Cylinder Friction

(To be removed) Friction in hydraulic cylinders

The Hydraulics (Isothermal) library will be removed in a future release. Use the Isothermal Liquid library instead. (since R2020a)

For more information on updating your models, see Upgrading Hydraulic Models to Use Isothermal Liquid Blocks.

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Libraries:
Simscape / Fluids / Hydraulics (Isothermal) / Hydraulic Cylinders

Description

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

The block approximates the friction force as

$$F=F_C·\left(1+\left(K_{brk}-1\right)·\exp \left(-c_v\left|v\right|\right)\right)sign\left(v\right)+f_{vfr}·v$$

$$F_C=F_{pr}+f_{cfr}\left(p_A+p_B\right)$$

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, the block introduces a small region, |v| ≤ v_th, around zero velocity where the friction force is linearly proportional to velocity

$$F=K·v$$

$$K=\frac{F_C\left(1+\left(K_{brk}-1\right)·\exp \left(-c_v{v}_{th}\right)\right)+f_{vfr}·v_{th}}{v_{th}}$$

where:

K	Proportionality coefficient
vth	Velocity threshold

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

Variables

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

Nominal values provide a way to specify the expected magnitude of a variable in a model. Using system scaling based on nominal values increases the simulation robustness. Nominal values can come from different sources, one of which is the Nominal Values section in the block dialog box or Property Inspector. For more information, see Modify Nominal Values for a Block Variable.

Ports

Conserving

A — Cylinder inlet

hydraulic

Hydraulic conserving port connected to the cylinder inlet.

B — Cylinder outlet

hydraulic

Hydraulic conserving port connected to the cylinder outlet.

R — Cylinder rod

mechanical translational

Mechanical translational conserving port associated with the cylinder rod.

C — Cylinder clamping structure

mechanical translational

Mechanical translational conserving port associated with the cylinder clamping structure.

Parameters

Preload force — Preload force caused by seal squeeze during assembly

10 N (default) | nonnegative scalar

Preload force caused by the seal squeeze during assembly.

Coulomb friction force coefficient — Proportionality coefficient for Coulomb friction force

1e-6 N/Pa (default) | nonnegative scalar

Coulomb friction coefficient. This value defines the proportionality between the Coulomb friction force and the pressure in cylinder chambers.

Breakaway friction increase coefficient — Friction force increase over Coulomb friction

1 (default) | scalar greater than or equal to 1

Friction force increase over the Coulomb friction. The Coulomb friction force, multiplied by this coefficient, is breakaway friction force.

Viscous friction coefficient — Proportionality coefficient between viscous friction force and relative velocity

100 N/(m/s) (default) | nonnegative scalar

Proportionality coefficient between the viscous friction force and the relative velocity.

Transition approximation coefficient — Approximation of transition between breakaway and Coulomb frictions

10 s/m (default) | positive scalar

Value of the coefficient c_v, which the block uses for the approximation of the transition between the breakaway and the Coulomb frictions. Assign this value based on the following considerations: the Stribeck friction component reaches approximately 5% of its steady-state value at velocity 3/c_v, and 2% at velocity 4/c_v, which makes it possible to develop an approximate relationship c_v ~= 4/v_min, where v_min is the relative velocity at which friction force has its minimum value. The default value, 10 s/m, corresponds to a minimum friction at a velocity of about 0.4 m/s.

Linear region velocity threshold — Small vicinity near zero velocity where friction force is linearly proportional to relative velocity

1e-4 m/s (default) | positive scalar

Small vicinity near zero velocity where the friction force is linearly proportional to the relative velocity. It is recommended that you use values in the range between 1e-6 and 1e-4 m/s.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2006b

R2023a: To be removed

The Hydraulics (Isothermal) library will be removed in a future release. Use the Isothermal Liquid library instead.

For more information on updating your models, see Upgrading Hydraulic Models to Use Isothermal Liquid Blocks.