# Cone Clutch

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

• Library:
• Simscape / Driveline / Clutches

## Description

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, FN, 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.

You can also enable faulting. When faulting occurs, the clutch will remain locked or will be unable to transmit power. Faults can occur at a specified time or due to an external trigger at port T.

### Clutch Geometry and Variables

The figure shows the cone clutch geometry.

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 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 FN.

Kinetic Friction

The kinetic friction torque is the product of four factors:

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

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. Therefore, 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:

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

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:

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

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).

### Velocity-Dependent Model

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

### Thermal Model

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

### Thermal, Velocity-Dependent Model

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

### Faults

You can enable faulty behavior in response to:

• Simulation time — Faulting occurs at a specified time.

• Simulation behavior — Faulting occurs in response to an external trigger. This exposes port T.

You can choose either or both of these settings for block faulting. If faulting is triggered, the clutch responds according to the Behavior when faulted setting for the remainder of the simulation. The fault options are:

• ```Cannot transmit power```

• ```Cannot unlock```

You can set the block to issue a fault report as a warning or error message in the Simulink Diagnostic Viewer with the Reporting when fault occurs parameter.

## Ports

### Input

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Physical signal port associated with the normal force. This signal is positive or zero. A signal of less than zero is interpreted as zero.

#### Dependencies

This port is visible only if, in the Geometry settings, the Shift linkage control parameter is set to ```Physical signal```. For more information, see Shift linkage control and Geometry Parameter Dependencies.

Physical signal port for an external fault trigger. Triggering occurs when the value is greater than 0.5. There is no unit associated with the trigger value.

#### Dependencies

This port is visible when Enable faults is set to `On` and Enable external fault trigger is set to `On`.

### Output

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Physical signal port associated with shift linkage position.

#### Dependencies

This port is visible only when, in the Geometry settings, the Shift linkage control parameter is set to ```Conserving port```. For more information, see Shift linkage control and Geometry Parameter Dependencies.

### Conserving

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Mechanical rotational conserving port associated with the driving (base) shaft. The clutch motion is measured as the slip ω = ωFωB, the angular velocity of follower relative to base.

Mechanical rotational conserving port associated with the driven or follower shaft

Thermal conserving port associated with heat flow.

#### Dependencies

This port is visible only when, in the Friction settings, the Friction model parameter is set to ```Temperature-dependent friction coefficients``` or ```Temperature and velocity-dependent friction coefficients```. For more information, see Friction model and Friction Parameter Dependencies.

Mechanical rotational conserving port associated with shift linkage.

#### Dependencies

This port is visible only when, in the Geometry settings, the Shift linkage control parameter is set to ```Conserving port```. For more information, see Shift linkage control and Geometry Parameter Dependencies.

## Parameters

expand all

### Geometry

The table shows how the visibility of some parameters depends on the option that you choose for other parameters. To learn how to read the table, see Parameter Dependencies.

Geometry Parameter Dependencies

Geometry
Contact surface maximum diameter
Contact surface minimum diameter
Cone half angle
```Physical signal``````Conserving port```

Exposes physical signal input port N

Exposes:

• Conserving port S

• Physical signal output port X

Outer conical diameter do.

Inner conical diameter di.

Half opening angle α of the cone geometry.

• `Physical signal` — Expose physical signal ports N, which inputs the normal force, and X, which outputs for the shift linkage travel.

• `Conserving port` — Expose conserving port, S, which is associated with shift linkage control.

#### Dependencies

The visibility of Shift Linkage settings and ports S, X, and N depend on this setting. For more information, see Geometry Parameter Dependencies.

These settings are visible only if, in the Geometry settings, the Shift linkage control parameter is set to `Conserving port`. For more information, see Shift linkage control and Geometry Parameter Dependencies.

Hard stop at back of shift linkage

Ring-hub clearance when disengaged

Ring stops stiffness

Ring stop damping

Linkage travel direction that disengages the clutch

### Friction

The table shows how the visibility of some ports, parameters, and settings depends on the option that you choose for other parameters. To learn how to read the table, see Parameter Dependencies.

Friction Parameter Dependencies

Friction
Friction model
```Fixed kinetic friction coefficient``````Velocity-dependent kinetic friction coefficient``````Temperature-dependent friction coefficients``````Temperature and velocity-dependent friction coefficients```

Exposes:

• Conserving port H

• Thermal parameters in the Friction settings

• Thermal Port settings

Exposes:

• Conserving port H

• Thermal parameters in the Friction settings

• Thermal Port settings

--Temperature vectorTemperature vector
-Relative velocity vector-Relative velocity vector
Static friction coefficientStatic friction coefficientStatic friction coefficient vectorStatic friction coefficient vector
Kinetic friction coefficientKinetic friction coefficient vectorKinetic friction coefficient vectorKinetic friction coefficient matrix
-Friction coefficient interpolation methodFriction coefficient interpolation methodFriction coefficient interpolation method
-Friction coefficient extrapolation methodFriction coefficient extrapolation methodFriction coefficient extrapolation method
Velocity toleranceVelocity toleranceVelocity toleranceVelocity tolerance
Threshold forceThreshold forceThreshold forceThreshold force
Viscous drag torque coefficientViscous drag torque coefficientViscous drag torque coefficientViscous drag torque coefficient

Parameterization method to model the kinetic friction coefficient. The options and default values for this parameter depend on the friction model that you select for the block. The options are:

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

• ```Velocity-dependent kinetic friction coefficient``` — Define the kinetic friction coefficient by one-dimensional table lookup based on the relative angular velocity between disks.

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

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

#### Dependencies

The friction model setting affects the visibility of other parameters, settings, and ports. For more information, see Friction Parameter Dependencies.

Input values for the relative velocity as a vector. The values in the vector must increase from left to right. The minimum number of values depends on the interpolation method that you select. For linear interpolation, provide at least two values per dimension. For smooth interpolation, provide at least three values per dimension.

#### Dependencies

This parameter is visible only when the Friction model parameter is set to ```Velocity-dependent kinetic friction coefficient``` or ```Temperature and velocity-dependent friction coefficients```. For more information, see Friction Parameter Dependencies.

Input values for the temperature as a vector. The minimum number of values depends on the interpolation method that you select. For linear interpolation, provide at least two values per dimension. For smooth interpolation, provide at least three values per dimension. The values in the vector must increase from left to right.

#### Dependencies

This parameter is visible only when the Friction model parameter is set to ```Temperature-dependent friction coefficients``` or ```Temperature and velocity-dependent friction coefficients```. For more information, see Friction Parameter Dependencies.

Static or peak value of the friction coefficient. The static friction coefficient must be greater than the kinetic friction coefficient.

#### Dependencies

this parameter is visible only when the Friction model parameter is set to ```Fixed kinetic friction coefficient``` or ```Velocity-dependent kinetic friction coefficient```. For more information, see Friction Parameter Dependencies.

Static, or peak, values of the friction coefficient as a vector. The vector must have the same number of elements as the temperature vector. Each value must be greater than the value of the corresponding element in the kinetic friction coefficient vector.

#### Dependencies

This parameter is visible only when the Friction model parameter is set to ```Temperature-dependent friction coefficients``` or ```Temperature and velocity-dependent friction coefficients```. For more information, see Friction Parameter Dependencies.

The kinetic, or Coulomb, friction coefficient. The coefficient must be greater than zero.

#### Dependencies

This parameter is visible only when the Friction model parameter is set to ```Fixed kinetic friction coefficient```. For more information, see Friction Parameter Dependencies.

Output values for kinetic friction coefficient as a vector. All values must be greater than zero.

If the Friction model parameter is set to

• ```Velocity-dependent kinetic friction coefficient``` — The vector must have same number of elements as relative velocity vector.

• ```Temperature-dependent friction coefficients``` — The vector must have the same number of elements as the temperature vector.

#### Dependencies

This parameter is visible only when the Friction model parameter is set to ```Velocity-dependent kinetic friction coefficient``` or ```Temperature-dependent friction coefficients```. For more information, see Friction Parameter Dependencies.

Output values for kinetic friction coefficient as a matrix. All the values must be greater than zero. The size of the matrix must equal the size of the matrix that is the result of the temperature vector × the kinetic friction coefficient relative velocity vector.

#### Dependencies

This parameter is visible only when the Friction model parameter is set to ```Temperature and velocity-dependent friction coefficients```. For more information, see Friction Parameter Dependencies.

Interpolation method for approximating the output value when the input value is between two consecutive grid points:

• `Linear` — Select this option to get the best performance.

• `Smooth` — Select this option to produce a continuous curve with continuous first-order derivatives.

For more information on interpolation algorithms, see the PS Lookup Table (1D) block reference page.

#### Dependencies

This parameter is visible only when the Friction model parameter is set to ```Velocity-dependent kinetic friction coefficient```, ```Temperature-dependent friction coefficients```, or ```Temperature and velocity-dependent friction coefficients```. For more information, see Friction Parameter Dependencies.

Extrapolation method for determining the output value when the input value is outside the range specified in the argument list:

• `Linear` — Select this option to produce a curve with continuous first-order derivatives in the extrapolation region and at the boundary with the interpolation region.

• `Nearest` — Select this option to produce an extrapolation that does not go above the highest point in the data or below the lowest point in the data.

• `Error` — Select this option to avoid going into the extrapolation mode when you want your data to be within the table range. If the input signal is outside the range of the table, the simulation stops and generates an error.

For more information on extrapolation algorithms, see the PS Lookup Table (1D) block reference page.

#### Dependencies

This parameter is visible only when the Friction model parameter is set to ```Velocity-dependent kinetic friction coefficient```, ```Temperature-dependent friction coefficients```, or ```Temperature and velocity-dependent friction coefficients```. For more information, see Friction Parameter Dependencies.

Relative velocity below which the two surfaces can lock. The surfaces lock if the torque across the B and F rotational ports is less than the product of the effective radius, the static friction coefficient, and the applied normal force.

The normal force applied to the physical signal port N is applied to the contact only if the amount of force exceeds the value of the Threshold force parameter. Forces below the Threshold force are not applied so there is no transmitted frictional torque.

Viscous drag torque coefficient.

### Initial Conditions

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, that is, as a single unit. An unlocked clutch allows the two shafts to spin at different velocities, resulting in slip between the clutch plates.

### Faults

Enable externally or temporally triggered faults. When faulting occurs, the clutch fails to unlock or cannot transmit power, according to the Behavior when faulted setting.

Set fault response. You can select the clutch faulting as either:

• ```Cannot transmit power```

• ```Cannot unlock```

#### Dependencies

To enable this parameter, set Enable faults to `On`.

Enables port T. A physical signal at port T that is greater than `0.5` triggers faulting.

#### Dependencies

To enable this parameter, set Enable faults to `On`.

Enables fault triggering at a specified time. When the Simulation time for fault event is reached, the clutch responds according to the Behavior when faulted setting.

#### Dependencies

To enable this parameter, set Enable faults to `On`.

When the Simulation time for fault event is reached, the clutch responds according to the Behavior when faulted setting.

#### Dependencies

To enable this parameter, set Enable faults to `On` and Enable temporal fault trigger to `On`.

Reporting preference for the fault condition. When reporting is set to `Warning` or `Error`, a message is displayed in the Simulink Diagnostic Viewer. When `Error` is selected, the simulation will stop if faulting occurs.

#### Dependencies

To enable this parameter, set Enable faults to `On`.

### Thermal Port

Thermal Port settings are visible only when, in the Friction settings, the Friction model parameter is set to ```Temperature-dependent friction coefficients``` or ```Temperature and velocity-dependent friction coefficients```. For more information, see Friction Parameter Dependencies.

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.

#### Dependencies

This parameter is only visible when, in the Friction settings, the Friction model parameter is set to ```Temperature-dependent friction coefficients``` or ```Temperature and velocity-dependent friction coefficients```. For more information, see Friction Parameter Dependencies.

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.

#### Dependencies

This parameter is only visible when, in the Friction settings, the Friction model parameter is set to ```Temperature-dependent friction coefficients``` or ```Temperature and velocity-dependent friction coefficients```. For more information, see Friction Parameter Dependencies.

## Version History

Introduced in R2011a