Cam-follower systems: experiments and simulations

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

19. System description Lumped parametersingle 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 Cam-follower systems: experiments and simulations

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

21. Outline • Introduction • System description (experimental set-up) • Mathematical modeling • Typical dynamics • Remarks and ongoing work 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 lawthat models the reset of the state variables when the impact occurs Cam-follower systems: experiments and simulations

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

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

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

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

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

29. Detachment Cam-follower systems: experiments and simulations

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

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

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

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

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

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

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

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

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

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

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