Volumetric Contact Dynamics Models and Validation

Transcription

1 Volumetric Contact Dynamics s and Validation Mike Boos and John McPhee Department of Systems Design Engineering University of Waterloo Canada May 26, 2010 Mike Boos and John McPhee Volumetric Contact Dynamics s and Validation 1/ 28

2 Outline 1 2 Volumetric model Friction forces 3 Experimental apparatus 4 Quasi-static experiments Dynamic experiments 5 Mike Boos and John McPhee Volumetric Contact Dynamics s and Validation 2/ 28

3 Outline 1 2 Volumetric model Friction forces 3 Experimental apparatus 4 Quasi-static experiments Dynamic experiments 5 Mike Boos and John McPhee Volumetric Contact Dynamics s and Validation 3/ 28

4 Figure: Dextre at the tip of Canadarm2 (Gonthier, 2007). Mike Boos and John McPhee Volumetric Contact Dynamics s and Validation 4/ 28

5 Contact s Electrical Connectors Alignment Sleeve SPDM OTCM 36" Micro Fixture Alignment Pins 28" 12" Coarse Alignment Bumper Point contact models Small contact patches only Simple, convex geometries No rolling resistance, spinning friction torque Battery Battery Worksite FEM Worksite Figure: ISS battery box (Gonthier, 2007). Too complex for real-time Mike Boos and John McPhee Volumetric Contact Dynamics s and Validation 5/ 28

6 Contact s Point contact models Small contact patches only Simple, convex geometries No rolling resistance, spinning friction torque Falling ISS battery box: real-time (Gonthier, 2007) FEM Too complex for real-time Mike Boos and John McPhee Volumetric Contact Dynamics s and Validation 5/ 28

7 Volumetric contact model Ball-table simulation: real-time (Gonthier, 2007) Mike Boos and John McPhee Volumetric Contact Dynamics s and Validation 6/ 28

8 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. Mike Boos and John McPhee Volumetric Contact Dynamics s and Validation 7/ 28

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

10 Goals 1 Experimentally validate the normal force components of the volumetric contact dynamics model 2 Demonstrate parameter identification for this model Mike Boos and John McPhee Volumetric Contact Dynamics s and Validation 8/ 28

11 Outline Volumetric model Friction forces 1 2 Volumetric model Friction forces 3 Experimental apparatus 4 Quasi-static experiments Dynamic experiments 5 Mike Boos and John McPhee Volumetric Contact Dynamics s and Validation 9/ 28

12 Volumetric model Volumetric model Friction forces f N k v Figure: The modified Winkler elastic foundation model (Gonthier, 2007). Mike Boos and John McPhee Volumetric Contact Dynamics s and Validation 10/ 28

13 Volumetric properties Volumetric model Friction forces Bi Kw s fs,j(s) nj 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 n - contact normal J s - surface-inertia tensor J v - volume-inertia tensor Mike Boos and John McPhee Volumetric Contact Dynamics s and Validation 11/ 28

14 Volumetric model Friction forces V Normal force f n = k v V (1 + av cn )n n v cn S Mike Boos and John McPhee Volumetric Contact Dynamics s and Validation 12/ 28

15 Rolling resistance Volumetric model Friction forces V Rolling resistance torque τ r = k v a J s ω t n ω t S Mike Boos and John McPhee Volumetric Contact Dynamics s and Validation 13/ 28

16 Friction Volumetric model Friction forces The model can include tangential friction forces and spinning friction torque. Friction forces (Gonthier et al., 2007) f t = µ c f n v ct v avg τ s = µ cf n V v avg J s ω n Mike Boos and John McPhee Volumetric Contact Dynamics s and Validation 14/ 28

17 Outline Experimental apparatus 1 2 Volumetric model Friction forces 3 Experimental apparatus 4 Quasi-static experiments Dynamic experiments 5 Mike Boos and John McPhee Volumetric Contact Dynamics s and Validation 15/ 28

18 Normal force experiments Experimental apparatus Volumetric stiffness (k v ) Increase force on payload quasi-statically Measure normal forces (f N ) and displacements (δ) V = πr 2 δ f N = k v V Mike Boos and John McPhee Volumetric Contact Dynamics s and Validation 16/ 28

19 Normal force experiments Experimental apparatus Volumetric stiffness (k v ) Increase force on payload quasi-statically Measure normal forces (f N ) and displacements (δ) Damping (a) V = πr 2 δ f N = k v V (1 + av cn ) Drive the payload into contact plate at set velocities Measure forces (f N ) and displacements over time (δ, v cn ) Mike Boos and John McPhee Volumetric Contact Dynamics s and Validation 16/ 28

20 Apparatus Experimental apparatus Cylindrical payload Force sensor Linear encoder Encoder reference Contact surface Mike Boos and John McPhee Volumetric Contact Dynamics s and Validation 17/ 28

21 Outline Quasi-static experiments Dynamic experiments 1 2 Volumetric model Friction forces 3 Experimental apparatus 4 Quasi-static experiments Dynamic experiments 5 Mike Boos and John McPhee Volumetric Contact Dynamics s and Validation 18/ 28

22 Quasi-static results with elastomer Quasi-static experiments Dynamic experiments Measured data fit Relatively low stiffness for elastomer Contact force (N) Volumetric stiffness k v = N/m Displacement (µm) Mike Boos and John McPhee Volumetric Contact Dynamics s and Validation 19/ 28

23 Quasi-static results with aluminum Quasi-static experiments Dynamic experiments Contact force (N) Measured data fit Contact between surface asperities at low pressure for aluminum Volumetric stiffness k v = N/m Displacement (µm) Mike Boos and John McPhee Volumetric Contact Dynamics s and Validation 20/ 28

24 Quasi-static experiments Dynamic experiments Dynamic experiment with elastomer at 2.25 mm/s Displacement (mm) Measured with damping no damping Damping forces are relatively small for elastomer, difficult to estimate damping factor 3.5 Force (N) Damping factor a = 45.4 s/m Time (s) Mike Boos and John McPhee Volumetric Contact Dynamics s and Validation 21/ 28

25 Quasi-static experiments Dynamic experiments Measured damping factors for elastomer Damping factor (s/m) Estimated factors value for α = 21.9 s/m Impact velocity (mm/s) value (Gonthier, 2007) a 1 e2 eff e eff v i n e eff = 1 αv i n Measured damping factors a = 45 ± 15 s/m Mike Boos and John McPhee Volumetric Contact Dynamics s and Validation 22/ 28

26 Outline 1 2 Volumetric model Friction forces 3 Experimental apparatus 4 Quasi-static experiments Dynamic experiments 5 Mike Boos and John McPhee Volumetric Contact Dynamics s and Validation 23/ 28

27 Volumetric contact dynamics model discussed Mike Boos and John McPhee Volumetric Contact Dynamics s and Validation 24/ 28

28 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 s and Validation 24/ 28

29 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 Mike Boos and John McPhee Volumetric Contact Dynamics s and Validation 24/ 28

30 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 Mike Boos and John McPhee Volumetric Contact Dynamics s and Validation 24/ 28

31 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 Mike Boos and John McPhee Volumetric Contact Dynamics s and Validation 24/ 28

32 Future work Damping testing at higher speeds and with aluminum Mike Boos and John McPhee Volumetric Contact Dynamics s and Validation 25/ 28

33 Future work Damping testing at higher speeds and with aluminum Sphere-on-plane contact Mike Boos and John McPhee Volumetric Contact Dynamics s and Validation 25/ 28

34 Future work Damping testing at higher speeds and with aluminum Sphere-on-plane contact Validation of friction contact model for translation and rotation Mike Boos and John McPhee Volumetric Contact Dynamics s and Validation 25/ 28

35 References Y. Gonthier. Contact Dynamics ling for Robotic Task Simulation. PhD thesis, University of Waterloo, 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 Mike Boos and John McPhee Volumetric Contact Dynamics s and Validation 26/ 28

36 Research supported by Mike Boos and John McPhee Volumetric Contact Dynamics s and Validation 27/ 28

37 Questions Mike Boos and John McPhee Volumetric Contact Dynamics s and Validation 28/ 28