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, ωF and ωB have the same sign. If they rotate in opposite directions, ωF and ωB have opposite signs. For model details, see Simple Gear Model.
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.
Fixed ratio gFB of
the follower axis to the base axis. The gear ratio must be strictly
positive. The default is
Direction of motion of the follower (output) driveshaft relative
to the motion of the base (input) driveshaft. The default is
opposite direction to input shaft.
Parameters for meshing losses vary with the block variant chosen—one with a thermal port for thermal modeling and one without it.
Two-element array with the viscous friction coefficients in
effect at the base and follower shafts. The default array,
0], corresponds to zero viscous losses.
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|
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, τCoul = gFBτidle + kτF. k is a proportionality constant. η is related to τCoul in the standard, preceding form but becomes dependent on load:
η = τF/[gFBτidle + (k + 1)τF] .
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|