Friction in contact between moving bodies

Mechanical Translational Elements

The Translational Friction block represents friction in contact between moving bodies. The friction force 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, *F _{S}*,
is the negatively sloped characteristics taking place at low velocities
(see [1]). The
Coulomb friction,

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

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

$${v}_{Coul}={v}_{brk}/10$$

$$v={v}_{R}-{v}_{C}$$

where

F | Friction force |

F_{C} | Coulomb friction |

F_{brk} | Breakaway friction |

v_{brk} | Breakaway friction velocity |

v_{St} | Stribek velocity threshold |

v_{Coul} | Coulomb velocity threshold |

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

v | Relative velocity |

f | Viscous friction coefficient |

The exponential function used in the Stribek 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 *v* = 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 force from R to C.

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

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

`25`

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

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

m/s.**Coulomb friction force**The Coulomb friction force, which is the friction that opposes motion with a constant force at any velocity. The default value is

`20`

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

`100`

N/(m/s).

The block has the following ports:

`R`

Mechanical translational conserving port.

`C`

Mechanical translational conserving port.

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

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