Simple Gear

Simple gear of base and follower wheels with adjustable gear ratio and friction losses




The Simple Gear block represents a gearbox that constrains the two connected driveline axes, base (B) and follower (F), to corotate with a fixed ratio that you specify. You can choose whether the follower axis rotates in the same or opposite direction as the base axis. If they rotate in the same direction, ωF and ωB have the same sign. If they rotate in opposite directions, ωF and ωB have opposite signs. For model details, see Simple Gear Model.

You can model the effects of heat flow and temperature change through an optional thermal conserving port. To expose the thermal port, right-click the block and select Simscape > Block choices > Show thermal port. Exposing the thermal port causes new parameters specific to thermal modeling to appear in the block dialog box.

Dialog Box and Parameters


Follower (F) to base (B) teeth ratio (NF/NB)

Fixed ratio gFB of the follower axis to the base axis. The gear ratio must be strictly positive. The default is 2.

Output shaft rotates

Direction of motion of the follower (output) driveshaft relative to the motion of the base (input) driveshaft. The default is In opposite direction to input shaft.

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

Viscous friction coefficients at base (B) and follower (F)

Two-element array with the viscous friction coefficients in effect at the base and follower shafts. The default array, [0 0], corresponds to zero viscous losses.

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 influences the starting meshing or friction losses by altering the component efficiency according to an efficiency vector that you specify. The default value is 300 K.

Simple Gear Model

Ideal Gear Constraint and Gear Ratio

Simple Gear imposes one kinematic constraint on the two connected axes:

rFωF = rBωB .

The follower-base gear ratio gFB = rF/rB = NF/NB. N is the number of teeth on each gear. The two degrees of freedom reduce to one independent degree of freedom.

The torque transfer is:

gFBτB + τFτloss = 0 ,

with τloss = 0 in the ideal case.

Nonideal Gear Constraint and Losses

In the nonideal case, τloss ≠ 0. For general considerations on nonideal gear modeling, see Model Gears with Losses.

In a nonideal gear pair (B,F), the angular velocity, gear radii, and gear teeth constraints are unchanged. But the transferred torque and power are reduced by:

  • Coulomb friction between teeth surfaces on gears B and F, characterized by efficiency η

  • Viscous coupling of driveshafts with bearings, parametrized by viscous friction coefficients μ

Constant Efficiency

In the constant efficiency case, η is constant, independent of load or power transferred.

Load-Dependent Efficiency

In the load-dependent efficiency case, η depends on the load or power transferred across the gears. For either power flow, τCoul = gFBτidle + kτF. k is a proportionality constant. η is related to τCoul in the standard, preceding form but becomes dependent on load:

η = τF/[gFBτidle + (k + 1)τF] .


  • Gear inertia is assumed negligible.

  • Gears are treated as rigid components.

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


BRotational conserving port representing the base shaft
FRotational conserving port representing the follower shaft
HThermal conserving port for thermal modeling


The sdl_simple_gear example model gives a basic example of a simple gear.

The sdl_backlash example model illustrates a gear with backlash.

The sdl_gearbox_efficiency example model measures the efficiency of a nonideal simple gear by comparing output to input power.

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