cam-follower systems: experiments and simulations by ricardo alzate university of naples –...
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Cam-follower systems: experiments and simulations
byRicardo Alzate
University of Naples – Federico IIWP6: Applications
Cam-follower systems: experiments and simulations
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Outline
• Introduction
• System description (experimental set-up)
• Mathematical modeling
• Typical dynamics
• Remarks and ongoing work
Cam-follower systems: experiments and simulations
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Outline
• Introduction
• System description (experimental set-up)
• Mathematical modeling
• Typical dynamics
• Remarks and ongoing work
Cam-follower systems: experiments and simulations
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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 …”
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Introduction
A cam-follower system
Taken from http://www.ul.ie
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Introduction
Cam-follower systems
general and relevant benchmark problem
The most common application
Internal combustion engines (ICE)
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Introduction
The 4 stroke engine
1 - Intake
2 - Compression
3 - Combustion
4 - Exhaust
Taken from http://en.wikipedia.org
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Introduction
Engine performance
Mechanical parts in close contact
Speed increasing:
valve floating
bouncing
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Introduction
Illustration of a cam-shaft based engine
Taken from http://en.wikipedia.org
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Introduction
Illustration of the valve-floating phenomenon
Taken from http://www.ul.ie
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Introduction
Damage: a piston striking a valve
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Introduction
Spring forced
disadvantages
wear of pieces (friction)
valve timing
desmodromic valves
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Introduction
Cam-follower = impact oscillator
Complex behaviour (transition to chaos)
Experimental validation of theoretical bifurcation based analysis
To apply nonlinear control techniques
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Outline
• Introduction
• System description (experimental set-up)
• Mathematical modeling
• Typical dynamics
• Remarks and ongoing work
Cam-follower systems: experiments and simulations
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System description
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System description
Cam-follower systems: experiments and simulations
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System description
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System description
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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
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System description
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Outline
• Introduction
• System description (experimental set-up)
• Mathematical modeling
• Typical dynamics
• Remarks and ongoing work
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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
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Mathematical model
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Mathematical model
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Mathematical model
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Outline
• Introduction
• System description (experimental set-up)
• Mathematical modeling
• Typical dynamics
• Remarks and ongoing work
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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)
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Permanent contact
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Detachment
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Periodic regime
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Transition to Chaos
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Chaos!
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Experimental bifurcation diagram
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Identification of system parameters
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Numerical bifurcation diagram
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Bifurcation diagrams num vs. exp
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Outline
• Introduction
• System description (experimental set-up)
• Mathematical modeling
• Typical dynamics
• Remarks and ongoing work
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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.
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Ongoing work
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Ongoing work
- Impact detection
- Phase plane plots
- Poincaré maps
- Experimental study of discontinuous second derivative
cam-shape
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Thanks for your attention !!