# Documentation

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# Variable Ratio Gear

Represent gear with controllable, variable gear ratio

Gears

## Description

The Variable Ratio Gear block represents a gearbox that constrains the two connected driveline axes, base (B) and follower (F), to corotate with a variable ratio that you can control. 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.

You specify the variable gear ratio as a function of time with the Simulink® input signal r. You specify the first derivative of the variable gear ratio as a function of time with the Simulink input signal v.

### Axis Motion and Constraint

The Variable Ratio Gear imposes a single constraint, specified by the variable gear ratio gFB(t), on the motions and torques of the two axes:

±gFB(t) = ωBF = τFB

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

### Effect of Coriolis Acceleration

With the Variable Ratio Gear block, you can choose to include or not include the effect of Coriolis acceleration on the gear motion. If you choose to include it, you must supply the first derivative, dgFB/dt, of the gear ratio as another Simulink input signal v.

The Coriolis acceleration is a nonlinear effect proportional to the angular velocity and the first derivative of the gear ratio:

dωB/dt = gFB·dωF/dt + ωF·dgFB/dt

 Caution:   If you do not include the Coriolis acceleration, simulation with the Variable Ratio Gear block will be inaccurate by an error proportional to dgFB/dt. If the gear ratio gFB changes rapidly, this error can be significant.If you include the Coriolis acceleration, the v derivative signal dgFB(t)/dt must be consistent with the r gear ratio signal gFB(t) to ensure accurate simulation.

### Effect of Linearization

If you simulate your model in linearization mode, the block holds the variable gear ratio gFB(t) fixed at its initial value, gFB(0).

## Dialog Box and Parameters

Follower and base rotate in opposite directions

Select to make the follower and base axes corotate in opposite directions. The default is selected.

Include Coriolis acceleration

Select to include the nonlinear effect of the nonzero first derivative of the variable gear ratio in the driveline dynamics. The default is unselected.