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.
Friction Modelling and Validation for a Volumetric Contact Dynamics Model
1. 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
2. Motivation
Volumetric Model
Experiments
Conclusions
Outline
1 Motivation
2 Volumetric Model
Volumetric model framework
Basic friction model framework
Bristle model
Contensou effect
3 Experiments
Overview and apparatus
Results
4 Conclusions
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 2/ 27
3. Motivation
Volumetric Model
Experiments
Conclusions
Outline
1 Motivation
2 Volumetric Model
Volumetric model framework
Basic friction model framework
Bristle model
Contensou effect
3 Experiments
Overview and apparatus
Results
4 Conclusions
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 3/ 27
4. Motivation
Volumetric Model
Experiments
Conclusions
Motivation
28"
36"
Micro Fixture 12"
Electrical
Connectors
Alignment Coarse
Sleeve Alignment Bumper
Alignment
Pins
SPDM
OTCM
Battery Worksite
Battery
Worksite
Figure: Dextre at the tip of Canadarm2. Figure: ISS battery box.
(Gonthier, 2007)
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 4/ 27
5. Motivation
Volumetric Model
Experiments
Conclusions
Motivation
Falling ISS battery box:
real-time.
Figure: Dextre at the tip of Canadarm2.
(Gonthier, 2007)
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 4/ 27
6. Motivation
Volumetric Model
Experiments
Conclusions
Contact Models
Point contact models
Small contact patches only
Simple, convex geometries
Efficient yet high-fidelity No rolling resistance,
simulations required spinning friction torque
FEM
Too complex for real-time
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 5/ 27
7. Motivation Volumetric model framework
Volumetric Model Basic friction model framework
Experiments Bristle model
Conclusions Contensou effect
Outline
1 Motivation
2 Volumetric Model
Volumetric model framework
Basic friction model framework
Bristle model
Contensou effect
3 Experiments
Overview and apparatus
Results
4 Conclusions
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 6/ 27
8. Motivation Volumetric model framework
Volumetric Model Basic friction model framework
Experiments Bristle model
Conclusions Contensou effect
Volumetric contact dynamics model
Gonthier and McPhee
Larger, more complex, and conforming contact patches
possible
Includes both translational (normal and friction forces) and
rotational (rolling resistance and spinning friction torque)
dynamics
Tippe-top simulation with volumetric contact model.
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 7/ 27
9. Motivation Volumetric model framework
Volumetric Model Basic friction model framework
Experiments Bristle model
Conclusions Contensou effect
Volumetric contact dynamics model
Gonthier and McPhee
Larger, more complex, and conforming contact patches
possible
Includes both translational (normal and friction forces) and
rotational (rolling resistance and spinning friction torque)
dynamics
Normal force model validated (Boos and McPhee, 2011)
Tippe-top simulation with volumetric contact model.
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 7/ 27
10. Motivation Volumetric model framework
Volumetric Model Basic friction model framework
Experiments Bristle model
Conclusions Contensou effect
Volumetric contact dynamics model
Gonthier and McPhee
Larger, more complex, and conforming contact patches
possible
Includes both translational (normal and friction forces) and
rotational (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
11. Motivation Volumetric model framework
Volumetric Model Basic friction model framework
Experiments Bristle model
Conclusions Contensou effect
Volumetric model
S
fn
B1
B1
δ(s)
kv s n
Contact plate
B2 B2
Figure: Modified Winkler elastic Force element
foundation model. df n = kv δ(s)n
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 8/ 27
12. Motivation Volumetric model framework
Volumetric Model Basic friction model framework
Experiments Bristle model
Conclusions Contensou effect
Volumetric model
S
S
B1
B1
ρs ρv
δ(s)
s n s n
sc p
Contact plate
pc
B2 B2
V = S δ(s)dS
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 9/ 27
13. Motivation Volumetric model framework
Volumetric Model Basic friction model framework
Experiments Bristle model
Conclusions Contensou effect
Volumetric model
S
S
B1
B1
ρs ρv
δ(s)
s n s n
sc p
Contact plate
pc
B2 B2
V = S δ(s)dS
pdV
pc = V
V
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 9/ 27
14. Motivation Volumetric model framework
Volumetric Model Basic friction model framework
Experiments Bristle model
Conclusions Contensou effect
Volumetric model
S
S
B1
B1
ρs ρv
δ(s)
s n s n
sc p
Contact plate
pc
B2 B2
V = S δ(s)dS Js = S ((ρs ·ρs )I−ρs ρs )δ(s)dS
pdV
pc = V
V
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 9/ 27
15. Motivation Volumetric model framework
Volumetric Model Basic friction model framework
Experiments Bristle model
Conclusions Contensou effect
Volumetric model
S
S
B1
B1
ρs ρv
δ(s)
s n s n
sc p
Contact plate
pc
B2 B2
V = S δ(s)dS Js = S ((ρs ·ρs )I−ρs ρs )δ(s)dS
pdV
pc = V
V Jv = V ((ρv · ρv )I − ρv ρv )dV
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 9/ 27
16. Motivation Volumetric model framework
Volumetric Model Basic friction model framework
Experiments Bristle model
Conclusions Contensou effect
Volumetric model
S
S
B1
B1
ρs ρv
δ(s)
s n s n
sc p
Contact plate
pc
B2 B2
V = S δ(s)dS Js = S ((ρs ·ρs )I−ρs ρs )δ(s)dS
2
J{s,v} n = rgyr V n
pdV
pc = V
V Jv = V ((ρv · ρv )I − ρv ρv )dV
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 9/ 27
17. Motivation Volumetric model framework
Volumetric Model Basic friction model framework
Experiments Bristle model
Conclusions Contensou effect
Normal Forces
df n = kv δ(s)(1 + a vn )n
a - damping factor
vn - relative normal velocity
fn
B1 τs
ft
τr
B2
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 10/ 27
18. Motivation Volumetric model framework
Volumetric Model Basic friction model framework
Experiments Bristle model
Conclusions Contensou effect
Normal Forces
df n = kv δ(s)(1 + a vn )n
a - damping factor
vn - relative normal velocity
fn
Normal force
f n = kv V (1 + a vcn )n
B1 τs
ft
τr vcn - relative normal velocity at
centroid
B2
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 10/ 27
19. Motivation Volumetric model framework
Volumetric Model Basic friction model framework
Experiments Bristle model
Conclusions Contensou effect
Normal Forces
df n = kv δ(s)(1 + a vn )n
a - damping factor
vn - relative normal velocity
fn
Normal force
f n = kv V (1 + a vcn )n
B1 τs
ft
τr vcn - relative normal velocity at
centroid
Rolling resistance torque
B2
τ r = kv a Js · ω t
ω t - relative tangential angular
velocity
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 10/ 27
20. Motivation Volumetric model framework
Volumetric Model Basic friction model framework
Experiments Bristle model
Conclusions Contensou effect
Basic friction model
df t = −µ dfn vt
vt - relative tangential velocity
fn
B1 τs
ft
τr
B2
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 11/ 27
21. Motivation Volumetric model framework
Volumetric Model Basic friction model framework
Experiments Bristle model
Conclusions Contensou effect
Basic friction model
df t = −µ dfn vt
vt - relative tangential velocity
fn Friction force
f t = −µ fn vsct
B1 τs
ft
vsct - relative tangential
τr velocity at centroid
B2
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 11/ 27
22. Motivation Volumetric model framework
Volumetric Model Basic friction model framework
Experiments Bristle model
Conclusions Contensou effect
Basic friction model
df t = −µ dfn vt
vt - relative tangential velocity
fn Friction force
f t = −µ fn vsct
B1 τs
ft
vsct - relative tangential
τr velocity at centroid
Spinning friction torque
B2 2
τ s = −µ rgyr fn ω n
ω n - relative normal angular
velocity
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 11/ 27
23. Motivation Volumetric model framework
Volumetric Model Basic friction model framework
Experiments Bristle model
Conclusions Contensou effect
Stick-slip state
Average surface velocity
vavg = vsct · vsct + (rgyr |ω n |)2
2
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 12/ 27
24. Motivation Volumetric model framework
Volumetric Model Basic friction model framework
Experiments Bristle model
Conclusions Contensou effect
Stick-slip state
Average surface velocity
vavg = vsct · vsct + (rgyr |ω n |)2
2
Stick-slip state
2
vavg
−
v2
s=e s vs - Stribeck velocity
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 12/ 27
25. Motivation Volumetric model framework
Volumetric Model Basic friction model framework
Experiments Bristle model
Conclusions Contensou effect
Stick-slip state
Average surface velocity
vavg = vsct · vsct + (rgyr |ω n |)2
2
Stick-slip state
2
vavg
−
v2
s=e s vs - Stribeck velocity
Maximum friction coefficient
µmax = µC + (µS − µC ) s
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 12/ 27
26. Motivation Volumetric model framework
Volumetric Model Basic friction model framework
Experiments Bristle model
Conclusions Contensou effect
Stick-slip state
Average surface velocity
vavg = vsct · vsct + (rgyr |ω n |)2
2
Stick-slip state
2
vavg
−
v2
s=e s 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
27. Motivation Volumetric model framework
Volumetric Model Basic friction model framework
Experiments Bristle model
Conclusions Contensou effect
Bristle model
fN
Bristle properties
Deformation: zsc
Rotation: θn
Contact sites
Surface asperities (‘bristles’) in
contact.
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 13/ 27
28. Motivation Volumetric model framework
Volumetric Model Basic friction model framework
Experiments Bristle model
Conclusions Contensou effect
Bristle model
fN
Bristle properties
Deformation: zsc
Rotation: θn
Parameters
Stiffness: σo
Contact sites
Damping: σ1
Surface asperities (‘bristles’) in
contact.
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 13/ 27
29. Motivation Volumetric model framework
Volumetric Model Basic friction model framework
Experiments Bristle model
Conclusions Contensou effect
Tangential friction forces
Friction force
f t = −fn (sat(σo zsc + σ1 zsc , µmax ) + σ2 vsct )
˙
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 14/ 27
30. Motivation Volumetric model framework
Volumetric Model Basic friction model framework
Experiments Bristle model
Conclusions Contensou effect
Tangential friction forces
Friction force
f t = −fn (sat(σo zsc + σ1 zsc , µmax ) + σ2 vsct )
˙
Bristle deformation rate
1 σo
zsc = s vsct + (1 − s) σ1 µC dir (vsct , v ) − σ1 zsc
˙
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 14/ 27
31. Motivation Volumetric model framework
Volumetric Model Basic friction model framework
Experiments Bristle model
Conclusions Contensou effect
Spinning friction torque
Spinning friction torque
2 ˙ µ
τ s = −rgyr fn sat σo θn + σ1 θn , rmax + σ2 ωn n
gyr
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 15/ 27
32. Motivation Volumetric model framework
Volumetric Model Basic friction model framework
Experiments Bristle model
Conclusions Contensou effect
Spinning friction torque
Spinning friction torque
2 ˙ µ
τ s = −rgyr fn sat σo θn + σ1 θn , rmax + σ2 ωn n
gyr
Bristle deformation rate
µC
θn = s ωn + (1 − s) σ1 rgyr sgn(ωn ) − σo θn
˙
σ1
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 15/ 27
33. Motivation Volumetric model framework
Volumetric Model Basic friction model framework
Experiments Bristle model
Conclusions Contensou effect
The Contensou effect
Translational friction forces vC
tend to ‘cancel out’ as angular ωr
C
velocity increases.
vB
ωr
v
A B
vA
ωr ω
vD
D
ωr
v << ωr (Gonthier, 2007)
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 16/ 27
34. Motivation Volumetric model framework
Volumetric Model Basic friction model framework
Experiments Bristle model
Conclusions Contensou effect
The Contensou effect
Translational friction forces vC
tend to ‘cancel out’ as angular ωr
C
velocity increases.
vB
ωr
Contensou factors
v
|vsct | rgyr |ωn | A B
Cv = vavg Cω = vavg vA
ωr ω
vD
D
ωr
v << ωr (Gonthier, 2007)
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 16/ 27
35. Motivation Volumetric model framework
Volumetric Model Basic friction model framework
Experiments Bristle model
Conclusions Contensou effect
The Contensou effect
Translational friction forces vC
tend to ‘cancel out’ as angular ωr
C
velocity increases.
vB
ωr
Contensou factors
v
|vsct | rgyr |ωn | A B
Cv = vavg Cω = vavg vA
ωr ω
We now need to update the D
vD
slipping coefficient in our ωr
bristle dyanmics equations to
v << ωr (Gonthier, 2007)
include these factors.
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 16/ 27
36. Motivation
Volumetric Model Overview and apparatus
Experiments Results
Conclusions
Outline
1 Motivation
2 Volumetric Model
Volumetric model framework
Basic friction model framework
Bristle model
Contensou effect
3 Experiments
Overview and apparatus
Results
4 Conclusions
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 17/ 27
37. Motivation
Volumetric Model Overview and apparatus
Experiments Results
Conclusions
Friction force experiments
Identify parameters
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 18/ 27
38. Motivation
Volumetric Model Overview and apparatus
Experiments Results
Conclusions
Friction force experiments
Identify parameters Verify parameters
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 18/ 27
39. Motivation
Volumetric Model Overview and apparatus
Experiments Results
Conclusions
Friction force experiments
Identify parameters Verify parameters Contensou effect
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 18/ 27
40. Motivation
Volumetric Model Overview and apparatus
Experiments Results
Conclusions
Friction apparatus
Rotational
motor
Linear
motor
Linear
Cylindrical encoder
payload
Contact Encoder
surface reference
x x
y y
z 3DOF force sensors z
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 19/ 27
41. Motivation
Volumetric Model Overview and apparatus
Experiments Results
Conclusions
Static friction, tangential motion
Coefficient of static friction
0.25
Force measurements
Force measurements adjusted by rotation
0.2
Friction over normal force magnitudes
0.15
0.1
0.05
0
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Displacement (mm)
Average µS ≈ 0.2
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 20/ 27
42. Motivation
Volumetric Model Overview and apparatus
Experiments Results
Conclusions
Static friction, tangential motion
Coefficient of static friction Bristle parameters
0.25 0.3
Force measurements Measured coefficients
Force measurements adjusted by rotation Model − bristle stiffness only
0.25 Model − bristle stiffness and damping
0.2
Friction over normal force magnitudes
0.2
Coefficient of friction
0.15
0.15
0.1 0.1
0.05
0.05
0
0 −0.05
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Displacement (mm) Time (s)
Average µS ≈ 0.2 σo ≈ 4500 m−1 σ1 ≈ 300 sm−1
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 20/ 27
43. Motivation
Volumetric Model Overview and apparatus
Experiments Results
Conclusions
Dynamic friction, tangential motion
Coefficient of kinetic friction
0.35
0.3
Coefficient of friction
0.25
0.2
0.15
0.1
0.05
0
0 1 2 3 4 5 6 7 8 9
Time (s)
Average µC ≈ 0.2
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 21/ 27
44. Motivation
Volumetric Model Overview and apparatus
Experiments Results
Conclusions
Rotational motion
Coefficient of static friction
0.2
0.15
Coefficient of friction
0.1
0.05
0
−0.05
0 0.5 1 1.5 2 2.5
Rotation (degrees)
Average µS ≈ 0.2
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 22/ 27
45. Motivation
Volumetric Model Overview and apparatus
Experiments Results
Conclusions
Rotational motion
Coefficient of static friction Coefficient of kinetic friction
0.2 0.35
0.3
0.15
0.25
Coefficient of friction
Coefficient of friction
0.1
0.2
0.15
0.05
0.1
0
0.05
−0.05 0
0 0.5 1 1.5 2 2.5 0 1 2 3 4 5 6 7 8 9 10
Rotation (degrees) Time (s)
Average µS ≈ 0.2 Average µC ≈ 0.2
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 22/ 27
46. Motivation
Volumetric Model Overview and apparatus
Experiments Results
Conclusions
Contensou effect
Tangential friction force Spinning friction torque
0.45 0.45
Measured coefficients Measured coefficients
0.4 Model coefficients 0.4 Model coefficients
0.35 0.35
Coefficient of Friction
Coefficient of Friction
0.3 0.3
0.25 0.25
0.2 0.2
0.15 0.15
0.1 0.1
0.05 0.05
0 0
0 1 2 3 4 5 0 1 2 3 4 5
Time (s) Time (s)
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 23/ 27
47. Motivation
Volumetric Model
Experiments
Conclusions
Outline
1 Motivation
2 Volumetric Model
Volumetric model framework
Basic friction model framework
Bristle model
Contensou effect
3 Experiments
Overview and apparatus
Results
4 Conclusions
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 24/ 27
48. Motivation
Volumetric Model
Experiments
Conclusions
Conclusions
Volumetric contact dynamics model discussed
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 25/ 27
49. Motivation
Volumetric Model
Experiments
Conclusions
Conclusions
Volumetric contact dynamics model discussed
Experimental procedure and apparatus developed for friction
force parameter identification and validation
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 25/ 27
50. Motivation
Volumetric Model
Experiments
Conclusions
Conclusions
Volumetric contact dynamics model discussed
Experimental procedure and apparatus developed for friction
force parameter identification and validation
Parameters identified and verified for translation and rotation
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 25/ 27
51. Motivation
Volumetric Model
Experiments
Conclusions
Conclusions
Volumetric contact dynamics model discussed
Experimental procedure and apparatus developed for friction
force parameter identification and validation
Parameters identified and verified for translation and rotation
Contensou effect demonstrated and Contensou factors
validated
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 25/ 27
52. Motivation
Volumetric Model
Experiments
Conclusions
Research supported by
Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 26/ 27
53. Motivation
Volumetric Model
Experiments
Conclusions
Questions
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