Dual clutch transmission that applies torque to the drive shaft
Powertrain Blockset / Transmission / Transmission Systems
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 lockup and clutch friction
Locked rotational dynamics
Unlocked rotational dynamics
To specify the block efficiency calculation, for Efficiency factors, select either of these options.
Setting  Block 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:

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 singleclutch
commands that result in equivalent drive shaft torque. To use your
own clutch control signals, select Control mode parameter External
control
.
Based on the clutch lockup condition, the block implements one of these friction models.
If  Clutch Condition  Friction Model 

$\begin{array}{l}{\omega}_{i}\ne N{\omega}_{d}\\ \text{or}\\ {T}_{S}<\left{T}_{f}N{w}_{i}{b}_{i}\right\end{array}$  Unlocked  $$\begin{array}{l}{T}_{f}={T}_{k}\\ \text{where,}\\ {T}_{k}={F}_{c}{R}_{eff}{\mu}_{k}\mathrm{tanh}\left[4\left(\frac{{w}_{i}}{N}{w}_{d}\right)\right]\\ {T}_{s}={F}_{c}{R}_{eff}{\mu}_{s}\\ {R}_{eff}=\frac{2({R}_{o}{}^{3}{R}_{i}{}^{3})}{3({R}_{o}{}^{2}{R}_{i}{}^{2})}\end{array}$$ 
$\begin{array}{l}{\omega}_{i}=N{\omega}_{t}\\ \text{and}\\ {T}_{S}\ge \left{T}_{f}N{b}_{i}{\omega}_{i}\right\end{array}$  Locked 
T_{f} = T_{s} 
The equations use these variables.
ω_{t}  Output drive shaft speed 
ω_{i}  Input drive shaft speed 
ω_{d}  Drive shaft speed 
${b}_{i}$  Viscous damping 
F_{c}  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 
μ_{s}  Coefficient of static friction 
μ_{k}  Coefficient of kinetic friction 
To model the rotational dynamics when the clutch is locked, the block implements these equations.
$\begin{array}{l}{\dot{\omega}}_{d}{J}_{N}={\eta}_{N}{T}_{d}\frac{{\omega}_{i}}{N}{b}_{N}+N{T}_{i}\\ {\omega}_{i}=N{\omega}_{d}\end{array}$
The block determines the input torque, T_{i}, through differentiation.
The equations use these variables.
ω_{i}  Input drive shaft speed 
ω_{d}  Drive shaft speed 
N  Engaged gear 
b_{N}  Engaged gear viscous damping 
J_{N}  Engaged gear inertia 
η_{N}  Engaged gear efficiency 
T_{d}  Drive shaft torque 
T_{i}  Applied input torque 
To model the rotational dynamics when the clutch is unlocked, the block implements this equation.
${\dot{\omega}}_{d}{J}_{N}=N{T}_{f}{\omega}_{d}{b}_{N}+{T}_{d}$
where:
ω_{d}  Drive shaft speed 
N  Engaged gear 
b_{N}  Engaged gear viscous damping 
J_{N}  Engaged gear inertia 
T_{d}  Drive shaft torque 
T_{i}  Applied input torque 
For the power accounting, the block implements these equations.
Bus Signal  Description  Variable  Equations  



 Engine power  P_{eng}  ${\omega}_{i}{T}_{i}$ 
PwrDiffrntl  Differential power  P_{diff}  ${\omega}_{d}{T}_{d}$  
 PwrEffLoss  Mechanical power loss  P_{effloss}  ${\omega}_{d}{T}_{d}\left({\eta}_{N}1\right)$  
PwrDampLoss  Mechanical damping loss  P_{damploss}  ${b}_{N}{\omega}_{d}^{2}\text{}{b}_{in}{\omega}_{i}^{2}$  
PwrCltchLoss  Clutch power loss  P_{mech}  When locked: $$0$$ When unlocked: $${T}_{k}\left({\omega}_{i}N{\omega}_{d}\right)$$  
 PwrStoredTrans  Rate change in rotational kinetic energy  P_{str}  When locked: $${\dot{\omega}}_{i}{\omega}_{i}({J}_{in}+\frac{{J}_{N}}{{N}^{2}})$$ When unlocked: $${J}_{in}{\dot{\omega}}_{i}{\omega}_{i}+{J}_{N}{\dot{\omega}}_{d}{\omega}_{d}$$ 
The equations use these variables.
b_{N}  Engaged gear viscous damping 
J_{N}  Engaged gear rotational inertia 
J_{in}  Flywheel rotational inertia 
η_{N}  Engaged gear efficiency 
N  Engaged gear ratio 
T_{i}  Applied input torque, typically from the engine crankshaft or dual mass flywheel damper 
T_{d}  Applied load torque, typically from the differential or drive shaft 
ω_{d}  Initial input drive shaft rotational velocity 
ω_{i}, ώ_{i}  Applied drive shaft angular speed and acceleration 