A little help with some math please...?

I think a reasonable model for the generator is an ideal AC voltage source with voltage proportional to frequency (essentially the unloaded curve)) in series with a resistor (winding resistance) and an inductor. The inductor is selected to produce the drooping light load curve, and the resistor is selected to tweek the fit on the high load.

Reply to
John Popelish
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This is something I've been scratching my head over for a couple of days...

I want to model a permanant-magnet type (bicycle) AC generator, to calculate its output at a given speed / load. Characteristics of the actual device can be seen here:

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(the plots are no-load and two different load values)

I know that the generator has a finite current limit, due to the induced current generating its own magnetic field (someone correct me if I'm wrong), and I can *see* what is occurring, but I just can't seem to define it mathmatically :o(

I need to calculate Vout as a function of rotational speed and load.

This is frustrating because it's pretty basic, but hopefully is one of those cases of just getting past the starting post. Before anyone asks, no this is not a homework project (FAR to many years since I was at college) nor anything further than hobbyist tinkering.

Thanks, Nick

Reply to
Nick.

Just do a curve-fit - you've got it right there: Effektivspannung In Volts per Fahrgeschweindigkelt In km/h. ;-P

It looks kinda like a log, but heck, you should be able to curve-fit something like that in only order 2. :-)

Good Luck! Rich

Reply to
Rich Grise

This is basically a permanent magnet dc motor operating as a generator. The equation for a pm dc motor is:

Vt = IR -kw

Where Vt is the terminal voltage, I the motor current, R the winding resistance, k a constant and w the rotational speed. The kw term is the back emf generated by the motor turning.

I am sure this will do for you with suitable alteration of the terms.

HTH

Ian

Reply to
Ian Bell

Agreed. The value of resistance that best fits the curves may approach zero.

Reply to
John Popelish

The inductor is probably the most important. Since frequency is proportional to rpm and inductive reactance is proportional to frequency, this makes the voltage self limiting at the design load.

Ted

Reply to
Ted Edwards

If the voltage source produces a voltage and frequency proportional to speed (what the graph shows for no load, for voltage, anyway), and the inductor has an impedance proportional to speed (since the generator frequency is proportional to bike speed), you get a constant current into any load resistance that is significantly lower than the inductor impedance. That point occurs for a different speed for each load resistance, at a lower speed for lower load resistances, and that is generally what the graph shows. No exponentials anywhere in the AC analysis.

Reply to
John Popelish

Hi Nick,

Ein zusätzliches Problem bei der Beschreibung dieses Systems ist die extrem nichtlineare Kennlinie der Leuchtmittel. Die sind es nämlich IMHO die den Gleichstromcharakter des ganzen Systemes einprägen. Glühobst neigt nämlich zu einer Art Stromkonstanter zu werden. Ich hab zu Hause noch ein Ladegert, das genau so seinen Strom einstellt und das gar nicht allzu schlecht. Sei doch mal so nett und mess das ganze für uns mal mit ohmschen Widerständen als Last aus.

Sorry for all english readers, german is much easer for me ;-)

Marte

Reply to
Marte Schwarz

Hi Marte

No worries... Google Translate sort of did the job :o) I'm not too sure what Glühobst means (Google translates to Glow Fruit)

As well as the graph mentioned, I also have some measured data, using resistive loads. (I suspect that the graph might've been measured using resistors) Good point, though.

Nick

Reply to
Nick.

I don't think that'll work John, because if you also plot (for a given speed/freq) voltage vs load, you will get an exponential-ish curve (up to the no-load voltage)

Reply to
Nick.

Thanks, I'll probably end up doing that. But.. one of the points of the exercise is to try to understand the principles behind what effectively is a few turns of wire wrapped around a revolving magnet. (20yrs ago this would've been fairly trivial, but I'm afraid I then hung up my soldering iron for a keyboard. Scary how much one forgets...)

On the practical side, all I want to do is vary the load (power a bulb, maybe two, charge a battery) based on speed. I can do that easily enough using measured data in a lookup table.

Cheers, Nick

Reply to
Nick.

Hi Nick,

Glühobst is a more general description for glowing things not only "-birnen" ;-) A "Quartzstrahler" (is it called glass-heating-cylinder?) is a nice example with a similar behaviour.

Well in the graph there was the explanation with 3W and 2.4 Watt lamps AFAIR. The differences in the graphs would be very interesting for me too. I use such a nabendynamo in my bike and want to design my accu-frontlight to use the daily energy as a standby-light in the frontlight too. I have a old bisy but it should be named buggy-light ;-)

Marte

Reply to
Marte Schwarz

I'm getting a pretty good fit using the following: (view in fixed-width font, eg. Courier)

1 Vout = ------------------------------------ SquareRoot[ (A/speed)^2 + B^2 ]

Where the parameters are

A & B = 1.1 & 0 for the no-load case A & B = 1.25 & 1/17.7 for the middle curve A & B = 1.4 & 1/7.9 for the lowest curve

Note: at low speed, Vout is approx = speed / A at very high speed, Vout is approx = 1 / B

Regards,

Mark

p.s. these parameters are not optimized least-squares values. I just overlayed your .gif file on an Excel graph and played around till things looked reasonable.

Reply to
redbelly

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