# Disc Friction Clutch

Friction clutch with disc plates that engage when plate pressure exceeds threshold

Libraries:
Simscape / Driveline / Clutches

## Description

The Disc Friction Clutch block represents a friction clutch with two flat friction plate sets that come into contact to engage. The clutch engages when the applied plate pressure exceeds an engagement threshold pressure. Once engaged, the plates experience frictional torques that enable them to transmit power between the base and follower driveshafts.

The clutch can be bidirectional or unidirectional. A bidirectional clutch can slip in the positive and negative directions. A unidirectional clutch can slip only in the positive direction. The slip direction is positive if the follower shaft spins faster than the base shaft and negative if it slips slower. The block defines the slip velocity as the difference

`$\omega ={\omega }_{\text{F}}-{\omega }_{\text{B}},$`

where:

• ω is the relative angular velocity or slip velocity.

• ωF is the angular velocity of the follower driveshaft.

• ωB is the angular velocity of the base driveshaft.

The block provides a physical signal input port P for the applied pressure between the clutch plates. The applied pressure must be greater than or equal to zero and has units of Pascals. If the input signal falls below zero, the block treats the plate pressure as zero.

You can also enable faulting. When faulting occurs, the clutch will remain locked or will be unable to transmit power. Faults can occur at a specified time or due to an external trigger at port T.

### Equations

The Disc Friction Clutch block is a simplified implementation of the Fundamental Friction Clutch block. The Fundamental Friction Clutch requires the kinetic and static friction limit torques as input signals. The Disc Friction Clutch does not require the input data. Instead, the block calculates the kinetic and static friction from the clutch parameters and the input pressure signal P.

When you apply a pressure signal above threshold, such that the applied pressure equals or exceeds the pressure threshold, that is, $P\ge {P}_{th}$, the block can apply two kinds of friction to the driveline motion, kinetic and static. The clutch applies kinetic friction torque only when one driveline axis is spinning relative to the other driveline axis. The clutch applies static friction torque when the two driveline axes lock and spin together. The block iterates through multistep testing to determine when to lock and unlock the clutch.

Kinetic Friction

The kinetic friction torque opposes the relative slip and is applied with an overall minus sign. Mathematically, the kinetic friction is the positive sum of viscous drag and surface contact friction torques:

`${\tau }_{k}=\mu \cdot \omega +{\tau }_{contact}.$`
• τK is the kinetic friction torque.

• μ is the viscous drag coefficient.

• ω is the relative angular velocity, or slip velocity.

• τcontact is the contact torque.

The contact friction is a product of six factors such that

`${\tau }_{contact}={k}_{K}\cdot D\cdot N\cdot {r}_{eff}\cdot {P}_{fric}\cdot A\ge 0,$`

where:

• kK is the dimensionless coefficient of kinetic friction of clutch discs, which is a function of ω.

• D is the clutch de-rating factor.

• N is the number of friction surfaces.

• reff is the effective torque radius, that is, the effective moment arm of clutch friction force.

• Pfric is the clutch friction capacity, such that ${P}_{fric}=\mathrm{max}\left[\left(P-{P}_{th}\right),0\right]$.

• A is the engagement surface area.

You specify the kinetic friction coefficient, kK, as either a constant or a tabulated discrete function of relative angular velocity ω. The tabulated function is assumed to be symmetric for positive and negative values of the relative angular velocity. Therefore, specify kK for positive values of ω only.

The clutch applies a normal force from its piston as the product of the clutch friction capacity, Pfric, and engagement surface area, A, on each of N friction surfaces. The pressure signal, P, should be nonnegative. If P is less than the pressure threshold. Pth, the clutch applies no friction at all.

The effective torque radius, reff, is the effective moment arm of clutch friction force, measured from the driveline axis, at which the kinetic friction forces are applied at the frictional surfaces. It is related to the geometry of the friction surface by:

`${r}_{\text{eff}}=\frac{2}{3}\frac{{r}_{\text{o}}{}^{3}-{r}_{\text{i}}{}^{3}}{{r}_{\text{o}}{}^{2}-{r}_{\text{i}}{}^{2}},$`

where, for a friction surface, modeled as an annular disc:

• ro is the outer disc radius.

• ri is the inner disc radius.

The clutch de-rating factor, D, accounts for clutch wear. For a new clutch, D is one. For a clutch approaching a uniform wear state:

`$D\to \frac{3}{4}\frac{{\left({r}_{o}+\text{​}{r}_{i}\right)}^{2}}{{r}_{o}{}^{2}+{r}_{o}{r}_{i}+\text{​}{r}_{i}{}^{2}}.$`

Static Friction

The static friction limit is related to the kinetic friction, setting ω to zero and replacing the kinetic with the static friction coefficient:

`${\tau }_{S}={k}_{S}\cdot D\cdot N\cdot {r}_{eff}\cdot {P}_{fric}\cdot A\ge 0.$`

where:

• τS is the static friction torque limit, which is the product of the static friction peak factor and the kinetic friction torque as ω approaches 0.

• kK is the dimensionless coefficient of static friction of clutch discs.

• D is the clutch de-rating factor.

• N is the number of friction surfaces.

• reff is the effective torque radius, that is, the effective moment arm of clutch friction force.

• Pfric is the clutch friction capacity, such that ${P}_{fric}=\mathrm{max}\left[\left(P-{P}_{th}\right),0\right]$.

• A is the engagement surface area.

${k}_{S}>{k}_{K}$, so that the torque τ needed across the clutch to unlock it by overcoming static friction is larger than the kinetic friction at the instant of unlocking, when $\omega =0.$.

The static friction torque range or limits are then defined symmetrically as

`${\tau }_{S}\equiv {\tau }_{S}^{+}=-{\tau }_{S}^{-}.$`

Wait State: Locking and Unlocking

The Wait state of the Disc Friction Clutch is identical to the Wait state of the Fundamental Friction Clutch, with the replacement of the positive kinetic friction condition, ${\tau }_{K}>0$, by the positive clutch friction capacity condition, the applied pressure equals or exceeds the pressure threshold, that is, $P\ge {P}_{th}$.

Power Dissipated by the Clutch

The power dissipated by the clutch is the absolute value of the product of slip velocity, ω, and the kinetic friction torque, τK, that is, $|\omega \cdot {\tau }_{K}|$. The clutch dissipates power only if it is both slipping, $\omega \ne 0$, and applying kinetic friction, ${\tau }_{k}>0$.

### Velocity-Dependent and Temperature-Dependent Friction Models

Velocity-Dependent Model

You can model the effects of rotational velocity change by selecting a velocity-dependent model. To choose a velocity-dependent model, in the Friction settings, set the Friction model parameter to ```Velocity-dependent kinetic friction coefficient```. For information about a friction model that depends on both velocity and temperature, see Thermal, Velocity-Dependent Model.

For the velocity-dependent model these related parameters become visible in the Friction settings:

• Relative velocity vector

• Kinetic friction coefficient vector

• Friction coefficient interpolation method

• Friction coefficient extrapolation method

Thermal Model

You can model the effects of heat flow and temperature change by selecting a temperature-dependent model. To choose a temperature-dependent model, in the Friction settings, set the Friction model parameter to ```Temperature-dependent friction coefficients```. For information about a friction model that depends on both velocity and temperature, see Thermal, Velocity-Dependent Model.

For the temperature-dependent model, thermal port H and these parameters are visible:

• In the Friction settings:

• Temperature vector

• Static friction coefficient vector

• Kinetic friction coefficient vector

• Friction coefficient interpolation method

• Friction coefficient extrapolation method

• In the Thermal Port settings:

• Thermal mass

• Initial Temperature

Thermal, Velocity-Dependent Model

You can model the effects of rotational velocity change and heat flow by selecting a velocity-dependent and temperature-dependent model. To choose a model that depends on both velocity and temperature, in the Friction settings, set the Friction model parameter to ```Temperature and velocity-dependent friction coefficients```.

For the velocity-dependent and temperature-dependent model, thermal port H and these related settings and parameters become visible:

• In the Friction settings:

• Relative velocity vector

• Temperature vector

• Static friction coefficient vector

• Kinetic friction coefficient matrix

• Friction coefficient interpolation method

• Friction coefficient extrapolation method

• In the Thermal Port settings:

• Thermal mass

• Initial Temperature

### Faults

You can enable faulty behavior in response to:

• Simulation time — Faulting occurs at a specified time.

• Simulation behavior — Faulting occurs in response to an external trigger. This exposes port T.

You can choose either or both of these settings for block faulting. If faulting is triggered, the clutch responds according to the Behavior when faulted setting for the remainder of the simulation. The fault options are:

• `Cannot transmit power`

• `Cannot unlock`

You can set the block to issue a fault report as a warning or error message in the Simulink Diagnostic Viewer with the Reporting when fault occurs parameter.

## Ports

### Input

expand all

Physical signal input port for the applied pressure between the clutch plates. This signal is positive or zero. A signal of less than zero is interpreted as zero.

Physical signal port for an external fault trigger. Triggering occurs when the value is greater than 0.5. There is no unit associated with the trigger value.

#### Dependencies

This port is visible when Enable faults is set to `On` and Enable external fault trigger is set to `On`.

### Conserving

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Rotational conserving port associated with the driving, or base, shaft.

Rotational conserving port associated with the driven, or follower, shaft.

Thermal conserving port associated with heat flow.

#### Dependencies

This port is visible only when, in the Friction settings, the Friction model parameter is set to ```Temperature-dependent friction coefficients``` or ```Temperature and velocity-dependent friction coefficients```. For more information, see Friction Parameter Dependencies and Friction model.

## Parameters

expand all

### Geometry

Parameterization method for modeling the clutch friction geometry.

#### Dependencies

The Effective torque radius parameter is visible only If this parameter is set to ```Define effective radius```:

These parameters are visible only If this parameter is set to `Define annular region`:

• Friction surface outside diameter

• Friction surface inside diameter

Effective moment arm radius, reff, that determines the kinetic friction torque inside the clutch.

#### Dependencies

This parameter is visible only if the Geometry model parameter is set to ```Define effective radius```.

Diameter, 2ro, across the outer edge of the friction disc annulus.

#### Dependencies

This parameter is visible only if the Geometry model parameter is set to ```Define annular region```.

Diameter, 2ri, across the inner edge of the friction disc annulus.

#### Dependencies

This parameter is visible only if the Geometry model parameter is set to ```Define annular region```.

Number, N, of friction-generating contact surfaces inside the clutch.

Effective area, A, of the clutch piston when the piston is applying pressure across the clutch.

Slip directions the clutch allows between its plates. A bidirectional clutch allows positive and negative slip velocities. A unidirectional clutch allows only positive slip velocities.

The unidirectional clutch is equivalent to a friction clutch connected in parallel to a one-way clutch that disengages only when the slip velocity becomes positive. To model a unidirectional clutch with slip in the negative direction, reverse the base and follower port connections.

### Friction

The table shows how the visibility of some ports, parameters, and settings depends on the option that you choose for other parameters. To learn how to read the table, see Parameter Dependencies.

Friction Parameter Dependencies

Friction
Friction model
```Fixed kinetic friction coefficient``````Velocity-dependent kinetic friction coefficient``````Temperature-dependent friction coefficients``````Temperature and velocity-dependent friction coefficients```

Exposes:

• Conserving port H

• Thermal Port settings

Exposes:

• Conserving port H

• Thermal Port settings

-Relative velocity vector-Relative velocity vector
--Temperature vectorTemperature vector
Static friction coefficientStatic friction coefficientStatic friction coefficient vectorStatic friction coefficient vector
Kinetic friction coefficientKinetic friction coefficient vectorKinetic friction coefficient vectorKinetic friction coefficient matrix
-Friction coefficient interpolation methodFriction coefficient interpolation methodFriction coefficient interpolation method
-Friction coefficient extrapolation methodFriction coefficient extrapolation methodFriction coefficient extrapolation method
De-rating factorDe-rating factorDe-rating factorDe-rating factor
Clutch velocity toleranceClutch velocity toleranceClutch velocity toleranceClutch velocity tolerance
Engagement threshold pressureEngagement threshold pressureEngagement threshold pressureEngagement threshold pressure

Parameterization method to model the kinetic friction coefficient. The options and default values for this parameter depend on the friction model that you select for the block. The options are:

• ```Fixed kinetic friction coefficient``` — Provide a fixed value for the kinetic friction coefficient.

• ```Velocity-dependent kinetic friction coefficient``` — Define the kinetic friction coefficient by one-dimensional table lookup based on the relative angular velocity between discs.

• ```Temperature-dependent friction coefficients``` — Define the kinetic friction coefficient by table lookup based on the temperature.

• ```Temperature and velocity-dependent friction coefficients``` — Define the kinetic friction coefficient by table lookup based on the temperature and the relative angular velocity between discs.

#### Dependencies

The friction model setting affects the visibility of other parameters, settings, and ports. For more information, see Friction Parameter Dependencies.

Input values for the relative velocity as a vector. The values in the vector must increase from left to right. The minimum number of values depends on the interpolation method that you select. For linear interpolation, provide at least two values per dimension. For smooth interpolation, provide at least three values per dimension.

#### Dependencies

This parameter is visible only if the Friction model parameter is set to ```Velocity-dependent kinetic friction coefficient``` or ```Temperature and velocity-dependent friction coefficients```. For more information, see Friction Parameter Dependencies.

Input values for the temperature as a vector. The minimum number of values depends on the interpolation method that you select. For linear interpolation, provide at least two values per dimension. For smooth interpolation, provide at least three values per dimension. The values in the vector must increase from left to right.

#### Dependencies

This parameter is visible only if the Friction model parameter is set to ```Temperature-dependent friction coefficients``` or ```Temperature and velocity-dependent friction coefficients```. For more information, see Friction Parameter Dependencies.

Static or peak value of the friction coefficient. The static friction coefficient must be greater than the kinetic friction coefficient.

#### Dependencies

This parameter is visible only when the Friction model parameter is set to ```Fixed kinetic friction coefficient``` or ```Velocity-dependent kinetic friction coefficient```. For more information, see Friction Parameter Dependencies.

Static, or peak, values of the friction coefficient as a vector. The vector must have the same number of elements as the temperature vector. Each value must be greater than the value of the corresponding element in the kinetic friction coefficient vector.

#### Dependencies

This parameter is visible only if the Friction model parameter is set to ```Temperature-dependent friction coefficients``` or ```Temperature and velocity-dependent friction coefficients```. For more information, see Friction Parameter Dependencies.

The kinetic, or Coulomb, friction coefficient. The coefficient must be greater than zero.

#### Dependencies

This parameter is visible only if the Friction model parameter is set to ```Fixed kinetic friction coefficient```. For more information, see Friction Parameter Dependencies.

Output values for kinetic friction coefficient as a vector. All values must be greater than zero.

If the Friction model parameter is set to

• ```Velocity-dependent kinetic friction coefficient``` — The vector must have same number of elements as relative velocity vector.

• ```Temperature-dependent friction coefficients``` — The vector must have the same number of elements as the temperature vector.

#### Dependencies

This parameter is visible only if the Friction model parameter is set to ```Velocity-dependent kinetic friction coefficient``` or ```Temperature-dependent friction coefficients```. For more information, see Friction Parameter Dependencies.

Output values for kinetic friction coefficient as a matrix. All the values must be greater than zero. The size of the matrix must equal the size of the matrix that is the result of the temperature vector × the kinetic friction coefficient relative velocity vector.

#### Dependencies

This parameter is visible only if the Friction model parameter is set to ```Temperature and velocity-dependent friction coefficients```. For more information, see Friction Parameter Dependencies.

Interpolation method for approximating the output value when the input value is between two consecutive grid points:

• `Linear` — Select this option to get the best performance.

• `Smooth` — Select this option to produce a continuous curve with continuous first-order derivatives.

For more information on interpolation algorithms, see the PS Lookup Table (1D) block reference page.

#### Dependencies

This parameter is visible only if the Friction model parameter is set to ```Velocity-dependent kinetic friction coefficient```, ```Temperature-dependent friction coefficients```, or ```Temperature and velocity-dependent friction coefficients```. For more information, see Friction Parameter Dependencies.

Extrapolation method for determining the output value when the input value is outside the range specified in the argument list:

• `Linear` — Select this option to produce a curve with continuous first-order derivatives in the extrapolation region and at the boundary with the interpolation region.

• `Nearest` — Select this option to produce an extrapolation that does not go above the highest point in the data or below the lowest point in the data.

• `Error` — Select this option to avoid going into the extrapolation mode when you want your data to be within the table range. If the input signal is outside the range of the table, the simulation stops and generates an error.

For more information on extrapolation algorithms, see the PS Lookup Table (1D) block reference page.

#### Dependencies

This parameter is visible only if the Friction model parameter is set to ```Velocity-dependent kinetic friction coefficient```, ```Temperature-dependent friction coefficients```, or ```Temperature and velocity-dependent friction coefficients```. For more information, see Friction Parameter Dependencies.

Dimensionless de-rating factor, D, that accounts for clutch disc wear by proportionately reducing clutch friction.

Maximum slip velocity at which the clutch can lock. The slip velocity is the signed difference between the base and follower shaft angular velocities, that is, $w={w}_{F}-{w}_{B}$. If the kinetic friction torque is nonzero and the transferred torque is within the static friction torque limits, then the clutch locks if the actual slip velocity falls below the velocity tolerance.

Minimum pressure Pth at which the clutch engages. If the pressure input signal falls below this threshold, the clutch automatically disengages.

### Viscous Losses

Viscous friction coefficient μ applied to the relative slip ω between the base and follower axes.

### Initial Conditions

Clutch state at the start of simulation. The clutch can be in one of two states, locked and unlocked. A locked clutch constrains the base and follower shafts to spin at the same velocity, that is, as a single unit. An unlocked clutch allows the two shafts to spin at different velocities, resulting in slip between the clutch plates.

### Faults

Enable externally or temporally triggered faults. When faulting occurs, the clutch fails to unlock or cannot transmit power, according to the Behavior when faulted setting.

Set fault response. You can select the clutch faulting as either:

• `Cannot transmit power`

• `Cannot unlock`

#### Dependencies

To enable this parameter, set Enable faults to `On`.

Enables port T. A physical signal at port T that is greater than `0.5` triggers faulting.

#### Dependencies

To enable this parameter, set Enable faults to `On`.

Enables fault triggering at a specified time. When the Simulation time for fault event is reached, the clutch responds according to the Behavior when faulted setting.

#### Dependencies

To enable this parameter, set Enable faults to `On`.

When the Simulation time for fault event is reached, the clutch responds according to the Behavior when faulted setting.

#### Dependencies

To enable this parameter, set Enable faults to `On` and Enable temporal fault trigger to `On`.

Reporting preference for the fault condition. When reporting is set to `Warning` or `Error`, a message is displayed in the Simulink Diagnostic Viewer. When `Error` is selected, the simulation will stop if faulting occurs.

#### Dependencies

To enable this parameter, set Enable faults to `On`.

### Thermal Port

Thermal Port settings are visible only when, in the Friction settings, the Friction model parameter is set to ```Temperature-dependent friction coefficients``` or ```Temperature and velocity-dependent friction coefficients```. For more information, see Friction Parameter Dependencies.

Thermal energy required to change the component temperature by a single degree. The greater the thermal mass, the more resistant the component is to temperature change.

#### Dependencies

This parameter is visible only when, in the Friction settings, the Friction model parameter is set to ```Temperature-dependent friction coefficients``` or ```Temperature and velocity-dependent friction coefficients```. For more information, see Friction Parameter Dependencies.

Component temperature at the start of simulation. The initial temperature alters the component efficiency according to an efficiency vector that you specify, affecting the starting meshing or friction losses. The default value is `300` `K`.

#### Dependencies

This parameter is only visible when, in the Friction settings, the Friction model parameter is set to ```Temperature-dependent friction coefficients``` or ```Temperature and velocity-dependent friction coefficients```. For more information, see Friction Parameter Dependencies.

## Version History

Introduced in R2011a