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American Journal of Physics -- February 2012 -- Volume 80, Issue 2, pp. 113

Chaotic motors

C. Laroche1, R. Labbé2, F. Pétrélis1, and S. Fauve1

1Laboratoire de Physique Statistique, Ecole Normale Supérieure, Université P. et M. Curie, Université Paris Diderot, CNRS, 24 rue Lhomond, F-75005 Paris, France
2Laboratorio de Turbulencia and GCTE, Departamento de Física, Facultad de Ciencia, Universidad de Santiago de Chile, USACH, Casilla 307, Correo 2, 9170022, Santiago, Chile

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We show that electric motors and dynamos can be used to illustrate most elementary instabilities or bifurcations discussed in courses on nonlinear oscillators and dynamical systems. These examples are easier to understand and display a richer behavior than the ones commonly used from mechanics, electronics, hydrodynamics, lasers, chemical reactions, and population dynamics. In particular, an electric motor driven by a dynamo can display stationary, Hopf, and codimension-two bifurcations by tuning the driving speed of the dynamo and the electric current in the stator of the electric motor. When the dynamo is driven at constant torque instead of constant rotation rate, chaotic reversals of the generated current and of the angular rotation of the motor are observed. Simple deterministic models are presented which capture the observed dynamical regimes.

© 2012 American Association of Physics Teachers

ACKNOWLEDGMENTS

R.L. is indebted to G. Bobadilla, S. Navarro and G. Palma, whose support made possible his participation in this work in the frame of a sabbatical year project.

Article Outline

  1. INTRODUCTION
  2. THE FARADAY DISK AND THE BULLARD DYNAMO
    1. A stationary bifurcation illustrated by the Bullard dynamo
    2. A Bullard dynamo driving a Faraday disk: Hopf and codimension-two bifurcations
  3. DYNAMO EXPERIMENTS USING UNIVERSAL MOTORS
  4. GENERATION OF ELECTRIC CURRENT FROM THE DYNAMO INSTABILITY OF A MOTOR
    1. Dynamo operated at fixed velocity
    2. Dynamo operated at fixed torque
  5. DYNAMICAL REGIMES OF A DYNAMO DRIVING A MOTOR
    1. Fixed velocity: A codimension-two bifurcation
    2. Fixed torque: Chaotic regimes
  6. CONCLUSION

KEYWORDS and PACS

Keywords

bifurcation, chaos, DC generators, educational courses, electric current, electric motors, electronic engineering education, oscillators, rotation, stators, tuning

PACS

  • 05.00.00

    Statistical physics, thermodynamics, and nonlinear dynamical systems

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History
Received Aug 2011
Accepted Nov 2011

PUBLICATION DATA

ISSN

0002-9505 (print)  
1943-2909 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Association of Physics Teachers

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1119/1.3664605

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