Cam-follower systems: experiments and simulations

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

Cam-follower systems: experiments and simulations

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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

Cam-follower systems: experiments and simulations

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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

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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System description

Cam-follower systems: experiments and simulations

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System description

Cam-follower systems: experiments and simulations

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System description

Cam-follower systems: experiments and simulations

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System description

Cam-follower systems: experiments and simulations

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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

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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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

Cam-follower systems: experiments and simulations

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Mathematical model

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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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 !!

r.alzate@unina.it