MotivationModel
ExperimentsResults
Conclusions
Volumetric Contact DynamicsModels and Validation
Mike Boos and John McPhee
Department of Systems Design EngineeringUniversity of Waterloo
Canada
May 26, 2010
Mike Boos and John McPhee Volumetric Contact Dynamics Models and Validation 1/ 28
MotivationModel
ExperimentsResults
Conclusions
Outline
1 Motivation
2 ModelVolumetric modelNormal forcesFriction forces
3 ExperimentsNormal forcesExperimental apparatus
4 ResultsQuasi-static experimentsDynamic experiments
5 Conclusions
Mike Boos and John McPhee Volumetric Contact Dynamics Models and Validation 2/ 28
MotivationModel
ExperimentsResults
Conclusions
Outline
1 Motivation
2 ModelVolumetric modelNormal forcesFriction forces
3 ExperimentsNormal forcesExperimental apparatus
4 ResultsQuasi-static experimentsDynamic experiments
5 Conclusions
Mike Boos and John McPhee Volumetric Contact Dynamics Models and Validation 3/ 28
MotivationModel
ExperimentsResults
Conclusions
Motivation
Figure: Dextre at the tip of Canadarm2 (Gonthier, 2007).
Mike Boos and John McPhee Volumetric Contact Dynamics Models and Validation 4/ 28
MotivationModel
ExperimentsResults
Conclusions
Contact Models
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).
Point contact models
Small contact patches only
Simple, convex geometries
No rolling resistance,spinning friction torque
FEM
Too complex for real-time
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MotivationModel
ExperimentsResults
Conclusions
Contact Models
Falling ISS battery box:real-time (Gonthier, 2007)
Point contact models
Small contact patches only
Simple, convex geometries
No rolling resistance,spinning friction torque
FEM
Too complex for real-time
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MotivationModel
ExperimentsResults
Conclusions
Volumetric contact model
Ball-table simulation: real-time (Gonthier, 2007)
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MotivationModel
ExperimentsResults
Conclusions
Volumetric contact model
Advantages
Larger, more complex, and conforming contact patchespossible
Includes both translational (normal and friction forces) androtational (rolling resistance and spinning friction torque)dynamics.
Validation of the model still required
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MotivationModel
ExperimentsResults
Conclusions
Volumetric contact model
Advantages
Larger, more complex, and conforming contact patchespossible
Includes both translational (normal and friction forces) androtational (rolling resistance and spinning friction torque)dynamics.
Validation of the model still required
Mike Boos and John McPhee Volumetric Contact Dynamics Models and Validation 7/ 28
MotivationModel
ExperimentsResults
Conclusions
Goals
1 Experimentally validate the normal force components of thevolumetric contact dynamics model
2 Demonstrate parameter identification for this model
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MotivationModel
ExperimentsResults
Conclusions
Volumetric modelNormal forcesFriction forces
Outline
1 Motivation
2 ModelVolumetric modelNormal forcesFriction forces
3 ExperimentsNormal forcesExperimental apparatus
4 ResultsQuasi-static experimentsDynamic experiments
5 Conclusions
Mike Boos and John McPhee Volumetric Contact Dynamics Models and Validation 9/ 28
MotivationModel
ExperimentsResults
Conclusions
Volumetric modelNormal forcesFriction forces
Volumetric model
fN
kv
Figure: The modified Winkler elastic foundation model (Gonthier, 2007).
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MotivationModel
ExperimentsResults
Conclusions
Volumetric modelNormal forcesFriction forces
Volumetric properties
nj
Kw
fs,j(s)
fs,i(s)
Contact Surface S
Contact Plate
ni
s
Bi
Bj
Figure: The contact surface between two deformable bodies (Gonthieret al., 2007).
Volumetric properties
V - volume of interference Js - surface-inertia tensorn - contact normal Jv - volume-inertia tensor
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MotivationModel
ExperimentsResults
Conclusions
Volumetric modelNormal forcesFriction forces
Normal forces
Normal force
fn = kvV (1 + avcn)nn
V
S
vcn
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MotivationModel
ExperimentsResults
Conclusions
Volumetric modelNormal forcesFriction forces
Rolling resistance
Rolling resistance torque
τ r = kv aJs · ωtn
V
S
ωt
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MotivationModel
ExperimentsResults
Conclusions
Volumetric modelNormal forcesFriction forces
Friction
The model can include tangential friction forces and spinningfriction torque.
Friction forces (Gonthier et al., 2007)
f t = −µcfn vctvavg
τ s = − µcfnV vavg
Js · ωn
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MotivationModel
ExperimentsResults
Conclusions
Normal forcesExperimental apparatus
Outline
1 Motivation
2 ModelVolumetric modelNormal forcesFriction forces
3 ExperimentsNormal forcesExperimental apparatus
4 ResultsQuasi-static experimentsDynamic experiments
5 Conclusions
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MotivationModel
ExperimentsResults
Conclusions
Normal forcesExperimental apparatus
Normal force experiments
V = πr2δ
fN = kvV
Volumetric stiffness (kv)
Increase force on payload quasi-statically
Measure normal forces (fN ) anddisplacements (δ)
Damping (a)
Drive the payload into contact plate at setvelocities
Measure forces (fN ) and displacementsover time (δ, vcn)
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MotivationModel
ExperimentsResults
Conclusions
Normal forcesExperimental apparatus
Normal force experiments
V = πr2δ
fN = kvV (1 + avcn)
Volumetric stiffness (kv)
Increase force on payload quasi-statically
Measure normal forces (fN ) anddisplacements (δ)
Damping (a)
Drive the payload into contact plate at setvelocities
Measure forces (fN ) and displacementsover time (δ, vcn)
Mike Boos and John McPhee Volumetric Contact Dynamics Models and Validation 16/ 28
MotivationModel
ExperimentsResults
Conclusions
Normal forcesExperimental apparatus
Apparatus
Force sensorCylindrical payload
Encoder reference Contact surface
Linear
encoder
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MotivationModel
ExperimentsResults
Conclusions
Quasi-static experimentsDynamic experiments
Outline
1 Motivation
2 ModelVolumetric modelNormal forcesFriction forces
3 ExperimentsNormal forcesExperimental apparatus
4 ResultsQuasi-static experimentsDynamic experiments
5 Conclusions
Mike Boos and John McPhee Volumetric Contact Dynamics Models and Validation 18/ 28
MotivationModel
ExperimentsResults
Conclusions
Quasi-static experimentsDynamic experiments
Quasi-static results with elastomer
20 40 60 80 100 120 140 160 1800.5
1
1.5
2
2.5
3
3.5
4
Displacement (µm)
Con
tact
forc
e (N
)
Measured dataModel fit
Relatively low stiffness forelastomer
Volumetric stiffness
kv = 2.71× 108N/m3
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MotivationModel
ExperimentsResults
Conclusions
Quasi-static experimentsDynamic experiments
Quasi-static results with aluminum
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.80
5
10
15
20
25
30
35
Displacement (µm)
Con
tact
forc
e (N
)
Measured dataModel fit
Contact between surfaceasperities at low pressure foraluminum
Volumetric stiffness
kv = 3.16× 1011N/m3
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MotivationModel
ExperimentsResults
Conclusions
Quasi-static experimentsDynamic experiments
Dynamic experiment with elastomer at 2.25 mm/s
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.090
0.05
0.1
0.15
0.2
Dis
plac
emen
t (m
m)
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Time (s)
For
ce (
N)
MeasuredModel with dampingModel no damping
Damping forces arerelatively small forelastomer, difficult toestimate dampingfactor
Damping factor
a = 45.4 s/m
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MotivationModel
ExperimentsResults
Conclusions
Quasi-static experimentsDynamic experiments
Measured damping factors for elastomer
1.6 1.8 2 2.2 2.4 2.6 2.8 3 3.20
10
20
30
40
50
60
Impact velocity (mm/s)
Dam
ping
fact
or (
s/m
)
Estimated factorsModel value for α = 21.9 s/m
Model value (Gonthier, 2007)
a ≈ 1−e2eff
eeff vin
eeff = 1− αvin
Measured damping factors
a = 45± 15 s/m
Mike Boos and John McPhee Volumetric Contact Dynamics Models and Validation 22/ 28
MotivationModel
ExperimentsResults
Conclusions
Outline
1 Motivation
2 ModelVolumetric modelNormal forcesFriction forces
3 ExperimentsNormal forcesExperimental apparatus
4 ResultsQuasi-static experimentsDynamic experiments
5 Conclusions
Mike Boos and John McPhee Volumetric Contact Dynamics Models and Validation 23/ 28
MotivationModel
ExperimentsResults
Conclusions
Conclusions
Volumetric contact dynamics model discussed
Experimental procedure and apparatus developed for normalforce parameter identification and validation
Quasi-static experiments show linear relationship betweenvolume of interference and contact force
Non-linearity at low pressure for aluminum likely due to surfaceasperities
Damping factors measured for elastomer over a low range ofspeeds
Mike Boos and John McPhee Volumetric Contact Dynamics Models and Validation 24/ 28
MotivationModel
ExperimentsResults
Conclusions
Conclusions
Volumetric contact dynamics model discussed
Experimental procedure and apparatus developed for normalforce parameter identification and validation
Quasi-static experiments show linear relationship betweenvolume of interference and contact force
Non-linearity at low pressure for aluminum likely due to surfaceasperities
Damping factors measured for elastomer over a low range ofspeeds
Mike Boos and John McPhee Volumetric Contact Dynamics Models and Validation 24/ 28
MotivationModel
ExperimentsResults
Conclusions
Conclusions
Volumetric contact dynamics model discussed
Experimental procedure and apparatus developed for normalforce parameter identification and validation
Quasi-static experiments show linear relationship betweenvolume of interference and contact force
Non-linearity at low pressure for aluminum likely due to surfaceasperities
Damping factors measured for elastomer over a low range ofspeeds
Mike Boos and John McPhee Volumetric Contact Dynamics Models and Validation 24/ 28
MotivationModel
ExperimentsResults
Conclusions
Conclusions
Volumetric contact dynamics model discussed
Experimental procedure and apparatus developed for normalforce parameter identification and validation
Quasi-static experiments show linear relationship betweenvolume of interference and contact force
Non-linearity at low pressure for aluminum likely due to surfaceasperities
Damping factors measured for elastomer over a low range ofspeeds
Mike Boos and John McPhee Volumetric Contact Dynamics Models and Validation 24/ 28
MotivationModel
ExperimentsResults
Conclusions
Conclusions
Volumetric contact dynamics model discussed
Experimental procedure and apparatus developed for normalforce parameter identification and validation
Quasi-static experiments show linear relationship betweenvolume of interference and contact force
Non-linearity at low pressure for aluminum likely due to surfaceasperities
Damping factors measured for elastomer over a low range ofspeeds
Mike Boos and John McPhee Volumetric Contact Dynamics Models and Validation 24/ 28
MotivationModel
ExperimentsResults
Conclusions
Future work
Damping testing at higher speeds and with aluminum
Sphere-on-plane contact
Validation of friction contact model for translation androtation
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MotivationModel
ExperimentsResults
Conclusions
Future work
Damping testing at higher speeds and with aluminum
Sphere-on-plane contact
Validation of friction contact model for translation androtation
Mike Boos and John McPhee Volumetric Contact Dynamics Models and Validation 25/ 28
MotivationModel
ExperimentsResults
Conclusions
Future work
Damping testing at higher speeds and with aluminum
Sphere-on-plane contact
Validation of friction contact model for translation androtation
Mike Boos and John McPhee Volumetric Contact Dynamics Models and Validation 25/ 28
MotivationModel
ExperimentsResults
Conclusions
References
Y. Gonthier. Contact Dynamics Modelling for Robotic TaskSimulation. PhD thesis, University of Waterloo, 2007.
Y. Gonthier, J. McPhee, and C. Lange. On the implementation ofcoulomb friction in a volumetric-based model for contactdynamics. In Proceedings of ASME IDETC, Las Vegas, Nevada,September 2007.
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MotivationModel
ExperimentsResults
Conclusions
Research supported by
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MotivationModel
ExperimentsResults
Conclusions
Questions
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