1. Cam-follower systems: experiments and simulations by Ricardo Alzate University of Naples – Federico II WP6: Applications

2. Cam-follower systems: experiments and simulations 2 Outline Introduction System description (experimental set-up) Mathematical modeling Typical dynamics Remarks and ongoing work

3. Cam-follower systems: experiments and simulations 3 Outline Introduction System description (experimental set-up) Mathematical modeling Typical dynamics Remarks and ongoing work

4. Cam-follower systems: experiments and simulations 4 Introduction [Norton02] “… A cam-follower system could be seen, as the predefined translation of a rigid body (called follower) as a consequence of a forcing imposing by a specially shaped piece of metal or other material (called cam). In other words the cam profile can be understood as a control action over the follower state …”

5. Cam-follower systems: experiments and simulations 5 Introduction A cam-follower system Taken from http://www.ul.iehttp://www.ul.ie

6. Cam-follower systems: experiments and simulations 6 Introduction Cam-follower systems general and relevant benchmark problem The most common application Internal combustion engines (ICE)

7. Cam-follower systems: experiments and simulations 7 Introduction The 4 stroke engine 1 - Intake 2 - Compression 3 - Combustion 4 - Exhaust Taken from http://en.wikipedia.orghttp://en.wikipedia.org

8. Cam-follower systems: experiments and simulations 8 Introduction Engine performance Mechanical parts in close contact Speed increasing: valve floating bouncing

9. Cam-follower systems: experiments and simulations 9 Introduction Illustration of a cam-shaft based engine Taken from http://en.wikipedia.orghttp://en.wikipedia.org

10. Cam-follower systems: experiments and simulations 10 Introduction Illustration of the valve-floating phenomenon Taken from http://www.ul.iehttp://www.ul.ie

11. Cam-follower systems: experiments and simulations 11 Introduction Damage: a piston striking a valve

12. Cam-follower systems: experiments and simulations 12 Introduction Spring forced disadvantages wear of pieces (friction) valve timing desmodromic valves

13. Cam-follower systems: experiments and simulations 13 Introduction Cam-follower = impact oscillator Complex behaviour (transition to chaos) Experimental validation of theoretical bifurcation based analysis To apply nonlinear control techniques

14. Cam-follower systems: experiments and simulations 14 Outline Introduction System description (experimental set-up) Mathematical modeling Typical dynamics Remarks and ongoing work

15. Cam-follower systems: experiments and simulations 15 System description

16. Cam-follower systems: experiments and simulations 16 System description

17. Cam-follower systems: experiments and simulations 17 System description

18. Cam-follower systems: experiments and simulations 18 System description

19. Cam-follower systems: experiments and simulations 19 System description Lumped parameter single degree of freedom produce enough information to characterize a cam- follower system Time diagrams trajectories continuous periodic harmonic (as an starting point) discontinuous second derivative time profile

20. Cam-follower systems: experiments and simulations 20 System description

21. Cam-follower systems: experiments and simulations 21 Outline Introduction System description (experimental set-up) Mathematical modeling Typical dynamics Remarks and ongoing work

22. Cam-follower systems: experiments and simulations 22 Mathematical modeling Unconstrained mode, or equation that describe the motion of the follower when there is not contact between it and the cam. Equation for the contact, that describes the system before detachment. Restitution law that models the reset of the state variables when the impact occurs

23. Cam-follower systems: experiments and simulations 23 Mathematical model

24. Cam-follower systems: experiments and simulations 24 Mathematical model

25. Cam-follower systems: experiments and simulations 25 Mathematical model

26. Cam-follower systems: experiments and simulations 26 Outline Introduction System description (experimental set-up) Mathematical modeling Typical dynamics Remarks and ongoing work

27. Cam-follower systems: experiments and simulations 27 Typical dynamics Permanent contact (ω < 125 rpm) Detachment (ω =125 rpm) Periodic regime (125 < ω < 155 rpm) Transition to Chaos (ω  155 rpm) Chaos (ω >155 rpm)

28. Cam-follower systems: experiments and simulations 28 Permanent contact

29. Cam-follower systems: experiments and simulations 29 Detachment

30. Cam-follower systems: experiments and simulations 30 Periodic regime

31. Cam-follower systems: experiments and simulations 31 Transition to Chaos

32. Cam-follower systems: experiments and simulations 32 Chaos!

33. Cam-follower systems: experiments and simulations 33 Experimental bifurcation diagram

34. Cam-follower systems: experiments and simulations 34 Identification of system parameters

35. Cam-follower systems: experiments and simulations 35 Numerical bifurcation diagram

36. Cam-follower systems: experiments and simulations 36 Bifurcation diagrams num vs. exp

37. Cam-follower systems: experiments and simulations 37 Outline Introduction System description (experimental set-up) Mathematical modeling Typical dynamics Remarks and ongoing work

38. Cam-follower systems: experiments and simulations 38 Remarks The cam-follower experimental rig built is a versatile and flexible tool for the experimental analysis of bifurcations in impacting systems, and complex dynamics derived.

39. Cam-follower systems: experiments and simulations 39 Ongoing work

40. Cam-follower systems: experiments and simulations 40 Ongoing work - Impact detection - Phase plane plots - Poincaré maps - Experimental study of discontinuous second derivative cam-shape

41. Cam-follower systems: experiments and simulations 41 Thanks for your attention !! r.alzate@unina.it