Model Gears with Losses

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.

Constant Efficiency

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. When no power is transmitted, Simscape uses the frictional torque equation.

• 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) + ForwardLossBackwardLoss)

where:

• 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. For blocks like the Leadscrew block that use Floss instead of Tf, the same expression applies in terms of force.