# Rotational Inerter

Two-port inertia in mechanical rotational systems

Libraries:
Simscape / Foundation Library / Mechanical / Rotational Elements

## Description

The Rotational Inerter block represents a device that has torque proportional to the rate of change of the relative angular velocity across the ports. It is essentially a two-port inertia that works on the velocity difference between the ports, not the absolute velocity.

Use this block in high performance suspension systems, to decouple weave and roll modes, or in applications where you need to model a passively tuned mass-spring-damper response.

The block is described with the following equations:

`$T=B\frac{d\omega }{dt}$`
`$\omega ={\omega }_{R}-{\omega }_{C}$`

where

• T is torque transmitted through the inerter.

• B is inertance.

• ω is relative angular velocity.

• ωR and ωC are absolute angular velocities of ports R and C, respectively.

The block positive direction is from port R to port C. This means that if the port R velocity is greater than that of port C, the block transmits torque from R to C.

### Variables

To set the priority and initial target values for the block variables prior to simulation, use the Initial Targets section in the block dialog box or Property Inspector. For more information, see Set Priority and Initial Target for Block Variables.

Nominal values provide a way to specify the expected magnitude of a variable in a model. Using system scaling based on nominal values increases the simulation robustness. Nominal values can come from different sources, one of which is the Nominal Values section in the block dialog box or Property Inspector. For more information, see Modify Nominal Values for a Block Variable.

## Ports

### Conserving

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Mechanical rotational conserving port associated with the rod, that is, the moving body.

Mechanical rotational conserving port associated with the case, that is, the stationary body.

## Parameters

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Proportionality coefficient between the torque and the rate of change of the relative angular velocity across the ports.

## Version History

Introduced in R2015b