Loaded-Contact Rotational Friction
Loaded-contact friction between two rotating surfaces
Libraries:
Simscape /
Driveline /
Brakes & Detents /
Rotational
Description
The Loaded-Contact Rotational Friction block simulates friction between two rotating surfaces loaded with a normal force.
The block is implemented as a structural component based on the Fundamental Friction Clutch block. From the locked state, the two surfaces unlock if the transmitted torque exceeds the static friction, as defined by the static coefficient of friction and current normal force. For details on how the locking and unlocking are modeled, see the Fundamental Friction Clutch block reference page.
Torque is transmitted for normal forces larger than the Threshold force parameter.
Equations
The block simulates friction between two rotating surfaces loaded with a normal force. When the two rotating surfaces are not locked, the transmitted torque is determined with the following equations:
where:
τ is the transmitted torque.
N is the normal force.
μ is the friction coefficient.
reff is the effective radius.
ro is the surface outside radius.
ri is the surface inside radius.
ω is the relative angular velocity.
τvisc is the viscous drag torque.
μvisc is the viscous drag torque coefficient.
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 Loaded-Contact Rotational Friction 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 clutch responds according to the Behavior when faulted setting for the remainder of the simulation. The fault options are:
Cannot transmit power
Cannot unlock
Limitations and Assumptions
The model does not account for inertia. Add inertia terms externally to the B and F ports as required.
The model computes the torque assuming a uniform distribution of the normal force.
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.
Conserving
B — Base
mechanical rotational
Rotational conserving port associated with the driving (base) surface.
F — Follower
mechanical rotational
Rotational conserving port associated with the driven (follower) surface.
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.
Parameters
Geometry
Geometry model — Parameterization method
Define effective
radius
(default) | Define annular
region
Parameterization method for the loaded-contact friction model:
Define effective radius
— Provide a value for the friction effective radius.Define annular region
— Define the friction effective radius in terms of the inside and outside diameters of the friction surface. If you select this option, the panel changes from its default.
Dependencies
The value of this parameter affects the visibility of other parameters in the Geometry settings.
Effective torque radius — Effective friction surface radius
130
mm
(default) | positive scalar
Effective radius reff. The value must be greater than zero.
Dependencies
This parameter is visible only if the
Geometry model parameter is
set to Define effective
radius
.
Friction surface outside diameter — Friction surface outer diameter
150
mm
(default) | positive scalar
Outside diameter, 2 * ro, of the friction surfaces. Must be greater than zero.
Dependencies
This parameter is visible only if the
Geometry model parameter is
set to Define annular
region
.
Friction surface inside diameter — Friction surface inner diameter
100
mm
(default) | positive scalar less than outer
diameter
Inside diameter, 2 * ri, of the friction surfaces. Must be greater than zero, but less than the friction surface outside diameter.
Dependencies
This parameter is visible only if the
Geometry model parameter is
set to Define annular
region
.
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:
| 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 discs.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 discs.
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 only visible when you set
the Friction model parameter
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 only visible when you set
the Friction model parameter
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 only visible when you set
the Friction model parameter
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 only visible when you set
the Friction model parameter
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 only visible when you set
the Friction model parameter
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 only visible when you set
the Friction model parameter
to Temperature and velocity-dependent
friction coefficients
. For more
information, see Friction Parameter Dependencies.
Friction coefficient interpolation method — Extrapolation 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 only visible when you set
the Friction model parameter
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 — Interpolation 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 only visible when you set
the Friction model parameter
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 Losses
Viscous drag torque coefficient — Viscous drag torque
0
N*m/(rad/s)
(default) | nonnegative scalar
Viscous drag coefficient, μvisc, for computing the drag torque. The coefficient depends on the type of operating fluid, fluid temperature, and the maximum distance between the surfaces.
Initial Conditions
Initial state — Initial clutch state
Unlocked
(default) | Locked
State of the internal Fundamental Friction Clutch block state at the start of simulation.
Locked
— Rotational ports B and F are initially locked together.Unlocked
— Rotational ports B and F are initially sliding relative to each other.
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.
Friction 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 — Response to fault trigger
Cannot transmit
power
(default) | Cannot
unlock
Behavior when a fault is triggered. You can select the faulting between the surfaces 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
.
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
To enable this parameter, set
Friction model to
Temperature-dependent friction
coefficients
or
Temperature and velocity-dependent
friction coefficients
.
Initial temperature — Initial temperature
300
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
To enable this parameter, set
Friction model to
Temperature-dependent friction
coefficients
or
Temperature and velocity-dependent
friction coefficients
.
Extended Capabilities
C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.
Version History
Introduced in R2011aR2024a: Model faults with the Simscape faults interface
The Loaded-Contact Rotational Friction block now supports the Simscape faults interface. To learn more, see Introduction to Simscape Faults.
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