Loaded-Contact Translational Friction

Loaded-contact friction between two sliding surfaces

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Libraries:
Simscape / Driveline / Brakes & Detents / Translational

Description

The Loaded-Contact Translational Friction block simulates friction between two sliding 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 exerted force 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.

Force is transmitted for normal forces larger than the Threshold force parameter.

Equations

The block simulates friction between two sliding surfaces loaded with a normal force. When the two sliding surfaces are not locked, the friction force is determined with these equations:

$$F = N· \mu · \text{sign}(v_{rel})+F_{\text{visc}} ,$$

$$F_{visc} = {\mu }_{\text{visc}}·v_{rel} ,$$

where:

• F is the transmitted force.

• N is the normal force.

• μ is the friction coefficient.

• v_rel is the relative velocity.

• F_visc is the viscous drag force.

• μ_visc is the viscous drag force coefficient.

Velocity-Dependent Model

You can model the effects of translational 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 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 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 translational 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

Faults

To model a fault in the Loaded-Contact Translational 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 body mass. Add mass terms externally to the B and F ports as required.

• The model computes the transmitted force 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 translational

Translational conserving port associated with the driving surface.

F — Follower

mechanical translational

Translational conserving port associated with the driven surface.

H — Heat flow

thermal

Thermal conserving port associated with heat flow.

Dependencies

To enable this parameter, set Friction model to Temperature-dependent friction coefficients or Temperature and velocity-dependent friction coefficients.

Parameters

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 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, .1, 1] m/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) | positive 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 m/s (default) | scalar

Relative velocity below which the two surfaces can lock. The surfaces lock if the torque across the B and F translational 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/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 — Translational ports B and F are initially locked together.

• Unlocked — Translational 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, first 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

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 R2011a

R2024a: Model faults with the Simscape faults interface

The Loaded-Contact Translational Friction block now supports the Simscape faults interface. To learn more, see Introduction to Simscape Faults.