# Cylinder Friction

Friction in hydraulic cylinders

## Library

Hydraulic Cylinders

## Description

The Cylinder Friction block simulates friction in the contact between moving bodies in hydraulic cylinders and is intended to be used primarily as a building block in combination with both the double- and single-acting cylinders to develop a cylinder model with friction. The friction force is simulated as a function of relative velocity and pressure, and is assumed to be the sum of Stribeck, Coulomb, and viscous components. The Coulomb friction force consists of the preload force, caused by the seal squeeze during assembly, and the force proportional to pressure. The sum of the Coulomb and Stribeck friction forces at zero velocity is often referred to as the breakaway friction force. For more information, see the Translational Friction block reference page.

The friction force is approximated with the following equations:

`$F={F}_{C}·\left(1+\left({K}_{brk}-1\right)·\mathrm{exp}\left(-{c}_{v}|v|\right)\right)sign\left(v\right)+{f}_{vfr}·v$`
`${F}_{C}={F}_{pr}+{f}_{cfr}\left({p}_{A}+{p}_{B}\right)$`

where

 F Friction force FC Coulomb friction Fpr Preload force fcfr Coulomb friction coefficient pA, pB Pressures in cylinder chambers Kbrk Breakaway friction force increase coefficient cv Transition coefficient v Relative velocity in the contact fvfr Viscous friction coefficient

To avoid discontinuity at v = 0, a small region |v| ≤ vth is introduced around zero velocity, where friction force is assumed to be linearly proportional to velocity:

`$F=K·v$`
`$K=\frac{{F}_{C}\left(1+\left({K}_{brk}-1\right)·\mathrm{exp}\left(-{c}_{v}{v}_{th}\right)\right)+{f}_{vfr}·{v}_{th}}{{v}_{th}}$`

where

 K Proportionality coefficient vth Velocity threshold

Connections R and C are mechanical translational conserving ports associated with the rod and case, respectively. Connections A and B are hydraulic conserving ports to be connected to ports A and B of the cylinder model, as shown in the following illustration. The force generated by the block always opposes relative motion between the rod and the case.

## Parameters

### Parameters Tab

The preload force, caused by the seal squeeze during assembly. The default value is `10` N.

Coulomb friction force coefficient

Coulomb friction coefficient, which defines the proportionality between the Coulomb friction force and the pressure in cylinder chambers. The default value is `1e-6` N/Pa.

Breakaway friction increase coefficient

The friction force increase over the Coulomb friction. The Coulomb friction force, multiplied by this coefficient, is referred to as breakaway friction force. The default value is `1`.

Viscous friction coefficient

Proportionality coefficient between the viscous 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).

Transition approximation coefficient

The parameter sets the value of coefficient cv, which is used for the approximation of the transition between the breakaway and the Coulomb frictions. Its value is assigned based on the following considerations: the Stribeck friction component reaches approximately 5% of its steady-state value at velocity `3`/cv, and 2% at velocity `4`/cv, which makes it possible to develop an approximate relationship cv ~= `4`/vmin, where vmin is the relative velocity at which friction force has its minimum value. By default, cv is set to `10` s/m, which corresponds to a minimum friction at velocity of about `0.4` m/s.

Linear region velocity threshold

The parameter sets the small vicinity near zero velocity, within which friction force is considered to be linearly proportional to the relative velocity. MathWorks recommends that you use values in the range between `1e-6` and `1e-4` m/s. The default value is `1e-4` m/s.

### Variables Tab

Use the Variables tab 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 (Simscape).

## Ports

The block has the following ports:

`A`

Hydraulic conserving port connected to the cylinder inlet.

`B`

Hydraulic conserving port connected to the cylinder outlet.

`R`

Mechanical translational conserving port associated with the cylinder rod.

`C`

Mechanical translational conserving port associated with the cylinder clamping structure.