# Rotational Friction

Friction in contact between rotating bodies

## 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
(see [1]). The
Coulomb friction,

*T*, results in a constant torque at any velocity. The viscous friction,

_{C}*T*, 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,

_{V}*T*. The friction is approximated with the following equations:

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

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

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

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

where

T | Friction torque |

T_{C} | Coulomb friction torque |

T_{brk} | Breakaway friction torque |

ω_{brk} | Breakaway friction velocity |

ω_{St} | Stribeck velocity threshold |

ω_{Coul} | Coulomb velocity threshold |

ω_{R}, ω_{C} | Absolute angular velocities of terminals R and C, respectively |

ω | Relative velocity |

f | 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 **Variables** tab in the block dialog box (or the
**Variables** section in the block Property Inspector). For more
information, see Set Priority and Initial Target for Block Variables.

## Parameters

**Breakaway friction torque**Breakaway friction torque, which is the sum of the Coulomb and the static frictions. It must be greater than or equal to the Coulomb friction torque value. The default value is

`25`

N*m.**Breakaway friction velocity**The velocity at which the Stribeck friction is at its peak. At this point, the sum of the Stribeck and Coulomb friction is the

**Breakaway friction force**. The default value is`0.1`

rad/s.**Coulomb friction torque**Coulomb friction torque, which is the friction that opposes rotation with a constant torque at any velocity. The default value is

`20`

N*m.**Viscous friction coefficient**Proportionality coefficient between the friction torque and the relative angular velocity. The parameter value must be greater than or equal to zero. The default value is

`100`

N*m/(rad/s).

## Ports

The block has the following ports:

`R`

Mechanical rotational conserving port.

`C`

Mechanical rotational conserving port.

## Examples

The Mechanical Rotational System with Stick-Slip Motion example illustrates the use of the Rotational Friction block in mechanical systems. The friction element is installed between the load and the velocity source, and there is a difference between the breakaway and the Coulomb frictions. As a result, stick-slip motion is developed in the regions of constant velocities.

## References

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

## Extended Capabilities

## See Also

Rotational Damper | Rotational Hard Stop | Rotational Spring

**Introduced in R2007a**