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.


B and F are rotational conserving ports representing, respectively, the base and follower gear wheels.

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

Friction model

List of friction models at various precision levels for estimating power losses due to meshing.

  • No meshing losses - Suitable for HIL simulation — Neglect friction between gear cogs. Meshing is ideal.

  • Constant efficiency — Reduce torque transfer by a constant efficiency factor. This factor falls in the range 0 < η ≤ 1 and is independent of load. Selecting this option exposes additional parameters.

     Constant efficiency

  • Load-dependent efficiency — Reduce torque transfer by a variable efficiency factor. This factor falls in the range 0 < η < 1 and varies with the torque load. Selecting this option exposes additional parameters.

     Load-Dependent Efficiency

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.

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

τloss = τCoul·tanh(4ωout/ωth) + μωout , τCoul = |τF|·(1 – η) .

The hyperbolic tangent regularizes the sign change in the Coulomb friction torque when the angular velocity changes sign.

Power FlowPower Loss ConditionOutput Driveshaft ωout
ForwardωBτB > ωFτFFollower, ωF
ReverseωBτB < ωFτFBase, ωB

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 negligible. It does not impact gear dynamics.

  • Gears are rigid. They do not deform.

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


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

The sdl_backlashsdl_backlash example model illustrates a gear with backlash.

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

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