# Automated Manual Transmission

Ideal automated manual transmission

• Library:
• Powertrain Blockset / Transmission / Transmission Systems

• ## Description

The Automated Manual Transmission block implements an ideal automated transmission (AMT). An AMT is a manual transmission with additional actuators and an electronic control unit (ECU) to regulate clutch and gear selection based on commands from a controller. The number of gears is specified via an integer vector with corresponding gear ratios, inertias, viscous damping, and efficiency factors. The clutch and synchronization engagement rates are linear and adjustable.

Use the block for:

• Power and torque capacity sizing

• Determining gear ratio impact on fuel economy and performance

To determine the rotational drive shaft speed and reaction torque, the Automated Manual Transmission block calculates:

• Clutch lock-up and clutch friction

• Locked rotational dynamics

• Unlocked rotational dynamics

To specify the block efficiency calculation, for Efficiency factors, select either of these options.

SettingBlock Implementation
`Gear only`

Efficiency determined from a 1D lookup table that is a function of the gear.

`Gear, input torque, input speed, and temperature`

Efficiency determined from a 4D lookup table that is a function of:

• Gear

• Input torque

• Input speed

• Oil temperature

### Clutch Control

The AMT delivers drive shaft torque continuously by controlling the pressure signals from the clutch. If you select Control type parameter `Ideal integrated controller`, the block generates idealized clutch pressure signals. To use your own clutch control signals, select Control type parameter ```External control```.

### Clutch Lock-Up and Clutch Friction

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

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

Tf = Ts

The equations use these variables.

 ωt Output drive shaft speed ωi Input drive shaft speed ωd Drive shaft speed ${b}_{i}$ Viscous damping Fc Applied clutch force N Engaged gear ${T}_{f}$ Frictional torque ${T}_{k}$ Kinetic frictional torque ${T}_{s}$ Static frictional torque ${R}_{eff}$ Effective clutch radius ${R}_{o}$ Annular disk outer radius ${R}_{i}$ Annular disk inner radius μs Coefficient of static friction μk Coefficient of kinetic friction

### Locked Rotational Dynamics

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

`$\begin{array}{l}{\stackrel{˙}{\omega }}_{d}{J}_{N}={\eta }_{N}{T}_{d}-\frac{{\omega }_{i}}{N}{b}_{N}+N{T}_{i}\\ {\omega }_{i}=N{\omega }_{d}\end{array}$`

The block determines the input torque, Ti, through differentiation.

The equations use these variables.

 ωi Input drive shaft speed ωd Drive shaft speed N Engaged gear bN Engaged gear viscous damping JN Engaged gear inertia ηN Engaged gear efficiency Td Drive shaft torque Ti Applied input torque

### Unlocked Rotational Dynamics

To model the rotational dynamics when the clutch is unlocked, the block implements this equation.

`${\stackrel{˙}{\omega }}_{d}{J}_{N}=N{T}_{f}-{\omega }_{d}{b}_{N}+{T}_{d}$`

where:

 ωd Drive shaft speed N Engaged gear bN Engaged gear viscous damping JN Engaged gear inertia Td Drive shaft torque Ti Applied input torque

### 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

`PwrEng`

Engine power

Peng

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

Differential power

Pdiff

${\omega }_{d}{T}_{d}$

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

• Positive signals indicate an input

• Negative signals indicate a loss

`PwrEffLoss`

Mechanical power loss

Peffloss

${\omega }_{d}{T}_{d}\left({\eta }_{N}-1\right)$
`PwrDampLoss`

Mechanical damping loss

Pdamploss

`PwrCltchLoss`

Clutch power loss

Pmech

When locked: $0$

When unlocked: $-{T}_{k}\left({\omega }_{i}-N{\omega }_{d}\right)$

`PwrStored` — Stored energy rate of change

• Positive signals indicate an increase

• Negative signals indicate a decrease

`PwrStoredTrans`

Rate change in rotational kinetic energy

Pstr

When locked: ${\stackrel{˙}{\omega }}_{i}{\omega }_{i}\left({J}_{in}+\frac{{J}_{N}}{{N}^{2}}\right)$

When unlocked: ${J}_{in}{\stackrel{˙}{\omega }}_{i}{\omega }_{i}+{J}_{N}{\stackrel{˙}{\omega }}_{d}{\omega }_{d}$

The equations use these variables.

 bN Engaged gear viscous damping JN Engaged gear rotational inertia Jin Flywheel rotational inertia ηN Engaged gear efficiency N Engaged gear ratio Ti Applied input torque, typically from the engine crankshaft or dual mass flywheel damper Td Applied load torque, typically from the differential or drive shaft ωd Initial input drive shaft rotational velocity ωi, ώi Applied drive shaft angular speed and acceleration

## Ports

### Input

expand all

Integer value of gear number to engage.

Clutch pressure command.

#### Dependencies

To create this port, select Control type parameter `External control`.

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

Applied load torque, Td, typically from the differential or driveshaft, in N·m.

Oil temperature, in K. To determine the efficiency, the block uses a 4D lookup table that is a function of:

• Gear

• Input torque

• Input speed

• Oil temperature

#### Dependencies

To create this port, set Efficiency factors to ```Gear, input torque, input speed, and temperature```.

### Output

expand all

Bus signal contains these block calculations.

SignalDescriptionVariableUnits

`Eng`

`EngTrq`

Input applied torque

Ti

N·m

`EngSpd`

Input drive shaft speed

ωi

`Diff`

`DiffTrq`

Output drive shaft torque

Tt

N·m

`DiffSpd`

Output drive shaft speed

ωt

`Cltch`

`CltchForce`

Applied clutch force

Fc

N

`CltchLocked`

Clutch lock status, Boolean:

• Locked — `0`

• Unlocked — `1`

N/A

N/A

`Trans`

`TransSpdRatio`

Speed ratio at time t

$\varphi \left(t\right)$

N/A

`TransEta`

Ratio of output power to input power

$\eta$

N/A

`TransGearCmd`

Commanded gear

Ncmd

N/A

`TransGear`

Engaged gear

N

N/A

`PwrInfo``PwrTrnsfrd`

`PwrEng`

Engine power

Peng

W
`PwrDiffrntl`

Differential power

Pdiff

W
`PwrNotTrnsfrd``PwrEffLoss`

Mechanical power loss

Peffloss

W
`PwrDampLoss`

Mechanical damping loss

Pdamploss

W
`PwrCltchLoss`

Clutch power loss

Pmech

W
`PwrStored``PwrStoredTrans`

Rate change in rotational kinetic energy

Pstr

W

Applied drive shaft angular speed input, ωi, in rad/s.

Drive shaft angular speed output, ωd, in rad/s.

## Parameters

expand all

The AMT delivers drive shaft torque continuously by controlling the pressure signals from the clutch. If you select Control type parameter `Ideal integrated controller`, the block generates idealized clutch pressure signals. To use your own clutch control signals, select Control type parameter ```External control```.

#### Dependencies

This table summarizes the port configurations.

Control ModeCreates Ports
```External control```

`CltchCmd`

To specify the block efficiency calculation, for Efficiency factors, select either of these options.

SettingBlock Implementation
`Gear only`

Efficiency determined from a 1D lookup table that is a function of the gear.

`Gear, input torque, input speed, and temperature`

Efficiency determined from a 4D lookup table that is a function of:

• Gear

• Input torque

• Input speed

• Oil temperature

#### Dependencies

Setting Parameter ToEnables
`Gear only`

Efficiency vector, eta

```Gear, input torque, input speed, and temperature```

Efficiency torque breakpoints, Trq_bpts

Efficiency speed breakpoints, omega_bpts

Efficiency temperature breakpoints, Temp_bpts

Efficiency lookup table, eta_tbl

Transmission

Input shaft inertia, in kg·m^2.

Input shaft damping, in N·m·s/rad.

Angular velocity, in rad/s.

Vector of integer gear commands used to specify the number of transmission speeds. Neutral gear is `0`. For example, you can set these parameter values.

To SpecifySet Gear number, G To
Four transmission speeds, including neutral`[0,1,2,3,4]`
Three transmission speeds, including neutral and reverse`[-1,0,1,2,3]`
Five transmission speeds, including neutral and reverse`[-1,0,1,2,3,4,5]`

Vector dimensions for the Gear number vector, Gear ratio vector, Transmission inertia vector, Transmission damping vector, and Efficiency vector parameters must be equal.

Torque breakpoints for efficiency table, in N·m.

#### Dependencies

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

Speed breakpoints for efficiency table, rad/s.

#### Dependencies

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

Temperature breakpoints for efficiency table, in K.

#### Dependencies

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

Vector of gear ratios (that is, input speed to output speed) with indices corresponding to the ratios specified in Gear number, G. For neutral, set the gear ratio to `1`. For example, you can set these parameter values.

To Specify Gear Ratios ForSet Gear number, G ToSet Gear ratio, N To
Four transmission speeds, including neutral`[0,1,2,3,4]``[1,4.47,2.47,1.47,1]`
Five transmission speeds, including neutral and reverse`[-1,0,1,2,3,4,5]``[-4.47,1,4.47,2.47,1.47,1,0.8]`

Vector dimensions for the Gear number vector, Gear ratio vector, Transmission inertia vector, Transmission damping vector, and Efficiency vector parameters must be equal.

Vector of gear rotational inertias, with indices corresponding to the inertias specified in Gear number, G, in kg·m^2. For example, you can set these parameter values.

To Specify Inertia ForSet Gear number, G ToSet Inertia, J To
Four gears, including neutral`[0,1,2,3,4]``[0.01,2.28,2.04,0.32,0.028]`
Inertia for five gears, including reverse and neutral`[-1,0,1,2,3,4,5]``[2.28,0.01,2.28,2.04,0.32,0.028,0.01]`

Vector dimensions for the Gear number vector, Gear ratio vector, Transmission inertia vector, Transmission damping vector, and Efficiency vector parameters must be equal.

Vector of gear viscous damping coefficients, with indices corresponding to the coefficients specified in Gear number, G, in N·m·s/rad. For example, you can set these parameter values.

To Specify Damping ForSet Gear number, G ToSet Damping, b To
Four gears, including neutral`[0,1,2,3,4]````[0.001,0.003,0.0025, 0.002,0.001]```
Five gears, including reverse and neutral`[-1,0,1,2,3,4,5]````[0.003,0.001,0.003, 0.0025,0.002,0.001,0.001]```

Vector dimensions for the Gear number vector, Gear ratio vector, Transmission inertia vector, Transmission damping vector, and Efficiency vector parameters must be equal.

Vector of gear mechanical efficiency, with indices corresponding to the efficiencies specified in Gear number, G. For example, you can set these parameter values.

To Specify Efficiency ForSet Gear number, G ToSet Efficiency, eta To
Four gears, including neutral`[0,1,2,3,4]``[0.9,0.9,0.9,0.9,0.95]`
Five gears, including reverse and neutral`[-1,0,1,2,3,4,5]````[0.9,0.9,0.9, 0.9,0.9,0.95,0.95]```

Vector dimensions for the Gear number vector, Gear ratio vector, Transmission inertia vector, Transmission damping vector, and Efficiency vector parameters must be equal.

#### Dependencies

To enable this parameter, set Efficiency factors to `Gear only`.

Table of gear mechanical efficiency, ηN as a function of gear, input torque, input speed, and temperature.

#### Dependencies

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

Transmission initial output rotational velocity, ωto, in rad/s. If you select Clutch initially locked, the block ignores the Initial output velocity, omega_o parameter value.

Initial gear to engage, Go.

Clutch and Synchronizer

Pressure input filter time constant, τc, in s.

Time required for gear selection and synchronization, ts, in s.

Time required to engage and disengage the clutch during shift events, tc, in s.

#### Dependencies

To create this parameter, select Control type parameter `Ideal integrated controller`.

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

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

Dimensionless clutch disc coefficient of static friction, μs.

Dimensionless clutch disc coefficient of kinetic friction, μk.

Select to lock clutch initially.

#### Dependencies

To create this parameter, select Control type parameter `Ideal integrated controller`.

Select to initially lock synchronizer.

## Version History

Introduced in R2017a