# Cylinder Friction (IL)

**Libraries:**

Simscape /
Fluids /
Isothermal Liquid /
Actuators /
Auxiliary Components

## Description

The Cylinder Friction (IL) block models friction on a moving cylinder. The total friction is a combination of 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 Stribeck and viscous forces are calculated in the same way as for the Simscape Foundational Library Translational Friction block.

### The Stribeck Friction and Viscous Friction Forces

The Stribeck friction force is the dominating friction component at low velocities. It is calculated as:

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

where:

*R*_{break,Coulomb}is the ratio of the breakaway force to the Coulomb force: $${R}_{Break,Coulomb}=\frac{{F}_{break}}{{F}_{Coulomb}}.$$*ν*is the velocity of the cylinder, $$\upsilon ={\upsilon}_{R}-{\upsilon}_{C}$$.*ν*_{static,th}is the threshold velocity for static torque:$${\upsilon}_{static,th}=\sqrt{2}{v}_{break},$$

where

*v*_{break}is the**Breakaway friction velocity**. A transition range is established between 0 and the threshold velocity for static torque to ensure smooth modeling of the friction force.*F*_{C}is introduced in The Coulomb Friction Force section below.

The viscous friction force is based on the **Viscous friction
coefficient** of 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 calculated as:

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

where *ν* is the relative velocity between ports
**R** and **C**
(*ν*_{R} –
*ν*_{C}), and
*ν*_{Coulomb,th} is the threshold velocity
for Coulomb force:

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

Note that the threshold velocity for Coulomb force is a different quantity than the threshold velocity for the static force, which is used 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 (the **Preload force**) and the pressure in the
cylinder:

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

where *f*_{Coulomb} is the
**Coulomb friction force coefficient**.
*P*_{A} and
*P*_{B}, the pressures at cylinder ports
**A** and **B**, are gauge pressures with
respect to the environmental pressure, specified either as atmospheric or another
user-defied value in the **Environment pressure specification**
parameter.

## Ports

### Conserving

## Parameters

## Extended Capabilities

## Version History

**Introduced in R2020a**