What I am getting at is a generally unrecognized phase delay that occurs in the magnetic domain.
Just let me verify that you really mean "domain" and not "domains".
The voltage induced into a coil is proportional to the time rate of change of the flux within the coil.
Yes, but I do not like your terminology.
The voltage is induced across the coil - not "into" a coil. The only electric thing flowing in the windings of a coil is current.
Some flux can come from say a moving magnet, but there is also a component coming from any current flowing in the coil, even if that current has been induced by the moving magnet.
Yes, and these two fluxes are exactly equal and opposite through a surface spanning the hole of an ideal shorted air coil.
So when we wish to accurately calculate the voltage applied to a load (and the current flowing in that load) we have to take account of the effect of the coil's inductance that adds its own self-flux to the flux coming from the magnet. Under normal operating conditions that self-flux is usually negligible so we ignore it.
I don't know what you mean by "normal operating conditions".
To me a normal operating condition for a coil is a condition that maximizes the flux current flowing through it, because a coil inherently is a current device and any resistance to that current is just a sink to the energy stored in that coil.
But we can create the condition where the self-flux is dominant.
No, the induced current and flux that it creates is never larger than the externally applied flux, (when if we start from zero).
The word "dominant" implies "larger than".
If the flux from the magnet follows a sine wave then that condition is met when the load resistor is small compared to the reactance of the coil's self-inductance.
Inductive reactance implies a frequency domain analysis. I will not analyze the system this way because in such analysis the starting conditions are undefined.
If you want to continue this analysis with me you'll have to do a full transient state analysis - in other words: you must start from zero current and zero flux and zero force.
And under those conditions you get the coil current shifted by almost 90 degrees from where it would be normally.
"Normally" compared to what?
That modifies considerably the torque waveform on the drive shaft,
But torque is not proportional to the flux - it is proportional to the gradient of the magnetic flux density. Thus you cannot assume that the torque is in phase with the flux magnitude.
The attached pdf was written some years ago and illustrates the phasor diagram for the applied flux from the moving magnet, the self-flux from the coil current (called Lenz flux)
I know Cyril Smith's work.
and the resulting flux that delivers the induced voltage.
Flux does not deliver voltage. Flux magnitude is not even proportional to the voltage. The rate of change of flux is.
The only thing that is proportional to the flux magnitude is the induced current in an ideal shorted coil (if you start from zero).
The paper also looks into the power waveforms and energy flows (a) at the mechanical input shaft and (b) at the electrical load where at large phase angles the power to the load is not delivered coincidentally with power taken from the shaft.
The mechanical input (torque) is not proportional to the magnitude of flux. Flux does not cause any mechanical attraction - it's gradient does. It's not surprising that the torque is not in phase with the flux.
Over parts of the cycle the shaft torque is negative, but note this is not the usual cogging torque associated with magnets moving relative to some ferromagnetic material.
If you mean the negative torque on a magnet moving relative to a coil, then this is nothing unusual. Just take a look at
my animation of the bouncing magnet over an ideal shorted coil. The force acts on it in both directions periodically.
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Topic: Piston Project (Read 19961 times)
