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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 Mike Boos and John McPhee Friction for a Volumetric Contact Dynamics Model 27/ 27