The current provided by a Bullard dynamo (left) is used to
drive a Faraday disk (right).

Fixed Torque Dynamo and Motor

The Fixed Torque Dynamo and Motor Model solves the coupled differential equations for an electric motor driven by a dynamo (generator). The model can be used as a simple example to illustrate elementary instabilities or bifurcations discussed in courses about nonlinear oscillators and dynamical systems. When the dynamo is driven at constant torque, chaotic reversals of the generated current and of the angular rotation of the motor are observed.

Simplified dynamical equations for the dynamo angular velocity Ω1, motor angular velocity Ω2 and current I (see Laroche et al.) are

where L is the inductance, R is the total resistance, J is the moment of inertia, and T is the torque applied to the dynamo. The stator current Is produces the magnetic field B0 in the motor. When the dynamo armature rotates with angular velocity Ω1, a voltage Ω1Φ(Is) is generated where K is the dynamo efficiency and I0 is the saturation current. The saturation function Φ(I) is also used in the Ω2 (motor) ODE because we assume that the identical devices. (Laroche et al. use washing machine motors in their experiments.)

The following parameters are fixed in the model.

Parameter	Variable	Value	Units
moment of inertia	J	1.38E-4	kg/m^2
inductance	L	0.11	H
saturation current	I0	1.8	A

efficiency	K	0.17	V/(rad s)

The stator current Is (A), torque T (N m), and resistance R (ohm) are adjustable.

References

C. Laroche, R. Labbe, F. Petrelis and S. Fauve, "Chaotic Motors," American Journal of Physics, (in press).
A. Cox, Computer Program FARADAY DISK DYNAMO MODEL, Version 1.0 (2009), WWW Document, (http://www.compadre.org/Repository/document/ServeFile.cfm?ID=9417).

Credits:

The Fixed Torque Dynamo and Motor Mode was developed by Wolfgang Christian using the Easy Java Simulations (EJS) version 4.3 authoring and modeling tool.

You can examine and modify a compiled EJS model if you run the model (double click on the model's jar file), right-click within a plot, and select "Open EJS Model" from the pop-up menu. You must, of course, have EJS installed on your computer. Information about EJS is available at: <http://www.um.es/fem/Ejs/> and in the OSP ComPADRE collection <http://www.compadre.org/OSP/>.