Simple Gear with Variable Efficiency

Gear set with parallel-axis rotation and variable meshing efficiency




The block represents a simple gear train with variable meshing efficiency. The gear train transmits torque at a specified ratio between base and follower shafts arranged in a parallel configuration. Shaft rotation can occur in equal or opposite directions. Gear losses are optional. They include meshing and viscous bearing losses. To specify the variable meshing efficiency, the block contains a physical signal port that you can use to input a general time-varying signal. Inertia and compliance effects are ignored.

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. Specify the associated thermal parameters for the component.



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

Enter the gear ratio. This is the fraction of follower over base gear teeth numbers, NF/NB. The ratio must be positive. The default value is 2.

Output shaft rotates

Select the relative rotation between shafts. This is the rotation direction of the output shaft with respect to the input shaft. Options include equal or opposite directions. The default setting is In opposite direction to input shaft.

Meshing Losses

Minimum efficiency

Enter the smallest efficiency value allowed for the gear. The efficiency is the power ratio between output and input shafts. The physical signal input saturates for values below the minimum efficiency or above 1. The minimum efficiency must be positive. The default value is 0.01.

Follower power threshold

Enter the follower shaft power above which full efficiency factor is in effect. A hyperbolic tangent function smooths the efficiency factor between zero when at rest and the value provided by the temperature-efficiency lookup table when at the power threshold. The default value is 0.001 W.

Viscous Losses

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

Enter a two-element vector with the viscous friction coefficients of the base and follower gears. Coefficients must be positive. The default vector is [0 0]. The default unit is N*m/(rad/s).

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.

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.


  • 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
Was this topic helpful?