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Nonlinear dynamics in a cam-follower impacting system

Nonlinear dynamics in a cam-follower impacting system. Ricardo Alzate Ph.D. Student University of Naples FEDERICO II (SINCRO GROUP). Outline. Background Results Conjectures and open problems. Background. Application problem.

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Nonlinear dynamics in a cam-follower impacting system

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  1. Nonlinear dynamics in a cam-follower impacting system Ricardo Alzate Ph.D. Student University of Naples FEDERICO II (SINCRO GROUP)

  2. NLD in a cam-follower impacting system Outline • Background • Results • Conjectures and open problems

  3. NLD in a cam-follower impacting system Background

  4. NLD in a cam-follower impacting system Application problem Valve floating phenomena in cam-shaft based engines (performance reduction, piece-wearing and damage)

  5. NLD in a cam-follower impacting system Theoretical context Cam-follower systems are particular cases of: • Hybrid automata (constrained and unconstrained modes + reset) • Impact oscillator with surface forcing (nonsmooth dynamics and complex behaviour) • Broad application (mechanical tools)

  6. NLD in a cam-follower impacting system The system: features Experimental rig to validate theoretical approaches: • Flat-faced sliding follower driven by a rotating, shape selectable, eccentric cam (circular and discontinuous) with spring preload • High performance sensors (encoders and gyroscope) and actuator • Flexible storage and programming tools

  7. NLD in a cam-follower impacting system The experimental rig

  8. NLD in a cam-follower impacting system Results (circular shape case)

  9. NLD in a cam-follower impacting system Dynamics overview Low velocity region - contact condition Which phenomenon is behind this abrupt transition? Detachment and periodic regime A-periodic behaviour and chaos

  10. NLD in a cam-follower impacting system Modeling Mathematical representation of main events (see [1] for details): • Development of expression for unconstrained state vector evolution using Lagrangian approach • Transition rule between modes: impact law based on a single Newton’s restitution model • Numeric evaluation with event-driven algorithm (G. Osorio) [1]. R. Alzate, M. Di Bernardo, U. Montanaro and S. Santini. “Experimental and numerical verification of bifurcations and chaos in a cam-follower impacting system”, Nonlinear dynamics, Springer. 2007.

  11. NLD in a cam-follower impacting system Equations unconstrained constrained

  12. NLD in a cam-follower impacting system Identification Assignment of quantitative values for model parameters searching agreement with experimental data: • Geometric parameters • Physical parameters • Restitution coefficient

  13. NLD in a cam-follower impacting system Validation 110 rpm 150 rpm experimental numerical

  14. NLD in a cam-follower impacting system Dynamics: simulation

  15. NLD in a cam-follower impacting system Conjectures and open problems

  16. NLD in a cam-follower impacting system Conjectures: bif. cascade 1 ω[150,155] rpm • Is particular transition to chaos on scenario 1 consequence of interrupted chattering sequences? • Is such interruption of chattering due to grazing? • Is scenario 1 the particular transition observed in bifurcation map obtained experimentally?

  17. NLD in a cam-follower impacting system Conjectures: bif. cascade 1ω[150,155] rpm (2) • Fingered patterns

  18. NLD in a cam-follower impacting system Conjectures bif. cascade 2ω[135,160] rpm • How to predict analytically conditions for existence of the period doubling cascade? [Note that vector field under study is highly nonlinear] • Is scenario 2 detectable experimentally?

  19. NLD in a cam-follower impacting system Open problems • Development of a more accurate simulation algorithm and of an appropriated continuation algorithm

  20. NLD in a cam-follower impacting system Open problems (2) • Continuation of stable and unstable solutions and detection of smooth and DIB • Analysis for coexistence of attractors and computation for related basins of attraction • Experimental evidence of solutions • Analysis of discontinuous-cam case

  21. NLD in a cam-follower impacting system Conclusion We have studied a cam follower system with continuous cam profile, involving highly nonlinearities in associated model We have detected two main bifurcation scenarios Scenario 1 involves sudden transition to chaos with chattering solutions Scenario 2 involves a period doubling route to chaos The open problem regards numerical and experimental study of coexistence between such dynamics

  22. NLD in a cam-follower impacting system Thanks !!! r.alzate@unina.it

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