Inertia with Friction (AB)

Inertia with friction in angle-based rotational systems

Since R2026a

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  • Inertia with Friction (AB) block

Libraries:
Simscape / Foundation Library / Rotational / Elements

Description

The Inertia with Friction (AB) block represents an inertia with friction in angle-based rotational systems.

The Inertia with Friction (AB) block is essentially a structural component that consists of an Inertia (AB) block connected to port F of a Rotational Friction (AB) block. Port B of the Rotational Friction (AB) block is connected to an implicit reference.

Inertia with friction schematic

The friction torque is the sum of Stribeck, Coulomb, and viscous components. The sum of the Coulomb and Stribeck frictions at the vicinity of zero velocity is the breakaway friction, TBrk. The Coulomb and breakaway frictions are proportional to the normal force. The viscous friction is independent of normal force [1]. You can disable the individual frictional effects by setting the Breakaway friction coefficient, Coulomb friction coefficient, and Viscous friction coefficient parameters to 0.

The block uses the equations

tacc=t+tfriction

tacc=I⋅ω˙

tfriction=−2e(TBrk−TC)⋅exp(−(ωωSt)2)⋅ωωSt−TC⋅tanh(ωωC)−fv⋅ω

TBrk=rEff⋅μBrk⋅FN

TC=rEff⋅μC⋅FN

ωSt=ωBrk2

ωC=ωBrk/10

where:

  • tacc is torque proportional to inertia acceleration. Positive tacc corresponds to an inertia accelerating in the positive direction.

  • t is the port torque, which is the torque of the rotational network acting on the inertia. Positive t drives the inertia in the positive direction.

  • tfriction is the torque of the friction acting on the inertia. Positive tfriction opposes an inertia rotating in the negative direction.

  • I is inertia.

  • ω is the inertia angular velocity.

  • e is Euler's number.

  • TBrk is the breakaway friction torque.

  • TC is the Coulomb friction torque.

  • FN is the normal force of the inertia acting on the axis.

  • 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.

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. Use the Visible ports parameter to select whether to expose both ports or only one port, B or F, depending on your diagram layout. Because the two ports are rigidly connected to each other, the difference between the one-port and two-port variants is purely graphical.

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

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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

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

Dependencies

To enable this port, set the Visible ports parameter to either B and F or B.

Angle-based rotational conserving port that represents the follower connection. This port is rigidly connected to the base port.

Dependencies

To enable this port, set the Visible ports parameter to either B and F or F.

Parameters

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Main

Inertia value. The inertia is constant during simulation.

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

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

  • Variable — Specify the 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.

Ports

To improve block diagram readability, you can specify whether to expose both ports or only one port, B or F. Because the two ports are rigidly connected to each other, the difference between the one-port and two-port variants is purely graphical. Select the ports visible on the block icon:

  • B and F — Expose both ports, B and F.

  • B — Expose only port B.

  • F — Expose only port F.

References

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

Extended Capabilities

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

Version History

Introduced in R2026a

See Also

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