Dual Clutch Transmission

Dual clutch transmission that applies torque to the drive shaft

Libraries:
Powertrain Blockset / Transmission / Transmission Systems

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.

Setting Block Implementation

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: Gear Input torque Input speed Oil temperature

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.

If	Clutch Condition	Friction Model
$\begin{array}{l} ω_{i} \neq N ω_{d} \\ or \\ T_{S} < \| T_{f} - N w_{i} b_{i} \| \end{array}$	Unlocked	$\begin{array}{l} T_{f} = T_{k} \\ where, \\ T_{k} = F_{c} R_{e f f} μ_{k} \tanh [4 (\frac{w_{i}}{N} - w_{d})] \\ T_{s} = F_{c} R_{e f f} μ_{s} \\ R_{e f f} = \frac{2 (R_{o}^{3} - R_{i}^{3})}{3 (R_{o}^{2} - R_{i}^{2})} \end{array}$
$\begin{array}{l} ω_{i} = N ω_{t} \\ and \\ T_{S} \geq \| T_{f} - N b_{i} ω_{i} \| \end{array}$	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
$R_{e f f}$	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

Locked Rotational Dynamics

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

$\begin{array}{l} {\dot{ω}}_{d} J_{N} = η_{N} T_{d} - \frac{ω_{i}}{N} b_{N} + N T_{i} \\ ω_{i} = N ω_{d} \end{array}$

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

Unlocked Rotational Dynamics

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

${\dot{ω}}_{d} J_{N} = N T_{f} - ω_{d} b_{N} + T_{d}$

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

Power Accounting

For the power accounting, the block implements these equations.

Bus Signal			Description	Variable	Equations
`PwrInfo`	`PwrTrnsfrd` — Power transferred between blocks Positive signals indicate flow into block Negative signals indicate flow out of block	`PwrEng`	Engine power	P_eng	$ω_{i} T_{i}$
		`PwrDiffrntl`	Differential power	P_diff	$ω_{d} T_{d}$
	`PwrNotTrnsfrd` — Power crossing the block boundary, but not transferred Positive signals indicate an input Negative signals indicate a loss	`PwrEffLoss`	Mechanical power loss	P_effloss	$ω_{d} T_{d} (η_{N} - 1)$
		`PwrDampLoss`	Mechanical damping loss	P_damploss	$- b_{N} ω_{d}^{2} - b_{i n} ω_{i}^{2}$
		`PwrCltchLoss`	Clutch power loss	P_mech	When locked: $0$ When unlocked: $- T_{k} (ω_{i} - N ω_{d})$
	`PwrStored` — Stored energy rate of change Positive signals indicate an increase Negative signals indicate a decrease	`PwrStoredTrans`	Rate change in rotational kinetic energy	P_str	When locked: ${\dot{ω}}_{i} ω_{i} (J_{i n} + \frac{J_{N}}{N^{2}})$ When unlocked: $J_{i n} {\dot{ω}}_{i} ω_{i} + J_{N} {\dot{ω}}_{d} ω_{d}$

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

Examples

Build Conventional Vehicle Model

Build a vehicle with an internal combustion engine using the conventional vehicle reference application.

Ports

Inputs

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Gear — Gear number to engage
`scalar`

Integer value of gear number to engage.

CltchACmd — Command for odd-numbered gears
`scalar`

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

Dependencies

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

CltchBCmd — Command for even-numbered gears
`scalar`

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

Dependencies

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

EngTrq — Applied torque
`scalar`

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

DiffTrq — Applied torque
`scalar`

Applied load torque, T_d, typically from the drive shaft, in N·m.

Temp — Oil temperature
`scalar`

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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Info — Bus signal
bus

Bus signal containing these block calculations.

Signal			Description	Variable	Units
`Eng`	`EngTrq`		Applied input torque, typically from the engine crankshaft or dual mass flywheel damper	T_i	N·m
`Eng`	`EngSpd`		Applied drive shaft angular speed input	ω_i	rad/s
`Diff`	`DiffTrq`		Applied load torque, typically from the differential	T_d	N·m
`Diff`	`DiffSpd`		Drive shaft angular speed output	ω_d	rad/s
`Cltch`	`CltchForce`		Applied clutch force	F_c	N
`Cltch`	`CltchLocked`		Clutch state	NA	NA
`Trans`	`TransSpd Ratio`		Input to output speed ratio at time t	Φ(t)	NA
	`TransEta`		Ratio of output power to input power	η_N	NA
	`TransGearCmd`		Commanded gear	N_cmd	NA
	`TransGear`		Engaged gear	N	NA
`PwrInfo`	`PwrTrnsfrd`	`PwrEng`	Engine power	P_eng	W
	`PwrTrnsfrd`	`PwrDiffrntl`	Differential power	P_diff	W
	`PwrNotTrnsfrd`	`PwrEffLoss`	Mechanical power loss	P_effloss	W
		`PwrDampLoss`	Mechanical damping loss	P_damploss	W
		`PwrCltchLoss`	Clutch power loss	P_mech	W
	`PwrStored`	`PwrStoredTrans`	Rate change in rotational kinetic energy	P_str	W

EngSpd — Angular speed
`scalar`

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

DiffSpd — Angular speed
`scalar`

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

Parameters

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Control mode — Specify control mode
`External control` (default) | `Ideal integrated controller`

Dependencies

This table summarizes the port configurations.

Control Mode	Creates Ports
`External control`	`CltchACmd`
`External control`	`CltchBCmd`

Efficiency factors — Specify efficiency calculation
`Gear only` (default) | `Gear, input torque, input speed, and temperature`

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

Setting Block Implementation

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: Gear Input torque Input speed Oil temperature

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 To Enables

Setting Parameter To	Enables
`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

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, Jin — Inertia
`0.1` (default) | `scalar`

Input shaft inertia, in kg·m^2.

Input shaft damping, bin — Damping
`0.001` (default) | `scalar`

Input shaft damping, in N·m·s/rad.

Initial input velocity, omegain_o — Angular velocity
`0` (default) | `scalar`

Angular velocity, in rad/s.

Efficiency torque breakpoints, Trq_bpts — Breakpoints
`[25 50 75 100 150 200 250]` (default) | `vector`

Torque breakpoints for efficiency table, in N·m.

Dependencies

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

Efficiency speed breakpoints, omega_bpts — Breakpoints
`[52.4 78.5 105 131 157 183 209 262 314 419 524]` (default) | `vector`

Speed breakpoints for efficiency table, in rad/s.

Dependencies

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

Efficiency temperature breakpoints, Temp_bpts — Breakpoints
`[313 358]` (default) | `vector`

Temperature breakpoints for efficiency table, in K.

Dependencies

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

Gear number vector, G — Specify number of transmission speeds
`[-1, 0, 1, 2, 3, 4, 5, 6, 7, 8]` (default) | `vector`

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

To Specify	Set 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]`