# Cylinder Friction (TL)

**Libraries:**

Simscape /
Fluids /
Thermal Liquid /
Actuators /
Auxiliary Components

## Description

The Cylinder Friction (TL) block models friction on a moving cylinder in a thermal liquid network. The total friction is a combination of the Stribeck, Coulomb, and viscous effects. The Coulomb friction component includes any initial force applied by the seal and the influence of pressure in the cylinder.

The block calculates the Stribeck and viscous forces using the same approach as the Simscape Foundational Library Translational Friction block.

### The Stribeck Friction and Viscous Friction Forces

The Stribeck friction force, *F _{Stribeck}*, is the
dominating friction component at low velocities. The block uses the equation

$${F}_{Stribeck}=\sqrt{2e}\left({R}_{break,Coulomb}-1\right)\cdot {F}_{C}\left(\frac{\upsilon}{{\upsilon}_{static,th}}\right){e}^{-{\left(\frac{\upsilon}{{\upsilon}_{static,th}}\right)}^{2}},$$

where:

*R*is the value of the_{break,Coulomb}**Breakaway to Coulomb friction force ratio**parameter, $${R}_{Break,Coulomb}=\frac{{F}_{break}}{{F}_{Coulomb}}.$$*ν*is the velocity of the cylinder, $$\upsilon ={\upsilon}_{R}-{\upsilon}_{C}$$.*ν*is the threshold velocity for static torque_{static,th}$${\upsilon}_{static,th}=\sqrt{2}{v}_{break},$$

where

*v*is the value of the_{break}**Breakaway friction velocity**parameter. The block establishes a transition range between 0 and the threshold velocity for static torque to ensure smooth modeling of the friction force.*F*is the Coulomb frictional force._{C}

The viscous friction force is based on the value of the **Viscous friction
coefficient** parameter for the working fluid,
*f _{viscous}*, and is proportional to
the cylinder velocity

$${F}_{viscous}={f}_{viscous}\upsilon .$$

### The Coulomb Friction Force

The Coulomb friction force is a force that acts normal to the friction surface. The cylinder motion creates a radial stress inside the fixed cylinder casing, which increases as the cylinder compresses the internal fluid. The radial stress is normal to the cylinder motion, and results in a Coulomb friction force that opposes cylinder motion.

The Coulomb frictional force is

$${F}_{Coulomb}={F}_{c}\mathrm{tanh}\left(\frac{\upsilon}{{\upsilon}_{Coulomb,th}}\right),$$

where *ν* is the relative velocity between ports
**R** and **C**,
*ν _{R}* –

*ν*.

_{C}*ν*is the threshold velocity for the Coulomb force,

_{Coulomb,th}$${\upsilon}_{Coulomb,th}=\frac{{v}_{break}}{10}.$$

The threshold velocity for the Coulomb force is a different quantity than the threshold velocity for the static force, which the block uses to calculate the Stribeck friction force, although they both act as a threshold region to ensure smooth modeling of the Coulomb and Stribeck forces.

*F _{C}* is the force contribution from seal preloading
and the pressure in the cylinder,

$${F}_{C}={F}_{preload}+{f}_{Coulomb}({P}_{A}+{P}_{B}),$$

where:

*F*is the value of the_{preload}**Preload force**parameter.*f*is the value of the_{Coulomb}**Coulomb friction force coefficient**parameter.*P*and_{A}*P*are the pressures at cylinder ports_{B}**A**and**B**, respectively. These values are gauge pressures with respect to the environmental pressure. You can specify these values either as atmospheric or another user-defied value by using the**Environment pressure specification**parameter.

## Ports

### Conserving

## Parameters

## Extended Capabilities

## Version History

**Introduced in R2023b**