Understanding the complex dynamics of a cam-follower

impacting system

Understanding the complex dynamics of a cam-follower

impacting system

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

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The Cam-follower SystemThe Cam-follower System

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

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

[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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The Valve TrainThe Valve Train

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

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

4-stroke engine

1. Intake 2. Compression

3. Combustion 4. Exhaust

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Undesired DynamicsUndesired DynamicsDesired behavior (keeping contact)

Undesired behavior (VALVE FLOATING)Damage from a piston striking a valve

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Theoretical contextTheoretical 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)

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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QuestionsQuestions

1. How to model a cam-follower system ?

2. Is it possible to simulate the system taking into account the presence of impacts after detachment (valve floating) ?

3. Can you predict the value of the cam rotational speed where detachment occurs ?

4. Can the system behave chaotically ? When ?

5. Can we eliminate chaos by appropriate redesign or control algorithms ?

[HINT: Assume eccentric circular cam shape]

1. How to model a cam-follower system ?

2. Is it possible to simulate the system taking into account the presence of impacts after detachment (valve floating) ?

3. Can you predict the value of the cam rotational speed where detachment occurs ?

4. Can the system behave chaotically ? When ?

5. Can we eliminate chaos by appropriate redesign or control algorithms ?

[HINT: Assume eccentric circular cam shape]

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ReferencesReferences

The web !Literature on impact oscillatorsPiecewise-smooth dynamical systems

The web !Literature on impact oscillatorsPiecewise-smooth dynamical systems