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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.
Fixed ratio g_{FB} of the follower axis to the base axis. The gear ratio must be strictly positive. The default is 2.
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.
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(4ω_{out}/ω_{th}) + μω_{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} + kτ_{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.