Compound Planetary Gear

Planetary gear train with stepped planet gear set

  • Library:
  • Simscape / Driveline / Gears

Description

The Compound Planetary Gear block represents a planetary gear train with composite planet gears. Each composite planet gear is a pair of rigidly connected and longitudinally arranged gears of different radii. One of the two gears engages the centrally located sun gear while the other engages the outer ring gear.

Compound Planetary Gear

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

To increase the fidelity of the gear model, 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 only. To model the inertias of the carrier, sun, and ring gears, connect Simscape Inertia blocks to ports C, S, and R.

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 model variant that includes a thermal port. Specify the associated thermal parameters for the component.

Equations

Ideal Gear Constraints and Gear Ratios

The Compound Planetary Gear block imposes two kinematic and two geometric constraints on the three connected axes and the fourth, internal wheel (planet):

rCωC = rSωS+ rP1ωP , rC = rS + rP1 ,(1)
rRωR = rCωC+ rP2ωP , rR = rC + rP2 .(2)

The ring-planet gear ratio is gRP = rR/rP2 = NR/NP2 and the planet-sun gear ratio is gPS = rP1/rS = NP1/NS. N is the number of teeth on each gear. In terms of these ratios, the key kinematic constraint is:

(1 + gRP·gPS)ωC = ωS + gRP·gPSωR .(3)

The four degrees of freedom reduce to two independent degrees of freedom. The gear pairs are (1,2) = (P2,R) and (S,P1).

Warning

The gear ratio gRP must be strictly greater than one.

The torque transfers are:

gRPτP2 + τRτloss(P2,R) = 0 , gPSτS + τP1τloss(S,P1) = 0 ,(4)

with τloss = 0 in the ideal case.

Nonideal Gear Constraints and Losses

In the nonideal case, τloss0. See Model Gears with Losses.

Limitations and Assumptions

Ports

Conserving

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Rotational conserving port associated with the planet gear carrier.

Rotational conserving port associated with the ring gear.

Rotational conserving port associated with the sun gear.

Thermal conserving port associated with heat flow.

Dependencies

This port is visible only when Block choices is set to Show thermal port.

Exposing this port makes related parameters visible.

Parameters

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Main

Fixed ratio, gRP, of the ring gear to the planet gear. The gear ratio must be strictly greater than 1.

Fixed ratio, gPS, of the planet gear to the sun gear. The gear ratio must be strictly positive.

Meshing Losses

The parameters that are visible in the Meshing Losses settings depend on the thermal and friction models that you choose for the block. For more information, see Thermal Modeling and Friction model.

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.

Dependencies

This parameter is visible only if Block choices is set to No thermal port.

Selecting Constant efficiency makes related parameters visible.

Vector of torque transfer efficiencies, [ηSP ηRP], for sun-planet and ring-carrier gear wheel pair meshings, respectively.

Dependencies

This parameter is visible only if Block choices is set to No thermal port and the Friction model parameter is set to Constant efficiency.

Array of power thresholds, pth, above which full efficiency factors apply, for the sun-carrier and planet-carrier, respectively. Below these 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 not visible only if the Friction model parameter is set to No meshing losses - Suitable for HIL simulation.

Array of temperatures used to construct a 1-D temperature-efficiency lookup table. The array values must increase from left to right. The temperature array must be the same size as each efficiency array.

Dependencies

This parameter is visible only if Block choices is set to Thermal port.

Array of mechanical efficiencies with power flowing from the sun gear to the planet gears. Each array value is the ratio of output power to input power at one of the temperatures in the temperature array. The temperature and efficiency arrays must be the same size.

Dependencies

This parameter is visible only if Block choices is set to Thermal port.

Array of mechanical efficiencies with power flowing from the ring gear to the planet gears. Each array value is the ratio of output power to input power at one of the temperatures in the temperature array. The temperature and efficiency arrays must be the same size.

Dependencies

This parameter is visible only if Block choices is set to Thermal port.

Viscous Losses

Array of viscous friction coefficients, [μS, μP], for the sun-carrier and planet-carrier gear motions, respectively.

Inertia

Moment of inertia of the combined planet gears. This value must be positive or zero. To ignore gear inertia, specify 0.

Thermal Port

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 visible only if Block choices is set to Thermal port.

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 visible only if Block choices is set to Thermal port.

More About

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Extended Capabilities

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

Introduced in R2011a