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

Mike Boos and John McPhee Volumetric Contact Dynamics Models and Validation 7/ 28

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

Mike Boos and John McPhee Volumetric Contact Dynamics Models and Validation 8/ 28

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

Mike Boos and John McPhee Volumetric Contact Dynamics Models and Validation 11/ 28

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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