Loaded-Contact Rotational Friction

Loaded-contact friction between two rotating surfaces

Library:
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.

You can also enable faulting. When faulting occurs, the surfaces 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.

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:

$τ = N \cdot μ \cdot r_{eff} \cdot sign (ω) + τ_{visc},$

$r_{eff} = \frac{2}{3} \cdot \frac{r_{o}^{3} - r_{i}^{3}}{r_{o}^{2} - r_{i}^{2}},$

$τ_{v i s c} = μ_{visc} \cdot ω,$

where:

τ is the transmitted torque.
N is the normal force.
μ is the friction coefficient.
r_eff is the effective radius.
r_o is the surface outside radius.
r_i is the surface inside radius.
ω is the relative angular velocity.
τ_visc is the viscous drag torque.
μ_visc 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.

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

Faulty Behavior

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.

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

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`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.

`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.

Conserving

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`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

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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 r_eff. 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 * r_o, 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 * r_i, 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. 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`
`Fixed kinetic friction coefficient`	`Velocity-dependent kinetic friction coefficient`	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 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

`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

`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, μ_visc, 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

`Enable faults` — Fault option
`Off` (default) | `On`

Enable externally or temporally triggered faults. When faulting occurs, the surfaces fail 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 faulting between the surfaces 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 surfaces respond 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 surfaces respond 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

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.

Documentation

Loaded-Contact Rotational Friction

Description

Equations

Velocity-Dependent Model

Thermal Model

Thermal, Velocity-Dependent Model

Faulty Behavior

Limitations and Assumptions

Ports

Input

N — Normal force physical signal

T — External fault trigger physical signal

Dependencies

Conserving

B — Base mechanical rotational

F — Follower mechanical rotational

H — Heat flow thermal

Dependencies

Parameters

Geometry

Geometry model — Parameterization method Define effective radius (default) | Define annular region

Dependencies

Effective torque radius — Effective friction surface radius 130 mm (default) | positive scalar

Dependencies

Friction surface outside diameter — Friction surface outer diameter 150 mm (default) | positive scalar

Dependencies

Friction surface inside diameter — Friction surface inner diameter 100 mm (default) | positive scalar less than outer diameter

Dependencies

Friction

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

Dependencies

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

Dependencies

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

Dependencies

Static friction coefficient — Static friction coefficient 0.35 (default) | scalar

Dependencies

Static friction coefficient vector — Static friction coefficient [.4, .38, .36] (default) | vector

Dependencies

Kinetic friction coefficient — Kinetic friction coefficient 0.3 (default) | positve scalar

Dependencies

Kinetic friction coefficient vector — Kinetic friction coefficient [.3, .22, .19] (default) | [.3, .28, .25] | vector

Dependencies

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

Dependencies

Friction coefficient interpolation method — Extrapolation method Linear (default) | Smooth

Dependencies

Friction coefficient extrapolation method — Interpolation method Linear (default) | Nearest | Error

Dependencies

Velocity tolerance — Relative velocity locking threshold 0.001 rad/s (default) | scalar

Threshold force — Normal contact force threshold 1 N (default) | scalar

Viscous Losses

Viscous drag torque coefficient — Viscous drag torque 0 N*m/(rad/s) (default) | nonnegative scalar

Initial Conditions

Initial state — Initial clutch state Unlocked (default) | Locked

Faults

Enable faults — Fault option Off (default) | On

Behavior when faulted — Set fault response Cannot transmit power (default) | Cannot unlock

Dependencies

Enable external fault trigger — External trigger option Off (default) | On

Dependencies

Enable temporal fault trigger — Temporal trigger option Off (default) | On

Dependencies

Simulation time for fault event — Time at which faulting is triggered 5 s (default) | positive scalar

Dependencies

Reporting when fault occurs — Fault condition report None (default) | Warning | Error

Dependencies

Thermal Port

Thermal mass — Thermal mass 50 kJ/K (default) | scalar

Dependencies

Initial temperature — Initial temperature 300 K (default) | scalar

Dependencies

Extended Capabilities

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See Also

Topics

Simscape Driveline Documentation

Support

`N` — Normal force
physical signal

`T` — External fault trigger
physical signal

`B` — Base
mechanical rotational

`F` — Follower
mechanical rotational

`H` — Heat flow
thermal

`Geometry model` — Parameterization method
`Define effective radius` (default) | `Define annular region`

`Effective torque radius` — Effective friction surface radius
`130` `mm` (default) | positive scalar

`Friction surface outside diameter` — Friction surface outer diameter
`150` `mm` (default) | positive scalar

`Friction surface inside diameter` — Friction surface inner diameter
`100` `mm` (default) | positive scalar less than outer diameter

`Friction model` — Friction model
`Fixed kinetic friction coefficient` (default) | `Velocity-dependent kinetic friction coefficient` | `Temperature-dependent friction coefficients` | `Temperature and velocity-dependent friction coefficients`

`Relative velocity vector` — Relative velocity
`[0, 100, 1000]` `rad/s` (default) | vector

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

`Static friction coefficient` — Static friction coefficient
`0.35` (default) | scalar

`Static friction coefficient vector` — Static friction coefficient
`[.4, .38, .36]` (default) | vector

`Kinetic friction coefficient` — Kinetic friction coefficient
`0.3` (default) | positve scalar

`Kinetic friction coefficient vector` — Kinetic friction coefficient
`[.3, .22, .19]` (default) | `[.3, .28, .25]` | vector

`Kinetic friction coefficient matrix` — Kinetic friction coefficient
`[.34, .32, .3; .3, .28, .25; .25, .2, .15]` (default) | matrix

`Friction coefficient interpolation method` — Extrapolation method
`Linear` (default) | `Smooth`

`Friction coefficient extrapolation method` — Interpolation method
`Linear` (default) | `Nearest` | `Error`

`Velocity tolerance` — Relative velocity locking threshold
`0.001` `rad/s` (default) | scalar

`Threshold force` — Normal contact force threshold
`1` `N` (default) | scalar

`Viscous drag torque coefficient` — Viscous drag torque
`0` `N*m/(rad/s)` (default) | nonnegative scalar

`Initial state` — Initial clutch state
`Unlocked` (default) | `Locked`

`Enable faults` — Fault option
`Off` (default) | `On`

`Behavior when faulted` — Set fault response
`Cannot transmit power` (default) | `Cannot unlock`

`Enable external fault trigger` — External trigger option
`Off` (default) | `On`

`Enable temporal fault trigger` — Temporal trigger option
`Off` (default) | `On`

`Simulation time for fault event` — Time at which faulting is triggered
`5 s` (default) | positive scalar

`Reporting when fault occurs` — Fault condition report
`None` (default) | `Warning` | `Error`

`Thermal mass` — Thermal mass
`50` `kJ/K` (default) | scalar

`Initial temperature` — Initial temperature
`300` `K` (default) | scalar

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