# Disk Friction Clutch

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

Clutches

## Description

This block represents a friction clutch with two flat friction plate sets that come into contact in order 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 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.

## Disk Friction Clutch Model

The Disk Friction Clutch is based on the Fundamental Friction Clutch. For the complete friction clutch model, consult the Fundamental Friction Clutch block reference page. This section discusses the simplified model implemented in the Disk Friction Clutch.

When you apply a pressure signal above threshold (PPth), the Disk Friction Clutch 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.

### Clutch Variable, State, and Mode Summary

This table summarizes the clutch variables.

Clutch Variables

SymbolDefinitionSignificance
ωRelative angular velocity (slip)ωFωB
ωTolSlip tolerance for clutch lockingSee the following model
P, PthClutch pressure and thresholdInput pressure applied to clutch discs;
threshold clutch pressure: Pth, P > 0.
PfricClutch friction capacitymax[(PPth), 0]
DClutch de-rating factorSee the following model
NNumber of friction surfacesSee the following model
AEngagement surface areaSee the following model
reffEffective torque radiusEffective moment arm of clutch friction force
kKKinetic friction coefficientDimensionless coefficient of kinetic friction of clutch discs. Function of ω.
kSStatic friction coefficientDimensionless coefficient of static friction of clutch discs.
μViscous drag coefficientSee the following model
τKKinetic friction torqueSee the following model
τSStatic friction torque limit(static friction peak factor)·(kinetic friction torque for ω → 0)
(See the following model)

### Relation to Fundamental Friction Clutch

Instead of requiring the kinetic and static friction limit torques as input signals, the Disk Friction Clutch calculates the kinetic and static friction from the clutch parameters and the input pressure signal P.

#### Kinetic Friction

The kinetic friction torque is the positive sum of viscous drag and surface contact friction torques:

τK = μω + τcontact .

(The kinetic friction torque opposes the relative slip and is applied with an overall minus sign.) The contact friction is a product of six factors:

τcontact = kK·D·N·reff·Pfric·A ≥ 0 .

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, so that you need to 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 Pth, the clutch applies no friction at all.

The effective torque radius reff is the effective radius, 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:

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

ro and ri are the outer and inner radii, respectively, of the friction surface, modeled as an annular disk.

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:

τS = kS·D·N·reff·Pfric·A ≥ 0 .

kS > kK, 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 ω = 0.

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

τSτS+ = –τS .

#### 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 (τK > 0) by the positive clutch friction capacity condition (PPth).

#### Power Dissipated by the Clutch

The power dissipated by the clutch is |ω·τK|. The clutch dissipates power only if it is both slipping (ω ≠ 0) and applying kinetic friction (τK > 0).

## Modeling Thermal Effects

You can model the effects of heat flow and temperature change through an optional thermal conserving port. By default, the thermal port is hidden. To expose the thermal port, right-click the block in your model and, from the context menu, select Simscape > Block choices. Choose a variant that includes a thermal port. Specify the associated thermal parameters for the component.

## Ports

`B`

Rotational conserving port that represents the base driveshaft

`F`

Rotational conserving port that represents the follower driveshaft

`P`

Physical signal input port for the applied pressure between the clutch plates

`H`

Thermal conserving port. The thermal port is optional and is hidden by default. To expose the port, select a variant that includes a thermal port.

## Parameters

### Geometry

Force action region

Select a parameterization method to model the clutch friction geometry. The default method is `Define effective radius`.

• `Define effective radius` — Model friction geometry in terms of disk radius.

• `Define annular region` — Model friction geometry in terms of annulus dimensions. If you select this option, the visible parameters change.

### Friction

Friction model

Select a parameterization method to model the kinetic friction coefficient. The options and default values for this parameter depend on the variant that you select for the block.

The options are:

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

• Is only visible if you use the default variant of the block

• Is the default method for parameterizing the default variant of the block

• Affects the visibility of other parameters

• `Table lookup kinetic friction coefficient` — Define the kinetic friction coefficient by one-dimensional table lookup based on the relative angular velocity between disks. This option:

• Is only visible if you use the default variant of the block

• Affects the visibility of other parameters

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

• Is only visible if you use a thermal variant of the block

• Is the default method for parameterizing the thermal variant of the block

• Affects the visibility of other parameters

• ```Temperature and speed-dependent kinetic friction coefficient``` — Define the kinetic friction coefficient by table lookup based on the temperature and the relative angular velocity between disks. This option:

• Is only visible if you use the thermal variant of the block

• Affects the visibility of other parameters

De-rating factor

Dimensionless de-rating factor D that accounts for clutch disk wear by proportionately reducing clutch friction. The default value is `1`.

Clutch velocity tolerance

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. The default value is `0.001` `rad/s`.

Engagement threshold pressure

Minimum pressure Pth at which the clutch engages. If the pressure input signal falls below this threshold, the clutch automatically disengages. The default value is `100` `Pa`.

### Viscous Drag

Viscous drag torque coefficient

Viscous friction coefficient μ applied to the relative slip ω between the base and follower axes. The default value is `0` `N*m/(rad/s)`.

### Initial Conditions

Initial state

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, i.e., as a single unit. An unlocked clutch allows the two shafts to spin at different velocities, resulting in slip between the clutch plates. The default setting is `Unlocked`.

### Thermal Port

These thermal parameters are only visible when you select a block variant that includes a thermal port.

Thermal mass

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. The default value is `25` `kJ/K`.

Initial temperature

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`.