Cone Clutch
Friction clutch with conical plates that engage when normal force
exceeds threshold
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
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
FN.
Kinetic FrictionThe kinetic friction torque is the product of four
factors:
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:
do and
di are
the contact surface maximum and minimum diameters,
respectively.
Static FrictionThe static friction limit is related to the kinetic friction,
setting ω to zero and replacing the
kinetic with the static friction coefficient:
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:
The range
[τS–,
τS+]
is used by the Fundamental Friction Clutch.
Engagement and Locking ConditionsThe 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 ClutchThe 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:
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:
Faulty Behavior
You can enable faulty behavior in response to:
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
expand all
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.
T
— External fault trigger
physical signal
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
expand all
X
— Shift linkage position
physical signal
Physical signal port associated with shift
linkage position.
Dependencies
This port is visible only when, in the
settings, the
Shift linkage control
parameter is set to Conserving
port
. For more information, see
Shift linkage control and Geometry Parameter Dependencies.
Conserving
expand all
B
— Base
mechanical rotational
Mechanical rotational conserving port
associated with the driving (base) shaft. The
clutch motion is measured as the
slip
ω =
ωF–
ωB, 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
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 |
Shift linkage control
|
Physical
signal | Conserving
port |
Exposes
physical signal input port
N | Exposes:
|
Contact surface maximum diameter
— Outer diameter
150
mm
(default) | positive scalar
Outer conical diameter
do.
Contact surface minimum diameter
— Inner diameter
100
mm
(default) | positive scalar
Inner conical diameter
di.
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 stop damping
— Ring stop damping
1e3
N/(m/s)
(default) | nonnegative scalar
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.
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:
| Exposes:
|
- | - | 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) | positve 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:
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
Enable faults
— Fault option
Off
(default) | On
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.
Behavior when faulted
— Set fault response
Cannot transmit
power
(default) | Cannot
unlock
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
.
Enable external fault trigger
— External trigger option
Off
(default) | 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
.
Enable temporal fault trigger
— Temporal trigger option
Off
(default) | 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
.
Simulation time for fault event
— Time at which faulting is triggered
5 s
(default) | positive scalar
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 when fault occurs
— Fault condition report
None
(default) | Warning
| Error
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 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
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Generate C and C++ code using Simulink® Coder™.
Introduced in R2011a