Cone Clutch

Cone clutch with plates that engage when normal force exceeds threshold

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Libraries:
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, 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.

Clutch Geometry and Variables

The figure shows the cone clutch geometry.

Clutch Variables

Parameter	Definition	Significance
do	Outer diameter of the conical contact surface	See the preceding figure
di	Inner diameter of the conical contact surface	See the preceding figure
α	Cone half angle	See the preceding figure
ω	Relative angular velocity (slip)	ωF – ωB
ωTol	Slip tolerance for clutch locking	See the following model
FN	Normal force applied to conical surfaces	Normal force applied, if greater than threshold: FN > Fth
α	Cone half-angle	See the preceding figure
reff	Effective torque radius	Effective moment arm of clutch friction force
kK	Kinetic friction coefficient	Dimensionless coefficient of kinetic friction of conical friction surfaces. Function of ω.
kS	Static friction coefficient	Dimensionless coefficient of static friction of conical friction surfaces.
τK	Kinetic friction torque	See the following model
τS	Static 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 F_N.

Kinetic Friction

The kinetic friction torque is the product of four factors:

$${\tau }_K=k_K\cdot F_N\cdot r_{eff}\cdot \mathrm{sgn}(\omega )$$

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, ω. The tabulated function is assumed to be symmetric for positive and negative values of the relative angular velocity. Therefore, 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:

$$r_{\text{eff}}=\frac{1}{3\sin \alpha }\frac{d_o{}^3-d_i{}^3}{d_o{}^2-d_i{}^2}$$

d_o and d_i 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:

$$T_S=k_S\cdot F_N\cdot r_{eff}\ge 0$$

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.

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: 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.

Power Dissipated by the Clutch

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).

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.

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.

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.

Faults

To model a fault in the Cone Clutch block, in the Faults section, click the Add fault hyperlink next to the fault that you want to model. For more information about fault modeling, see Fault Behavior Modeling and Fault Triggering.

When you trigger a fault, the block responds according to the setting of the Behavior when faulted parameter for the remainder of the simulation. The fault options are:

• Cannot transmit power

• Cannot unlock

Ports

Input

N — Normal force

physical signal

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.

Output

X — Shift linkage position

physical signal

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

B — Base

mechanical rotational

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

F — Follower

mechanical rotational

Mechanical rotational conserving port associated with the driven or follower shaft

H — Heat flow

thermal

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.

S — Shift linkage

mechanical rotational

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

Geometry

The table shows how the visibility of some parameters depends on the option that you choose for other parameters.

Geometry Parameter Dependencies

Geometry
Contact surface maximum diameter
Contact surface minimum diameter
Cone half angle
Shift linkage control
Physical signal			Conserving port
Exposes physical signal input port N			Exposes: Conserving port S Physical signal output port X Shift Linkage settings

Contact surface maximum diameter — Outer diameter

150 mm (default) | positive scalar

Outer conical diameter d_o.

Contact surface minimum diameter — Inner diameter

100 mm (default) | positive scalar

Inner conical diameter d_i.

Cone half angle — Cone half angle

12 deg (default) | positive scalar

Half opening angle α of the cone geometry.

Shift linkage control — Shift linkage model

Physical signal (default) | Conserving port

Shift linkage control model:

• 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.

Shift Linkage

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 — Hard stop

On (default) | Off

Hard stop at back of shift linkage

Ring-hub clearance when disengaged — Ring-hub clearance

3 mm (default) | nonnegative scalar

Ring-hub clearance when disengaged

Ring stop stiffness — Ring stop stiffness

10e5 N/m (default) | nonnegative scalar

Ring stops stiffness

Ring stop damping — Ring stop damping

1e3 N/(m/s) (default) | nonnegative scalar

Ring stop damping

Shift linkage viscous friction coefficient — Shift linkage viscous friction

100 N/(m/s) (default) | positive scalar

Shift linkage viscous friction coefficient

Linkage travel direction — Disengagement travel direction

Positive shift linkage displacement engages clutch (default) | Negative shift linkage displacement engages clutch

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.

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 vector		Temperature vector
-	Relative velocity vector		-		Relative velocity vector
Static friction coefficient	Static friction coefficient		Static friction coefficient vector		Static friction coefficient vector
Kinetic friction coefficient	Kinetic friction coefficient vector		Kinetic friction coefficient vector		Kinetic friction coefficient matrix
-	Friction coefficient interpolation method		Friction coefficient interpolation method		Friction coefficient interpolation method
-	Friction coefficient extrapolation method		Friction coefficient extrapolation method		Friction coefficient extrapolation method
Velocity tolerance	Velocity tolerance		Velocity tolerance		Velocity tolerance
Threshold force	Threshold force		Threshold force		Threshold force
Viscous drag torque coefficient	Viscous drag torque coefficient		Viscous drag torque coefficient		Viscous drag torque coefficient

Friction model — Friction model

Fixed kinetic friction coefficient (default) | Velocity-dependent kinetic friction coefficient | Temperature-dependent friction coefficients | Temperature and velocity-dependent friction coefficients

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.

Relative velocity vector — Relative velocity

[0, 100, 1000] rad/s (default) | vector

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.

Temperature vector — Temperature

[280, 300, 320] K (default) | increasing vector

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 friction coefficient — Static friction coefficient

0.35 (default) | scalar

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 friction coefficient vector — Static friction coefficient

[.4, .38, .36] (default) | vector

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.

Kinetic friction coefficient — Kinetic friction coefficient

0.3 (default) | positive scalar

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.

Kinetic friction coefficient vector — Kinetic friction coefficient

[.3, .22, .19] (default) | [.3, .28, .25] | vector

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.

Kinetic friction coefficient matrix — Kinetic friction coefficient

[.34, .32, .3; .3, .28, .25; .25, .2, .15] (default) | matrix

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.

Friction coefficient interpolation method — Interpolation method

Linear (default) | Smooth

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.

Friction coefficient extrapolation method — Extrapolation method

Linear (default) | Nearest | Error

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.

Velocity tolerance — Relative velocity locking threshold

0.001 rad/s (default) | scalar

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.

Threshold force — Normal contact force threshold

1 N (default) | scalar

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 — Viscous drag torque

0 (default) | nonnegative scalar

Viscous drag torque coefficient.

Initial Conditions

Initial state — Initial clutch state

Unlocked (default) | Locked

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

To modify the faults, create a fault and, in the block dialog, click Open fault properties. In the Property Inspector, click the Fault behavior link to open the faults.

Clutch fault — Option to model friction fault

Add fault

Whether to model a fault in the block. To add a fault, click the Add fault hyperlink.

Behavior when faulted — Clutch friction fault response

Cannot transmit power (default) | Cannot unlock

Fault response. You can select the clutch faulting as either:

• Cannot transmit power

• Cannot unlock

Dependencies

To enable this parameter, enable faults for the block by clicking the Add fault hyperlink.

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 mass — Thermal mass

50 kJ/K (default) | scalar

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.

Initial temperature — Initial temperature

300 K (default) | scalar

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.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2011a

R2024a: Model faults with the Simscape faults interface

The Cone Clutch block now supports the Simscape faults interface. To learn more, see Introduction to Simscape Faults.