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.

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.

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

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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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

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Rotational conserving port associated with the driving (base) surface.

Rotational conserving port associated with the driven (follower) surface.

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

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 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```.

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```.

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. 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 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.

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 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 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.

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.

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.

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.

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.

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.

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 Losses

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

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.

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.

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.

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