Understanding the complex dynamics of a camfollower impacting system

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Understanding the complex dynamics of a
cam-follower impacting system

• R. Alzate, M. di Bernardo, S. Santini

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The Cam-follower System
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

• Cams are used to convert rotary motion into
  reciprocating motion. The motion created can be
  simple and regular or complex and irregular
• Some external downward force (usually a spring
  and gravity) pushes the follower down making it
  keep contact with the cam

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The Valve Train
4-stroke engine

• Cam-follower systems represents a very general
  and relevant benchmark problem since they are
  widely used in several mechanical engineering
  devices, e.g. automated production machines
• The most common application is related with the
  valve train of an internal combustion engines
  (ICE)
• The effectiveness of an ICE is funded on the
  proper working of the cam-follower mechanism

• Intake 2. Compression
• 3. Combustion 4. Exhaust

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Undesired Dynamics
Desired behavior (keeping contact)
Undesired behavior (VALVE FLOATING)
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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)

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Questions

• How to model a cam-follower system ?
• Is it possible to simulate the system taking into
  account the presence of impacts after detachment
  (valve floating) ?
• Can you predict the value of the cam rotational
  speed where detachment occurs ?
• Can the system behave chaotically ? When ?
• Can we eliminate chaos by appropriate redesign or
  control algorithms ?
• HINT Assume eccentric circular cam shape

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References

• The web !
• Literature on impact oscillators
• Piecewise-smooth dynamical systems