# Rotational Friction

Friction in contact between rotating bodies

**Library:**Simscape / Foundation Library / Mechanical / Rotational Elements

## Description

The Rotational Friction block represents friction in contact between rotating bodies. The friction torque is simulated as a function of relative velocity and is assumed to be the sum of Stribeck, Coulomb, and viscous components, as shown in the following figure.

The Stribeck friction, *T*_{S}, is the negatively
sloped characteristics taking place at low velocities [1]. The Coulomb friction,
*T*_{C}, results in a constant torque at any velocity.
The viscous friction, *T*_{V}, opposes motion with the
torque directly proportional to the relative velocity. The sum of the Coulomb and Stribeck
frictions at the vicinity of zero velocity is often referred to as the breakaway friction,
*T*_{brk}. The friction is approximated with the
following equations:

$$T=\sqrt{2e}\left({T}_{brk}-{T}_{C}\right)\cdot \mathrm{exp}\left(-{\left(\frac{\omega}{{\omega}_{St}}\right)}^{2}\right)\cdot \frac{\omega}{{\omega}_{St}}+{T}_{C}\cdot \mathrm{tanh}\left(\frac{\omega}{{\omega}_{Coul}}\right)+f\omega $$

$${\omega}_{St}={\omega}_{brk}\sqrt{2}$$

$${\omega}_{Coul}={\omega}_{brk}/10$$

$$\omega ={\omega}_{R}-{\omega}_{C}$$

where

*T*is friction torque.*T*_{C}is Coulomb friction torque.*T*_{brk}is breakaway friction torque.*ω*_{brk}is breakaway friction velocity.*ω*_{St}is Stribeck velocity threshold.*ω*_{Coul}is Coulomb velocity threshold.*ω*_{R}and*ω*_{C}are absolute angular velocities of ports**R**and**C**, respectively.*ω*is relative velocity.*f*is viscous friction coefficient.

The exponential function used in the Stribeck portion of the force equation is continuous and decays at velocity magnitudes greater than the breakaway friction velocity.

The hyperbolic tangent function used in the Coulomb portion of the force equation ensures
that the equation is smooth and continuous through *ω* = 0, but quickly reaches its full value at nonzero velocities.

The block positive direction is from port **R** to port
**C**. This means that if the port **R** velocity is
greater than that of port **C**, the block transmits torque from
**R** to **C**.

### 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.

## Ports

### Conserving

## Parameters

## Model Examples

## References

[1] Armstrong, B. and C.C. de Wit,
*Friction Modeling and Compensation*, The Control Handbook, CRC Press,
1995.

## Extended Capabilities

## Version History

**Introduced in R2007a**

## See Also

Rotational Damper | Rotational Hard Stop | Rotational Spring