Compound Planetary Gear

Planetary gear train with stepped planet gear set


Simscape / Driveline / Gears


This 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 Sun-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, 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 variant that includes a thermal port. Specify the associated thermal parameters for the component.

Compound Planetary Gear Model

Ideal Gear Constraints and Gear Ratios

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

rCωC = rSωS+ rP1ωP , rC = rS + rP1 ,

rRωR = rCωC+ rP2ωP , rR = rC + rP2 .

The ring-planet gear ratio gRP = rR/rP2 = NR/NP2 and the planet-sun gear ratio 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 .

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


The gear ratio gRP must be strictly greater than one.

The torque transfers are:

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

with τloss = 0 in the ideal case.

Nonideal Gear Constraints and Losses

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



CRotational conserving port representing the planet gear carrier
RRotational conserving port representing the ring gear
SRotational conserving port representing the sun gear
HThermal conserving port for thermal modeling



Ring (R) to planet (P) teeth ratio (NR/NP)

Fixed ratio gRP of the ring gear to the planet gear. The gear ratio must be strictly greater than 1. The default is 2.

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

Fixed ratio gPS of the planet gear to the sun gear. The gear ratio must be strictly positive. The default is 1.

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

 With Thermal Port

Viscous Losses

Sun-carrier and planet-carrier viscous friction coefficients

Vector of viscous friction coefficients [μS μP] for the sun-carrier and planet-carrier gear motions, respectively. The default is [0 0].

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


Planet gear inertia

Moment of inertia of the combined planet gears. This value must be positive or zero. Enter 0 to ignore gear inertia. The default value is 0 kg*m^2.

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™.