# Cone Clutch

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

Clutches

## Description

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.

### Ports

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 = ωFωB, 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.

## Dialog Box and Parameters

### Geometry

Contact surface maximum diameter

Outer conical diameter do. The default is `150`.

From the drop-down list, choose units. The default is millimeters (`mm`).

Contact surface minimum diameter

Inner conical diameter di. The default is `100`.

From the drop-down list, choose units. The default is millimeters (`mm`).

Cone half angle

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

Friction model

Select how to model the dimensionless Coulomb kinetic friction coefficient kK 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 kS applied to the normal force across the clutch when the clutch is locked. Must be larger than kK. The default is `0.35`.

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, $w={w}_{F}-{w}_{B}$. The clutch locks if the actual slip velocity falls below the velocity tolerance and if other conditions are present—i.e., if the kinetic friction torque is nonzero and if the transferred torque is within the static friction torque limits. The default value is `0.001` rad/s.

Threshold force

Minimum normal force Fth 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`).

### 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`.

## Cone Clutch Model

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 FN, 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.

### Clutch Geometry and Variable Summary

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

Clutch Variables

ParameterDefinitionSignificance
doOuter diameter of the conical contact surfaceSee the preceding figure
diInner diameter of the conical contact surfaceSee the preceding figure
αCone half angleSee the preceding figure
ωRelative angular velocity (slip)ωFωB
ωTolSlip tolerance for clutch lockingSee the following model
FNNormal force applied to conical surfacesNormal force applied, if greater than threshold: FN > Fth
αCone half-angleSee the preceding figure
reffEffective torque radiusEffective moment arm of clutch friction force
kKKinetic friction coefficientDimensionless coefficient of kinetic friction of conical friction surfaces. Function of ω.
kSStatic friction coefficientDimensionless coefficient of static friction of conical friction surfaces.
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

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 FN. See the Fundamental Friction Clutch reference page for more information about the friction clutch.

#### Kinetic Friction

The kinetic friction torque is the product of four factors:

τK = kK·FN·reff·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 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 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 conical friction surface geometry by:

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

do and di are the contact surface maximum and minimum diameters, respectively.

#### 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·FN·reff ≥ 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 limit defines symmetric static friction torque limits as:

τSτS+ = –τS .

The range [τS, τS+] is used by the Fundamental Friction Clutch.

#### Engagement and Locking Conditions

The clutch engages (transmits torque) when the conical friction surfaces are subject to a positive normal force and generate kinetic friction: FN > 0 and τK> 0.

The clutch locks if and only if it is engaged, and the slip is less than the velocity tolerance: |ω| < ωTol.

#### 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).