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Slip clutch based on friction between conical surfaces

This block represents a friction clutch with a conical contact interface. The conical interface creates a wedging action between the clutch components, a cone and a cup, thereby reducing the normal force required for clutch engagement.

The cup component connects rigidly to the drive shaft, spinning with it as a unit. The cone component connects rigidly to the driven shaft, which sits in axial alignment with the drive shaft. The clutch engages when the cone slides toward the cup and presses tightly against its internal surface.

Friction at the cone-cup contact interface enables the clutch to transmit rotational power between the drive and driven shafts. The friction model of this block includes both static and kinetic friction contributions, the latter of which leads to power dissipation during slip between the cone and cup components.

Cone clutches find real-world application in synchromesh gearboxes, which synchronize the drive and driven shaft speeds to enable smoother engagement between transmission gears. For block model details, see Cone 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 N that represents the normal force (in newtons) applied between the friction surfaces in contact. This signal should be positive or zero. A signal N less than zero is interpreted as zero.

**Contact surface maximum diameter**The outer conical diameter

*d*_{o}. The default is`150`.From the drop-down list, choose units. The default is millimeters (

`mm`).**Contact surface minimum diameter**The inner conical diameter

*d*_{i}. The default is`100`.From the drop-down list, choose units. The default is millimeters (

`mm`).**Cone half angle**The half opening angle

*α*of the cone geometry. The default is`12`.From the drop-down list, choose units. The default is degrees (

`deg`).

**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`.**Velocity tolerance**Sets the minimum 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`).**Threshold force**The minimum normal force

*F*_{th}needed to engage the clutch. This lower bound applies to the physical signal input normal force N. If N falls below this value, the clutch applies no normal force. The default is`1`.From the drop-down list, choose units. The default is newtons (

`N`).

The Cone 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 specialized model implemented in the Cone Clutch.

When you apply a normal force *F*_{N},
the Cone 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.

The figure shows the cone clutch geometry and some model parameters. Refer to the table for a summary of variable descriptions.

**Clutch Variables**

Parameter | Definition | Significance |
---|---|---|

d_{o} | Outer diameter of the conical contact surface | See the preceding figure |

d_{i} | Inner diameter of the conical contact surface | See the preceding figure |

α | Cone half angle | See the preceding figure |

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

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

F_{N} | Normal force applied to conical surfaces | Normal force applied, if greater than threshold: F_{N} > F_{th} |

α | Cone half-angle | See the preceding figure |

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

k_{K} | Kinetic friction coefficient | Dimensionless coefficient of kinetic friction of conical friction
surfaces. Function of ω. |

k_{S} | Static friction coefficient | Dimensionless coefficient of static friction of conical friction surfaces. |

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) |

The Cone Clutch is based on the Fundamental Friction Clutch.
Instead of requiring the kinetic and static friction limit torques
as input signals, the Cone Clutch calculates the kinetic and static
friction from the clutch parameters and the input normal force signal *F*_{N}.
See the Fundamental Friction Clutch reference page for more information
about the friction clutch.

The kinetic friction torque is the product of four factors:

*τ*_{K} = *k*_{K}·*F*_{N}·*r*_{eff}·sgn(*ω*)
.

The kinetic friction torque opposes the relative slip and is
applied with an overall minus sign. It changes sign when *ω* changes
sign.

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 *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 conical friction surface geometry
by:

*d*_{o} and *d*_{i} are
the contact surface maximum and minimum diameters, respectively.

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}·*F*_{N}·*r*_{eff} ≥
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 limit defines symmetric *static
friction torque limits* as:

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

The range [*τ*_{S}^{–}, *τ*_{S}^{+}]
is used by the Fundamental Friction Clutch.

The clutch engages (transmits torque) when the conical friction
surfaces are subject to a positive normal force and generate kinetic
friction: *F*_{N} >
0 and *τ*_{K}>
0.

The clutch locks if and only if it is engaged, and the slip
is less than the velocity tolerance: |*ω*|
< *ω*_{Tol}.

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).

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