# Disk Friction Clutch

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

**Library:**Simscape / Driveline / Clutches

## Description

The Disk 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.*ω*is the angular velocity of the follower driveshaft._{F}*ω*is the angular velocity of the base driveshaft._{B}

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 Disk 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 Disk 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:

$${\tau}_{k}=\mu \cdot \omega +{\tau}_{contact}.$$

*τ*is the kinetic friction torque._{K}*μ*is the viscous drag coefficient.*ω*is the relative angular velocity, or slip velocity.*τ*is the contact torque._{contact}

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:

*k*is the dimensionless coefficient of kinetic friction of clutch discs, which is a function of_{K}*ω*.*D*is the clutch de-rating factor.*N*is the number of friction surfaces.*r*is the effective torque radius, that is, the effective moment arm of clutch friction force._{eff}*P*is the clutch friction capacity, such that $${P}_{fric}=\mathrm{max}\left[\left(P-{P}_{th}\right),0\right]$$._{fric}*A*is the engagement surface area.

You specify the *kinetic friction coefficient*,
*k _{K}*, 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

*k*for positive values of

_{K}*ω*only.

The clutch applies a normal force from its piston as the product of the clutch
friction capacity, *P _{fric}*, 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.

*P*, the clutch applies no friction at all.

_{th}The *effective torque radius*,
*r _{eff}*, 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 disk:

*r*is the outer disk radius._{o}*r*is the inner disk radius._{i}

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:

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

**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:

*τ*is the static friction torque limit, which is the product of the static friction peak factor and the kinetic friction torque as_{S}*ω*approaches 0.*k*is the dimensionless coefficient of kinetic friction of clutch discs, which is a function of_{K}*ω*.*D*is the clutch de-rating factor.*N*is the number of friction surfaces.*r*is the effective torque radius, that is, the effective moment arm of clutch friction force._{eff}*P*is the clutch friction capacity, such that $${P}_{fric}=\mathrm{max}\left[\left(P-{P}_{th}\right),0\right]$$._{fric}*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 Disk 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,
*τ _{K}*, that is, $$\left|\omega \cdot {\tau}_{K}\right|$$. 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**

### Faulty Behavior

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

### Conserving

## Parameters

## Extended Capabilities

**Introduced in R2011a**