Gear train for transferring power to separate shafts spinning at different speeds
This block represents a gear train for transferring power from one drive shaft to two driven shafts. A combination of simple and bevel gear constraints enable the driven shafts to spin at different speeds, when necessary, and in different directions. One example is an automobile differential, which during a turn enables the inner and outer wheels to spin at different speeds, these depending on the turning radius of each individual wheel.
Any of the shafts can provide the input that drives the remaining two shafts. The differential converts this input into rotation, torque, and power at the driven shafts. The drive gear ratio, which you specify directly in the block dialog box, helps determine the angular velocity of each driven shaft. For more information, see Differential Gear Model
This block is a composite component with three underlying blocks:
The figure shows the connections between the three blocks.
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.
Select the placement of the bevel crown gear with respect to
the center-line of the gear assembly. The default is
right of the center-line.
Fixed ratio gD of
the carrier gear to the longitudinal driveshaft gear. The default
Parameters for meshing losses vary with the block variant chosen—one with a thermal port for thermal modeling and one without it.
Vector of viscous friction coefficients [μS μD]
for the sun-carrier and longitudinal driveshaft-casing gear motions,
respectively. The default is
From the drop-down list, choose units. The default is newton-meters/(radians/second)
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
Differential imposes one kinematic constraint on the three connected axes:
ωD = ±(1/2)gD(ωS1 + ωS2) ,
with the upper (+) or lower (–) sign valid for the differential crown to the right or left, respectively, of the center-line. The three degrees of freedom reduce to two independent degrees of freedom. The gear pairs are (1,2) = (S,S) and (C,D). C is the carrier.
The sum of the lateral motions is the transformed longitudinal motion. The difference of side motions ωS1 – ωS2 is independent of the longitudinal motion. The general motion of the lateral shafts is a superposition of these two independent degrees of freedom, which have this physical significance:
One degree of freedom (longitudinal) is equivalent to the two lateral shafts rotating at the same angular velocity (ωS1 = ωS2) and at a fixed ratio with respect to the longitudinal shaft.
The other degree of freedom (differential) is equivalent to keeping the longitudinal shaft locked (ωD = 0) while the lateral shafts rotate with respect to each other in opposite directions (ωS1 = –ωS2).
The torques along the lateral axes, τS1 and τS2, are constrained to the longitudinal torque τD in such a way that the power flows into and out of the gear, less any power loss Ploss, sum to zero:
ωS1τS1 + ωS2τS2 + ωDτD – Ploss= 0 .
When the kinematic and power constraints are combined, the ideal case yields:
gDτD = 2(ωS1τS1 + ωS2τS2) / (ωS1 + ωS2) .
In the nonideal case, τloss ≠ 0. See Model Gears with Losses.
Gear inertia is assumed negligible.
Gears are treated as rigid components.
Coulomb friction slows down simulation. See Adjust Model Fidelity.
These SimDriveline™ example models contain working examples of differential gears:
|D||Rotational conserving port representing the longitudinal driveshaft|
|S1||Rotational conserving port representing one of the sun gears|
|S2||Rotational conserving port representing one of the sun gears|
|H||Thermal conserving port for thermal modeling|