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Disk friction clutch or brake with kinetic and static friction and controllable pressure

A friction clutch transfers torque between two driveline axes by coupling them with friction. The Disk Friction Clutch block models a friction clutch based on disks in contact, with kinetic friction and static (locking) friction acting on the two axes. For model details, see Disk Friction Clutch Model.

B and F are rotational conserving ports representing, respectively,
the clutch input (base) and output (follower) driveshaft axes. The
clutch motion is measured as the *slip* *ω* = *ω*_{F}– *ω*_{B},
the angular velocity of follower relative to base.

The clutch requires a physical signal input P that represents the hydraulic pressure (in pascals) modulating the applied kinetic friction. This signal should be positive or zero. A signal P less than zero is interpreted as zero.

**Force action region**Select how to model the clutch friction geometry. The default 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 panel changes from its default.

**Number of friction surfaces**The number

*N*of friction-generating contact surfaces inside the clutch. The default is`4`.**Engagement piston area**The effective area

*A*of the clutch piston when the piston is applying pressure across the clutch. The default is`0.001`.From the drop-down list, choose units. The default is meters-squared (

`m^2`).

**Friction model**Select how to model the dimensionless Coulomb kinetic friction coefficient

*k*_{K}across the clutch when the clutch is slipping. The default is`Fixed kinetic friction coefficient`.`Fixed kinetic friction coefficient`— Model Coulomb kinetic friction in terms of a constant kinetic friction coefficient.`Table lookup kinetic friction coefficient`— Model Coulomb kinetic friction in terms of a kinetic friction coefficient lookup function defined at discrete relative velocity values. If you select this option, the panel changes from its default.

**Static friction coefficient**Dimensionless Coulomb static friction coefficient

*k*_{S}applied to the normal force across the clutch when the clutch is locked. Must be larger than*k*_{K}. The default is`0.35`.**De-rating factor**Dimensionless de-rating factor

*D*that accounts for clutch disk wear by proportionately reducing clutch friction. The default is`1`.**Clutch velocity tolerance**The minimum relative angular speed

*ω*_{Tol}above which the clutch cannot lock. Below this speed, the clutch can lock. The default is`1e-3`.From the drop-down list, choose units. The default is radians/second (

`rad/s`).**Engagement threshold pressure**The minimum pressure

*P*_{th}needed to engage the clutch. This lower bound applies to the physical signal input pressure P. If P falls below this value, the clutch applies no pressure. The default is`100`.From the drop-down list, choose units. The default is pascals (

`Pa`).

**Viscous drag torque coefficient**Viscous friction coefficient

*μ*applied to the relative slip*ω*between the base and follower axes. The default is`0`.From the drop-down list, choose units. The default is newton-meters/(radians/second) (

`N*m/(rad/s)`).

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 (*P* ≥ *P*_{th}),
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.

This table summarizes the clutch variables.

**Clutch Variables**

Symbol | Definition | Significance |
---|---|---|

ω | Relative angular velocity (slip) | ω_{F} – ω_{B} |

ω_{Tol} | Slip tolerance for clutch locking | See the following model |

P, P_{th} | Clutch pressure and threshold | Input pressure applied to clutch discs; threshold clutch pressure: P_{th}, P >
0. |

P_{fric} | Clutch friction capacity | max[(P – P_{th}),
0] |

D | Clutch de-rating factor | See the following model |

N | Number of friction surfaces | See the following model |

A | Engagement surface area | See the following model |

r_{eff} | Effective torque radius | Effective moment arm of clutch friction force |

k_{K} | Kinetic friction coefficient | Dimensionless coefficient of kinetic friction of clutch discs.
Function of ω. |

k_{S} | Static friction coefficient | Dimensionless coefficient of static friction of clutch discs. |

μ | Viscous drag coefficient | See the following model |

τ_{K} | Kinetic friction torque | See the following model |

τ_{S} | Static friction torque limit | (static friction peak factor)·(kinetic friction torque
for ω → 0)( See the following model) |

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*.

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

*τ*_{K} = *μ**ω* + *τ*_{contact} .

(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:

*τ*_{contact} = *k*_{K}·*D*·*N*·*r*_{eff}·*P*_{fric}·*A* ≥
0 .

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, so that you need to specify *k*_{K} for
positive values of *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 *P*_{th},
the clutch applies no friction at all.

The *effective torque radius* *r*_{eff} 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*_{o} and *r*_{i} 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:

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

τ_{S} = *k*_{S}·*D*·*N*·*r*_{eff}·*P*_{fric}·*A* ≥
0 .

*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 *ω* =
0.

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

*τ*_{S} ≡ *τ*_{S}^{+} =
–*τ*_{S}^{–} .

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 (*τ*_{K} >
0) by the positive clutch friction capacity condition (*P* ≥ *P*_{th}).

The power dissipated by the clutch is |*ω*·*τ*_{K}|.
The clutch dissipates power only if it is both slipping (ω ≠
0) and applying kinetic friction (*τ*_{K} >
0).

These SimDriveline™ example models contain working examples of disk friction clutches that change gear couplings:

Differential | Fundamental Friction Clutch | Torque Converter | Variable Ratio Transmission

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