Main Content

# Rotational Inertia

Ideal mechanical rotational inertia

Libraries:
Powertrain Blockset / Drivetrain / Couplings
Vehicle Dynamics Blockset / Powertrain / Drivetrain / Couplings

## Description

The Rotational Inertia block implements an ideal mechanical rotational inertia.

### Power Accounting

For the power accounting, the block implements these equations.

Bus Signal DescriptionVariableEquations

`PwrInfo`

`PwrTrnsfrd` — Power transferred between blocks

• Positive signals indicate flow into block

• Negative signals indicate flow out of block

`PwrR`

Mechanical power from base shaft

PTR

`PwrC`

Mechanical power from follower shaft

PTC

`PwrNotTrnsfrd` — Power crossing the block boundary, but not transferred

• Positive signals indicate an input

• Negative signals indicate a loss

`PwrDampLoss`

Power loss due to damping

Pd

${P}_{d}=-b{|\omega |}^{2}$

`PwrStored` — Stored energy rate of change

• Positive signals indicate an increase

• Negative signals indicate a decrease

`PwrStoredShft`

Rate change of stored internal torsional energy

Ps

${P}_{s}=\omega \stackrel{˙}{\omega }J$

The equations use these variables.

 TR Input torque TC Output torque ω Driveshaft angular velocity J Rotational inertia b Rotational viscous damping Pd Power loss due to damping Ps Rate change of stored internal torsional energy

## Ports

### Input

expand all

Applied input driveshaft torque, TR, in N·m.

#### Dependencies

To enable this port, for Port Configuration, select `Simulink`.

Load driveshaft torque, TC, in N·m.

#### Dependencies

To enable this port, for Port Configuration, select `Simulink`.

Angular velocity in rad/s. Torque is in N·m.

#### Dependencies

To enable this port, for Port Configuration, select `Two-way connection`.

Rotational inertia, in kg·m^2.

#### Dependencies

To create the `Inertia` port, select External inertia input.

### Output

expand all

Bus signal containing these block calculations.

SignalDescriptionVariableUnits
Trq

`R`

Applied input driveshaft torque

TRN·m

`C`

Output driveshaft torque

TCN·m

`Damp`

Damping torque

Td=bω

N·m

Spd

Angular driveshaft speed

ωrad/s
PwrInfo

`PwrTrnsfrd`

`PwrR`

Mechanical power from base shaft

PTR

W
`PwrC`

Mechanical power from follower shaft

PTC

W

`PwrNotTrnsfrd`

`PwrDampLoss`

Power loss due to damping

Pd

W

`PwrStored`

`PwrStoredShft`

Rate change of stored internal torsional energy

Ps

W

#### Dependencies

To enable this port, select Output Info bus.

Angular driveshaft speed, ω, in rad/s.

#### Dependencies

To enable this port, for Port Configuration, select `Simulink`.

Angular velocity in rad/s. Torque is in N·m.

#### Dependencies

To enable this port, for Port Configuration, select `Two-way connection`.

## Parameters

expand all

Block Options

Specify the port configuration.

#### Dependencies

Specifying `Simulink` creates these ports:

• `RTrq`

• `CTrq`

• `Spd`

Specifying `Two-way connection` creates these ports:

• `R`

• `C`

Select to create the `Info` output port.

#### Dependencies

To create the `Inertia` port, select External inertia input.

Parameters

Rotational inertia, in kg·m^2.

#### Dependencies

To enable this parameter, clear Input rotational inertia.

Torsional damping, in N·m· s/rad.

Initial angular velocity, in rad/s.

## Version History

Introduced in R2017a