficiency lookup table.

Each element is an efficiency that relates to a temperature in the Temperature vector. The length of the vector must be equal to the length of the Temperature vector. Each element in the vector must be in the range (0,1].

Dependencies

To enable this parameter, set Friction model to Temperature-dependent efficiency.

Planet-planet efficiency — Planet-planet efficiency

[.95, .9, .85] (default) | vector

Vector of output-to-input power ratios that describe the power flow from the small sun planet gears to the large sun planet gears, η_PP. The block uses the values to construct a 1-D temperature-efficiency lookup table.

Each element is an efficiency that relates to a temperature in the Temperature vector. The length of the vector must be equal to the length of the Temperature vector. Each element in the vector must be in the range (0,1].

Dependencies

To enable this parameter, set Friction model to Temperature-dependent efficiency.

Large sun-carrier, small sun-carrier, large sun planet-carrier and small sun planet-carrier power thresholds — Minimum efficiency power threshold for the large sun-carrier, small sun-carrier, large sun planet-carrier, and small sun planet-carrier gear couplings

[.001, .001, .001, .001] W (default) | vector

Vector of power thresholds above which the full efficiency factors apply. Enter the thresholds in the order large sun gear, small sun gear, large sun planet gears, and small sun planet gears, all relative to the gear carrier. Below these values, a hyperbolic tangent function smooths the efficiency factor.

When you set Friction model to Constant efficiency, the block lowers the efficiency losses to zero when no power is transmitted. When you set Friction model to Temperature-dependent efficiency, the block smooths the efficiency factors between zero when at rest and the values provided by the temperature-efficiency lookup tables at the power thresholds.

Dependencies

To enable this parameter, set Friction model to Temperature-dependent efficiency.

Viscous Losses

Large sun-carrier, small sun-carrier, large sun planet-carrier and small sun planet-carrier viscous friction coefficients — Gear viscous friction

[0, 0, 0, 0] N*m/(rad/s) (default) | vector

Vector of viscous friction coefficients, [μ_LS, μ_SS, μ_LSP, μ_SSP], for the large sun-carrier, small sun-carrier, large sun planet-carrier, and small sun planet-carrier gear motions, respectively.

Inertia

Inertia — Inertia model

off (default) | on

Inertia model for the block:

• Off — Model gear inertia.

• On — Neglect gear inertia.

Small sun gear inertia — Small sun gear inertia

0.001 kg*m^2 (default) | positive scalar

Small sun gear inertia.

Dependencies

To enable this parameter, set Inertia to On.

Large sun gear inertia — Large sun gear inertia

0.001 kg*m^2 (default) | positive scalar

Large sun gear inertia.

Dependencies

To enable this parameter, set Inertia to On.

Ring gear inertia — Ring gear inertia

0.001 kg*m^2 (default) | positive scalar

Ring gear inertia.

Dependencies

To enable this parameter, set Inertia to On.

Carrier gear inertia — Carrier gear inertia

0.001 kg*m^2 (default) | positive scalar

Carrier gear inertia.

Dependencies

To enable this parameter, set Inertia to On.

Carrier gear inner radius — Carrier gear inner radius

0.01 m (default) | positive scalar

Carrier gear inner radius.

Dependencies

To enable this parameter, set Inertia to On.

Carrier gear outer radius — Carrier gear outer radius

0.02 m (default) | positive scalar

Carrier gear outer radius.

Dependencies

To enable this parameter, set Inertia to On.

Inner planet gear spin inertia — Inner planet gear spin inertia

0.001 kg*m^2 (default) | positive scalar

Inertia of the inner planet gear about its own axis.

Dependencies

To enable this parameter, set Inertia to On.

Inner planet gear mass — Inner planet gear mass

0.001 kg (default) | positive scalar

Mass of the inner planet gear.

Dependencies

To enable this parameter, set Inertia to On.

Outer planet gear inertia — Outer planet gear inertia

0.001 kg*m^2 (default) | positive scalar

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

Dependencies

Tho enable this parameter, set Inertia to On.

Outer planet gear mass — Outer planet gear mass

0.001 kg (default) | positive scalar

Mass of the inner planet gear.

Dependencies

To enable this parameter, set Inertia to On.

Thermal Port

To enable these settings, set Friction model to Temperature-dependent efficiency.

Thermal mass — Thermal mass

50 J/K (default) | scalar

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

Dependencies

To enable this parameter, set Friction model to Temperature-dependent efficiency.

Initial temperature — Initial temperature

300 K (default) | scalar

Block temperature at the start of simulation. The initial temperature sets the initial component efficiencies according to their respective efficiency vectors.

Dependencies

To enable this parameter, set Friction model to Temperature-dependent efficiency.

More About

Hardware-in-the-Loop Simulation

For optimal simulation performance, set Friction model 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™.

Version History

Introduced in R2011a

R2024b: Inertia updates

You now can specify the inertia of all gear subcomponents including the sun, ring, and carrier gears. You also now can include the effects of planet procession in the planet inertia behavior.