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Coercive force of a Slinky?

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klugesmith

Sat May 23 2009, 12:09AM

Registered Member #2099 Joined: Wed Apr 29 2009, 12:22AM
Location: Los Altos, California
Posts: 1714

Maybe some transformer experts here can help where Google has failed me. I don't think this thread belongs in Projects unless it concludes with a useful design.

My old Variac box could use a passive ammeter driven by a current transformer. It was no challenge to get good performance from a commercial 200A:5A CT, and just as good from a 1.1-inch-OD, 13-gram toroidal transformer found at our electronics flea market. But what about people not so fortunately situated?

So yesterday I started playing with a 2-inch-OD toroidal core wound from a crate-banding strap discarded by Home Depot.
And with a 1.6-inch-OD Slinky spring. If possible, the composition and temper and surface insulation were to be as-found. Mitigation of eddy currents and hysteresis loss would be addressed if proved necessary by measurements or other research.

Eddy currents were never expected to be a show-stopper, and initial DC tests were promising. For example, the Slinky end-to-end resistance was measured to be 3.1 ohms when slightly extended, and almost 2 ohms fully collapsed with a modest axial load, so contacts between laminations are few & far between.

Hysteresis is another matter. The magnetizing current required by these cores might be ridiculously high for 10 amp CT application. Unlike "real" cores, both of my springy candidates have enough remanent field to pick up a sewing pin after being touched with a permanent magnet. (Though that's really about Br rather than Hc)
On the Internet, it's easy to find Hc values for transformer steels (less than 1 Oe or [EDIT] 100 A/m) and for some permanent magnet alloys (on the order of 1000 Oe). But I struggled to find any quantitative values for the middle ground -- ferrous products such as cold-rolled steel or spring steel, ordinarily specified for their mechanical properties rather than magnetic ones.

As a disciple of The Laboratory, I wound about 82 turns on the strapping toroid, and got almost no open circuit voltage with 5 A at 60 Hz threading the core. (The 200A:5A CT under same condition was substantially saturated, with narrow voltage spikes of well over 10 V on secondary). Then put 2 coils of 19 turns on the Slinky, ran 2 A through one of them, and got similarly disappointing response. Fortunately, there's a handle on a measurable magnetization characteristic. Driving 1 amp RMS into the 82 turn coil, whose DC resistance is 0.66 ohms, gives a distorted terminal voltage waveform reaching +- 2.4 volts, a readily measurable inductive reaction.

In the next few days I can dig out enough equipment to make a full B-H hysteresisgraph of these cores. With 1.2 KVA UPS transformer rewound for 4V secondary, and a few turns through CUT, can drive and sense (with resistive shunt) at least 1000 ampere-turns. Got a RFL model 916 fluxmeter (voltage integrator in a box) to infer the B flux from any modest sense winding. Heck, if losses heat core too fast I can submerge it in a bucket of water.

Meanwhile -- would anyone care to guess, or point to a reference, about the expected B-H behavior of these materials?
Or to offer general practical advice regarding this exercise?

Best regards to all.
-Rich

Steve Conner

Sat May 23 2009, 12:17PM

Registered Member #30 Joined: Fri Feb 03 2006, 10:52AM
Location: Glasgow, Scotland
Posts: 6706

Sounds interesting. There was a thread on my other favourite forum (sadly down for maintenance) about using salvaged transformer cores for high-power audio. I foolishly said that it was "easy to draw the B-H loop on a scope" and the original poster challenged me to post a schematic of the circuit I used. The problem is, I've never actually done it! So it'll be interesting to see what you come up with.

One related thing I'm interested in, is measuring the B-H characteristic of cores already inside tube amp output transformers. I have quite a collection of them, and I want to study how the non-linear magnetic behaviour affects the tone. I can't use 50 or 60Hz for this, since driving them to saturation would induce thousands of volts in the primary, which risks damaging these expensive transformers. I was thinking of using 5 or 10Hz from a big audio power amp instead.

WaveRider

Sat May 23 2009, 03:00PM

Registered Member #29 Joined: Fri Feb 03 2006, 09:00AM
Location: Hasselt, Belgium
Posts: 500

Though I have never done this myself, I would probably attempt to measure the differential inductance at a series of DC operating points. The process goes like this:

Put enough turns on your core such that the DC current expected to push the core into (or close to) saturation will not draw excessive current.
Apply a DC bias current to the windings.
Superimpose a small AC signal on the DC bias.
Measure the measured AC inductance as a function of the DC bias.
The average permeability of the core at a certain DC bias can be deduced from the measured AC inductance.
By recognising that the AC inductance is proportional to the derivative of permeability with respect to bias current (or applied H), you can construct a B-H curve.

Short of showing lots of formulas, I hope this makes sense. This is a standard way of measuring non-linear devices like transistors, diodes and other small signal devices. In this case, it relies on the use of a Taylor series approximation B and H

B(H) = B(H_dc) + dB(H_dc)/dH * delta H

H_dc is the H resulting from the DC bias current
delta_H is the small deviations from the DC conditions caused by the superposed AC signal. This is directly related to the small signal current. The derivative of B wrt to t yields a differential equation for mu in terms of the measured dH/dt (current measurement) and dB/dt (from an AC voltage measurement across the winding):

dB/dt = (mu + H_dc * dmu/dH) * d(delta_H)/dt

This can be solved numerically based on measurement data. The catch is that we need to know the initial magnetisation condition. For unmagnetised material, it can be assumed zero...however, a rigorous measurement system should account for initial magnatisation.... I need to think about this some more...

Cheers!

klugesmith

Sun May 24 2009, 05:00PM

Registered Member #2099 Joined: Wed Apr 29 2009, 12:22AM
Location: Los Altos, California
Posts: 1714

Got my first BH curves.
Steve, I'm sure this method would work at 5 or 10 Hz; in fact with a bipolar DC current source and hand-turned knob, one could do a BH trace from initially demagnetized state, up to deep saturation, then around the hysteresis loop.
WaveRider, you make an interesting point about small-signal permeability. Stay tuned!

I tested a commercial 200:5 current transformer in a setup like:

except the voltmeter and computer were replaced by an oscilloscope, and the bipolar power supply was replaced by: Variac, 12 V transformer, 12 V lamp + 0.1 ohm sense resistor + 3 turns through CTUT.
The fluxmeter is a voltage integrator with no deliberate low-frequency pole; instead there is a reset button and a ten-turn knob to adjust the offset voltage (drift rate). Not hard to make at home, but mine came via ebay and looks like

except for an older maker's badge.
To measure a static B field, you place sense coil in the field and reset the integrator. Then move sense coil to a place where the field is practically zero, and promptly read the integrator output. Calibration is simply a matter of knowing the number of turns and effective loop area. Could measure the Earth's field, or that of a 30T lab electromagnet, by simply turning the sense coil over.

Elapsed time in the lab was less than I am now spending to tell the story. Did this at work with an unfamiliar but glitzy digital 'scope. Could not find an X-Y (Ch2 vs Ch1) display mode, but easily saved time/voltage records to files for crunching by spreadsheet calculator.

I 'scoped the primary current (voltage across sense resistor), the secondary winding voltage, and the fluxmeter output voltage. Here is a representative display, and a spreadsheet chart of all the raw data from 3 different Variac settings.

In the spreadsheet I compared the fluxmeter record with a numerical integration of the coil voltage record. Very close match after scaling and -- this held me up a bit -- taking out the scope's offset voltage. Hint: successive peaks of integrated waveform should reach the same level; same as saying the true voltage, averaged over exactly one cycle, should be zero. Analog integration is not easy to beat for DC and very low frequencies.

Nuff said. Here is the BH chart. Scaling is a detail for another day. The round corners are real (not an artifact of fluxmeter) -- perhaps a manifestation of eddy current losses at 60 Hz?
-Rich

Steve Conner

Mon May 25 2009, 09:40AM

Registered Member #30 Joined: Fri Feb 03 2006, 10:52AM
Location: Glasgow, Scotland
Posts: 6706

Klugesmith wrote ...

Excellent!

The loop does look bigger than I expected for a commercial transformer core, but that could just be a scaling thing, as you say.

WaveRider

Wed May 27 2009, 07:11AM

Registered Member #29 Joined: Fri Feb 03 2006, 09:00AM
Location: Hasselt, Belgium
Posts: 500

Those are lovely results! Did you try a measurement of the spring-steel core that you made?

klugesmith

Fri May 29 2009, 08:28PM

Registered Member #2099 Joined: Wed Apr 29 2009, 12:22AM
Location: Los Altos, California
Posts: 1714

I'm pleased to report an answer to the question which titles this thread.
Last night, got a quantitative B-H hysteresisgraph of my Slinky core.

The big step for this session was to use fluxmeter along with an X-Y 'scope display, to see the B-H curve in realtime.
For primary winding stimulus I used Variac with a 2.5-volt, 10 A filament transformer and 0.1-ohm sense resistor.

The 200:5 CT and the 13g toroid gave familiar pictures. But the crate-strapping core with about 7 primary turns showed little evidence of magnetization up to about 40 ampere-turns. Harboring a faint suspicion about inter-lamination eddy currents, I turned to the Slinky, which was trusted in that department. Threaded it 19 times with a form of bifilar wire known as lamp cord, and connected the two conductors in series.

Cranked up the Variac and voila!, a loop opened on the 'scope display and expanded to form a textbook BH curve. Current peaks of 300 amp-turns came very close to saturation.

The X-axis crossings were at absolute currents of 160 amp-turns for this core.
That corresponds to the material property Hc = 1306 A/m = 16.4 oersteds.
On a logarithmic scale that's almost halfway along the path from transformer steel to alnico.
I haven't yet figured the scaling of volt-seconds (flux) axis, but expect B_sat to be about 2 T.

So the Slinky is ruled out for original instrument transformer application, which requires that magnetizing current be much less than the measured current. (Even if magnetization were linear, transformer voltage would be 90 degrees out of phase from magnetizing current).

Next steps: Go back and measure Hc of the strapping core. Then wind a core out of an -annealed- specimen of the same strapping. Sorry, I'm not ready to anneal my favorite little Slinky.

-Rich

p.s. now that I know how to edit-in new images here, going to add a picture of the 4 cores to the original post in this thread.

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