# Gearbox

Ideal rotational gearbox

• Library:
• Powertrain Blockset / Drivetrain / Couplings ## Description

The Gearbox block implements an ideal rotational gearbox. The block uses the gear inertias and damping to calculate the velocity response to the base and follower gear pair input torques.

In fuel economy and powertrain efficiency studies, you can use the Gearbox block to model ideal gear coupling and the power transfer between common driveline elements such as transmissions, engines, clutches, and differentials.

The Gearbox block uses these equations to approximate the transmission dynamics.

`$\begin{array}{l}{\stackrel{˙}{\omega }}_{B}{J}_{B}={\omega }_{B}{b}_{B}+\eta N{T}_{F}\\ {\stackrel{˙}{\omega }}_{F}{J}_{F}={\omega }_{F}{b}_{F}+\eta {T}_{F}\end{array}$`

This constraint equation reduces the system to a one DOF system.

`${\omega }_{B}=N{\omega }_{F}$`

To express the ideal torque transfer, the block uses this relationship.

`$\eta N{T}_{B}+{T}_{F}=0$`

### Efficiency

To account for the block efficiency, use the Efficiency factors parameter. This table summarizes the block implementation for each setting.

SettingImplementation

`Constant`

Constant efficiency that you can set with the Constant efficiency factor, eta parameter.

`Driveshaft torque, temperature and speed`

Efficiency as a function of base gear input torque, air temperature, and driveshaft speed. Use these parameters to specify the lookup table and breakpoints:

• Efficiency lookup table, eta_tbl

• Efficiency torque breakpoints, Trq_bpts

• Efficiency speed breakpoints, omega_bpts

• Efficiency temperature breakpoints, Temp_bpts

For the air temperature, you can either:

• Select Input temperature to create an input port.

• Set a Ambient temperature, Tamb parameter value.

To select the interpolation method, use the Interpolation method parameter. For more information, see Interpolation Methods (Simulink).

### 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

`PwrBase`

Mechanical power from base shaft

PBase

`PwrFlwr`

Mechanical power from follower shaft

PFlwr

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

• Positive signals indicate an input

• Negative signals indicate a loss

`PwrMechLoss`

Total power loss

Png

`PwrDampLoss`

Power loss due to damping

Pd

${P}_{d}=-\left({b}_{F}{|{\omega }_{F}|}^{2}+{b}_{B}{|{\omega }_{B}|}^{2}\right)$

`PwrStored` — Stored energy rate of change

• Positive signals indicate an increase

• Negative signals indicate a decrease

`PwrStoredShft`

Rate change of stored internal kinetic energy

Ps

${P}_{s}=\left({\omega }_{B}{\stackrel{˙}{\omega }}_{B}{J}_{B}+{\omega }_{F}{\stackrel{˙}{\omega }}_{F}{J}_{F}\right)$

The equations use these variables.

 TB Base gear input torque TF Follower gear output torque ωB Base gear angular velocity ωF Follower gear angular velocity JB Base gear rotational inertia JF Follower gear rotational inertia bB Base gear rotational viscous damping bF Follower gear rotational viscous damping N Torque transmission gear ratio η Gear efficiency Pt Total power Pd Power loss due to damping Ps Rate change of stored internal kinetic energy

## Ports

### Input

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Base gear input torque, TB, in N·m.

#### Dependencies

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

Follower gear output torque, TF, in N·m.

#### Dependencies

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

Base gear angular velocity, ωB, in rad/s. Base gear torque, TB, in N·m.

#### Dependencies

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

Ambient air temperature, Tair, in K.

#### Dependencies

To create this port:

• Set Efficiency factors to ```Driveshaft torque, speed and temperature```.

• Select Input ambient temperature.

### Output

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Bus signal containing these block calculations.

SignalDescriptionVariableUnits
Base

`BaseTrq`

Base gear input torque

TBN·m

`BaseSpd`

Base gear angular velocity

Flwr

`FlwrTrq`

Follower gear torque

TFN·m

`FlwrSpd`

Follower gear angular velocity

PwrInfo

`PwrTrnsfrd`

`PwrBase`

Mechanical power from base shaft

PBase

W
`PwrFlwr`

Mechanical power from follower shaft

PFlwr

W

`PwrNotTrnsfrd`

`PwrMechLoss`

Total gear power loss

Png

W
`PwrDampLoss`

Power loss due to damping

Pd

W

`PwrStored`

`PwrStoredShft`

Rate change of stored internal kinetic energy

Ps

W

Base gear angular velocity, ωB, in rad/s.

#### Dependencies

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

Follower gear angular velocity, ωF, in rad/s.

#### Dependencies

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

Follower gear angular velocity, ωF, in rad/s. Follower gear torque, TF, in N·m.

#### Dependencies

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

## Parameters

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#### Block Options

Specify the port configuration.

#### Dependencies

Specifying `Simulink` creates these ports:

• `BSpd`

• `FSpd`

• `BTrq`

• `FTrq`

Specifying `Two-way connection` creates these ports:

• `B`

• `F`

To account for the block efficiency, use the Efficiency factors parameter. This table summarizes the block implementation for each setting.

SettingImplementation

`Constant`

Constant efficiency that you can set with the Constant efficiency factor, eta parameter.

`Driveshaft torque, temperature and speed`

Efficiency as a function of base gear input torque, air temperature, and driveshaft speed. Use these parameters to specify the lookup table and breakpoints:

• Efficiency lookup table, eta_tbl

• Efficiency torque breakpoints, Trq_bpts

• Efficiency speed breakpoints, omega_bpts

• Efficiency temperature breakpoints, Temp_bpts

For the air temperature, you can either:

• Select Input temperature to create an input port.

• Set a Ambient temperature, Tamb parameter value.

To select the interpolation method, use the Interpolation method parameter. For more information, see Interpolation Methods (Simulink).

#### Dependencies

To enable this parameter, set Efficiency factors to `Driveshaft torque, speed and temperature`.

Select to specify that the output shaft rotates in the same direction as the input.

Select to create input port `AirTemp` for the ambient air temperature.

#### Dependencies

To enable this parameter, set Efficiency factors to `Driveshaft torque, speed and temperature`.

Base-to-follower gear ratio, dimensionless.

Base shaft inertia, in kg·m^2.

Follower shaft inertia, in kg·m^2.

Base viscous shaft damping, in N·m· s/rad.

Follower viscous shaft damping, in N·m· s/rad.

Base shaft initial velocity, in rad/s.

#### Efficiency

Constant efficiency, η.

#### Dependencies

To enable this parameter, set Efficiency factors to `Constant`.

Dimensionless array of values for efficiency as a function of:

• `M` input torques

• `N` input speed

• `L` air temperatures

Each value specifies the efficiency for a specific combination of torque, speed, and temperature. The array size must match the dimensions defined by the torque, speed, and temperature breakpoint vectors.

#### Dependencies

To enable this parameter, set Efficiency factors to `Driveshaft torque, speed and temperature`.

Vector of input torque, breakpoints for efficiency, in N·m.

#### Dependencies

To enable this parameter, set Efficiency factors to `Driveshaft torque, speed and temperature`.

Vector of speed, breakpoints for efficiency, in rad/s.

#### Dependencies

To enable this parameter, set Efficiency factors to `Driveshaft torque, speed and temperature`.

Vector of ambient temperature breakpoints for efficiency, in K.

#### Dependencies

To enable this parameter, set Efficiency factors to `Driveshaft torque, speed and temperature`.

Ambient air temperature, Tair, in K.

#### Dependencies

To enable this parameter:

• Set Efficiency factors to ```Driveshaft torque, speed and temperature```.

• Clear Input ambient temperature.

## Extended Capabilities

### C/C++ Code GenerationGenerate C and C++ code using Simulink® Coder™. 