SimDriveline™

Differential - Represent differential gear with specified gear ratio

Library

Gears

Description

The Differential block represents a differential gear that couples rotational motion about the longitudinal axis to rotational motion about two lateral axes.

Any one axis can be the input. In normal use, the longitudinal shaft is the input, and motion, torque, and power flow out through the lateral shafts. The output axes, in general, have different angular velocities. The longitudinal motion is divided by the drive gear ratio that you specify and then split between the two lateral shafts.

Differentials in drivelines often have a controllable clutch connecting the two output shafts. You can add this clutch control by appropriately connecting a Controllable Friction Clutch block to the Differential block.

Axis Motions and Constraints

The three rotational degrees of freedom, the longitudinal ω_B and the lateral ω_F1 and ω_F2, are subject to one gear constraint and reduce to two independent degrees of freedom. In terms of the drive gear ratio g_D, the longitudinal motion is related to the sum of the lateral motions:

ω_B = (1/2) · g_D(ω_F1 + ω_F2)

The sum of the lateral motions is this transformed longitudinal motion, once the longitudinal axis is connected. The difference of lateral motions ω_F1 – ω_F2 is independent of the longitudinal motion. These two independent degrees of freedom have this physical significance:

One degree of freedom (longitudinal) is equivalent to the two lateral shafts rotating at the same angular velocity (ω_F1 = ω_F2) 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 (ω_B = 0) while the lateral shafts rotate with respect to each other in opposite directions (ω_F1 = -ω_F2).

The general motion of the lateral shafts is a superposition of these two motions.

The torques along the lateral axes, τ_F1 and τ_F2, are constrained to the longitudinal torque τ_B in such a way that the power input equals the sum of the power outputs:

ω_Bτ_B = ω_F1τ_F1 + ω_F2τ_F2

When the kinematic and power constraints are combined,

g_Dτ_B = 2(ω_F1τ_F1 + ω_F2τ_F2) / (ω_F1 + ω_F2)

Warning All gear ratios must be strictly positive. If any gear ratio equals 0 or becomes negative at any time, a SimDriveline simulation stops with an error.

Dialog Box and Parameters

Drive gear ratio: Ratio g_D is twice the ratio of the input angular motion to the sum of the two output angular motions. This ratio must be strictly positive. The default is 1.

Example