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Friction Modelling and Validation for a Volumetric Contact Dynamics Model
Friction Modelling and Validation for a Volumetric Contact Dynamics Model
Friction Modelling and Validation for a Volumetric Contact Dynamics Model
Friction Modelling and Validation for a Volumetric Contact Dynamics Model
Friction Modelling and Validation for a Volumetric Contact Dynamics Model
Friction Modelling and Validation for a Volumetric Contact Dynamics Model
Friction Modelling and Validation for a Volumetric Contact Dynamics Model
Friction Modelling and Validation for a Volumetric Contact Dynamics Model
Friction Modelling and Validation for a Volumetric Contact Dynamics Model
Friction Modelling and Validation for a Volumetric Contact Dynamics Model
Friction Modelling and Validation for a Volumetric Contact Dynamics Model
Friction Modelling and Validation for a Volumetric Contact Dynamics Model
Friction Modelling and Validation for a Volumetric Contact Dynamics Model
Friction Modelling and Validation for a Volumetric Contact Dynamics Model
Friction Modelling and Validation for a Volumetric Contact Dynamics Model
Friction Modelling and Validation for a Volumetric Contact Dynamics Model
Friction Modelling and Validation for a Volumetric Contact Dynamics Model
Friction Modelling and Validation for a Volumetric Contact Dynamics Model
Friction Modelling and Validation for a Volumetric Contact Dynamics Model
Friction Modelling and Validation for a Volumetric Contact Dynamics Model
Friction Modelling and Validation for a Volumetric Contact Dynamics Model
Friction Modelling and Validation for a Volumetric Contact Dynamics Model
Friction Modelling and Validation for a Volumetric Contact Dynamics Model
Friction Modelling and Validation for a Volumetric Contact Dynamics Model
Friction Modelling and Validation for a Volumetric Contact Dynamics Model
Friction Modelling and Validation for a Volumetric Contact Dynamics Model
Friction Modelling and Validation for a Volumetric Contact Dynamics Model
Friction Modelling and Validation for a Volumetric Contact Dynamics Model
Friction Modelling and Validation for a Volumetric Contact Dynamics Model
Friction Modelling and Validation for a Volumetric Contact Dynamics Model
Friction Modelling and Validation for a Volumetric Contact Dynamics Model
Friction Modelling and Validation for a Volumetric Contact Dynamics Model
Friction Modelling and Validation for a Volumetric Contact Dynamics Model
Friction Modelling and Validation for a Volumetric Contact Dynamics Model
Friction Modelling and Validation for a Volumetric Contact Dynamics Model
Friction Modelling and Validation for a Volumetric Contact Dynamics Model
Friction Modelling and Validation for a Volumetric Contact Dynamics Model
Friction Modelling and Validation for a Volumetric Contact Dynamics Model
Friction Modelling and Validation for a Volumetric Contact Dynamics Model
Friction Modelling and Validation for a Volumetric Contact Dynamics Model
Friction Modelling and Validation for a Volumetric Contact Dynamics Model
Friction Modelling and Validation for a Volumetric Contact Dynamics Model
Friction Modelling and Validation for a Volumetric Contact Dynamics Model
Friction Modelling and Validation for a Volumetric Contact Dynamics Model
Friction Modelling and Validation for a Volumetric Contact Dynamics Model
Friction Modelling and Validation for a Volumetric Contact Dynamics Model
Friction Modelling and Validation for a Volumetric Contact Dynamics Model
Friction Modelling and Validation for a Volumetric Contact Dynamics Model
Friction Modelling and Validation for a Volumetric Contact Dynamics Model
Friction Modelling and Validation for a Volumetric Contact Dynamics Model
Friction Modelling and Validation for a Volumetric Contact Dynamics Model
Friction Modelling and Validation for a Volumetric Contact Dynamics Model
Friction Modelling and Validation for a Volumetric Contact Dynamics Model
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Friction Modelling and Validation for a Volumetric Contact Dynamics Model

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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 …

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.

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  • 1. Motivation Volumetric Model Experiments ConclusionsFriction 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 ConclusionsOutline 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 ConclusionsOutline 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 ConclusionsMotivation 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 ConclusionsMotivation 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 ConclusionsContact 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 effectOutline 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 effectVolumetric 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 effectVolumetric 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 effectVolumetric 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 effectVolumetric model S fn B1 B1 δ(s) kv s n Contact plate B2 B2Figure: Modified Winkler elastic Force elementfoundation 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 effectVolumetric model S S B1 B1 ρs ρv δ(s) s n s n sc p Contact plate pc B2 B2V = 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 effectVolumetric model S S B1 B1 ρs ρv δ(s) s n s n sc p Contact plate pc B2 B2V = S δ(s)dS pdVpc = 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 effectVolumetric model S S B1 B1 ρs ρv δ(s) s n s n sc p Contact plate pc B2 B2V = S δ(s)dS Js = S ((ρs ·ρs )I−ρs ρs )δ(s)dS pdVpc = 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 effectVolumetric model S S B1 B1 ρs ρv δ(s) s n s n sc p Contact plate pc B2 B2V = S δ(s)dS Js = S ((ρs ·ρs )I−ρs ρs )δ(s)dS pdVpc = 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 effectVolumetric model S S B1 B1 ρs ρv δ(s) s n s n sc p Contact plate pc B2 B2V = S δ(s)dS Js = S ((ρs ·ρs )I−ρs ρs )δ(s)dS 2 J{s,v} n = rgyr V n pdVpc = 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 effectNormal 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 effectNormal 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 effectNormal 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 effectBasic 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 effectBasic 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 effectBasic 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 effectStick-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 effectStick-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 effectStick-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 effectStick-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 effectBristle model fN Bristle properties Deformation: zsc Rotation: θn Contact sitesSurface asperities (‘bristles’) incontact. 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 effectBristle model fN Bristle properties Deformation: zsc Rotation: θn Parameters Stiffness: σo Contact sites Damping: σ1Surface asperities (‘bristles’) incontact. 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 effectTangential 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 effectTangential 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 effectSpinning 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 effectSpinning 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 effectThe 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 effectThe 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 effectThe 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 ConclusionsOutline 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 ConclusionsFriction 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 ConclusionsFriction 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 ConclusionsFriction 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 ConclusionsFriction 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 ConclusionsStatic 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 ConclusionsStatic 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 ConclusionsDynamic 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 ConclusionsRotational motionCoefficient 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 ConclusionsRotational motionCoefficient 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 ConclusionsContensou effectTangential 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 ConclusionsOutline 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 ConclusionsConclusions Volumetric contact dynamics model discussed Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 25/ 27
  • 49. Motivation Volumetric Model Experiments ConclusionsConclusions 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 ConclusionsConclusions 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 ConclusionsConclusions 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 ConclusionsResearch supported by Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 26/ 27
  • 53. Motivation Volumetric Model Experiments ConclusionsQuestions Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 27/ 27

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