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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.

**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`.

**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 angular velocity threshold**Enter the relative angular velocity above which full efficiency losses are included. Values below this threshold mark an efficiency transition region where the driving shaft becomes the driven shaft and vice-versa. The follower angular velocity threshold must be positive. Select a physical unit.

The default value is

`0.01`. The default unit is`rad/s`.

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} |

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.

Port | Description |
---|---|

B | Rotational conserving port representing the base shaft |

F | Rotational Conserving port representing the follower shaft |

Simple Gear | Variable Ratio Transmission

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