Cylinder Friction (TL)

Cylinder friction in a thermal liquid network

Since R2023b

• 

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_{break,Coulomb} is the value of the 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_static,th is the threshold velocity for static torque

  $${\upsilon }_{static,th}=\sqrt{2}{v}_{break},$$

  where v_break is the value of the 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_C is the Coulomb frictional force.

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

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

where ν is the relative velocity between ports R and C, ν_R – ν_C. ν_Coulomb,th is the threshold velocity for the Coulomb force,

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

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_preload is the value of the Preload force parameter.

• f_Coulomb is the value of the Coulomb friction force coefficient parameter.

• P_A and P_B are the pressures at cylinder ports 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

A — Liquid port

thermal liquid

Thermal liquid conserving port associated with the liquid entry or exit point to the orifice.

B — Liquid port

thermal liquid

Thermal liquid conserving port associated with the liquid entry or exit point to the orifice.

C — Mechanical port velocity

mechanical translational

Mechanical translational conserving port associated with the cylinder housing motion.

R — Mechanical port velocity

mechanical translational

Mechanical translational conserving port associated with the cylinder rod motion.

Parameters

Same fluid on both sides — Option to model same fluid on both sides of block

on (default) | off

Whether to model the same fluid on both sides of the block. If you select this parameter, the block propagates fluid properties through the block. Clear this parameter to model each chamber as a different fluid, where each chamber is connected to an isolated fluid network.

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, $$R_{Break,Coulomb}=\frac{F_{break}}{F_{Coulomb}}.$$

Breakaway friction velocity — Threshold for motion against friction force

0.1 m/s (default) | positive scalar

Threshold for the cylinder moving against the friction force.

Preload force — Initial force in cylinder due to seal assembly

20 N (default) | scalar

Initial force in the cylinder due to the seal assembly. The block uses this parameter to calculate the Coulomb friction force.

Coulomb friction force coefficient — Coulomb friction force coefficient

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

Coulomb friction force coefficient. The block uses this parameter to calculate the Coulomb friction force.

Viscous friction coefficient — Viscous friction coefficient

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

Viscous friction coefficient. The block uses this parameter to calculate the viscous friction force.

Environment pressure specification — Pressure reference source

Atmospheric pressure (default) | Specified pressure

Pressure reference to use 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 R2023b

R2024a: Model different fluids on each side of the block

Clear the new Same fluid on both sides parameter to block the propagation of fluid properties and model each chamber as a different fluid connected to its own isolated fluid network.