Doing the Math

[Kingfish]

I believe we have taken the Halbach AF arraignment about as far as one could go, and the next step would be one of procurement. Plainly, the Halbach arrangement requires custom shapes to leverage the greatest performance. Spot-checking pricing, I have noted that the materials cost has risen over 30% since May. The validity of the path now comes into question:

• What happens if we use off-the-shelf materials instead?
• How would the design change?
• What is the cost-benefit?
• What other possibilities exist for AF?

Perhaps now is the time to explore a simpler design, a non-Halbach AF array

Assumptions:

• From previous studies we understand that thickness plays a large role in field strength.
• We also understand that the Halbach arraignment effectively doubled the magnetic flux density onto one face at the expense of the opposite face.
• Without using Halbach, AF designs benefit most by completing the magnetic circuit with high-permeability back-plates.
• The addition of said materials does not contribute to issues related with iron-core stators; they are separate.

Let’s embrace an alternative view and explore this new direction with vigor!

Appending TOC.

1. Math Modeling
2. Axial Flux Design, Halbach, Ironless-Stator, Axial Motor
3. Axial Flux Design, Non-Halbach, Ironless-Stator, Axial Motor

...one moment please as I update the sections...
KF

[Kingfish]

Axial Flux Design, Non-Halbach, Ironless-Stator, Axial Motor

Magnetic Circuit:
With non-Halbach arrangements the magnets are configured identical to the internal rotor with alternating N-S magnets separated by a distance in-between; the objects should not touch. The magnetic backing material should have a high-permeability factor: Magnetic Steel is an ideal choice though not the only one. I prefer not to give up the Aluminum 70XX-series alloy for support and weight; those calculations should be retained. Let’s explore the concept of using the laminations for backing.

We have two paths:

• Using a full backing plate
• Using wedge-shapes placed in-between

Using CAD and FEMM I modeled-up a comparison using ¼-in thick magnets with a 5mm air gap and 3mm thick M-43 Magnetic Steel having an Electrical Conductivity of 2.6 MS/m with roughly 5 laminations. Figure 25 shows the visual comparison.



Taking the integral across the center air gap, the left design with the full plate yields an average B.n of -0.715 T, whereas the right design with the wedges -0.617 T. Clearly the wedge option will not suffice.

I think it would be interesting to explore the various thickness and permeance qualities of laminate materials although perhaps it is more expedient to save that calculation near the end when we have a better understanding of the actual materials available and their associated costs. In brief, the backing plate offers the best choice for this design heading forward.

Comments?

My next post will consider off-the-shelf shapes.
~KF

[BrushlessinSeattle]

Hey KF,
Greetings from across the lake. I’ve read most of this discussion - good work so far. Ive been working on a similar motor (axial flux DD). From all of my calculations, Femm analyses and spreadsheets I’ve concluded that its feasible....just, but weight is a major consideration. To achieve sufficient flux density it seems necessary to use heavy backing plates or a Halbach array. Obviously I favor Halbach, but, as you know, custom magnets aren't cheap. So, I started thinking about ways to create a Halbach array with off the shelf magnets. This is what I have so far (excuse my bad CAD):

rsz_halbach.png

(12.82 KiB) Downloaded 87 times

The square magnets are these:
http://www.magnet4sale.com/10-pcs-N42-Neodymium-Magnets-3-8-Cube-NdFeB-Magnets-DIAGONALLY-MAGNETIZED.html

The wedges would also be off the shelf but I will need to research whats out there and see whether any would fit the bill.
The Femm analysis looks pretty good – about 0.8 T in the air gap.
Feasible? What do you think?
Just trying to keep the Halbach dream alive!

-BiS

[rhitee05]

Sorry I've been absent for a while. Stupid grad school, making me do work and such.

KF:
I think the standard magnet approach using flux rings is perfectly viable. The main consideration here is for the flux ring to be sufficiently thick that it doesn't saturate. FEMM will tell you this, so long as you have an appropriate material model, and it's also pretty easy to test after it's built. Laminations won't hurt, but I don't think they're really necessary. The flux ring shouldn't experience very much time-varying field, so I think the gains would be pretty small. It can't hurt, though, and I suppose it might be easier to find good magnetic steel in lamination-thickness pieces.

Brushless:
Welcome. I don't think I've seen a Halbach arrangement exactly like the one you propose, using a combination of 90-deg and 45-deg magnets. Standard arrays generally only use one or the other, and I've also seen an array using a combination of 30-deg and 60-deg magnets (the CSIRO motor). Have you tried a linear simulation of that array type?

I'm not sure if the geometry you propose with both square and wedge magnets will work, though. If you use standard wedge-shaped magnets you'll have wedge-shaped gaps between them. It seems like you'd need wedge magnets with a special shape to make that work. I'd love for you to correct me if you've figured out how to make it work. Keep in mind the earlier discussion between KF and myself that you don't want to leave air gaps between the Halbach magnets or it'll mess with the flux strength and distribution.

[Kingfish]

Halbach w/ Wedge and fillers:
Greetings Brushless! Welcome aboard

You have my admiration for posing your design; I too considered the layout early on. <nods> Eric correctly pointed out (as he did so with me earlier) that the Halbach arrangement requires all surfaces to touch for best efficiency. Other factors that influenced the decision move on:

• The cross-section of the magnets should be consistent between N-S and L-R (or diagonal) poles. Effects of varying widths: Reference FEMM Studies – Part V
• The highest pole-count off-the-shelf wedges available are 16, meaning a gearing of 8:1. The rotor would spin much faster than what we want for a BMX-to-700mm hub motor, though is well suited if reduction is planned.
• The cube-magnet approach was dropped due to the complicated assembly envisioned, opting instead for the simplicity of the custom-shape, or in this next chapter – common bar magnets.
• Cost: The bar magnets are less expensive than the cumulative cube magnets. Although I must admit the layout you propose is much less expensive than a custom-shaped magnet, and it is here that we must explore those merits!

Flux Ring:
Hi Eric
Saturation noted & flagged. I did a little study using different permeability and quickly concluded that the choice of material affects the flux greatly and therefore requires diligence to source what is commercially available in relation to manufacturing costs (stamping/machining/post-processing). Short-story: I need to find out what my local machinist is using for prototyping. I am open to cost-effective materials if anyone should like to offer up experience.

More in a moment… KF

[Kingfish]

Layouts:
I am still wedded to the 32-pole/16:1 gearing of Plan-D and do not wish to part with much of the research. Plan-D in brief:

• 32 Poles / 16:1
• 30 Teeth / 10 teeth per phase
• Magnet length = 20 mm (preferential designs for both 4 and 5 mm)
• Each Copper winding is 3 mm wide x 33 turns
• r = 90 mm / 0.090 m.
• F = Ï„ / r = 33.9 / 0.090 m = 377 N
• 2-Stators/3-Rotors

Working up a model for comparison, two new layouts using bar magnets are presented below in Figure 26.

• Layout A: Plan-D (Halbach illustrated simply with 2-magnets per pole).
• Layout B: Displays the use of 1.0 x 0.5-inch wide bar magnets with a small air gap in-between at the ID.
• Layout C: Same as B except 2.0 x 0.5-inch wide bar magnets with a small air gap in-between at the ID.
• The Yellow circle is the OD of a Nine Continent 280X hub motor for reference. Note that A & B fit neatly within the physical limits (as per design), whereas with C the actual finished assembly will increase the diameter from roughly 8 inches to nearly 10.
• Because we are not using Halbach arrangements it is presumed that we must increase other physical quotients to make up for the deficiency. I took the liberty of drawing the length of the magnets of A across B & C for reference (two red lines).
• Though B offers slightly longer lengths the Torque-arm is smaller and the magnets would need to be taller than 5 mm. The fact is I would not consider magnets less than ¼ inch (6.35 mm) high.
• Layout C is better suited in that the average Torque-arm is essentially the same as in Plan-D, although the magnet length is larger and the goal of creating a motor smaller than a 9C would not be met.
• There are shorter magnets; I can source 1.5-inch long magnets however that particular manufacturer has different heights and Gauss strengths.
• As an alternative (not shown), use the 1.0-inch long magnets at the same Torque-arm radius as Plan-D and just move on.

Privately, Layout C appeals to me as a candidate for a motorcycle hub.

Clearly there are many factors we could play with. FEMM studies shortly.
~KF

[BrushlessinSeattle]

Rhitee,
I'm fairly sure that the geometry will work. If you start with a ring of wedge magnets:

rsz_11halbach2.png

(25.85 KiB) Downloaded 123 times

...and then push them out along radial lines that bisect each magnet, you end up with rectangular gaps:

rsz_2halbach4.png

(32.42 KiB) Downloaded 123 times

In the gaps you could place horizontally magnetized block magnets. Im glad you questioned my use of diagonally magnetized block mags. It was a hunch, but after some Femming I discovered that simple block magnets at 90 degrees are more effective - thats a good thing.

KF,
It looks like your well on your way to a final design. I'll share my latest findings with you anyway - food for thought if nothing else.

Heres a Femm analysis at the midpoint (halfway between the inner and outer edges of the magnets):

midpoint.PNG

(111.52 KiB) Not downloaded yet

Im using 1cm thick magnets and a 1cm airgap

The average flux density is around 0.74T. Its higher as you move towards the center and lower as you move outwards - this will be no surprise to you given your earlier work

If I were to remove the intermediate magnets and slap a big, 1cm thick, steel plate on each side, I would get about .79T. A little better but at the cost of lbs of weight. I have to ride up Pine St towards Capitol Hill!

Wedge shaped intermediates would be better but would need to be custom made. This array is far from perfect but it would be cheap to implement and could be significantly lighter than a back-plate design.

Having said all of that, Im a complete amateur when it comes to this stuff. If I've made mistakes please let me know

[liveforphysics]

BrushlessinSeattle, Kingfish, (and other Seattle guys if they want)-

I bought a boatload of magnets to build halbach arrays for axial flux motors, and other materials, bearings, carbon fiber plate for the rotors, etc.

You're welcome to all stop-by sometime and have a little get together or BBQ to discuss/plan building some badass motors.

[Arlo1]

Im not invited

[Kingfish]

I think a local tribe pow-wow is in order! Arlo, git on down here!

Luke, name a date/time and let’s go from there. Pot-luck? Tell us what you want us to bring.

Brushless, just a couple of questions:

1. What is your targeted system geometry? Hub, out/inboard motor?
2. What is the size of the driving wheel(s)?
3. What is the top-speed that you intend?
4. What is your target voltage?

From that information we will be able to provide more substantial feedback.

Pine St.-Capitol Hill: Oh I know that route! I thought a good urban hill-climber was the one Luke and I took after a day of exploring SeaFair, beginning at Lake-WA Blvd/Lake Park Dr (at the park) up McClellan then north on MLK to E. Madison @WOT, then SE up on over the hill and down past Broadway, and at this point we corked around looking for food and wound up at about 8th and Marion (sushi). They’re all big long steep hills we take for granted in a car. IMM, Seattle has steep hills that parallel SF: How about that winding-burner from Alaskan Way to 5th Ave up Marion? With the right voltage, battery, and controller (likely modified) ~ any urban hill is possible (and 2WD is better).

Smokin' KF

[Arlo1]

I think a local tribe pow-wow is in order! Arlo, git on down here!

Luke, name a date/time and let’s go from there. Pot-luck? Tell us what you want us to bring.

Brushless, just a couple of questions:

1. What is your targeted system geometry? Hub, out/inboard motor?
2. What is the size of the driving wheel(s)?
3. What is the top-speed that you intend?
4. What is your target voltage?

From that information we will be able to provide more substantial feedback.

Pine St.-Capitol Hill: Oh I know that route! I thought a good urban hill-climber was the one Luke and I took after a day of exploring SeaFair, beginning at Lake-WA Blvd/Lake Park Dr (at the park) up McClellan then north on MLK to E. Madison @WOT, then SE up on over the hill and down past Broadway, and at this point we corked around looking for food and wound up at about 8th and Marion (sushi). They’re all big long steep hills we take for granted in a car. IMM, Seattle has steep hills that parallel SF: How about that winding-burner from Alaskan Way to 5th Ave up Marion? With the right voltage, battery, and controller (likely modified) ~ any urban hill is possible (and 2WD is better).

Smokin' KF

Im in I love pushing my self to lern as fast as possible and I have a axial flux project to start very soon so....
But I am looking at things and I dont see the benifate of a Halbach aray just yet and could someone explaing in laymans terms the reason it would be a benifit?

[Kingfish]

Arlo, for sure friend

The single primary difference between a Halbach Array (HA) and traditional motor magnet arrangements is that the HA consists of at least two magnets to create a single pole, and minimum four magnets to create the N-S pairing. Excellent short-subject here:

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

The primary value is that the magnetic field & associated flux density are flipped to one side as oppose to both sides experiencing forces. The field is not precisely doubled, though in layman’s terms it is effectively so, and this lends itself to significantly enhanced characteristics desirable in both magnetic levitation and drive systems where space is at a premium.

The HA also eliminates the “Flux Ring” associated with non-HA AF orientations. Without the Flux Ring, the magnetic circuit would leak from the system ~ and actually based on the FEMM studies it is better to say “flood”, for without the ring there is nothing but air to constrain the field. The HA, by implied physical arrangement, redirects the lossy field with measurably superior effectiveness over the flux ring.

With linear or even radial systems HA is pretty economical, however in the axial arrangement the magnets need to be wedge-shaped and in physical contact. It is this wedge-shape that is expensive for custom designs. It is definitely a huge tooling cost as Thud had pointed out earlier. The special feat of correct engineering requires that the design of the object fit within reasonable production, timely manner, and cost-effective. The raw materials must also be readily available.

<soapbox: ON>

When I began this study I initially had costs for a 2-rotor/1-stator down to around $600 for magnets ~ and I thought that was livable for a one-off prototype. Now I am looking at $2000 per wheel and it’s no longer a viable option. Small thread on the price shift. I think we can do better.

<soapbox: Off>

Using the same philosophy as we have with the HobbyKing LiPos for building battery packs, we leverage the mass-production units to construct a reasonable AF solution. Let’s grab some common inexpensive stock and make do with it! Note that the significant part of this challenge is that each magnet supplier is slightly differentiated on height, width, length, strength, and heat-tolerance: It takes a willingness to compromise on the ideal, and a spreadsheet to keep track of the assets.

I am going to pick one supplier, roll the numbers, and see where and how we can bake this AF cake into an equally tasty HA-alternative. Then we’ll pick another supplier and do the same. As we canvas and survey the possibilities, our additive comprehension of the indefinite envelope for opportunity will resolve as tangible, and once there we should be able to articulate a wide assortment of solutions.

Make sense? KF

[Arlo1]

Thanks kingfish. The most important part was the magnets doubble (or close to it) the flux on the one side all I knew was it canceled the flux on one side. This makes more sense now.

[BrushlessinSeattle]

KF, you asked:

What is your targeted system geometry? Hub, out/inboard motor?
What is the size of the driving wheel(s)?
What is the top-speed that you intend?
What is your target voltage?

1.Axial DD motor, built on a customized hub. I’ve built an experimental version of the hub. It comprises of two 1/3 length hubs which are separated on the axle so as to expose the center section of the axle (total of 4 bearings) . A stator could be attached to this exposed section. The rotors would then attach to each side of the split hub and possibly to the spokes at the outer circumference (if the radius is sufficiently big). Whether using a hub that is split in this way is a workable approach remains to be seen. Its clearly going to affect the structural integrity of the wheel but I hope to get away with it. Connecting the outer edge of the rotors to the spokes will help.
2.26”
3.25mph (or more)
4.No idea

LiveFor Physics,
Ive got a crazy work schedule right now which keeps me busy most evenings but I’d love to come by and see what you have going on, talk about motors etc… and you have carbon-fiber! That’s awesome. Afternoons?

[liveforphysics]

Im not invited

You've got a permanent invite to anything I'm doing Arlo*

*unless it involves girls in a quanity less than 3.

[liveforphysics]

Potluck sounds great.

I work nights, and generally 5-6days a week of >12hrs shifts. So I can make afternoons work if I sacrifice sleep (which is fine).

I need to pick my place up a bit though first. lol It looks kinda like a UFO carrying racecar and motor parts just exploded in there at the moment. lol

Maybe roll the dice and try my luck with another Craigslist maid, and try not to have it end badly (as all previous maid experience as gone...lol)

[liveforphysics]

Also, back onto the topic of this thread, have you folks seen this axial-flux hubmotor?

viewtopic.php?f=2&t=22255

[Arlo1]

Im not invited

You've got a permanent invite to anything I'm doing Arlo*

*unless it involves girls in a quanity less than 3.

Haha thanks man but I dont waste my time with girls anymore wait that came out wrong lol

[Kingfish]

Im not invited

You've got a permanent invite to anything I'm doing Arlo*

*unless it involves girls in a quanity less than 3.

Haha thanks man but I dont waste my time with girls anymore wait that came out wrong lol

Arlo, I think you meant to post that comment here: http://endless-sphere.com/forums/viewtopic.php?f=3&t=19479

~KF

[Arlo1]

Haha too funny! I am going to sit and read through this thread as soon as I can! And get started on the mini vierson multi layered axial flux motor for a practice run! Then the big motor will be for the drag bike! The good and bad news is the boss has a guy trying to get us $20 000 to get it off the ground! (Also bad because like luke I have to many projects and am not ready) But like Luke I also love the challange!

[Arlo1]

So luke warns me not to run an axial flux with out a halbach or an iron backing behind the magnets is this true and why? Is it just efficiency that suffers or more?

[Kingfish]

Arlo, you have brought up the $64,000 Question!

Allow me to direct your attention to the Figure 27A below:


The Magnets are ¼-inch / 6.35 mm thick using N42 material.

On the Left, we have a 2-Rotor non-Halbach Array (NHA). The backing plate – though illustrated, is set to exactly the same non-magnetic material at the rotor = Aluminum 7075. The Magnetic Flux field passes unhindered or constrained in any observable manner. The Right side is identical except that we have 3-Rotors.

Taking the Integral diagonal through the cross-section yields:

• Left: Average B.n = -0.561521 Tesla
• Right: Average B.n = -0.60282 Tesla

Seems kinda weak relative to a Halbach Array (HA) especially for the magnet thickness. Let’s change the backing plate material and observe the change. The backing plates are 3 mm thick total and the material = M-43, which is about 5 laminations. Figure 27B illustrates the profound change.



Taking the Integral diagonal through the cross-section yields:

• Left: Average B.n = -0.717422 Tesla
• Right: Average B.n = -0.690459 Tesla

The Left side is clearly improved by 0.15 T whilst the Right Side by 0.09 T.

For reference, let’s compare that to a HA with 6 mm thick N42 magnets as indicated in Figure 27C.



Taking the Integral diagonal through the cross-section yields:

• Left: Average B.n = 0.809887 Tesla
• Right: Average B.n = -0.751268 Tesla

Well, I believe we can readily ascertain that the Halbach Array provides substantial improvement overall ~ but we knew that. Yet there are still unanswered questions about the NHA, such as effects of design manipulation and the cost benefits.

EDIT: Forgot to add L & R to Fig-27C measurements.

More in a bit, KF

[Biff]

Well, I believe we can readily ascertain that the Halbach Array provides substantial improvement overall ~ but we knew that. Yet there are still unanswered questions about the NHA, such as effects of design manipulation and the cost benefits.

The benefit of the Hallbach isn't that clear to me. You have a lot more magnetic material in the Hallbach array than you do in the NHA design, if they both had the same amount of magnetic material which one would have the higher flux density in the airgap?

If I see the diagonal line used for integration correctly it looks like it is just in the airgap where the flux travels, rather than a vertical line through the entire length of the airgap. I see that the Hallbach has only 2 magnetic flux paths, but the NHA has 3, What is the total area where the flux travels between the rotor and stator. It is more of the total flux that interacts between the rotor and stator that determines its ability to perform work rather than flux density. If you can get more flux travelling past the rotor with the hallbach array for a given space then you can get a higher power density which would be the advantage.

[Kingfish]

Hi Biff

“…if they both had the same amount of magnetic material which one would have the higher flux density in the airgap?”

The amount of magnetic material is double to create a single pole for the HA as oppose to the NHA. Therefore the cost of the custom-shape HA is compounded. There are advantages and disadvantages to this, however – at this point in the thread we are focused on reducing that cost greatly by using off-the-shelf magnets, and to do that we need to make a few compromises:

• We lose our optimum shape.
• We gain a lossy air gap between the magnetic poles along the rotor face.
• We need to add a Flux Ring to capture the stray field, arrest flux leakage, and better concentrate the density between the rotors.
• The Flux Ring adds cost and complexity.
• The off-the-shelf magnets generally have lower Strength, thus we need to add more thickness to compensate.

To conclude, the configurations are as different as are apples and oranges. Imagine how inexpensive a linear HA would be to a NHA! And yet – the cost is prohibitive for prototyping an AF machine. Once production starts, this financial aspect would reduce with each completed assembly – so long as your magnet supply is solvent.

“If I see the diagonal line used for integration correctly… <snip>”

• The pole-count for the examples given above is the same for both HA and NHA: 32 poles/16 pole-pairs.
• At the mid-point of the magnet the average radius arm is also the same at 0.09 m.
• The Halbach magnets have a consistent cross-section whereas the NHA will have a very small air gap at the base and a very large one at the top: It deceptive looks like there are more poles with the NHA.
• We need only to model one N-S pole interaction for HA, though the NHA modeling requires terminating poles, hence there is an extra pole pair to balance the other side and this allows us to take a proper measurement through the air gap of the middle pole pair.
• Regardless of the configuration, the HA has higher Flux Density over the NHA with or w/o employment of the backing plates. And actually the HA would be higher if we used 6.35 mm thick magnets rather than 6 mm (I reused one of my earlier models for this comparison).
• Lastly, when comparing designs, there is no need to calculate the entire flux density of the system when a segment will suffice: Figure 27C representing a HA clearly has a higher flux density over Figure 27B NHA.

More...

[Arlo1]

What was the pull force rating of the magnets on the most effiecient motor (world record holder)? Could one not just figure out how to make a higher pullforce rated magnet??