## Documentation Center |

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, *ω*_{F} and *ω*_{B} have
the same sign. If they rotate in opposite directions, *ω*_{F} and *ω*_{B} 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.

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

*g*_{FB}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`.

**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.`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.

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

*r*_{F}*ω*_{F} = *r*_{B}*ω*_{B} .

The follower-base gear ratio *g*_{FB} = *r*_{F}/*r*_{B} = *N*_{F}/*N*_{B}. *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:

*g*_{FB}*τ*_{B} + *τ*_{F} – *τ*_{loss} =
0 ,

with *τ*_{loss} =
0 in the ideal case.

In the nonideal case, *τ*_{loss} ≠
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*

*τ*_{loss} = *τ*_{Coul}·tanh(4*ω*_{out}/*ω*_{th})
+ *μ**ω*_{out} ,
*τ*_{Coul} = |*τ*_{F}|·(1
– *η*) .

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

Power Flow | Power Loss Condition | Output Driveshaft ω_{out} |
---|---|---|

Forward | ω_{B}τ_{B} > ω_{F}τ_{F} | Follower, ω_{F} |

Reverse | ω_{B}τ_{B} < ω_{F}τ_{F} | Base, ω_{B} |

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

In the load-dependent efficiency case, *η* depends
on the load or power transferred across the gears. For either power
flow, *τ*_{Coul} = *g*_{FB}*τ*_{idle} + *k**τ*_{F}. *k* is
a proportionality constant. *η* is related
to *τ*_{Coul} in the standard,
preceding form but becomes dependent on load:

*η* = *τ*_{F}/[*g*_{FB}*τ*_{idle} +
(*k* + 1)*τ*_{F}]
.

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.

Was this topic helpful?