# Torque Converter

Three-part torque converter consisting of an impeller, turbine, and stator

• Libraries:
Powertrain Blockset / Transmission / Torque Converters

## Description

The Torque Converter block implements a three-part torque converter consisting of an impeller, turbine, and stator with an optional clutch lock-up capability. The block can simulate driving (power flowing from impeller to turbine) and coasting (power from turbine dissipated in torque converter hydraulic fluid).

You can specify torque converter characteristics:

• Speed ratio — Ratio of turbine angular speed to impeller angular speed

• Torque ratio — Ratio of turbine torque to impeller torque

• Capacity factor parameterization — Function of input speed or input torque

Optional clutch lock-up configurations include:

• No lock-up — Model fluid-coupling only

• Lock-up — Model automatic clutch engagement

• External lock-up — Model clutch pressure as input from an external signal ### Dynamics

Clutch Lock-Up Condition and Clutch Friction

Based on the clutch lock-up condition, the block implements these friction models.

IfClutch ConditionFriction Model
$\begin{array}{l}{\omega }_{i}\ne {\omega }_{t}\\ \text{or}\\ {T}_{S}<|\frac{{J}_{t}}{\left({J}_{i}+{J}_{t}\right)}\left[{T}_{i}+{T}_{f}-{\omega }_{i}\left({b}_{t}+{b}_{i}\right)\right]|\end{array}$Unlocked$\begin{array}{l}{T}_{f}={T}_{k}\\ \text{where:}\\ {T}_{k}={F}_{c}{R}_{eff}{m}_{k}\mathrm{tanh}\left[4\left({\omega }_{i}-{\omega }_{t}\right)\right]\\ {T}_{s}={F}_{c}{R}_{eff}{m}_{s}\\ {R}_{eff}=\frac{2\left({R}_{o}{}^{3}-{R}_{i}{}^{3}\right)}{3\left({R}_{o}{}^{2}-{R}_{i}{}^{2}\right)}\end{array}$
$\begin{array}{l}{\omega }_{i}={\omega }_{t}\\ \text{and}\\ {T}_{S}\ge |\frac{{J}_{t}}{\left({J}_{i}+{J}_{t}\right)}\left[{T}_{i}+{T}_{f}-{w}_{t}\left({b}_{t}+{b}_{i}\right)+{w}_{t}{b}_{t}\right]|\end{array}$Locked

Tf = Ts

Locked Rotational Dynamics

To model the rotational dynamics if the clutch is locked, the block implements equations.

`$\begin{array}{l}\stackrel{˙}{\omega }\left({J}_{i}+{J}_{t}\right)={T}_{i}-\omega \left({b}_{i}+{b}_{t}\right)+{T}_{ext}\\ \omega ={\omega }_{i}={\omega }_{t}\end{array}$`

The rotational velocity represents both the impeller and turbine rotational velocities.

Unlocked Rotational Dynamics

To model the rotational dynamics if the clutch is unlocked, the block implements equations.

To approximate the torque multiplication lag between the impeller and turbine, you can specify the parameter Fluid torque response time constant (set to 0 to disable), tauc [s].

### 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

`PwrImp`

Applied impeller power

Pimp

${\omega }_{i}{T}_{i}$
`PwrTurb`

Applied turbine output power

Pturb

${\omega }_{t}{T}_{t}$

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

• Positive signals indicate an input

• Negative signals indicate a loss

`PwrDampLoss`

Mechanical damping loss

Pdamploss

$-{b}_{t}{\omega }_{t}^{2}-{b}_{i}{\omega }_{i}^{2}$

`PwrFluidCplingLoss`

Heat loss to transmission fluid

Pflloss

$-\left({T}_{p}{\omega }_{i}-{T}_{hyd}{\omega }_{t}\right)$

`PwrCltchLoss`

Clutch slip power loss

Pcltloss

$-{T}_{k}\left({\omega }_{i}-{\omega }_{t}\right)$

`PwrStored` — Stored energy rate of change

• Positive signals indicate an increase

• Negative signals indicate a decrease

`PwrStoredImp`

Rate change in impeller rotational kinetic energy

Pstrimp

${\stackrel{˙}{\omega }}_{i}{\omega }_{i}{J}_{i}$

`PwrStoredTurb`

Rate change in turbine rotational kinetic energy

Pstrturb

${\stackrel{˙}{\omega }}_{t}{\omega }_{t}{J}_{t}$

The block implements equations that use these variables.

 ${T}_{f}$ Frictional torque ${T}_{k}$ Kinetic frictional torque ${T}_{s}$ Static frictional torque ${T}_{i}$ Applied input torque ${T}_{p}$ Impeller reaction torque ${T}_{ext}$ Externally applied turbine torque $\psi \left(\varphi \right)$ Torque conversion capacity factor $\zeta \left(\varphi \right)$ Torque ratio ${\omega }_{i}$ Impeller rotational shaft speed ${\omega }_{t}$ Turbine rotational shaft speed ${J}_{i}$ Impeller rotational inertia ${J}_{t}$ Turbine rotational inertia ${b}_{i}$ Impeller rotational viscous damping ${b}_{t}$ Turbine rotational viscous damping ${R}_{eff}$ Effective clutch radius ${R}_{o}$ Annular disk outer radius ${R}_{i}$ Annular disk inner radius

## Ports

### Inputs

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Applied input torque, typically from the engine crankshaft or dual mass flywheel, in N·m.

Applied turbine torque, typically from the transmission, in N·m.

Applied clutch force, typically from a hydraulic actuator, in N.

#### Dependencies

To create this port, select `External lock-up input` for the Lock-up clutch configuration parameter.

### Output

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Bus signal containing these block calculations.

SignalDescriptionUnits

`Imp`

`ImpTrq`

Applied input torque

N·m

`ImpSpd`

Impeller rotational shaft speed

`Turb`

`TurbTrq`

Applied turbine torque

N·m

`TurbSpd`

Turbine rotational shaft speed

`Cltch`

`CltchForce`

Applied clutch force

N

`CltchLocked`

Clutch locked or unlocked state

N/A

`TrqConv`

`TrqConvSpdRatio`

Turbine to impeller speed ratio

N/A

`TrqConvEta`

Torque conversion efficiency

N/A

`PwrInfo`

`PwrTrnsfrd`

`PwrImp`

Applied impeller power

W

`PwrTurb`

Applied turbine output power

W

`PwrNotTrnsfrd`

`PwrDampLoss`

Mechanical damping loss

W

`PwrFluidCplingLoss`

Heat loss to transmission fluid

W

`PwrCltchLoss`

Clutch slip power loss

W

`PwrStored`

`PwrStoredImp`

Rate change in impeller rotational kinetic energy

W

`PwrStoredTurb`

Rate change in turbine rotational kinetic energy

W

Impeller rotational shaft speed, ${\omega }_{i}$, in rad/s.

Turbine rotational shaft speed, ${\omega }_{t}$, in rad/s.

## Parameters

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Configuration

To ModelSelect
Fluid-coupling only`No lock-up`
Automatic clutch engagement`Lock-up`
Clutch pressure as input from an external signal```External lock-up input```

#### Dependencies

To enable the Clutch parameters, select `Lock-up` or ```External lock-up input``` for the Lock-up clutch configuration parameter.

Torque Converter

Impeller shaft inertia, in kg·m^2.

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

Turbine shaft inertia, in kg·m^2.

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

Initial impeller shaft velocity, in rad/s.

Initial turbine shaft velocity, in rad/s.

Vector of turbine speed to impeller speed ratios. Breakpoints for the capacity and torque multiplication vectors.

To Set Factor Ratio toSelect
Impeller angular velocity to square root impeller torque```Input speed / sqrt(input torque)```
Impeller absorbed torque to square of impeller angular velocity```Absorbed torque / input speed^2```

Capacity factor parameterization SettingCapacity Vector Units
```Input speed / sqrt(input torque)```(rad/s)/(N·m)^0.5
```Absorbed torque / input speed^2```N·m/(rad/s)^2

Vector of turbine torque to impeller speed ratios.

To account for the delay in torque calculations due to changing input torque, specify the fluid torque transfer time constant, in s.

Interpolates the torque ratio and capacity factor functions between the discrete relative velocity values.

Clutch

The effective radius, ${R}_{eff}$, used with the applied clutch friction force to determine the friction force, in m. The effective radius is defined as:

`${R}_{eff}=\frac{2\left({R}_{o}{}^{3}-{R}_{i}{}^{3}\right)}{3\left({R}_{o}{}^{2}-{R}_{i}{}^{2}\right)}$`

The equation uses these variables.

 ${R}_{o}$ Annular disk outer radius ${R}_{i}$ Annular disk inner radius

#### Dependencies

To enable the Clutch parameters, select `Lock-up` or ```External lock-up input``` for the Lock-up clutch configuration parameter.

Dimensionless clutch disc coefficient of static friction.

#### Dependencies

To enable the Clutch parameters, select `Lock-up` or ```External lock-up input``` for the Lock-up clutch configuration parameter.

Dimensionless clutch disc coefficient of kinetic friction.

To enable the Clutch parameters, select `Lock-up` or `External lock-up input` for the Lock-up clutch configuration parameter.

#### Dependencies

To enable this parameter, select `Lock-up` or `External lock-up input` for the Lock-up clutch configuration parameter.

Set speed ratio threshold that engages clutch lock-up.

#### Dependencies

To enable this parameter, select `Lock-up` for the Lock-up clutch configuration parameter.

Set the minimum impeller speed that engages clutch lock-up, in rad/s.

#### Dependencies

To enable this parameter, select `Lock-up` for the Lock-up clutch configuration parameter.

Set the minimum impeller speed that disengages clutch lock-up, in rad/s.

#### Dependencies

To enable this parameter, select `Lock-up` for the Lock-up clutch configuration parameter.

Open loop clutch lock-up force gain, in N.

#### Dependencies

To enable this parameter, select `Lock-up` for the Lock-up clutch configuration parameter.

Open loop clutch lock-up time constant, in s.

#### Dependencies

To enable this parameter, select `Lock-up` for the Lock-up clutch configuration parameter.

## Version History

Introduced in R2017a