Friction Modelling and Validation for a Volumetric Contact Dynamics Model
53
Motivation Volumetric Model Experiments Conclusions Friction Modelling and Validation for a Volumetric Contact Dynamics Model Mike Boos and John McPhee Department of Systems Design Engineering University of Waterloo Canada May 30, 2012 Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 1/ 27
description
A volumetric contact dynamics model has been proposed for the purpose of generating reliable and rapid simulations of contact dynamics. Forces and moments between bodies in contact can be expressed in terms of the volume of interference between the undeformed geometries. This allows for the modelling of contact between complex geometries and relatively large contact surfaces. It also permits the modelling of rotational dynamics, such as spinning friction torque or the Contensou effect, when friction forces are distributed over a larger surface area. However, the volumetric model requires experimental validation. Models for simple geometries in contact have been developed for both translational and rotational motion; an apparatus has been developed to experimentally validate these models. This paper focuses on validation of the volumetric friction contact models. Measurements of forces and displacements will be used to identify the parameters related to the friction force, i.e.\ the bristle stiffness and damping, and coefficients of friction for metallic surfaces. The experimental measurements are compared with simulated results to assess the validity of the volumetric friction model.
Transcript of Friction Modelling and Validation for a Volumetric Contact Dynamics Model
MotivationVolumetric Model
ExperimentsConclusions
Friction Modelling and Validation for aVolumetric Contact Dynamics Model
Mike Boos and John McPhee
Department of Systems Design EngineeringUniversity of Waterloo
Canada
May 30, 2012
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 1/ 27
MotivationVolumetric Model
ExperimentsConclusions
Outline
1 Motivation
2 Volumetric ModelVolumetric model frameworkBasic friction model frameworkBristle modelContensou effect
3 ExperimentsOverview and apparatusResults
4 Conclusions
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 2/ 27
MotivationVolumetric Model
ExperimentsConclusions
Outline
1 Motivation
2 Volumetric ModelVolumetric model frameworkBasic friction model frameworkBristle modelContensou effect
3 ExperimentsOverview and apparatusResults
4 Conclusions
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 3/ 27
MotivationVolumetric Model
ExperimentsConclusions
Motivation
Figure: Dextre at the tip of Canadarm2.
Electrical
Connectors
Alignment
Sleeve
Alignment
Pins
Micro Fixture
Coarse
Alignment Bumper
36"28"
12"
Battery WorksiteBattery
Worksite
SPDM
OTCM
Figure: ISS battery box.
(Gonthier, 2007)
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 4/ 27
MotivationVolumetric Model
ExperimentsConclusions
Motivation
Figure: Dextre at the tip of Canadarm2.
Falling ISS battery box:real-time.
(Gonthier, 2007)
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 4/ 27
MotivationVolumetric Model
ExperimentsConclusions
Contact Models
Efficient yet high-fidelitysimulations required
Point contact models
Small contact patches only
Simple, convex geometries
No rolling resistance,spinning friction torque
FEM
Too complex for real-time
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 5/ 27
MotivationVolumetric Model
ExperimentsConclusions
Volumetric model frameworkBasic friction model frameworkBristle modelContensou effect
Outline
1 Motivation
2 Volumetric ModelVolumetric model frameworkBasic friction model frameworkBristle modelContensou effect
3 ExperimentsOverview and apparatusResults
4 Conclusions
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 6/ 27
MotivationVolumetric Model
ExperimentsConclusions
Volumetric model frameworkBasic friction model frameworkBristle modelContensou effect
Volumetric contact dynamics model
Gonthier and McPhee
Larger, more complex, and conforming contact patchespossible
Includes both translational (normal and friction forces) androtational (rolling resistance and spinning friction torque)dynamics
Normal force model validated (Boos and McPhee, 2011)
Friction model validation still required
Tippe-top simulation with volumetric contact model.
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 7/ 27
MotivationVolumetric Model
ExperimentsConclusions
Volumetric model frameworkBasic friction model frameworkBristle modelContensou effect
Volumetric contact dynamics model
Gonthier and McPhee
Larger, more complex, and conforming contact patchespossible
Includes both translational (normal and friction forces) androtational (rolling resistance and spinning friction torque)dynamics
Normal force model validated (Boos and McPhee, 2011)
Friction model validation still required
Tippe-top simulation with volumetric contact model.
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 7/ 27
MotivationVolumetric Model
ExperimentsConclusions
Volumetric model frameworkBasic friction model frameworkBristle modelContensou effect
Volumetric contact dynamics model
Gonthier and McPhee
Larger, more complex, and conforming contact patchespossible
Includes both translational (normal and friction forces) androtational (rolling resistance and spinning friction torque)dynamics
Normal force model validated (Boos and McPhee, 2011)
Friction model validation still required
Tippe-top simulation with volumetric contact model.
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 7/ 27
MotivationVolumetric Model
ExperimentsConclusions
Volumetric model frameworkBasic friction model frameworkBristle modelContensou effect
Volumetric model
B1
B2
fn
kv
Figure: Modified Winkler elasticfoundation model.
B1
B2
n
S
δ(s)
s
Contact plate
Force element
dfn = kvδ(s)n
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 8/ 27
MotivationVolumetric Model
ExperimentsConclusions
Volumetric model frameworkBasic friction model frameworkBristle modelContensou effect
Volumetric model
B1
B2
n
S
δ(s)
s
Contact plate
B1
B2
n
S
pc
sc
ρs ρv
sp
V =∫S δ(s)dS
pc =∫V pdV
V
Js =∫S((ρs ·ρs)I−ρsρs)δ(s)dS
Jv =∫V ((ρv · ρv)I− ρvρv)dV
J{s,v}n = r2gyrV n
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 9/ 27
MotivationVolumetric Model
ExperimentsConclusions
Volumetric model frameworkBasic friction model frameworkBristle modelContensou effect
Volumetric model
B1
B2
n
S
δ(s)
s
Contact plate
B1
B2
n
S
pc
sc
ρs ρv
sp
V =∫S δ(s)dS
pc =∫V pdV
V
Js =∫S((ρs ·ρs)I−ρsρs)δ(s)dS
Jv =∫V ((ρv · ρv)I− ρvρv)dV
J{s,v}n = r2gyrV n
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 9/ 27
MotivationVolumetric Model
ExperimentsConclusions
Volumetric model frameworkBasic friction model frameworkBristle modelContensou effect
Volumetric model
B1
B2
n
S
δ(s)
s
Contact plate
B1
B2
n
S
pc
sc
ρs ρv
sp
V =∫S δ(s)dS
pc =∫V pdV
V
Js =∫S((ρs ·ρs)I−ρsρs)δ(s)dS
Jv =∫V ((ρv · ρv)I− ρvρv)dV
J{s,v}n = r2gyrV n
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 9/ 27
MotivationVolumetric Model
ExperimentsConclusions
Volumetric model frameworkBasic friction model frameworkBristle modelContensou effect
Volumetric model
B1
B2
n
S
δ(s)
s
Contact plate
B1
B2
n
S
pc
sc
ρs ρv
sp
V =∫S δ(s)dS
pc =∫V pdV
V
Js =∫S((ρs ·ρs)I−ρsρs)δ(s)dS
Jv =∫V ((ρv · ρv)I− ρvρv)dV
J{s,v}n = r2gyrV n
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 9/ 27
MotivationVolumetric Model
ExperimentsConclusions
Volumetric model frameworkBasic friction model frameworkBristle modelContensou effect
Volumetric model
B1
B2
n
S
δ(s)
s
Contact plate
B1
B2
n
S
pc
sc
ρs ρv
sp
V =∫S δ(s)dS
pc =∫V pdV
V
Js =∫S((ρs ·ρs)I−ρsρs)δ(s)dS
Jv =∫V ((ρv · ρv)I− ρvρv)dV
J{s,v}n = r2gyrV n
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 9/ 27
MotivationVolumetric Model
ExperimentsConclusions
Volumetric model frameworkBasic friction model frameworkBristle modelContensou effect
Normal Forces
B1
B2
τ s
τ r
fn
f t
dfn = kvδ(s)(1 + a vn)n
a - damping factor
vn - relative normal velocity
Normal force
fn = kvV (1 + a vcn)n
vcn - relative normal velocity atcentroid
Rolling resistance torque
τ r = kv aJs · ωt
ωt - relative tangential angularvelocity
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 10/ 27
MotivationVolumetric Model
ExperimentsConclusions
Volumetric model frameworkBasic friction model frameworkBristle modelContensou effect
Normal Forces
B1
B2
τ s
τ r
fn
f t
dfn = kvδ(s)(1 + a vn)n
a - damping factor
vn - relative normal velocity
Normal force
fn = kvV (1 + a vcn)n
vcn - relative normal velocity atcentroid
Rolling resistance torque
τ r = kv aJs · ωt
ωt - relative tangential angularvelocity
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 10/ 27
MotivationVolumetric Model
ExperimentsConclusions
Volumetric model frameworkBasic friction model frameworkBristle modelContensou effect
Normal Forces
B1
B2
τ s
τ r
fn
f t
dfn = kvδ(s)(1 + a vn)n
a - damping factor
vn - relative normal velocity
Normal force
fn = kvV (1 + a vcn)n
vcn - relative normal velocity atcentroid
Rolling resistance torque
τ r = kv aJs · ωt
ωt - relative tangential angularvelocity
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 10/ 27
MotivationVolumetric Model
ExperimentsConclusions
Volumetric model frameworkBasic friction model frameworkBristle modelContensou effect
Basic friction model
B1
B2
τ s
τ r
fn
f t
df t = −µdfnvt
vt - relative tangential velocity
Friction force
f t = −µ fnvsct
vsct - relative tangentialvelocity at centroid
Spinning friction torque
τ s = −µ r2gyrfnωn
ωn - relative normal angularvelocity
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 11/ 27
MotivationVolumetric Model
ExperimentsConclusions
Volumetric model frameworkBasic friction model frameworkBristle modelContensou effect
Basic friction model
B1
B2
τ s
τ r
fn
f t
df t = −µdfnvt
vt - relative tangential velocity
Friction force
f t = −µ fnvsct
vsct - relative tangentialvelocity at centroid
Spinning friction torque
τ s = −µ r2gyrfnωn
ωn - relative normal angularvelocity
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 11/ 27
MotivationVolumetric Model
ExperimentsConclusions
Volumetric model frameworkBasic friction model frameworkBristle modelContensou effect
Basic friction model
B1
B2
τ s
τ r
fn
f t
df t = −µdfnvt
vt - relative tangential velocity
Friction force
f t = −µ fnvsct
vsct - relative tangentialvelocity at centroid
Spinning friction torque
τ s = −µ r2gyrfnωn
ωn - relative normal angularvelocity
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 11/ 27
MotivationVolumetric Model
ExperimentsConclusions
Volumetric model frameworkBasic friction model frameworkBristle modelContensou effect
Stick-slip state
Average surface velocity
v2avg = vsct · vsct + (rgyr|ωn|)2
Stick-slip state
s = e−
v2avgv2s vs - Stribeck velocity
Maximum friction coefficient
µmax = µC + (µS − µC) sCan add lag to s for dwell time dependency.
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 12/ 27
MotivationVolumetric Model
ExperimentsConclusions
Volumetric model frameworkBasic friction model frameworkBristle modelContensou effect
Stick-slip state
Average surface velocity
v2avg = vsct · vsct + (rgyr|ωn|)2
Stick-slip state
s = e−
v2avgv2s vs - Stribeck velocity
Maximum friction coefficient
µmax = µC + (µS − µC) sCan add lag to s for dwell time dependency.
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 12/ 27
MotivationVolumetric Model
ExperimentsConclusions
Volumetric model frameworkBasic friction model frameworkBristle modelContensou effect
Stick-slip state
Average surface velocity
v2avg = vsct · vsct + (rgyr|ωn|)2
Stick-slip state
s = e−
v2avgv2s vs - Stribeck velocity
Maximum friction coefficient
µmax = µC + (µS − µC) s
Can add lag to s for dwell time dependency.
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 12/ 27
MotivationVolumetric Model
ExperimentsConclusions
Volumetric model frameworkBasic friction model frameworkBristle modelContensou effect
Stick-slip state
Average surface velocity
v2avg = vsct · vsct + (rgyr|ωn|)2
Stick-slip state
s = e−
v2avgv2s vs - Stribeck velocity
Maximum friction coefficient
µmax = µC + (µS − µC) sCan add lag to s for dwell time dependency.
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 12/ 27
MotivationVolumetric Model
ExperimentsConclusions
Volumetric model frameworkBasic friction model frameworkBristle modelContensou effect
Bristle model
fN
Contact sites
Surface asperities (‘bristles’) incontact.
Bristle properties
Deformation: zsc
Rotation: θn
Parameters
Stiffness: σo
Damping: σ1
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 13/ 27
MotivationVolumetric Model
ExperimentsConclusions
Volumetric model frameworkBasic friction model frameworkBristle modelContensou effect
Bristle model
fN
Contact sites
Surface asperities (‘bristles’) incontact.
Bristle properties
Deformation: zsc
Rotation: θn
Parameters
Stiffness: σo
Damping: σ1
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 13/ 27
MotivationVolumetric Model
ExperimentsConclusions
Volumetric model frameworkBasic friction model frameworkBristle modelContensou effect
Tangential friction forces
Friction force
f t = −fn (sat(σo zsc + σ1 zsc, µmax) + σ2 vsct)
Bristle deformation rate
zsc = svsct + (1− s)(1σ1 µC dirε(vsct, vε)− σo
σ1 zsc
)
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 14/ 27
MotivationVolumetric Model
ExperimentsConclusions
Volumetric model frameworkBasic friction model frameworkBristle modelContensou effect
Tangential friction forces
Friction force
f t = −fn (sat(σo zsc + σ1 zsc, µmax) + σ2 vsct)
Bristle deformation rate
zsc = svsct + (1− s)(1σ1 µC dirε(vsct, vε)− σo
σ1 zsc
)
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 14/ 27
MotivationVolumetric Model
ExperimentsConclusions
Volumetric model frameworkBasic friction model frameworkBristle modelContensou effect
Spinning friction torque
Spinning friction torque
τ s = −r2gyr fn(sat(σo θn + σ1 θn,
µmaxrgyr
)+ σ2 ωn
)n
Bristle deformation rate
θn = s ωn + (1− s)(
µCσ1 rgyr sgn(ωn)− σo
σ1 θn
)
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 15/ 27
MotivationVolumetric Model
ExperimentsConclusions
Volumetric model frameworkBasic friction model frameworkBristle modelContensou effect
Spinning friction torque
Spinning friction torque
τ s = −r2gyr fn(sat(σo θn + σ1 θn,
µmaxrgyr
)+ σ2 ωn
)n
Bristle deformation rate
θn = s ωn + (1− s)(
µCσ1 rgyr sgn(ωn)− σo
σ1 θn
)
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 15/ 27
MotivationVolumetric Model
ExperimentsConclusions
Volumetric model frameworkBasic friction model frameworkBristle modelContensou effect
The Contensou effect
Translational friction forcestend to ‘cancel out’ as angularvelocity increases.
Contensou factors
Cv =|vsct|vavg
Cω =rgyr|ωn|vavg
We now need to update theslipping coefficient in ourbristle dyanmics equations toinclude these factors.
C
A Bv
ωvA
vB
vC
vDD
ω r
ω r
ω r
ω r
v << ωr (Gonthier, 2007)
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 16/ 27
MotivationVolumetric Model
ExperimentsConclusions
Volumetric model frameworkBasic friction model frameworkBristle modelContensou effect
The Contensou effect
Translational friction forcestend to ‘cancel out’ as angularvelocity increases.
Contensou factors
Cv =|vsct|vavg
Cω =rgyr|ωn|vavg
We now need to update theslipping coefficient in ourbristle dyanmics equations toinclude these factors.
C
A Bv
ωvA
vB
vC
vDD
ω r
ω r
ω r
ω r
v << ωr (Gonthier, 2007)
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 16/ 27
MotivationVolumetric Model
ExperimentsConclusions
Volumetric model frameworkBasic friction model frameworkBristle modelContensou effect
The Contensou effect
Translational friction forcestend to ‘cancel out’ as angularvelocity increases.
Contensou factors
Cv =|vsct|vavg
Cω =rgyr|ωn|vavg
We now need to update theslipping coefficient in ourbristle dyanmics equations toinclude these factors.
C
A Bv
ωvA
vB
vC
vDD
ω r
ω r
ω r
ω r
v << ωr (Gonthier, 2007)
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 16/ 27
MotivationVolumetric Model
ExperimentsConclusions
Overview and apparatusResults
Outline
1 Motivation
2 Volumetric ModelVolumetric model frameworkBasic friction model frameworkBristle modelContensou effect
3 ExperimentsOverview and apparatusResults
4 Conclusions
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 17/ 27
MotivationVolumetric Model
ExperimentsConclusions
Overview and apparatusResults
Friction force experiments
Identify parameters
Verify parameters Contensou effect
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 18/ 27
MotivationVolumetric Model
ExperimentsConclusions
Overview and apparatusResults
Friction force experiments
Identify parameters Verify parameters
Contensou effect
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 18/ 27
MotivationVolumetric Model
ExperimentsConclusions
Overview and apparatusResults
Friction force experiments
Identify parameters Verify parameters Contensou effect
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 18/ 27
MotivationVolumetric Model
ExperimentsConclusions
Overview and apparatusResults
Friction apparatus
Cylindrical
payload
Rotational
motor
Linear
motor
Encoder
reference
Linear
encoder
3DOF force sensors
Contact
surface
z
y
x
z
y
x
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 19/ 27
MotivationVolumetric Model
ExperimentsConclusions
Overview and apparatusResults
Static friction, tangential motion
Coefficient of static friction
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50
0.05
0.1
0.15
0.2
0.25
Displacement (mm)
Friction o
ver
norm
al fo
rce m
agnitudes
Force measurements
Force measurements adjusted by rotation
Average µS ≈ 0.2
Bristle parameters
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1−0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
Time (s)
Coeffic
ient of fr
ictio
n
Measured coefficients
Model − bristle stiffness only
Model − bristle stiffness and damping
σo ≈ 4500 m−1 σ1 ≈ 300 sm−1
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 20/ 27
MotivationVolumetric Model
ExperimentsConclusions
Overview and apparatusResults
Static friction, tangential motion
Coefficient of static friction
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50
0.05
0.1
0.15
0.2
0.25
Displacement (mm)
Friction o
ver
norm
al fo
rce m
agnitudes
Force measurements
Force measurements adjusted by rotation
Average µS ≈ 0.2
Bristle parameters
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1−0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
Time (s)C
oeffic
ient of fr
ictio
n
Measured coefficients
Model − bristle stiffness only
Model − bristle stiffness and damping
σo ≈ 4500 m−1 σ1 ≈ 300 sm−1
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 20/ 27
MotivationVolumetric Model
ExperimentsConclusions
Overview and apparatusResults
Dynamic friction, tangential motion
Coefficient of kinetic friction
0 1 2 3 4 5 6 7 8 90
0.05
0.1
0.15
0.2
0.25
0.3
0.35
Time (s)
Coeffic
ient of fr
iction
Average µC ≈ 0.2
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 21/ 27
MotivationVolumetric Model
ExperimentsConclusions
Overview and apparatusResults
Rotational motion
Coefficient of static friction
0 0.5 1 1.5 2 2.5−0.05
0
0.05
0.1
0.15
0.2
Rotation (degrees)
Coeffic
ient of fr
iction
Average µS ≈ 0.2
Coefficient of kinetic friction
0 1 2 3 4 5 6 7 8 9 100
0.05
0.1
0.15
0.2
0.25
0.3
0.35
Time (s)
Coeffic
ient of fr
iction
Average µC ≈ 0.2
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 22/ 27
MotivationVolumetric Model
ExperimentsConclusions
Overview and apparatusResults
Rotational motion
Coefficient of static friction
0 0.5 1 1.5 2 2.5−0.05
0
0.05
0.1
0.15
0.2
Rotation (degrees)
Coeffic
ient of fr
iction
Average µS ≈ 0.2
Coefficient of kinetic friction
0 1 2 3 4 5 6 7 8 9 100
0.05
0.1
0.15
0.2
0.25
0.3
0.35
Time (s)C
oeffic
ient of fr
iction
Average µC ≈ 0.2
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 22/ 27
MotivationVolumetric Model
ExperimentsConclusions
Overview and apparatusResults
Contensou effect
Tangential friction force
0 1 2 3 4 50
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
Time (s)
Co
eff
icie
nt
of
Frictio
n
Measured coefficients
Model coefficients
Spinning friction torque
0 1 2 3 4 50
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
Time (s)
Co
eff
icie
nt
of
Frictio
n
Measured coefficients
Model coefficients
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 23/ 27
MotivationVolumetric Model
ExperimentsConclusions
Outline
1 Motivation
2 Volumetric ModelVolumetric model frameworkBasic friction model frameworkBristle modelContensou effect
3 ExperimentsOverview and apparatusResults
4 Conclusions
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 24/ 27
MotivationVolumetric Model
ExperimentsConclusions
Conclusions
Volumetric contact dynamics model discussed
Experimental procedure and apparatus developed for frictionforce parameter identification and validation
Parameters identified and verified for translation and rotation
Contensou effect demonstrated and Contensou factorsvalidated
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 25/ 27
MotivationVolumetric Model
ExperimentsConclusions
Conclusions
Volumetric contact dynamics model discussed
Experimental procedure and apparatus developed for frictionforce parameter identification and validation
Parameters identified and verified for translation and rotation
Contensou effect demonstrated and Contensou factorsvalidated
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 25/ 27
MotivationVolumetric Model
ExperimentsConclusions
Conclusions
Volumetric contact dynamics model discussed
Experimental procedure and apparatus developed for frictionforce parameter identification and validation
Parameters identified and verified for translation and rotation
Contensou effect demonstrated and Contensou factorsvalidated
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 25/ 27
MotivationVolumetric Model
ExperimentsConclusions
Conclusions
Volumetric contact dynamics model discussed
Experimental procedure and apparatus developed for frictionforce parameter identification and validation
Parameters identified and verified for translation and rotation
Contensou effect demonstrated and Contensou factorsvalidated
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 25/ 27
MotivationVolumetric Model
ExperimentsConclusions
Research supported by
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 26/ 27
MotivationVolumetric Model
ExperimentsConclusions
Questions
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 27/ 27
