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 ( μ s ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaeWaaeaacq aH8oqBdaWgaaWcbaGaam4CaaqabaaakiaawIcacaGLPaaaaaa@3A63@ 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 ( μ d ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaeWaaeaacq aH8oqBdaWgaaWcbaGaamizaaqabaaakiaawIcacaGLPaaaaaa@3A54@ 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 σ 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aaS baaSqaaiaaicdaaeqaaaaa@389F@ .

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 σ 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aaS baaSqaaiaaigdaaeqaaaaa@38A0@ .

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 σ 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aaS baaSqaaiaaikdaaeqaaaaa@38A1@ .

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.

TORQUE_FROM_PRELOAD ≥0.

This is a mandatory parameter and it must be specified.

Recommended Value: Not available.

Ball_Radius Specifies the radius of the spherical connector.

BALL_RADIUS > 0.

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]
Torque_From_Preload real [F][L]
Ball_Radius real [L]

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
TORQUE_FROM_PRELOAD = 526.882
BALL_RADIUS         = 10.0