Cylinder Friction (IL)

Adds friction to cylinders with moving components

Since R2020a

• 

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:

$$F_{Coulomb}=F_c\tanh \left(\frac{\upsilon }{{\upsilon }_{Coulomb,th}}\right),$$

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

A — Liquid port

isothermal liquid

Liquid entry or exit point to the orifice.

B — Liquid port

isothermal liquid

Liquid entry or exit point to the orifice.

C — Mechanical port velocity, m/s

mechanical translational

Mechanical port for cylinder housing motion, in m/s.

R — Mechanical port velocity, m/s

mechanical translational

Mechanical port for cylinder rod motion, in m/s.

Parameters

Breakaway to Coulomb friction force ratio — Ratio of breakaway force to Coulomb friction force

1.2 (default) | positive scalar

Ratio of the breakaway force to the Coulomb friction force.

Breakaway friction velocity — Threshold for motion against friction force

0.1 m/s (default) | positive scalar

Threshold for movement against friction force.

Preload force — Initial force in cylinder due to seal assembly

20 N (default) | scalar

Initial force in the cylinder due to seal assembly.

Coulomb friction force coefficient — Coulomb friction force coefficient

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

Coulomb friction force coefficient.

Viscous friction coefficient — Viscous friction coefficient

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

Viscous friction coefficient. This parameter is used to calculate the viscous friction force.

Environment pressure specification — Pressure reference source

Atmospheric pressure (default) | Specified pressure

Identifies pressure reference for the Coulomb friction calculation.

Environment pressure — User-defined pressure reference

0.101325 MPa (default) | positive scalar

User-defined pressure reference for the Coulomb friction calculation.

Dependencies

To enable this parameter, set Environment pressure specification to Specified pressure.

Extended Capabilities

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

Version History

Introduced in R2020a