While the Simscape™ Driveline™ library contains a Planetary Gear, you can create your own custom planetary gear using the Planetary Subcomponents sublibrary. The sdl_custom_planetary_gear example model combines three Sun-Planet Bevel subgears into a masked subsystem to model a coupled planetary gear train. The model uses an Ideal Angular Velocity Source to place a fixed velocity demand on the gearbox input, while damping the system on both the input and output driveshafts with Rotational Dampers.
Custom Planetary Gear System and Subsystem
The blocks of the Simscape Driveline Gears Library contain optional built-in models of frictional losses, allowing you to represent nonideal gear couplings. In a nonideal gear pair (1,2), the angular velocity, gear radii, gear teeth constraints, and gear ratio g12 = r2/r1 = ω1/ω2 are unchanged. The transferred torque and power are reduced by:
Coulomb friction between imperfectly meshing teeth surfaces on gears 1 and 2, parameterized by an efficiency η, 0 < η ≤ 1. This efficiency depends on the torque load on the teeth. But it is often approximated as constant.
Viscous coupling of driveshafts with bearings, parameterized by viscous friction coefficients μ.
In the simplest nonideal gear loss model, the efficiency η12 of meshing in gear pair (1,2) is constant, independent of load (torque or power transferred).
The friction loss represented by η12 is effectively applied in full only if the transmitted power is greater than the power threshold pth. Below this value, a hyperbolic tangent function smooths the efficiency factor, lowering the efficiency losses to zero when no power is transmitted.
For gear sets with a carrier, η12 represents the ordinary efficiency, defined when the carrier is not moving.
For gears with different efficiencies for the forward and reverse power flow:
ForwardLoss = (1 – ηFB), ηFB is the torque transfer efficiency from the follower shaft to the base shaft.
BackwardLoss = (1/ηBF – 1), where ηBF is the torque transfer efficiency from the base shaft to the follower shaft.
The frictional torque is calculated as:
Tf = T / 2((ForwardLoss + BackwardLoss)tanh(4p / pth) + ForwardLoss – BackwardLoss)
T is the transferred torque.
p is the transferred power.
pth is the power threshold at the base shaft above which full efficiency losses are in effect.
For certain gear models, such as the Simple Gear, efficiency is assumed equal for both the forward and reverse power flow, ηBF = ηFB.
Making η dependent on the load is a way to make the loss model more accurate. For an example of load-dependent efficiency, see the Simple Gear block reference page.
Making η dependent on the geometry of gear meshing is another way to make the loss model more accurate. For an example of geometry-dependent efficiency, see the Leadscrew block reference page.
On a driveshaft mounted to a gear wheel by lubricated, nonideal bearings, the viscous friction experienced by the axis is controlled by the viscous friction coefficient μ. The viscous friction torque on a driveshaft "a" is –μa·ωa, where ωa is the angular velocity of the driveshaft with respect to its mounting or carrier (if a carrier is present).
Here, you revisit the sdl_simple_transmission model in Model a Two-Speed Transmission with Braking. You reconfigure the Simple Gears to model power loss due to nonideal meshing. The effect of viscous bearing losses is ignored.
Open the sdl_simple_transmission model and simulate to check the ideal gear behavior.
Open the Simple Gear 5:1 and Simple Gear 2:1 blocks.
Under Meshing Losses, in the Friction
model drop-down list, choose
Constant efficiency for
both. Enter efficiencies less than 1, but greater than 0. For example,
for the 5:1 gear, enter 0.7; and for the 2:1 gear, enter 0.95.
Leave the other settings as they are, including zero viscosity. Close the blocks.
Restart the model. The driveline runs at a lower efficiency and slightly smaller angular velocities, because of the power losses. If you enter different efficiency factors for the two gears, the effect of the loss is different if you switch between gears.
Experiment with load-dependent efficiency. In the Friction
model drop-down menu, choose
efficiency instead. In that case, you need more efficiency
model details to specify.