Dual Clutch Transmission

Dual clutch transmission that applies torque to the drive shaft

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Description

The Dual Clutch Transmission block implements a dual clutch transmission (DCT). In a DCT, two clutches apply mechanical torque to the drive shaft. Odd gears engage one clutch, while even gears engage the secondary clutch. 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. You can provide external clutch signals or configure the block to generate idealized internal clutch signals. The block implements the transmission model with minimal parameterization or computational cost.

Use the block to model a simplified automated manual transmission (AMT) 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 Dual Clutch 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 DCT delivers drive shaft torque continuously by controlling the pressure signals from both clutches. If you select Control mode parameter Ideal integrated controller, the block generates idealized clutch pressure signals. The block uses the maximum pressure from each clutch to approximate the single-clutch commands that result in equivalent drive shaft torque. To use your own clutch control signals, select Control mode 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
ωiNωdorTS<|TfNwibi|UnlockedTf=Tkwhere,Tk=FcReffμktanh[4(wiNwd)]Ts=FcReffμsReff=2(Ro3Ri3)3(Ro2Ri2)
ωi=NωtandTS|TfNbiωi|Locked

Tf = Ts

The equations use these variables.

ωt

Output drive shaft speed

ωi

Input drive shaft speed

ωd

Drive shaft speed

bi

Viscous damping

Fc

Applied clutch force

N

Engaged gear

Tf

Frictional torque

Tk

Kinetic frictional torque

Ts

Static frictional torque

Reff

Effective clutch radius

Ro

Annular disk outer radius

Ri

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.

ω˙dJN=ηNTdωiNbN+NTiωi=Nωd

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.

ω˙dJN=NTfωdbN+Td

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

ωiTi
PwrDiffrntl

Differential power

Pdiff

ωdTd

PwrNotTrnsfrd — Power crossing the block boundary, but not transferred

  • Positive signals indicate an input

  • Negative signals indicate a loss

PwrEffLoss

Mechanical power loss

Peffloss

ωdTd(ηN1)
PwrDampLoss

Mechanical damping loss

Pdamploss

bNωd2 binωi2

PwrCltchLoss

Clutch power loss

Pmech

When locked: 0

When unlocked: Tk(ωiNωd)

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: ω˙iωi(Jin+JNN2)

When unlocked: Jinω˙iωi+JNω˙dωd

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

Inputs

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Integer value of gear number to engage.

Clutch pressure command for odd-numbered gears, between 0 and 1.

Dependencies

To create this port, select Control mode parameter External control.

Clutch pressure command for even-numbered gears, between 0 and 1.

Dependencies

To create this port, select Control mode 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 drive shaft, 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

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Bus signal containing these block calculations.

SignalDescriptionVariableUnits
EngEngTrq

Applied input torque, typically from the engine crankshaft or dual mass flywheel damper

Ti

N·m

EngSpd

Applied drive shaft angular speed input

ωi

rad/s

DiffDiffTrq

Applied load torque, typically from the differential

Td

N·m

DiffSpd

Drive shaft angular speed output

ωd

rad/s

CltchCltchForce

Applied clutch force

Fc

N

CltchLocked

Clutch state

NA

NA

TransTransSpd Ratio

Input to output speed ratio at time t

Φ(t)

NA

TransEta

Ratio of output power to input power

ηN

NA

TransGearCmd

Commanded gear

Ncmd

NA

TransGear

Engaged gear

N

NA

PwrInfoPwrTrnsfrd

PwrEng

Engine power

Peng

W
PwrDiffrntl

Differential power

Pdiff

W
PwrNotTrnsfrdPwrEffLoss

Mechanical power loss

Peffloss

W
PwrDampLoss

Mechanical damping loss

Pdamploss

W
PwrCltchLoss

Clutch power loss

Pmech

W
PwrStoredPwrStoredTrans

Rate change in rotational kinetic energy

Pstr

W

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

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

Parameters

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The DCT delivers drive shaft torque continuously by controlling the pressure signals from both clutches. If you select Control mode parameter Ideal integrated controller, the block generates idealized clutch pressure signals. The block uses the maximum pressure from each clutch to approximate the single-clutch commands that result in equivalent drive shaft torque. To use your own clutch control signals, select Control mode parameter External control.

Dependencies

This table summarizes the port configurations.

Control ModeCreates Ports
External control

CltchACmd

CltchBCmd

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.

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, in 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 integers 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, Damping vector, and Efficiency vector parameters must be equal.

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, 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, 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, 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, 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

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

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

Time required to engage clutch, tc, in s.

Dependencies

To create this parameter, select Control mode parameter Ideal integrated controller.

The effective radius, Reff, used with the applied clutch friction force to determine the friction force, in m. The effective radius is defined as:

Reff=2(Ro3-Ri3)3(Ro2-Ri2)

The equation uses these variables.

Ro

Annular disk outer radius

Ri

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.

Selecting this parameter initially locks the clutch.

Dependencies

To create this parameter, select Control mode parameter Ideal integrated controller.

Selecting this parameter initially locks the synchronizer.

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