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General electronics => Electronic Circuits => Topic started by: klugesmith on November 01, 2019, 12:54:17 AM

Title: Measuring permanent magnets
Post by: klugesmith on November 01, 2019, 12:54:17 AM
Looks like this is the most appropriate sub-forum.  The transformer sections, where people talk about about magnetic induction in steel, ferrite, and air, are under High Voltage -- which is not involved here.

I'm about to do some measurements on the magnet assembly from a loudspeaker.  Will be using the fluxmeter method, which is "dynamic" and requires a sense coil.  But unlike Hall effect (and fluxgate, proton spin precession, etc.), the Fluxmeter method can measure magnetic flux in a solid iron bar just as easily as in empty space.  Analogous to a clip-on ammeter or current sensor with a hole through the middle, through which you could run an insulated wire or a beam of charged particles.  Are any other readers here proficient with voltage-integrating fluxmeters?

A friend gave me the ferrite magnet assembly from a broken loudspeaker.  I guess it weighs more than 5 kg (11 lbs), and the annular gap is wider (about 1/4 inch) than any I've seen before.  In an eddy current braking (drag) demonstration, a 58-mm-diameter Coke can with the bottom cut out settles slowly into the gap.   Analogous to familiar demonstration of strong magnet falling slowly inside a vertical copper pipe.

Us nerds need to know how many amperes are eddying, and that depends on the magnet gap's height and radial B value.   Sure, we could get a reasonable estimate of the B value, after just measuring the terminal velocity of a falling metal tube, and calculating its weight and electrical conductance.  I want to get the B value, and its spatial distribution, more directly.

Here's a fluxmeter sense coil made for the purpose.  The "former" is a bit of 2-inch Sch40 plastic pipe, with a hacksaw-width groove near one end. In the groove are five turns of 34 AWG magnet wire.

To measure the static B value at some place in a magnet gap, commonly you start with a sense coil at the place of interest.  Reset the fluxmeter (analog voltage integrator), then rapidly move the sense coil to a place with negligible B strength.   The instrument reading (in volt-seconds), divided by sense coil turns count and effective area, tells you the initial flux density.

With this loudspeaker magnet, I will start by reading the flux change between sense coil all the way in (bottom of inner pole piece) and all the way out.  Now how much is the flux concentrated in the section of interest (thickness of upper steel plate)?
No need to control or measure any coil velocity, or shape of any voltage pulse on an oscilloscope.
Just repeat the coil-withdrawing experiment with different initial positions, each time getting the volt-seconds integral from the digital readout on fluxmeter's front panel  (which has buttons to select the decade range, in kilo maxwell turns).

Anybody got a better idea?  Any guesses about whether the maximum static B is more than 1 tesla?  More than 1.5 T?
Any guesses about what fraction of the total flux runs above and below the steel top plate?

Is youtube a good place to post videos?  How about Flickr, or Imgur?  Do any sensible people use Facebook to present videos to the general public?  Or for any other useful purpose?  Thanks!

Title: Re: Measuring permanent magnets
Post by: klugesmith on November 02, 2019, 09:25:45 PM
First real measurement of the radial flux density, B, indicated 0.60 teslas. That's much lower than I'd guessed at the beginning.  It's roughly consistent with last night's initial SWAG, based on a copper pipe's physical parameters and rate of descent, judged by eye.  I still don't know the sign, which could be checked with a magnetic compass at a safe distance.

Today's measurement is based on the lifting power of current in a voice coil. 
That value, in newtons per ampere, is identical to a loudspeaker parameter called Bl, in tesla-meters.  Product of flux density B and the length of wire in the magnet gap.  Ain't the SI system nice here?  Some presentations found on the Internet suggest that 20 T-m is an ordinary value in powerful woofer drivers.

My hobby lab style sometimes seeks quick gratification from materials and tools on hand.  Buying new stuff, or having to clean up and find lost stuff, is no fun.
Today's "voice coil" started with a tube wound from 1-inch-wide paper, and some glue, using copper pipe as a mandrel.  It has 12 turns of 26 AWG magnet wire, from a 5-lb spool that I _did_ find under cobwebs and dust. 
It's driven by an adjustable DC power supply, whose digital current meter has a resolution of 0.01 ampere.
The resisting force is a stack of nickels (USA $0.05 coins) which are taken to be 5 gram weights.

Picture also shows that the ferrite ring magnets are far from concentric with the steel pole parts.  I drew an eccentric circle on top plate directly above the inner edge of the ferrite parts.  Is that just from sloppy assembly, or is it on purpose?  Could be to leave more space for some other part in original Sunfire powered subwoofer box.  Like the eccentric jet engine inlets on 737's, which are to increase the ground clearance.

For N_nickels = 0 to 4, I recorded the current at which voice coil began to rise from its support.
To get the most out of the few significant digits, I let Excel figure a straight-line fit:

The slope works out to 1.26 N/A, which we take as the Bl value.
The average coil diameter, times pi, times the number of turns, gives us wire length l = 2.107 meters.   So we infer that B = about 0.60 teslas, around the middle of the gap, at the radius of this coil.

The flux density in this magnet will be about 27% greater at the inner pole face than at the outer pole face, simply because of the radial geometry.  But the force factor, in N/A, doesn't depend on the radial position of any turn in a voice coil.  A turn near the outside is in a weaker B field, but has a proportionately greater length of wire, so contributes the same amount toward total "thrust".  It crosses the same total amount of magnetic flux (in webers or maxwells) per millimeter of axial displacement.

[edit] Just determined the sign, without finding a compass or applying left or right hand rule.  The magnet assembly _is_ the compass.  Suspended with axis horizontal, it turns until the annular end plate (outside pole) faces magnetic south.  The inner pole is connected to end plate which faces magnetic north.

Title: Re: Measuring permanent magnets
Post by: klugesmith on November 03, 2019, 03:38:32 AM
The first voltage integration measurement, using green-wire sense coil shown in OP, gave a thought-provoking result.  To agree with the approximate B value in previous post (0.60 T in middle of gap), we'd need that flux density within the entire 15-mm height of top plate, and almost as much fringing flux above and below the top plate.

My RFL model 916 fluxmeter looks like the one in this stock image, except the printed company name and logo are different.

Usage example: Set range buttons to 10 x 10^3 kilomaxwell turns; put sense coil all the way in; push the integrator Reset button; pull sense coil all the way out (& turn it orthogonal to magnet axis).  Read instrument digital display: 0.153. 

That indicates 1.53 million maxwell turns.  Same as 0.0153 volt-seconds.  One could get that number by capturing induced-voltage pulse on an oscilloscope and calculating its area.
Dividing by the number of turns in green-wire sense coil, 5, gives us 306 kilomaxwells (3.06 milliwebers).  That's the total amount of flux, radiating from center pole piece, that the sense coil crossed in one complete stroke. 

Suppose the flux were uniformly dense in the 1.5-cm-high gap next to top plate, and zero everywhere else.  Multiplying the gap height by our coil circumference, 17.6 cm, gives us the cross-sectional area penetrated by the flux bundle: 26.3 cm^2  (0.0026 m^2).  Dividing the known total flux by that area gives the average flux density: 11600 gauss (1.16 tesla), at the radius of our sense coils.

The flux density measured in previous post, with less care, was barely half of that value.  I bet it's the right value for middle of the gap.  The measurement using green-wire coil includes all the flux above and below the gap.

To profile the flux distribution along Z axis, at a given radius, one could use a Hall effect probe moved from place to place.  Mind the calibration, nonlinearity, and temperature sensitivity of the Hall probe (the ones that go up to whole teslas are very expensive).
We can do it just as accurately with the green-wire coil, measuring the flux change between intermediate positions and "infinity" (all the way out).  It would be educational to look at the fringing flux in simulation, e.g. with FEMM.  Remember, simulations (including SPICE) are tools to help us observe the behavior of models of real things.

[edit] Results are in from first flux-vs-Z sweep, with primitive hand-held vertical position control.
58% of the total measured flux is above or below the top plate zone (Z = 0 to +1.5 cm) when it crosses the imaginary cylinder scanned by our sense coil.
The top plate zone has 42% of total flux (129 kilomaxwells), at average density of only 4900 gausses (0.49 teslas).

Here's a snip from drawing showing a longitudinal section of magnet assembly, and sense coil in Z=0 position.

Does this stuff mostly make sense?  Is it too pedantic about things that are well known, or are seen as easy, or are of little interest at this forum?
Title: Re: Measuring permanent magnets
Post by: haversin on November 03, 2019, 06:01:36 PM
Nice work. I believe the voltage induced by the sense coil is caused by the rate of change of magnetic flux through the coil (perpendicular to plane of the coil). You are trying to measure the flux density parallel to the plane of the coil. The 3.06 milliwebers you are measuring is the flux inside the center post at z = -4.5 If you made a small sense coil and placed it perpendicular to the magnetic field inside the top plate gap, zeroed the integrator and then took the small sense coil out to a zero field place and divide the flux reading by the area of small coil times number of turns, I bet you would get close to the 0.6 T.
Title: Re: Measuring permanent magnets
Post by: davekni on November 04, 2019, 01:56:57 AM
My first thought is exactly what haversin suggested, a small coil, well under 1.5cm diameter (at least in direction being pulled).  However, there's already enough information in kugesmith's last test.  The field within the gap is proportional to the derivative of total flux vs. initial test coil position.  From the graph, it appears that the flux changes from ~80 to ~220 kilomaxwells over the range of 0cm to 1.5cm, a 140 kilomaxwell change over 1.5cm.  That 140 kilomaxwells must be passing laterally through the gap.  For a gap area of 26.3 cm^2 (0.00263 m^2), the field is (0.0014 weber / 0.00263 m^2 =  0.53 Teslas).

An average over the 1.5cm height of 0.53 Teslas may be perfectly consistent with 0.6 Teslas at the center.  Earlier this year I ran some magnetic field simulations for some linear-motor design options at work.  I was surprised how much field spreads out at the ends of the pole pieces.  It was a dose of reality on the difficulty of producing efficient linear motors, and the value of tight clearances.

If the data had enough resolution, the points at 0.5cm and 1.0cm could be used to generate a center field value.  I didn't see any detectable slope change over the 0 to 1.5cm range.  If that's accurate, then the field really is 0.53 Teslas over the entire gap.

BTW, I hadn't seen a commercial flux meter before your picture of one above.  I'd built my own in 1991 for a work project, which I now use occasionally for home projects.  The scope integration version works well too, especially with a scope that includes area-under-curve as a measurement option.
Title: Re: Measuring permanent magnets
Post by: klugesmith on November 04, 2019, 04:50:08 AM
Thanks for the feedback, guys.  Hats off to Dave for making a voltage integrator for this purpose. You need a very delicate knob to adjust the amplifier's input offset voltage, which determines the rate that output drifts when input voltage is zero. I think the model 916 has three switchable capacitors and about 8 switchable resistors, with lots of range redundancy -- like bicycle gearing.   When I integrated digital-oscilloscope waveforms for fluxmetering a transformer, I found the scope channel offset voltage to be hugely significant.  Needs to be numerically taken out to make the integral of an AC cycle return to its starting point, or to have flat lines before and after a coil-moving event like we're talking about here.

Following haversin's lead, I'm going to 1) stick with SI units and 2) flip the chart to show flux difference from infinity instead of flux difference from root of the magnet's "center bar".  I think it was handy, when everybody used cgs units, that the maxwell is a very small amount of flux in most engineering applications.  Technical trainers could often equate it with one discrete "line of force".  Follow the "line" along its whole loop, since it has no beginning or end.

Before haversin's comment, I'd overlooked that our 3.06 mWb represents total flux in the center bar at its root.  That would make the average B value 1.67 T.  There's the bottleneck (duh!). 

If we temporarily pretend that sense coil is barely outside the center bar, the "dF vs z" curve shows a decline from 3.06 mWb at the root to 2.18 at bottom of "gap", 0.89 at top of "gap", and 0.26 mWb at the top end of center bar.  As Dave said, that flux had to go somewhere, and had to get there by passing into air at the outer surface of center bar.  So between any two values of z, we can divide the delta F by the area of associated short cylindrical section, and correctly get the average radial flux density in air next to the cylinder. I think the B field orientation there is almost purely radial (axial component very small, unlike inside the steel) because of large permeability ratio.

Couldn't resist making some sketches to go with unfamiliar directional interpretations of what I think is called Faraday's law.

The "flux perpendicular to plane of coil" is a simple place to start.
Change of flux, inferred from the induced voltage-time integral, tells us the average B inside a sense coil with area As. If the coil is around a highly permeable bar like a transformer core, we can figure the average B within the core area Ac.
Next pictures are like some in physics books, where the B field doesn't change but the sense coil moves or changes area.

The last one is classic sliding-bar problem.  If the bar is moving vertically, there's an induced voltage proportional to B times the rate that area is swept by the bar.  (If we allow current to flow, the Lorentz force resists the motion of the bar, and power V * I matches the mechanical power needed to keep the bar moving).

I think my rectangular-coil drawings are representative of horizontal sense coil in a loudspeaker magnet, if we take a viewpoint from the magnet axis.  Think of the air gap unrolled to lie flat, and the direction of B is parallel to the direction from which we are viewing the gap.  The real green-wire sense coil corresponds to the lower horizontal segment of rectangular coils in the drawing.

But wait, there's more.  Faraday's law remains valid for flux not perpendicular to plane of sense coil.  In fact the coil doesn't need to be flat, for example it could be shaped like the seam on a baseball.  And we can choose any surface that's bounded by the coil.  For real B fields the answer will always be the same: how much flux threads the sense coil "loop"?  You can't pick up more or less flux by any distortion of the sense surface.
Title: Re: Measuring permanent magnets
Post by: klugesmith on November 04, 2019, 11:46:34 PM
Dusted off a FEA program called FEMM and entered the axisymmetric magnet geometry.  Included air vent hole along the axis, but none of the large chamfers on four corners.  It's my first use of permanent magnet material in that program.  First guess from PM materials library, with default strength, at first glance gives realistic flux values in center bar.  The concentric spherical shells are some kind of boundary condition that approximates an infinite universe, and was set up by a built-in wizard.  I'm impressed.  Hats off to David Meeker!

For a different problem, anybody know of a magnetostatic simulator that can handle real 3-D models, and does not cost an arm and a leg?
Or have access to one, and has time to enter a model about twice as complex as the one shown below?  Thanks.

[edit] Replaced a previous image after 1) adding chamfers to the model, 2) adding a contour for field charting (red line, matching the radius of existing sense coil), and 3) playing with the field chart.

Chart notes:
|B| is just like it came from FEMM simulation, using default value for the "Ceramic 5" magnet material strength.
"center bar flux" is by me, from integrating |B|, scaled to start at 0.306 to match measured "root" value from yesterday.
"B^2" is by me, with arbitrary vertical scale.  It's what will matter when we calculate the eddy current drag on falling pipes.

Who else remembers the movie "Close Encounters of the Third Kind", and its musical note sequence?

General note: FEA makes it easy to gain insight and make glitzy presentations.  But when lab measurements disagree with FEA, start with assumption that the FEA needs adjusting.
Title: Re: Measuring permanent magnets
Post by: davekni on November 05, 2019, 04:57:59 AM
Nice FEA simulation!  At first the flux dip at the center of the pole piece surprised me, but it now makes sense.  My crude 2D simulations were for NeFeB magnets directly as pole pieces, so low permeability, with no flux dip at the center.

Yes, offset is critical for flux measurement (voltage integration).  For scope measurements, manual subtraction of the volt-second area from a period prior and/or after the motion is needed for accuracy.  My 1991 meter design measured offset prior to and after the coil motion (measurement window), then interpolated to the center of the measurement window.  That handled linear drift in offset as well as fixed offset voltage.  Microprocessor SW ran that offset calculation prior to result display.  (Interpolation because it waited longer after the pulse for a stable period to measure offset.)

The easier part for my design was having a single scale range.  It was for manufacturing calibration of a sensor, so the expected results were in a relatively-narrow range.  (Did incluide two sensitivity levels for voltage amplitude to trigger a measurement.)

How much did you need to scale B to get 0.306 integral?  Shouldn't you scale the first B plot by that same factor?

Thank you for the interesting topic.
Title: Re: Measuring permanent magnets
Post by: klugesmith on November 05, 2019, 10:16:24 PM
You're welcome, Dave.  This is fun.

Re. previous scaling of simulated flux to match lab measurement: that was done with no attention to inch/cm and 2pi factors.

When done more carefully, after refining the simulation geometry (but not adjusting any material properties),
the match is shockingly close.  On the order of 1%.  Is that because of a lucky coincidence, or because PM ferrites are pretty standard materials (with standard magnetization)?  Maybe the saturating center bar is acting as a flux regulator.  I've made no effort to note the magnet temperature in these experiments.

Recent fluxmeter measurements consistently say 1.523e6 maxwell turns, 2.5 mm above the root of center bar.  3.046 mWb.
Steel area of the hollow center bar is 15.2 cm^2.  If measured flux were all in the steel, average B would be 2.00 T.

The simulation at same z position, with focus on normal (axial) component of B, shows
B range 1.967 to 1.984 T in the steel, average 1.975 T, steel flux 3.004 mWb.
B range 0.025 to 0.032 T inside the hole, for flux of 0.009 mWb.
B range 0.044 to 0.057 T between steel OD and sense coil radius, for flux of 0.036 mWb.
Total flux 3.049 mWb, which is 0.1% more than we measured with fluxmeter.   ::)  Fluxmeter has not been calibrated since I bought it on ebay about 10 years ago.

Next part: refined z sweep with fluxmeter.  A paper sleeve fits closely outside the felt coating of center bar, and inside the sense coil pipe.  It was rolled on a clear plastic pipe with just the right diameter (what I call "serendipity of fit"), that served in a bong 40 years ago.  Together, they guide the sense coil with hardly any freedom of motion except for z and theta.

Here's a chart of the measured fluxes, and computed radial flux density vs z (at the radius of our sense coil).

Some zones were re-measured after looking ugly in B chart, which turned out to be a computation blunder due to irregular spacing of z values.

The simulation can give insight about how the flux profile changes with radius, and concentrates near the edges of inner and outer pole pieces.
Of course B is systematically lower as we move away from the axis.  Green curve is from simulation at the radius of real sense coil.

Here are a couple of loose ends to be tied, before we close the book on this measurement exercise.

A fish scale says the magnet + handle weigh about 7.5 kg (17 lb).

Conventional direction of flux is radially outward in the gap, from N to S pole outside the magnet. Returning S to N pole inside the magnet.

If I were teaching electromagnetic stuff, I would never ask students to remember the signs.  Right hand rule, OK, but which finger goes with which field variable?  In practice, if 50% of new designs were backwards on the first try, almost all of them could be made right by swapping 2 wires or changing 1 character in software. (note 1)

Who can tell us about sign conventions in 3-phase AC power?  Do plugs and receptacles, or wire insulation colors, have a defined phase order?  When installing 3-phase electric motors, do electricians try to get the rotation right more than 50% of the time?  (Swap any two wires to reverse it.)

Note 1. A space probe bringing comet dust to earth crashed in the desert, because an accelerometer (to trigger parachute) had been installed upside down.
Title: Re: Measuring permanent magnets
Post by: davekni on November 06, 2019, 03:38:25 AM
Impressive precision and patience in measurement taking!  Great to see the simulation-experiment match, more the shape and details than the absolute value.  The absolute match is probably part luck and part precision.  If I recall correctly from my last look, there are primarily two varieties of ceramic magnets, one cheap and weak version, and a more common comparatively strong version.

As you mentioned, temperature is significant too.  My big 110lb levitron (levitating spinning magnet top) needs adjustment with just a few degrees of temperature change (~3C).  It's a combination of the 55lbs of ceramic base magnets (and 55lb of steel), and the small spinning NeFeB top.  (That's another fun simulation project.  Per simulation, there is a roughly +-1% range of stable weight range for the top, with given magnet strengths.)
Title: Re: Measuring permanent magnets
Post by: klugesmith on November 17, 2019, 03:02:45 AM
The first B measurement in this thread was based on the lifting force of a coil ( newtons per ampere = teslas X meters of wire ).
Yesterday there was time to do it with more care, and with witnesses. 
This time the answer was B_max = 0.50 T, very close to the results from fluxmetering and simulation.

Same 12-turn red-wire coil as pictured above, but different ballast and much better mechanical guidance. The coil is taped to a short piece of 2" Type L copper pipe, altogether weighing 29.50 g (0.289 N), sliding on a central post with less slop than before.  275 mA was the minimum current at which the coil could stay up at a sweet spot & not fall into the abyss.   As indicated by panel meter on a different lab power supply, far short of NIST-traceable instrumentation.  Bl product is 1.052 N/A = 1.052 T-m, from 2.107 m of red wire.

If the original subwoofer's Bl product had been 21 T-m, it would have needed 20 times more turns (effectively) in the main magnetic field.  Maybe just as many extra turns outside the main field, above and below, for reasonable linearity at large excursions.  A compulsive reverse engineer could figure the wire gauge to get 500-700 turns within estimated voice coil length and thickness.  What resistance would that have at room temperature?  How much more resistance after 100 degree temperature rise?
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