Halbach Axial Flux Motor

Hobby Friendly Cubes

For those that want the job of assembling the discs to be made easier they have pre-drilled cubes of both directions available:

http://www.kjmagnetics.com/proddetail.asp?prod=B888-3



...this would make mounting the magnets very easy because all you need is an aluminum disc and some bolts and nuts to attach the magnets.

Don't overtighten... these magnets can crack easily... but this would at least make getting things glued together easier.

The Disc-to-Magnet Calculation

Look at a standard bicycle chainring. Each tooth is separated by exactly 1/2". With the Halbach array you need two magnets for each pole, so in effect if you use 1/4" magnets then the spacing of the magnets will be about the same as a bicycle sprocket.

30 tooth sprocket -> 60 magnets -> 30 poles -> 3 Phases -> 10 Pole count (360 rpm @ 60hz)

...so if you know the size of a bicycle chainring you can guess the size of the disc you need.

Another way is:

1/4" (0.25) * 60 = 15 / Pi (3.1415) = 4.77" diameter

But if you don't want to mess with the teeth of the sprocket then you can use a larger one and mount on the sides. (a better idea) I have a 43 tooth aluminum sprocket already and it has solid material from a diameter of 5.25" to 6.25" which would allow me to install 1/4" magnets without overcrowding. It might be easier this way.

N52 magnets are 12% stronger than the other ones:

http://www.kjmagnetics.com/proddetail.asp?prod=B444-N52



6451 Gauss

64 magnets for $25

Hi Safe,
I think this may be worth viewing
Found an animation of a Halbach array (Femm simulation) at

http://www.thebackshed.com/Windmill/FORUM1/forum_posts.asp?TID=1458&PN=1&TPN=3

Page 3 posted by Dinges on that site.
Shows the varing magnetic field strength in Halbach Array with Airgap from 1mm to 19mm. Magnets are
(10mmx10mm)N40
Luka

Accepting The Impossible

A week ago I would not have imagined that the Halbach was even possible. At this point there has been enough information (to my satisfaction) to be able to accept that this idea is for real.

Halbach arrays:

Double the magnetic strength on one side and cancel on the other.

Allow motors to be designed that use no iron and have tight flux circles.

Magnets are available for purchase in many sizes and often at very reasonable prices. (my likely purchase is going to be only $25)

Torque is a measure of magnet strength times radius from the axle upon which it rotates and so big discs with small magnets will generate impressive performance.

It looks like regular RC ESC's can be used as a controller.

Efficiency can be as high as 95-97%.

...it's almost "too good to be true" so there is a natural inability to adjust to something that breaks everything you were used to believing.

How Much Is Enough?

http://en.wikipedia.org/wiki/Rare-earth_magnet

http://en.wikipedia.org/wiki/Remanence

The top of the line Nd2Fe14B (sintered) magnets have Remanence values of 1.0-1.4. Your basic Unite motor ceramic magnets, Sr-ferrite (sintered), are going to have Remanence values of 0.2-0.4.

So roughly speaking the Neodymium magnets are going to be somewhere around 3-5 stronger based on volume.

If the radius of a Unite motor is 2" and the volume of the magnets are:

0.25 * 2.0 * 2.5 * 4 = 5 cubic inches

...then if you divide the volume:

5 cubic inches / 3-5 (say 4) = 1.25 cubic inches of Neodymium "equivalent"

Now if you start with 60 Neodymium cubes of 0.25 square you get:

60 * 0.25 * 0.25 *0.25 = 0.9375 cubic inches

So before we even start to think about the disc radius we are ALMOST equal in magnet strength to a Unite. Now lets adjust the magnet strength to the larger radius. We assume a new radius of 3" for the Halbach:

0.9375 * 3 / 2 (the Unite radius) = 1.40625 "equivalent" volume by comparison.

We should be able to conclude:

The Halbach disc will have 1.40625 / 1.25 = 112% of the magnetic strength of a 1000 watt Unite motor.

...this appears to be about right for a 1000 watt motor.

Larger?

Let's use the same small magnets and just have more of them on a bigger disc. If you start with 80 Neodymium cubes of 0.25 square you get:

80 * 0.25 * 0.25 *0.25 = 1.25 cubic inches

We assume a new radius of 4" for the Halbach:

1.25 * 4 / 2 (the Unite radius) = 2.5 "equivalent" volume by comparison.

We should be able to conclude:

The Halbach disc will have 2.5 / 1.25 = 200% of the magnetic strength of a 1000 watt Unite motor.

...this appears to be about right for a 2000 watt motor.

Magnets Purchased



http://cgi.ebay.com/100-Neodymium-M...emQQptZLH_DefaultDomain_0?hash=item5ad492a6cd

100 Neodymium Magnet Cubes 1/4"

$24.95 + $5 = $29.95

----------------------------------

The strength is N42 which is 12% less strong compared to the N52, but on a "price-per-magnetism" basis this is cheaper for more.

64 of N52 : $25 + "shippping" (probably 5$) = $30

100 of N42 : $25 + 5$ = $29.95

64 (N52) * 1.12 = 72 "equivalent magnetism"

...so the bottom line is you get 100 / 72 = 38% more magnetism this way.

Note: A 48 tooth chainring means that there is room for 48 * 2 = 96 cubes... exactly what I had in mind. (so the spacing is already done for me)

Stats:

Phases : 3

Poles : 48

Pole Count : 48 / 3 = 16

Total Halbach Magnets : 48 * 2 = 96 (purchased 100)

Motor Speed : (24" wheel)

60 Hz - 225 rpm - 16.1 mph

120 Hz - 450 rpm - 32.1 mph

180 Hz - 675 rpm - 48.2 mph

Power Output : 2000+ watts based on magnet comparisons

Total Magnet Weight : 192 grams = 0.423 lbs

Force vs Air Gap



http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html

Let's assume that the current in the wire is equal to I.

Now we add that the "air gap" between the wire and (in our case) a Halbach magnet disc is r.

We arrive at some value for the value of B.

If we then double the "effective current" in the wire by stacking up more turns of wire (or use thicker wire) then we might say that the new current value is (say) 2I. This then produces a magnetic field of 2B.

...what this is going to mean is that if we use the same "air gap" with a stronger magnetic field (B) then the "relative losses" due to that "air gap" DECREASE compared to the initial case. (that's the hopeful thought anyway)

-------------------------------

If you have a choice of using a stator that wraps all the way around the rotor or to use a stator that wraps around HALF the rotor... you can now DOUBLE the magnet strength of the half rotor and might get half the "air gap" losses.

Using a partial stator design might actually IMPROVE efficiency from the "air gap" perspective. (the hope)

Does that make sense?

The losses are decreased in the absolute, but since it's linear the losses might be the same overall. Hmmmm... from the standpoint of losses there might be no difference. Maybe we need to check.

--------------------------------

Let's try some numbers:

I = 1, r = 0.001, B = 0.0002T

...let's call this the "perfect case".

Now we figure what a normal "air gap" actually is:

I = 1, r = 0.002, B = 0.0001T (50% loss due to the "air gap")

Let's now try for the larger field:

I = 2, r = 0.001, B = 0.0004T

...again we figure what a normal "air gap" actually is:

I = 2, r = 0.002, B = 0.0002T (50% loss due to the "air gap")

-----------------------------------

So in the end it just doesn't seem to matter... (it's linear)

Small Halbach Motor Kit

http://gyroscope.com/images/halbach/circularhalbachmanual.pdf

This idea could be used for ebikes if you used the bigger magnets. (like 1/2" x 1/2" x 1/2" cubes)

If you wanted "insane power" you could use:

http://www.kjmagnetics.com/proddetail.asp?prod=BX0X0X0-N52&cat=168



Dimensions: 1" x 1" x 1" thick
Tolerances: ±0.002" x ±0.002" x ±0.002"
Material: NdFeB, Grade N52
Plating/Coating: Ni-Cu-Ni (Nickel)
Magnetization Direction: Thru Thickness
Weight: 4.34 oz. (122.9 g)
Pull Force, Case 1: 94.60 lbs
Pull Force, Case 2: 94.60 lbs
Surface Field: 6451 Gauss
Max Operating Temp: 176ºF (80ºC)
Brmax: 14,800 Gauss
BHmax: 52 MGOe

http://www.teicontrols.com/notes/SeminarEE155/MaglevVehicles.pdf

"The configuration of rare-earth cobalt magnets, called a Halbach array, concentrates the magnetic field on one side of the array as shown in Figure 7. Magnetic field strength is the "square root of 2" times greater than a conventional ironless array of the same volume."

All those previous magnet calculations actually need to be INCREASED in favor of the Halbach by about 40%.

The Halbach array is so awesome.

You get to increase the radius of the magnets. (Torque = Force * Radius)

...and you get a "free" 40% on top of that.