Disc Clutch

Idealized disc clutch coupler

Libraries:
Powertrain Blockset / Drivetrain / Couplings

Description

The Disc Clutch block implements an idealized disc clutch coupler. The block couples the rotary input and output shafts through an idealized friction model. To determine the output torque, the block uses friction parameters, relative slip velocity, and applied input pressure.

In fuel economy and powertrain efficiency studies, you can use the Disc Clutch block to model the mechanical power transfer between common driveline elements such as transmissions, engines, and differentials.

To approximate the torque response, the Disc Clutch block implements friction and dynamic models that depend on the clutch lockup condition. The block determines the locked or unlocked condition based on an idealized dry clutch friction model. This table summarizes the logic the block uses to determine the clutch condition.

Clutch Condition	When
Unlocked	$\begin{array}{l} ω_{i} \neq ω_{o} \\ or \\ T_{f m a x} < \| \frac{J_{o} T_{i} - (J_{o} b_{i} - J_{i} b_{o}) ω_{i / o}}{J_{o} + J_{i}} \| \end{array}$
Locked	$\begin{array}{l} ω_{i} = ω_{o} \\ and \\ T_{f m a x} < \| T_{i} - \frac{J_{i} (b_{i} + b_{o}) ω_{i}}{J_{o} + J_{i}} + b_{o} ω_{i} \| \end{array}$

This table summarizes the friction and dynamic models that the block uses for locked or unlocked clutch conditions.

Clutch Condition	Friction Model	Dynamic Model
Unlocked	$\begin{array}{l} T_{f m a x} = T_{k} \\ where, \\ T_{k} = N_{d i s c} P_{c} A_{e f f} R_{e f f} μ_{k} \tanh [4 (ω_{i} - ω_{o})] \\ R_{e f f} = \frac{2 (R_{o}^{3} - R_{i}^{3})}{3 (R_{o}^{2} - R_{i}^{2})} \end{array}$ and $P_{c} = \max (P_{c} - P_{e n g}, 0)$	$\begin{array}{l} {\dot{ω}}_{i} J_{i} = T_{i} - T_{f} - ω_{i} b_{i} \\ {\dot{ω}}_{o} J_{o} = T_{f} + T_{o} - ω_{o} b_{o} \end{array}$
Locked	$\begin{array}{l} T_{f m a x} = T_{s} \\ where, \\ T_{s} = N_{d i s c} P_{c} A_{e f f} R_{e f f} μ_{s} \\ R_{e f f} = \frac{2 (R_{o}^{3} - R_{i}^{3})}{3 (R_{o}^{2} - R_{i}^{2})} \end{array}$	$\begin{array}{l} {\dot{ω}}_{i} (J_{o} + J_{i}) = T_{o} - ω_{i} (b_{i} + b_{o}) + T_{i} \\ ω_{i} = ω_{o} \end{array}$

Power Accounting

For the power accounting, the block implements these equations.

Bus Signal			Description	Equations
`PwrInfo`	`PwrTrnsfrd` — Power transferred between blocks Positive signals indicate flow into block Negative signals indicate flow out of block	`PwrBase`	Applied base power	$ω_{i} T_{i}$
		`PwrFlwr`	Applied follower output power	$ω_{o} T_{o}$
	`PwrNotTrnsfrd` — Power crossing the block boundary, but not transferred Positive signals indicate an input Negative signals indicate a loss	`PwrDampLoss`	Damping power loss	$- b_{o} ω_{o}^{2} - b_{i} ω_{i}^{2}$
		`PwrCltchSlipLoss`	Clutch slip power loss	$- T_{k} (ω_{i} - ω_{o})$
	`PwrStored` — Stored energy rate of change Positive signals indicate an increase Negative signals indicate a decrease	`PwrStoredBase`	Rate change in base rotational kinetic energy	${\dot{ω}}_{i} ω_{i} J_{i}$
		`PwrStoredFlwr`	Rate change in follower rotational kinetic energy	${\dot{ω}}_{o} ω_{o} J_{o}$

The equations use these variables.

ω_i	Input shaft angular speed
ω_o	Output shaft angular speed
b_i	Input shaft viscous damping
b_o	Output shaft viscous damping
J_i	Input shaft moment of inertia
J_o	Output shaft moment of inertia
T_f	Frictional torque
T_i	Net input torque
T_k	Kinetic frictional torque
T_o	Net output torque
T_s	Static frictional torque
T_fmax	Maximum frictional torque before slipping
P_c	Applied clutch pressure
P_eng	Engagement pressure
A_eff	Effective area
N_disc	Number of frictional discs
R_eff	Effective clutch radius
R_o	Annular disk outer radius
R_i	Annular disk inner radius
R_e	Effective tire radius while under load and for a given pressure
μ_s	Coefficient of static friction
μ_k	Coefficient of kinetic friction

Examples

Build Conventional Vehicle Model

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

Ports

Input

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Press — Applied clutch pressure
`scalar`

Base gear input torque, P_c, in N·m^2.

BTrq — Applied input torque
`scalar`

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

Dependencies

To create this port, for Port Configuration, select Simulink.

FTrq — Applied load torque
`scalar`

Applied load torque, T_o, typically from the differential or drive shaft, in N·m.

Dependencies

To create this port, for Port Configuration, select Simulink.

B — Applied drive shaft angular speed and torque
two-way connector port

Applied drive shaft angular speed, ω_i, in rad/s. Applied drive shaft torque, T_i, in N·m.

Dependencies

To create this port, for Port Configuration, select Two-way connection.

Output

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Info — Bus signal
bus

Bus signal containing these block calculations.

Signal			Description	Units
`Base`	`BTrq`		Applied input torque, typically from the engine crankshaft or dual mass flywheel damper	N·m
`Base`	`BSpd`		Applied drive shaft angular speed input	rad/s
`Flwr`	`FTrq`		Applied load torque, typically from the differential	N·m
`Flwr`	`FSpd`		Drive shaft angular speed output	rad/s
`Cltch`	`CltchForce`		Applied clutch force	N
	`CltchLocked`		Clutch lock status	NA
	`CltchSpdRatio`		Clutch speed ratio	NA
	`CltchEta`		Clutch power transmission efficiency	NA
`PwrInfo`	`PwrTrnsfrd`	`PwrBase`	Applied base power	W
	`PwrTrnsfrd`	`PwrFlwr`	Applied follower output power	W
	`PwrNotTrnsfrd`	`PwrDampLoss`	Damping power loss	W
	`PwrNotTrnsfrd`	`PwrCltchSlipLoss`	Clutch slip power loss	W
	`PwrStored`	`PwrStoredBase`	Rate change in base rotational kinetic energy	W
	`PwrStored`	`PwrStoredFlwr`	Rate change in follower rotational kinetic energy	W

BSpd — Angular speed
`scalar`

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

Dependencies

To create this port, for Port Configuration, select Simulink.

FSpd — Angular speed
`scalar`

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

Dependencies

To create this port, for Port Configuration, select Simulink.

F — Output velocity and torque
two-way connector port

Output drive shaft angular speed, ω_oi, in rad/s. Output drive shaft torque, T_o, in N·m.

Dependencies

To create this port, for Port Configuration, select Two-way connection.

Parameters

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Block Options

Port Configuration — Specify configuration
`Simulink` (default) | `Two-way connection`

Specify the port configuration.

Dependencies

Specifying Simulink creates these ports:

BSpd
FSpd
BTrq
FTrq

Specifying Two-way connection creates these ports:

Clutch force equivalent net radius, Reff — Radius
`1` (default) | `scalar`

Clutch force equivalent net radius, in m.

Number of disks, Ndisk — Ratio
`1` (default) | `scalar`

Number of disks, dimensionless.

Effective applied pressure area, Aeff — Pressure area
`.01` (default) | `scalar`

Effective applied pressure area, in m^2.

Engagement pressure threshold, Peng — Pressure threshold
`0` (default) | `scalar`

Pressure to engage clutch, in Pa.

Input shaft inertia, Jin — Inertia
`.1` (default) | `scalar`

Input shaft inertia, in kg·m^2.

Output shaft inertia, Jout — Inertia
`.1` (default) | `scalar`

Output shaft inertia, in kg·m^2.

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

Kinetic friction coefficient, dimensionless.

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

Static friction coefficient, dimensionless.

Input shaft viscous damping, bin — Damping
`.001` (default) | `scalar`

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

Output shaft viscous damping, bout — Damping
`.001` (default) | `scalar`

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

Initial input shaft velocity, win_o — Initial velocity
`0` (default) | `scalar`

Input shaft initial velocity, in rad/s.

Initial output shaft velocity, wout_o — Initial velocity
`0` (default) | `scalar`

Input shaft initial velocity, in rad/s.

Clutch actuation time constant, tauC — Constant
`.01` (default) | `scalar`

Clutch actuation time constant, in s.

Disc Clutch

Description

Power Accounting

Examples

Build Conventional Vehicle Model

Ports

Input

Press — Applied clutch pressure scalar

BTrq — Applied input torque scalar

Dependencies

FTrq — Applied load torque scalar

Dependencies

B — Applied drive shaft angular speed and torque two-way connector port

Dependencies

Output

Info — Bus signal bus

BSpd — Angular speed scalar

Dependencies

FSpd — Angular speed scalar

Dependencies

F — Output velocity and torque two-way connector port

Dependencies

Parameters

Port Configuration — Specify configuration Simulink (default) | Two-way connection

Dependencies

Clutch force equivalent net radius, Reff — Radius 1 (default) | scalar

Number of disks, Ndisk — Ratio 1 (default) | scalar

Effective applied pressure area, Aeff — Pressure area .01 (default) | scalar

Engagement pressure threshold, Peng — Pressure threshold 0 (default) | scalar

Input shaft inertia, Jin — Inertia .1 (default) | scalar

Output shaft inertia, Jout — Inertia .1 (default) | scalar

Kinetic friction coefficient, muk — Coefficient .3 (default) | scalar

Static friction coefficient, mus — Coefficient .5 (default) | scalar

Input shaft viscous damping, bin — Damping .001 (default) | scalar

Output shaft viscous damping, bout — Damping .001 (default) | scalar

Initial input shaft velocity, win_o — Initial velocity 0 (default) | scalar

Initial output shaft velocity, wout_o — Initial velocity 0 (default) | scalar

Clutch actuation time constant, tauC — Constant .01 (default) | scalar

Start simulation with clutch locked — Select to initially lock clutch off (default) | on

Extended Capabilities

C/C++ Code Generation Generate C and C++ code using Simulink® Coder™.

Version History

See Also

Press — Applied clutch pressure
`scalar`

BTrq — Applied input torque
`scalar`

FTrq — Applied load torque
`scalar`

B — Applied drive shaft angular speed and torque
two-way connector port

Info — Bus signal
bus

BSpd — Angular speed
`scalar`

FSpd — Angular speed
`scalar`

F — Output velocity and torque
two-way connector port

Port Configuration — Specify configuration
`Simulink` (default) | `Two-way connection`

Clutch force equivalent net radius, Reff — Radius
`1` (default) | `scalar`

Number of disks, Ndisk — Ratio
`1` (default) | `scalar`

Effective applied pressure area, Aeff — Pressure area
`.01` (default) | `scalar`

Engagement pressure threshold, Peng — Pressure threshold
`0` (default) | `scalar`

Input shaft inertia, Jin — Inertia
`.1` (default) | `scalar`

Output shaft inertia, Jout — Inertia
`.1` (default) | `scalar`

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

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

Input shaft viscous damping, bin — Damping
`.001` (default) | `scalar`

Output shaft viscous damping, bout — Damping
`.001` (default) | `scalar`

Initial input shaft velocity, win_o — Initial velocity
`0` (default) | `scalar`

Initial output shaft velocity, wout_o — Initial velocity
`0` (default) | `scalar`

Clutch actuation time constant, tauC — Constant
`.01` (default) | `scalar`

Start simulation with clutch locked — Select to initially lock clutch
`off` (default) | `on`

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.