Friction clutch with conical plates that engage when normal force exceeds threshold

**Library:**Simscape / Driveline / Clutches

The Cone Clutch block represents a friction clutch with a conical contact interface. The conical interface reduces the normal force required for clutch engagement by creating a wedging action between the clutch components, a cone and a cup. Cone clutch applications include synchromesh gearboxes, which synchronize the drive and driven shaft speeds to enable smoother engagement between transmission gears.

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.

The Cone Clutch block is based on the Fundamental Friction Clutch block. For the complete friction clutch model, see Fundamental Friction Clutch. This section discusses the specialized model implemented in the Cone Clutch block.

When you apply a normal force, *F _{N}*,
the Cone Clutch block can apply two kinds of
friction, kinetic and static, to the driveline motion. 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.

**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 block is based on the
Fundamental Friction
Clutch block. Instead of requiring the
kinetic and static friction limit torques as input signals, the
Cone Clutch block calculates
the kinetic and static friction from the clutch parameters and the
input normal force signal
*F _{N}*.

The kinetic friction torque is the product of four factors:

$${\tau}_{K}={k}_{K}\cdot {F}_{N}\cdot {r}_{eff}\cdot \mathrm{sgn}(\omega )$$

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,

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:

$${r}_{\text{eff}}=\frac{1}{3\mathrm{sin}\alpha}\frac{{d}_{o}{}^{3}-{d}_{i}{}^{3}}{{d}_{o}{}^{2}-{d}_{i}{}^{2}}$$

*d _{o}* and

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

$${T}_{S}={k}_{S}\cdot {F}_{N}\cdot {r}_{eff}\ge 0$$

*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:

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

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 (

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**

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 settings 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**

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**

Dog Clutch | Double-Sided Synchronizer | Fundamental Friction Clutch | Logic-Controlled Clutch | Synchronizer | Unidirectional Clutch