1. Understanding the complex dynamics of a cam-follower impacting system
R. Alzate, M. di Bernardo, S. Santini

2. 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

3. 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

4. Undesired Dynamics Desired behavior (keeping contact)
Undesired behavior (VALVE FLOATING)
Damage from a piston striking a valve

5. 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. 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]

7. References The web ! Literature on impact oscillators
Piecewise-smooth dynamical systems