# Friction Block

Friction parameters for the LuGre model are defined in the Friction block as shown in the following table:
Parameter Name Dimension
Mu_Static Specifies the static friction coefficient $\left({\mu }_{s}\right)$ in the connector.

MU_STATIC > 0.

This is a mandatory parameter and it must be specified.

Recommended Value: 0.5

Mu_Dynamic Specifies the dynamic friction coefficient $\left({\mu }_{d}\right)$ in the connector.

0 ≤ MU_DYNAMIC ≤ MU_STATIC.

This is a mandatory parameter and it must be specified.

Recommended Value: 0.3

Analysis_Modes Specifies the analysis modes for which the frictional effect is on. The choices are the strings:
• ‘STATICS_AND_DYNAMICS’
• ‘DYNAMICS_ONLY’

This is an optional parameter that defaults to ‘DYNAMICS_ONLY’. Both static and dynamic frictions are considered.

Recommended Value: ‘STATICS_AND_DYNAMICS’.

Effect Specifies the types of friction models to support. Available options are:
• ‘STICTION’
• ‘SLIDING’

This is a mandatory parameter and it must be specified.

Recommended Value: ‘SLIDING’.

Transition_Velocity The absolute velocity at which the friction transitions from dynamic friction to static friction. TRANSITION_VELOCITY > 0.

This is a mandatory parameter and it must be specified.

Recommended Value: 0.1 mm/second.

Bristle_Stiffness

Specifies the bristle stiffness in the LuGre model. Usually represented as ${\sigma }_{0}$ .

BRISTLE_STIFFNESS > 0.

This is a mandatory parameter and it must be specified.

Recommended Value: 100.0/mm.

Bristle_Damping Defines the damping coefficient for the pre-displacement (or stiction) regime. Its main role is to damp out bristle vibrations in the pre-displacement regime. Usually represented as ${\sigma }_{1}$ .

BRISTLE_DAMPING ≥0.

This is a mandatory parameter and it must be specified.

Recommended Value: 0.316 second/mm.

Slip_Damping

Specifies the coefficient for the viscous damping force that occurs when relative sliding actually begins. Usually represented as ${\sigma }_{2}$ .

SLIP_DAMPING ≥ 0.

This is a mandatory parameter and it must be specified.

Recommended Value: 0.0004 second/mm.

Torque_From_Preload Specifies the preload friction torque in the Spherical Connectors.

This is a mandatory parameter and it must be specified.

Recommended Value: Not available.

Ball_Radius Specifies the radius of the spherical connector.

This is a mandatory parameter and it must be specified.

Recommended Value: Not available.

The following table describes the type and dimension for the various input parameters. Abbreviations are: [F] = force, [L] = length, [T] = time.
Parameter Name Type Dimension
Mu_Static real No-Units
Mu_Dynamic real No-Units
Analysis_Modes real -
Effect real -
Transition_Velocity real [L][T-1]
Bristle_Stiffness real [L-1]
Bristle_Damping real [T][L-1]
Slip_Damping real [T][L-1]
The example below shows the specification of a LuGre Friction block in the .gbs file:
\$---------------------------------------------------------------
[LUGRE_FRICTION]
MU_STATIC           = 0.0
MU_DYNAMIC          = 0.0
ANALYSIS_MODES      = 'STATICS_AND_DYNAMICS'
EFFECT              = 'SLIDING'
USE_FORCE           = 'YES'
TRANSITION_VELOCITY = 0.1000
BRISTLE_STIFFNESS   = 0.0100
BRISTLE_DAMPING     = 0.31625
SLIP_DAMPING        = 0.0008