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.

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

Locked Rotational Dynamics

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

$\begin{array}{l} \dot{ω} (J_{i} + J_{t}) = T_{i} - ω (b_{i} + b_{t}) + T_{e x t} \\ ω = ω_{i} = ω_{t} \end{array}$

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.

$\begin{array}{l} {\dot{ω}}_{i} J_{i} = T_{i} - ω_{i} b_{i} - T_{f} - T_{p} \\ {\dot{ω}}_{t} J_{t} = T_{e x t} - ω_{t} b_{t} + T_{f} + T_{t} \\ T_{p} = ω_{i}^{2} ψ (ϕ) \\ T_{t} = T_{p} ζ (ϕ) \end{array}$

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			Description	Variable	Equations
`PwrInfo`	`PwrTrnsfrd` — Power transferred between blocks Positive signals indicate flow into block Negative signals indicate flow out of block	`PwrImp`	Applied impeller power	P_imp	$ω_{i} T_{i}$
		`PwrTurb`	Applied turbine output power	P_turb	$ω_{t} T_{t}$
	`PwrNotTrnsfrd` — Power crossing the block boundary, but not transferred Positive signals indicate an input Negative signals indicate a loss	`PwrDampLoss`	Mechanical damping loss	P_damploss	$- b_{t} ω_{t}^{2} - b_{i} ω_{i}^{2}$
		`PwrFluidCplingLoss`	Heat loss to transmission fluid	P_flloss	$- (T_{p} ω_{i} - T_{h y d} ω_{t})$
		`PwrCltchLoss`	Clutch slip power loss	P_cltloss	$- T_{k} (ω_{i} - ω_{t})$
	`PwrStored` — Stored energy rate of change Positive signals indicate an increase Negative signals indicate a decrease	`PwrStoredImp`	Rate change in impeller rotational kinetic energy	P_strimp	${\dot{ω}}_{i} ω_{i} J_{i}$
		`PwrStoredTurb`	Rate change in turbine rotational kinetic energy	P_strturb	${\dot{ω}}_{t} ω_{t} J_{t}$

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
$T_{e x t}$	Externally applied turbine torque
$ψ (ϕ)$	Torque conversion capacity factor
$ζ (ϕ)$	Torque ratio
$ω_{i}$	Impeller rotational shaft speed
$ω_{t}$	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
$R_{e f f}$	Effective clutch radius
$R_{o}$	Annular disk outer radius
$R_{i}$	Annular disk inner radius

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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ImpTrq — Applied impeller torque
`scalar`

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

TurbTrq — Applied turbine torque
`scalar`

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

Clutch Force — Applied clutch force
`scalar`

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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Info — Bus signal
bus

Bus signal containing these block calculations.

Signal			Description	Units
`Imp`	`ImpTrq`		Applied input torque	N·m
`Imp`	`ImpSpd`		Impeller rotational shaft speed	rad/s
`Turb`	`TurbTrq`		Applied turbine torque	N·m
`Turb`	`TurbSpd`		Turbine rotational shaft speed	rad/s
`Cltch`	`CltchForce`		Applied clutch force	N
`Cltch`	`CltchLocked`		Clutch locked or unlocked state	N/A
`TrqConv`	`TrqConvSpdRatio`		Turbine to impeller speed ratio	N/A
`TrqConv`	`TrqConvEta`		Torque conversion efficiency	N/A
`PwrInfo`	`PwrTrnsfrd`	`PwrImp`	Applied impeller power	W
	`PwrTrnsfrd`	`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
	`PwrStored`	`PwrStoredTurb`	Rate change in turbine rotational kinetic energy	W

ImpSpd — Impeller speed
`scalar`

Impeller rotational shaft speed, $ω_{i}$ , in rad/s.

TurbSpd — Turbine speed
`scalar`

Turbine rotational shaft speed, $ω_{t}$ , in rad/s.

Parameters

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Configuration

Lock-up clutch configuration — Select lock-up clutch configuration
`Lock-up` (default) | `No lock-up` | `External lock-up input`

To Model	Select
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, Ji — Inertia
`.1` (default) | `scalar`

Impeller shaft inertia, in kg·m^2.

Impeller shaft viscous damping, bi — Viscous damping coefficient
`.001` (default) | `scalar`

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

Turbine shaft inertia, Jt — Inertia
`.1` (default) | `scalar`

Turbine shaft inertia, in kg·m^2.

Turbine shaft viscous damping, bt — Viscous damping coefficient
`.001` (default) | `scalar`

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

Initial impeller shaft velocity, omegai_o — Angular velocity
`0` (default) | `scalar`

Initial impeller shaft velocity, in rad/s.

Initial turbine shaft velocity, omegat_o — Angular velocity
`0` (default) | `scalar`

Initial turbine shaft velocity, in rad/s.

Speed ratio vector, phi — Ratio
`[ 0 0.50 0.60 0.70 0.80 0.87 0.92 0.94 0.96 0.97]` (default) | `vector`

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

Capacity factor parameterization — Select factor ratio type
`Input speed / sqrt(input torque)` (default) | `Absorbed torque / input speed^2`

To Set Factor Ratio to	Select
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 vector, psi — Vector
`[12.2938 12.8588 13.1452 13.6285 14.6163 16.2675 19.3503 22.1046 29.9986 50.00]` (default) | `vector`

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

Torque ratio vector, zeta — Vector
`[2.2320 1.5462 1.4058 1.2746 1.1528 1.0732 1.0192 0.9983 0.9983 0.9983]` (default) | `vector`

Vector of turbine torque to impeller speed ratios.

Fluid torque response time constant (set to 0 to disable), tauTC — Time constant
`.02` (default) | `scalar`

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

Interpolation method — Select interpolation method
`Linear` (default) | `Flat` | `Nearest`

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

Clutch

Clutch force equivalent net radius, Reff — Effective radius
`.3` (default) | `scalar`

The effective radius, $R_{e f f}$ , used with the applied clutch friction force to determine the friction force, in m. The effective radius is defined as:

$R_{e f f} = \frac{2 (R_{o}^{3} - R_{i}^{3})}{3 (R_{o}^{2} - R_{i}^{2})}$

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.

Static friction coefficient, mus — Coefficient
`1.2` (default) | `scalar`

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.

Kinetic friction coefficient, muk — Coefficient
`1` (default) | `scalar`

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.

Initially lock clutch — Select to initially lock clutch
`off` (default) | `on`

Dependencies

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