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.
The block models the effects of heat flow and temperature change through an optional thermal port. To expose the thermal port, right-click the block and select Simscape > Block choices > Show thermal port. Exposing the thermal port causes new parameters specific to thermal modeling to appear in the block dialog box.
Enter the gear ratio. This is the fraction of follower over
base gear teeth numbers, NF/NB. The ratio must be positive. The default
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
opposite direction to input shaft.
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
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
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
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
Component temperature at the start of simulation. The initial
temperature influences the starting meshing or friction losses by
altering the component efficiency according to an efficiency vector
that you specify. The default value is
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 + τF – τloss = 0 ,
with τloss = 0 in the ideal case.
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 Flow||Power Loss Condition||Output Driveshaft ωout|
|Forward||ωBτB > ωFτF||Follower, ωF|
|Reverse||ωBτB < ωFτF||Base, ωB|
Gear inertia is assumed negligible.
Gears are treated as rigid components.
Coulomb friction slows down simulation. See Adjust Model Fidelity.
|B||Rotational conserving port representing the base shaft|
|F||Rotational conserving port representing the follower shaft|
|H||Thermal conserving port for thermal modeling|