The document describes experiments conducted to validate a volumetric contact dynamics model. Quasi-static experiments showed a linear relationship between contact force and volume of interference for an elastomer and aluminum. Dynamic experiments measured damping factors for an elastomer. Future work is planned to test damping at higher speeds and with aluminum.

1. Motivation
Model
Experiments
Results
Conclusions
Volumetric Contact Dynamics
Models and Validation
Mike Boos and John McPhee
Department of Systems Design Engineering
University of Waterloo
Canada
May 26, 2010
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2. Motivation
Model
Experiments
Results
Conclusions
Outline
1 Motivation
2 Model
Volumetric model
Normal forces
Friction forces
3 Experiments
Normal forces
Experimental apparatus
4 Results
Quasi-static experiments
Dynamic experiments
5 Conclusions
Mike Boos and John McPhee Volumetric Contact Dynamics Models and Validation 2/ 28

3. Motivation
Model
Experiments
Results
Conclusions
Outline
1 Motivation
2 Model
Volumetric model
Normal forces
Friction forces
3 Experiments
Normal forces
Experimental apparatus
4 Results
Quasi-static experiments
Dynamic experiments
5 Conclusions
Mike Boos and John McPhee Volumetric Contact Dynamics Models and Validation 3/ 28

4. Motivation
Model
Experiments
Results
Conclusions
Motivation
Figure: Dextre at the tip of Canadarm2 (Gonthier, 2007).
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5. Motivation
Model
Experiments
Results
Conclusions
Contact Models
28"
36"
Micro Fixture 12" Point contact models
Electrical
Connectors
Alignment
Sleeve
Coarse
Alignment Bumper
Small contact patches only
Alignment
Simple, convex geometries
Pins
No rolling resistance,
SPDM
OTCM
spinning friction torque
Battery Worksite
Battery
FEM
Worksite
Too complex for real-time
Figure: ISS battery box (Gonthier,
2007).
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6. Motivation
Model
Experiments
Results
Conclusions
Contact Models
Point contact models
Small contact patches only
Simple, convex geometries
No rolling resistance,
spinning friction torque
FEM
Falling ISS battery box:
Too complex for real-time
real-time (Gonthier, 2007)
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7. Motivation
Model
Experiments
Results
Conclusions
Volumetric contact model
Ball-table simulation: real-time (Gonthier, 2007)
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8. Motivation
Model
Experiments
Results
Conclusions
Volumetric contact model
Advantages
Larger, more complex, and conforming contact patches
possible
Includes both translational (normal and friction forces) and
rotational (rolling resistance and spinning friction torque)
dynamics.
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9. Motivation
Model
Experiments
Results
Conclusions
Volumetric contact model
Advantages
Larger, more complex, and conforming contact patches
possible
Includes both translational (normal and friction forces) and
rotational (rolling resistance and spinning friction torque)
dynamics.
Validation of the model still required
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10. Motivation
Model
Experiments
Results
Conclusions
Goals
1 Experimentally validate the normal force components of the
volumetric contact dynamics model
2 Demonstrate parameter identification for this model
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11. Motivation
Model Volumetric model
Experiments Normal forces
Results Friction forces
Conclusions
Outline
1 Motivation
2 Model
Volumetric model
Normal forces
Friction forces
3 Experiments
Normal forces
Experimental apparatus
4 Results
Quasi-static experiments
Dynamic experiments
5 Conclusions
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12. Motivation
Model Volumetric model
Experiments Normal forces
Results Friction forces
Conclusions
Volumetric model
fN
kv
Figure: The modified Winkler elastic foundation model (Gonthier, 2007).
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13. Motivation
Model Volumetric model
Experiments Normal forces
Results Friction forces
Conclusions
Volumetric properties
Bi
Kw
s nj
fs,j (s)
ni
fs,i (s)
Contact Surface S
Contact Plate Bj
Figure: The contact surface between two deformable bodies (Gonthier
et al., 2007).
Volumetric properties
V - volume of interference Js - surface-inertia tensor
n - contact normal Jv - volume-inertia tensor
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14. Motivation
Model Volumetric model
Experiments Normal forces
Results Friction forces
Conclusions
Normal forces
V
Normal force
vcn
f n = kv V (1 + avcn )n
n
S
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15. Motivation
Model Volumetric model
Experiments Normal forces
Results Friction forces
Conclusions
Rolling resistance
V
Rolling resistance torque
τ r = kv a Js · ω t n
ωt
S
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16. Motivation
Model Volumetric model
Experiments Normal forces
Results Friction forces
Conclusions
Friction
The model can include tangential friction forces and spinning
friction torque.
Friction forces (Gonthier et al., 2007)
vct
f t = −µc fn vavg
µc f
τ s = − V v n Js · ω n
avg
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17. Motivation
Model
Normal forces
Experiments
Experimental apparatus
Results
Conclusions
Outline
1 Motivation
2 Model
Volumetric model
Normal forces
Friction forces
3 Experiments
Normal forces
Experimental apparatus
4 Results
Quasi-static experiments
Dynamic experiments
5 Conclusions
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18. Motivation
Model
Normal forces
Experiments
Experimental apparatus
Results
Conclusions
Normal force experiments
Volumetric stiffness (kv )
Increase force on payload quasi-statically
Measure normal forces (fN ) and
displacements (δ)
V = πr2 δ
fN = kv V
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19. Motivation
Model
Normal forces
Experiments
Experimental apparatus
Results
Conclusions
Normal force experiments
Volumetric stiffness (kv )
Increase force on payload quasi-statically
Measure normal forces (fN ) and
displacements (δ)
Damping (a)
Drive the payload into contact plate at set
V = πr2 δ velocities
fN = kv V (1 + avcn ) Measure forces (fN ) and displacements
over time (δ, vcn )
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20. Motivation
Model
Normal forces
Experiments
Experimental apparatus
Results
Conclusions
Apparatus
Force sensor
Cylindrical payload
Linear
encoder
Encoder reference Contact surface
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21. Motivation
Model
Quasi-static experiments
Experiments
Dynamic experiments
Results
Conclusions
Outline
1 Motivation
2 Model
Volumetric model
Normal forces
Friction forces
3 Experiments
Normal forces
Experimental apparatus
4 Results
Quasi-static experiments
Dynamic experiments
5 Conclusions
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22. Motivation
Model
Quasi-static experiments
Experiments
Dynamic experiments
Results
Conclusions
Quasi-static results with elastomer
4
Measured data
Model fit
3.5
Relatively low stiffness for
3
elastomer
Contact force (N)
2.5
2
Volumetric stiffness
1.5
kv = 2.71 × 108 N/m3
1
0.5
20 40 60 80 100 120 140 160 180
Displacement (µm)
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23. Motivation
Model
Quasi-static experiments
Experiments
Dynamic experiments
Results
Conclusions
Quasi-static results with aluminum
35
Measured data
Model fit
30 Contact between surface
25
asperities at low pressure for
aluminum
Contact force (N)
20
15
Volumetric stiffness
10
kv = 3.16 × 1011 N/m3
5
0
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
Displacement (µm)
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24. Motivation
Model
Quasi-static experiments
Experiments
Dynamic experiments
Results
Conclusions
Dynamic experiment with elastomer at 2.25 mm/s
0.2
Displacement (mm)
0.15
0.1
Damping forces are
0.05 relatively small for
0
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 elastomer, difficult to
5
Measured
estimate damping
4.5 Model with damping
4
Model no damping factor
3.5
3
Force (N)
2.5
2
Damping factor
1.5
1
a = 45.4 s/m
0.5
0
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
Time (s)
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25. Motivation
Model
Quasi-static experiments
Experiments
Dynamic experiments
Results
Conclusions
Measured damping factors for elastomer
60
Model value (Gonthier, 2007)
50
1−e2eff
a≈ i
eeff vn
Damping factor (s/m)
40
i
eeff = 1 − αvn
30
20
Measured damping factors
10
Estimated factors
Model value for α = 21.9 s/m a = 45 ± 15 s/m
0
1.6 1.8 2 2.2 2.4 2.6 2.8 3 3.2
Impact velocity (mm/s)
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26. Motivation
Model
Experiments
Results
Conclusions
Outline
1 Motivation
2 Model
Volumetric model
Normal forces
Friction forces
3 Experiments
Normal forces
Experimental apparatus
4 Results
Quasi-static experiments
Dynamic experiments
5 Conclusions
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27. Motivation
Model
Experiments
Results
Conclusions
Conclusions
Volumetric contact dynamics model discussed
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28. Motivation
Model
Experiments
Results
Conclusions
Conclusions
Volumetric contact dynamics model discussed
Experimental procedure and apparatus developed for normal
force parameter identification and validation
Mike Boos and John McPhee Volumetric Contact Dynamics Models and Validation 24/ 28

29. Motivation
Model
Experiments
Results
Conclusions
Conclusions
Volumetric contact dynamics model discussed
Experimental procedure and apparatus developed for normal
force parameter identification and validation
Quasi-static experiments show linear relationship between
volume of interference and contact force
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30. Motivation
Model
Experiments
Results
Conclusions
Conclusions
Volumetric contact dynamics model discussed
Experimental procedure and apparatus developed for normal
force parameter identification and validation
Quasi-static experiments show linear relationship between
volume of interference and contact force
Non-linearity at low pressure for aluminum likely due to surface
asperities
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31. Motivation
Model
Experiments
Results
Conclusions
Conclusions
Volumetric contact dynamics model discussed
Experimental procedure and apparatus developed for normal
force parameter identification and validation
Quasi-static experiments show linear relationship between
volume of interference and contact force
Non-linearity at low pressure for aluminum likely due to surface
asperities
Damping factors measured for elastomer over a low range of
speeds
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32. Motivation
Model
Experiments
Results
Conclusions
Future work
Damping testing at higher speeds and with aluminum
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33. Motivation
Model
Experiments
Results
Conclusions
Future work
Damping testing at higher speeds and with aluminum
Sphere-on-plane contact
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34. Motivation
Model
Experiments
Results
Conclusions
Future work
Damping testing at higher speeds and with aluminum
Sphere-on-plane contact
Validation of friction contact model for translation and
rotation
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35. Motivation
Model
Experiments
Results
Conclusions
References
Y. Gonthier. Contact Dynamics Modelling for Robotic Task
Simulation. PhD thesis, University of Waterloo, 2007.
Y. Gonthier, J. McPhee, and C. Lange. On the implementation of
coulomb friction in a volumetric-based model for contact
dynamics. In Proceedings of ASME IDETC, Las Vegas, Nevada,
September 2007.
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36. Motivation
Model
Experiments
Results
Conclusions
Research supported by
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37. Motivation
Model
Experiments
Results
Conclusions
Questions
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