Rotational Friction (AB)

Friction in contact between rotating bodies in angle-based rotational systems

Since R2026a

expand all in page
  • Rotational Friction (AB) block

Libraries:
Simscape / Foundation Library / Rotational / Elements

Description

The Rotational Friction (AB) block represents friction in contact between rotating bodies. The friction torque is the sum of Stribeck, Coulomb, and viscous components.

Friction torque diagram

The sum of the Coulomb and Stribeck frictions at the vicinity of zero velocity is the breakaway friction. The Coulomb and breakaway frictions are proportional to the normal force. The viscous friction is independent of normal force [1].

The block uses the equations

t=−2e(TBrk−TC)⋅exp(−(ωRelωSt)2)⋅ωRelωSt−TC⋅tanh(ωRelωC)−fv⋅ωRel

TBrk=rEff⋅μBrk⋅FN

TC=rEff⋅μC⋅FN

ωSt=ωBrk2

ωC=ωBrk/10

ωRel=ωF−ωB

θRel=θF−θB

where:

  • t is the friction torque.

  • e is Euler's number.

  • TBrk is the breakaway friction torque.

  • TC is the Coulomb friction torque.

  • FN is the normal force.

  • rEff is the effective friction torque radius.

  • μBrk is the breakaway friction coefficient.

  • μC is the Coulomb friction coefficient.

  • fv is the viscous friction coefficient.

  • ωBrk is the breakaway friction angular velocity.

  • ωSt is the angular velocity threshold for the Stribeck torque.

  • ωCoul is the angular velocity threshold for the Coulomb torque.

  • ωRel is the relative angular velocity between ports.

  • ωB and ωF are the angular velocities of ports B and F, respectively.

  • θRel is the relative angle between ports.

  • θB and θF are the angles of ports B and F, respectively.

You can specify normal force as a parameter, Normal force, or as the input signal at port N, depending on the setting of the Normal force specification parameter.

B and F are angle-based rotational conserving ports. For positive relative angle, port F has a more positive angle than port B. The friction torque acts from port B on port F. Positive friction torque drives port F in the positive direction.

Variables

To set the priority and initial target values for the block variables prior to simulation, use the Initial Targets section in the block dialog box or Property Inspector. For more information, see Set Priority and Initial Target for Block Variables.

Nominal values provide a way to specify the expected magnitude of a variable in a model. Using system scaling based on nominal values increases the simulation robustness. Nominal values can come from different sources, one of which is the Nominal Values section in the block dialog box or Property Inspector. For more information, see Modify Nominal Values for a Block Variable.

Examples

Interpreting Angle in the Angle-Based Rotational Domain

Interpreting Angle in the Angle-Based Rotational Domain

Set up and interpret angles in angle-based rotational models. It provides background information to explain the underlying concepts. The angle-based rotational domain tracks angle, θ, and rotational velocity, ω, at every node. Use angle-based rotational blocks to model rotational systems where knowing multiple component angles is important.

Interpreting Torque in the Angle-Based Rotational Domain

Interpreting Torque in the Angle-Based Rotational Domain

Describes how to interpret torques in a Simscape™ angle-based rotational network. It outlines the key concepts for understanding the signs of logged torques. It examines rotational spring systems driven by torque sources at different ends, as well as a rotational system of inertias, to illustrate the torque behavior.

Ports

Input

expand all

Physical signal input port for the control signal that specifies the normal force. If the signal becomes negative, the block saturates the input value to 0.

Dependencies

To enable this port, set the Normal force specification parameter to Variable.

Conserving

expand all

Angle-based rotational conserving port that represents the base connection.

Angle-based rotational conserving port that represents the follower connection.

Parameters

expand all

Select whether the normal force applied to the block is constant or variable:

  • Constant — Specify normal force by using the Normal force parameter value.

  • Variable — Specify normal force by using the physical signal at port N.

Force applied to the block in the direction normal to the motion. The block calculates the breakaway friction torque and the Coulomb friction torque based on this value, the Effective friction torque radius value, and the proportionality coefficients, Breakaway friction coefficient and Coulomb friction coefficient.

Dependencies

To enable this parameter, set Normal force specification to Constant.

Effective friction torque radius, rEff. The block uses this parameter, together with the proportionality coefficients, to calculate the breakaway friction torque and the Coulomb friction torque.

Coefficient for calculating the breakaway friction torque, which is the sum of the Coulomb and the static frictions, based on the normal force. The parameter value must be greater than or equal to the Coulomb friction coefficient value.

Angular velocity at which the Stribeck friction is at its peak. At this point, the sum of the Stribeck and Coulomb frictions is the breakaway friction torque. This parameter specifies the velocity threshold, which affects the tradeoff between the simulation accuracy and speed.

Coefficient for calculating the Coulomb friction torque, which is the friction that opposes motion, based on the normal force.

Proportionality coefficient between the friction torque and the relative velocity. Viscous losses do not depend on the normal force.

References

[1] White, F. M., Fluid Mechanics, 7th Ed, Section 6.8. McGraw-Hill, 2011.

Extended Capabilities

expand all

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2026a

See Also

| | |