Doing the Math

[Arlo1]

Awesome!

[Kingfish]

FEMM Studies – Part VII

Eric, I wish to post this series as the last of the physical studies before moving on to magnetic circuits.

Lensing Effect:
In the next series, the boundaries remained the same: 0.5 to 0.9 T. I observed that the geometry lent itself to lensing when in a particular configuration. Many years ago I became an early student of magnetic lensing when working directly across the street from the world’s largest magnetic fusion facility at Lawrence Livermore National Laboratories in 1985. The question in my mind is how malleable is the field shape and strength given the primitive shapes at our (theoretical) disposal?


Figure 22A: Same as 21D with 4 mm high Halbach magnets, 3 mm high center magnets on the left, and 4 mm high center magnets on the right. In addition, I have added thin Focusing Magnets (FM) to each external rotor; left-side is 1 mm high, and the right-side is 2 mm. This does a nice job of aligning the FD perpendicular to the magnetic face, and homogenizes the distribution within the stator region, with the right-side profoundly enhanced. But this arraignment is very complicated, and I’d wager expensive. Nice peak density though!


Figure 22B: Let’s step back and evaluate the focusing magnets with a single center magnet array. Left-side is 4 mm high with a pair of 2 mm high FM. Right-side uses 5 mm high instead of 4 mm. Check out the peak FD! When I modeled this arrangement I had to go reset the boundaries for Figures 21 and 22. Notice the profound X-Pattern between the Halbach arrays. Maybe the center magnet width could be reduced; let’s investigate.


Figure 22C: Oh this is definitely a step-backward and very much in the same vain Figure 20 series. Less is not more. What if we reverse and grow wider?


Figure 22D: On the left 4 mm high magnets, Halbach and center poles are the same width. The FM are unchanged at 2 mm high. Right-side is 5 mm high. The left-side had a broader density though I think Figure 21B has better peak, however the right-side is arguably enhanced. Let’s take this one more step.


Figure 22E: Left-side 4 mm high Halbach and center poles, with 2 mm high FM on each side and again as a pair applied to the center rotor. On the right-side I increased the center pole to 6 mm high. Both sides experience peak FD near 0.9 T.

Conclusions:
The FD can be focused more effectively by placing smaller geometrics in key locations. However it is unfortunate that with manufacturing being what it is that we are limited with using rectangular shapes as oppose to curves or splines - and therefore would like to conclude this aspect of investigation.

Leaving this subject; moving on to Magnetic Circuits.
~KF

[Kingfish]

FEMM Studies – Part VIII

Magnetic Circuits:
After studying the examples in FEMM, I selected two configurations and reinstated the stator coil geometries.

Eric, allow me to explain what I did to create these models.

1. We are focused on 2-Stators/3-Rotors;
2. Stators follow the Plan-D except we now have double the windings, therefore the Current drops from 1.6 A for a single Stator to 0.8 A for a double. Additionally, I defined a single circuit of i = 0.8 A
3. All magnets are NdFeB 52, in either 4 or 5 mm thickness.
4. The Winding material is 1 mm Magnetic Wire with an Electrical Conductivity of 58 MS/m.
5. I am using a new material definition of Aluminum 7075 with an Electrical Conductivity of 20.88 MS/m.
6. Each Copper section (there are two-pairs) belongs to Circuit i with 33 turns.
7. Plots are 0.5 to 0.9 T

Figure 23A: 4mm high magnets. Looks great! We can observe what might be the influence of the winding upon the Flux Density.


Figure 23B: 5 mm high magnets. This has an anomaly and appears unaffected by the winding. I rebuilt the model from scratch and there was no change.

Eric, I am going to PM the files over to you; maybe you can spot my error. I did do a little bit of toying around but I will wait for your direction because I feel like I’m fly-fishing in the dark without a flashlight.

Thanks, KF

[rhitee05]

There was only one thing wrong with your model - direction. You modeled the coil correctly, but on one side the number of turns needs to be negative to indicate the opposite current direction. Even so, you wouldn't see any difference. Try looking at this:

Stator Only.png

Stator Only - all magnets replaced by Al 7075

(37.42 KiB) Downloaded 188 times

If you look at the scales, you'll see that the fields due to the stator currents are a very small fraction of the PM fields. The change in the combined fields is almost a rounding error. Now, for some analysis using the model you sent!
(AF-Mag-2S-4mm-Circuit)

The first useful result is to simply show what the normal component of B is at the stator. I added a couple of nodes at either side of the magnet arrays, midpoint between the first and second rotors where the first stator would be located. On the analysis screen you can use the contour tool to define a contour along any path between nodes (as many nodes as you like). Direction matters (a sign change), I went bottom-to-top. You can then hit the plot button, which gives you a selection of values to plot along the length of your contour. If you select B.n, it gives the plot shown below:

Stator Contour.png

Normal component of B along stator

(72.49 KiB) Not downloaded yet

Just as the graphics show, there is a nice even distribution of flux across each pole.

Another useful thing would be to see how much flux is passing through our coil. Using another set of nodes we define a contour through the center of the coil, and use the line integral function. If we choose B.n it gives us the total flux in Wb and the average flux in T:

Coil Flux.png

Flux coupled through coil

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Now we're getting somewhere more useful. We can make one more calculation which gets us the number we're really looking for - torque. Using the block select function on the analysis page, we can select the 4 blocks which make up the coils. Clicking the integral button gives us a number of options. We can choose Lorentz Force, which does the J x B integral for us:

Lorentz Force.png

Calculation of force on coil

(52.09 KiB) Downloaded 188 times

We can use this number to get an estimate of torque production. But, hang on one second before you hit the calculator.

It's useful to note here that only the upper 2 coil blocks are really contributing anything to the force. You can verify this by re-calculating the integral with only those blocks selected, but it should be obvious since the flux density is very small for the lower blocks. If we modify the model for a case where both sides of the coil are producing force we get the expected 2x increase:

Lorentz Force2.png

Calculation of force on wider coil

(52.67 KiB) Downloaded 188 times

Now, to take those force numbers and get something useful out of them. The first thing we have to understand is the model. This is a planar model, which is basically a 2D case with some assumed thickness. The thickness doesn't affect any of the magnetic calculations, but it does affect the force calculation (the L term in the equation). KF made this model with 1mm thickness. So, we multiply the calculated force by the actual width of the magnets (20 mm), then use the average radius (90 mm) to calculate torque.

With those numbers I get:
0.0706N * 20 * 0.090m = 0.127 N-m torque for the 2nd case (both coils producing torque)
0.0326N * 20 * 0.090m = 0.059 N-m torque for the original case

If memory serves, the current design was 10 coils/phase, so total torque would be ~1.3 N-m. A little comparison shows that is nowhere near the 33.9 N-m design torque. Something seems amiss in either calculations or model...

[Kingfish]

There was only one thing wrong with your model - direction. You modeled the coil correctly, but on one side the number of turns needs to be negative to indicate the opposite current direction. <snip>

D'oh! Thank you for pointing this out

With the first plot, other than delete the materials for the rest of the model, what were the precise steps you took to model the coils?

Also thanks for spotting my units issue; my bad

<snip> If memory serves, the current design was 10 coils/phase, so total torque would be ~1.3 N-m. A little comparison shows that is nowhere near the 33.9 N-m design torque. Something seems amiss in either calculations or model...

I think I can help with that. Let’s accept the reported value:

0.0706N * 20 * 0.090m = 0.127 N-m torque for the 2nd case (both coils producing torque)

And that there are 10 coils/phase; 10 * 0.127 N-m = 1.27 N-m / phase.

From Plan-D

32 Poles / 16:1, 30 Teeth / 10 teeth per phase
F = Ï„ / r = 33.9 / 0.090 m = 377 N
Wheel spins at 7 rps.
@ 16:1 & 7 rps, the Frequency (f) = 7 * 16 = 112 Hz
The original problem has Current (I) = 44 A.
We calculated that the actual Current/Phase = I/√3 = 44 A / 1.732 = 25.4 A / single phase of a 3-phase circuit.
Therefore 25.4 A / 112 = 0.227 A / phase
However – we changed the original radius from 0.3048 m to 0.09 m for Plan-D, a factor of 3.387. Therefore the new phase current is
0.227 * 3.387 = 0.769 ≈ 0.8 A

This is the actual value applied to the coils in the model; math is validated.

What happens if we reverse the math for Torque / phase?

Given 1.27 N-m / phase, @ 112 Hz * 3-phases =>
1.27 * 112 * √3 = 246 N-m applied Torque per second

Would this not imply that our magnetic utilization is very good?
What did we miss?
~KF

[rhitee05]

With the first plot, other than delete the materials for the rest of the model, what were the precise steps you took to model the coils?

Changing the magnets to non-magnetic material and correcting the coil so the lower block has -33 turns were the only changes. Run the analysis and the resulting field will be that solely due to the current.

From Plan-D

32 Poles / 16:1, 30 Teeth / 10 teeth per phase
F = Ï„ / r = 33.9 / 0.090 m = 377 N
Wheel spins at 7 rps.
@ 16:1 & 7 rps, the Frequency (f) = 7 * 16 = 112 Hz
The original problem has Current (I) = 44 A.
We calculated that the actual Current/Phase = I/√3 = 44 A / 1.732 = 25.4 A / single phase of a 3-phase circuit.
Therefore 25.4 A / 112 = 0.227 A / phase
However – we changed the original radius from 0.3048 m to 0.09 m for Plan-D, a factor of 3.387. Therefore the new phase current is
0.227 * 3.387 = 0.769 ≈ 0.8 A

This is the actual value applied to the coils in the model; math is validated.

What happens if we reverse the math for Torque / phase?

Given 1.27 N-m / phase, @ 112 Hz * 3-phases =>
1.27 * 112 * √3 = 246 N-m applied Torque per second


Would this not imply that our magnetic utilization is very good?
What did we miss?

Ah, now I think I see where the issue lies. The torque production and the electrical frequency are unrelated! We can show this using dimensional analysis - frequency is not a unit-less quantity - Hz is 1/s, so if you take amps and divide by Hz, now you get A-s which is not what you want. Similarly, if you take N-m and multiply by Hz, you get N-m/s - I'm not even sure what that is, but it ain't torque! Sorry I didn't catch this sooner.

Let's back up to the current calculation. I agree with you to the point where we say 44 / sqrt(3) = 25.4 A per phase. All of these should be RMS values, so no further correction is necessary. If we take that current value and plug it into the FEMM model, and change the model depth to the proper 20 mm, we get a J x B force of 44.5 N, or 445N total over the 10 poles, or finally 770.8N for all 3 phases with the factor of sqrt(3). That works out to 69.4 N-m torque. That's significantly more than the initial design value (about 104% more), but this is a dual-stator design and the flux density is ~0.75T vs. the 0.5T value used in the prior calculations.

A much better result.

[Kingfish]

Yea!

OK, I clearly see that I am still stuck in the sandbox with my maths - but at least there is a rainbow on the horizon

This sound to me that we are likely on par with 3 mm magnets, and much better with 4 mm then - and just about on target.

Let me get to fiddling about then and see if I can replicate your steps.

Mucho pleased & many thanks! KF

[rhitee05]

Another very useful thing to do with modeling is to figure out the structural forces due to the magnetic fields. An axial-flux motor has a powerful tendency for the two rotors to crush together due to magnetic attraction. The structure of the motor has to withstand this, and in particular the rotors must have thrust bearings or other appropriate measures. We can use FEMM to estimate this force for the structural design.

First, some theoretical background. It's not a trivial task to calculate force due to two permanent magnets. There are formulas for simple cases, like two dipole magnets in free space. There are no formulas for something like a motor, but there is a general technique which can be used to find the force indirectly. We can use basic physics to find that F = - grad(Wm), where Wm is the stored energy in the magnetic field and grad() is the gradient (directional derivative).

I can illustrate this using a simple example. Lifting an object off the ground gives it some gravitational potential energy. We need to do some work in order to lift the object, and simple conservation of energy tells us that the increase in potential energy is equal to the work done, where work is E = F * d, force times distance. We can apply the above principle to find the force. We know that potential energy is U = m*g*h. To find the vertical force, we find dU/dh, which gives us F = - dU/dh = - m*g. This is a fairly obvious result - we already know the force on the ball is its weight (mass * gravity) in the downward direction. But this illustrates how our calculation will work.

In the motor, there is energy stored in the magnetic field (ignoring the windings for now, speaking only of the permanent magnets). Specifically, we can look at the energy stored in the fields contained within the motor airgap (note that in the coreless case this includes the entire volume between the rotors). If the magnets are pressed directly together, there is no airgap; this is the zero-potential case, just like an object sitting on the ground. As we pull the magnets apart, the potential increases, and by finding the derivative of the stored energy we can find the force. In some cases this can be done analytically, but in our case we will use FEMM and approximate the derivative using the limit definition: limit dWm/dx = (Wm(x+dx) - Wm(x)) / dx, as dx -> 0. That is, we can find the stored energy Wm for our model, Wm(x), then we will shift the element of interest (one rotor) very slightly and find it again, Wm(x+dx), then we can take the difference and divide by the shift dx. As dx approaches zero the result will approach the true value of the derivative. Since we are using a numerical model with limited resolution, we can't make dx too small or error will swamp the useful signal.

... and I'm going to leave it there for now. I don't believe the numbers I got from the first set of calculations, so I want to do a little verification before I post any numbers here. It might be a few days before I have time to get around to that. In the meantime, here's a Google Books link which explains the above:

http://books.google.com/books?id=2CbvXE4o5swC&pg=PA601&lpg=PA601&dq=calculating+magnetic+force+via+potential+energy&source=bl&ots=3WXTrxu3e5&sig=z7sDrimfYb-Bp0Wobbq0VIi8nYU&hl=en&ei=2ROzTL6rFYKKlweYqJjlDw&sa=X&oi=book_result&ct=result&resnum=2&ved=0CBkQ6AEwATgK#v=onepage&q&f=false

[Kingfish]

BeamBoy Studies - Part I

I’ve been off-line on this thread for a while and actually working in the background with Eric on the FEMM calculations, and he is correct that we must account for the structural forces on our motor design.

After FEMM another tool that I find useful is BeamBoy: A Beam Analysis Tool. I have version 2.2 which is easily found through an Internet search. I don’t have access to Mathematica and at $10k a seat I am in no hurry to purchase a license – however it is the software of choice for generating proper calculus. In the meantime we poor folk must eat with plasticware – and BeamBoy - though lightweight, does a good job at forking over the data.

Breaking down model for study:

• Exterior Rotor faces (covers)
• Magnets
• Internal Rotor

Observations:

• The forces of attraction on the Internal Rotor with magnets nearly cancel out (though one may wish to study the shear forces internally). The calculations suggested deflections were less than 5% of 1 mm per side.
• The forces between the opposing Halbach magnets are weaker than the forces between the Internal Rotor and the External Rotor magnets. We will address this momentarily.

To study the model with our limited tools, we analyze the cross-section of the forces acting upon the External Rotor through one magnetic pole. It helps that we are a coreless design which adds economy to the calculations.

Presumptions:

• Generally, in the United States our supply of aluminum plate is cheaper if ordered in inches. Therefore I used two sizes of plate for the study: 0.125-in/3.17mm and 0.1875-in/4.76mm.
• In a previous correspondence between Eric and I the forces of attraction were suggested to be 78N.

Instructions for BeamBoy:

1. On Launch, select metric units and a Beam Length (Outside R) = 0.124 m
2. Add Simple Supports at 0.1165 m and at 0.024 m (theoretical points between the Bearing OD and the Fastener Bolt Circle)
3. Add Point Load at 0.090 m (Plan-D midpoint) of 78 N
4. Add Beam Properties:
   
   1. Modulus of Elasticity = 71.7 GPa (Aluminum 7075-T6XX)
   2. Select Calculate:
      
      1. Rectangle
      2. Solid
      3. Width = 28 mm (2 magnets width for Halbach * 14 mm)
      4. Height = 4.7625 mm = 0.1875 inch (typical)
      5. Select Calculate, “Use these values”, Continue
   3. Calculate|Calculate Stress and Deflection (Ctrl-R)
5. Bottom Diagram: Deflection at the OD of the Hub is 0.178 mm.

I think we can live with 0.2 mm of deflection.

What happens if we twiddle with a couple of parameters though?

Hmmm, KF

[Kingfish]

BeamBoy Studies - Part II

Curious about the potential forces for various magnet heights, I performed a two-track analysis across a spectrum of dimensions.

Borrowing from earlier Halbach calculations I developed a spreadsheet which provided the essential theoretical data. Then I developed slightly more elaborate FEMM studies to provide the measured data. Using this approach we get a sense of the high and low margins – and the limits across the material heights, all which is useful for evaluating the structural behavior.



Figure 24 Explained:
The top-most formula is used to derive the theoretical peak flux density for a Halbach array. Much earlier in the thread I had considered using ¼-inch N52 cube magnets and I simply grabbed a copy of those rough calcs. To the right of that list is the study continued with various magnet thicknesses from 3 to 12 mm. The two rows of conditional formatting below that are:

• Peak Flux Density in Tesla (T) from low to high.
• The difference between present and prior result.

It is easy to observe that the economic benefits are slowly reduced as height of the material increases.

The middle formula calculates the Force (F) of attraction between opposing magnetic faces. To simplify my Excel calculations I split the task into two parts before totaling. The Theoretical is given first: This is the Force of attraction between the entire distance (internal rotor excluded) between the two Halbach arrays.

From the adjusted FEMM models, I integrated along a line passing through the cross-section of the flux corner-to-corner between the External Magnet-Pole and the Internal Magnet-Pole, and this value is registered as Average Measured Flux Density. Recalculating using the FEMM data, we can see that the Forces are stronger between measured poles than between the Halbach arrays.

I noted a trend and went further to calculate the difference between the theoretical and the measured Flux Density and the values suggest a constant derivation or error; something worth noting.

Choosing the worst case:
The thing about engineering is this: Never assume your model is absolutely correct; you know... shit happens. I have been considering the 4 mm tall magnets as the best economic solution, although going to 5 mm has merit as well. If I won the Lotto – sure 6 mm would even do, however 8 mm is out of reach. Now that I have agreed not to build an 8 mm, let’s use it for the ultimate material stress.

Using the Instruction for BeamBoy in Part I with a 4.7625 mm thick beam and 138 N Force, the deflection from the center is 0.315 mm at the point of where the hub spokes attach. We can do a lot to reduce that value, namely by carving the External Rotor out from a thicker plate and employing ribbing, leaving the 4.7625 mm thick part at the magnet backing; anything to shorten that unreinforced thin section. It should be noted that 0.315 mm deflection is pretty dang good because the actual deflection at the magnet face where the coils are located is about 0.2 mm which is what we really care about.

Going one step farther – just for peace of mind – using the same model I changed the Force to 300 N: The deflection where the spokes mount is close to 0.7 mm, and at the magnet-coil surface approaches 0.5 mm or nearly 50% of our air gap. Without optimization, with the wildest magnetic forces applied to a motor that likely cannot be assembled, the structural integrity of the design should still allow the wheel to spin – in theory.

Neat, huh? KF

[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

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...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.