Doing the Math

[liveforphysics]

I love all your awesome work on motors and controllers Lebowski. Very very cool stuff.

I agree with your airpath thoughts, and it wouldn't take much for vanes to make it move some air if you spin it fast enough. Air moves at the square of RPM in those types of pumps, so you get roughly nothing at low speeds, and then at high speeds it comes on strong.

[rhitee05]

I've thought about PCB-stator axial-flux motors before. It's an attractive idea from the ease-of-manufacture standpoint. Luke is right that heat will always be an issue, also you'll likely never achieve the same kind of power density as a conventional stator design because the copper fill is fairly low (lots of fiberglass volume compared to copper). However, I don't think these are necessarily fatal flaws.

One way to improve the copper fill would be to go to a multi-layer board design. 4, 6, even more layers, possibly with the same coil pattern on each wired in parallel. The big disadvantage here is heat in the inner layers, as they will be fairly well insulated by the fiberglass. A possible solution might be to go with quite heavy copper on the outer layers and the standard 1/2-oz in the inner. The relative resistances will ensure that most of the current flows on the outer layers, to keep heat under control in the inner layers. A generous amount of vias would also help conduct heat to the outer layers where it has a chance to be removed by airflow. Multi-layer boards are more expensive, though, so it might be more economical to just use a 2-layer board with super-heavy copper. You might be able to use a thinner board than the standard 0.062", although there would be a tradeoff in structural rigidity.

I think the big thing to extract both reasonable power and reasonable power density would be to a) make the air gap super-small and b) use a multi-stator design. Since the PCB is thin and has good manufacturing tolerances, you could make the air gap very narrow, less than 0.1". That would give you very good flux density in the gap and thus a better Kt value, which would take the sting away from the lower current density. Now stack 3, 4, 5 of those stators together with n+1 magnet rotors, and you could probably get to some useful values of torque and power.

I don't think this would ever be a super-high performance design along the lines of what Luke likes. But, it might be something relatively simple to build, and perhaps an interesting engineering challenge to see what can be extracted.

[Kingfish]

Eric, that is precisely the route I am studying: Multilayer board with heavy copper clad, fat as I can fit traces. I use the PCB Trace Width Calculator to characterize options and note the heat rise. Don’t want a lot of heat; bad for business.

The problem with parallel traces though is that the current will never balance, so instead I thought of running the turns in series through the layers for a higher count, and then each stator is in parallel as you suggested with at least 2 stators and 3 rotors – as a starting point. Adding one more stator-rotor pair increases the output (F) by roughly √2; not quite 50% - but hey we’re already here so let’s throw another log on the fire.

The part where I took a tangent this last week is exploring how more turns reduce the current, but then we’re going to get more resistance (heat) and require more voltage. I’ve crafted a pretty happy model, though I don’t yet know how to get it to report the voltage back out; losses – yes, wattage – yes, system voltage - no. Running the Lua scripts is incouraging though. If the magnets didn't cost a kidney I would order up 256 pieces right now

For the pcb, I am thinking 3.175mm (1/8th inch) thick FR-4 to initialize the proof-of-concept stator, although I am searching for a tougher laminated substrate. Toying with a heat sink idea: Wouldn’t a couple of layers of solid copper work to pull heat from the board so long as I didn’t fill the center of the windings?

Electric Steel
Been doing my reading and modeling on M-19, M-4, plain iron from McMaster-Carr (not the ductile stuff) 1018 and 1006 Steel. The “Iron” material in FEMM performs the best, and all other materials appear to reduce the flux density (B) – and it has to be at least ¼ inch thick to drop B below 2T at 100% frequency; at 0Hz the flux ring is supersaturated above 5T.

The devil’s in the details: Hate to sell my real soul, though I might sell’m my leather sole… he can have both of them.

~KF

[rhitee05]

The problem with parallel traces though is that the current will never balance, so instead I thought of running the turns in series through the layers for a higher count, and then each stator is in parallel

Does it matter if the current balance is perfect? If the copper on each layer is identical and they're connected in parallel, it's something akin to stranded wire. If more current flows through the (thicker) outer layers, then less heat will be generated in the inner layers where it's hard to get rid of.

Adding one more stator-rotor pair increases the output (F) by roughly √2; not quite 50%

I don't think I understand why it wouldn't be a 2x increase in torque. Is there some other factor you're including that partially cancels that out?

Toying with a heat sink idea: Wouldn’t a couple of layers of solid copper work to pull heat from the board so long as I didn’t fill the center of the windings?

That would help with the heat, but eddy currents would bite you instead.

[liveforphysics]

You need to make use of every bit of copper available. If it's a 6 layer board or something, each layer needs to be as thick of copper as they make, then you need to figure out how many turns you're going to need (which is going to be a lot with no core if you want to have reasonable inductance), and then you need to make every layer as thick as physically possible to get the number of turns in you need. Anywhere you made it less thick would just be additional resistive loss and heating in an area that is all ready going to be nearly impossible to cool. The concept of balancing thickness between inside and outside layers is fundamentally flawed, you need to just do anything possible to reduce copper losses, and the layers should all be parallel. The ones that heat up faster will increase in resistance and get less of the current load naturally.

You're going to be in a situation where it may be impossible to even get 10% copper fill factor (haven't worked the math though, maybe you can find some super thick trace PCBs?" You are going to have extremely low continuous power, lots of motor heating problems, and lower than typical safe motor coil temperatures as well.

Keep in mind, even the 98% efficient CISRO motor would burn up at just 1.8kw, and it had WAY better copper fill and WAY higher efficiency than is even theoretically possible with your design.

[Njay]

A couple of loose thoughts:

1) Multilayer may get you a board so heavy that you'll drill holes to reduce weight - drill plated holes near the tracks to increase heat dissipation

2) Increase motor diameter - more torque. I've played a few time with this idea of having a motor almost as large as a wheel. It would have coils (maybe magnets; never really decided on that) and a comutator with brushes at the highest point, fixed to the bike's frame, with some magnets. The increased diameter would compensate for the "single pole".

[rhitee05]

You need to make use of every bit of copper available. If it's a 6 layer board or something, each layer needs to be as thick of copper as they make, then you need to figure out how many turns you're going to need (which is going to be a lot with no core if you want to have reasonable inductance), and then you need to make every layer as thick as physically possible to get the number of turns in you need. Anywhere you made it less thick would just be additional resistive loss and heating in an area that is all ready going to be nearly impossible to cool. The concept of balancing thickness between inside and outside layers is fundamentally flawed, you need to just do anything possible to reduce copper losses, and the layers should all be parallel. The ones that heat up faster will increase in resistance and get less of the current load naturally.

Totally agree with you that having as much copper as possible is desirable. I don't think you can rely on the thermal coefficient of resistance to handle the balancing, however. If you assume that 120 C is the maximum allowed temp, copper only has 39% more resistance at 120 C than at 20 C. That's not going to be enough to do much balancing if the inner layers don't have a path to dissipate heat. They'll just get too hot and de-laminate the board.

With a multi-layer board, I don't think there's any way around it except that you'd have to use a huge number of vias to conduct heat outward. If you did that, then the heat transfer might be good enough that you could use thick copper on all layers and rely on the thermal coefficient to regulate things.

Copper fill is definitely going to be low. Just tossing out some numbers, 6-oz copper would be 8.4 mils thick. If you put that on a regular 2-layer board with 60-mil FR4, it's about 28% copper by volume. Once you start actually cutting the traces that'll drop, so maybe 15-20% at best. You might be able to hit 50% if you do a really custom board with 6,8 layers of heavy copper and thin FR4 between.

You'd definitely want to make it as big (radius) as feasible. The issue there is that it's going to be hella expensive to make big, custom PCBs that you're only using the outer 2-3" of. I had an idea that you could maybe design it in partial arcs so that one PCB would be an arc-shaped piece, maybe containing a unit of 3 coils. It would be much more space-efficient to tile a bunch of those onto a sheet of material. Then you'd assemble the stator by stacking them together in an over-lapping fashion (there would be some important details in exactly how this was done, and you might end up needing some extra structure to stiffen the assembly).

[Lebowski]

I would take some 2 x 4 mm copper bar, isolate it by sheeting it with heatshrink tubing. Wind the bar
in a flat coil, solder one opposite it so you got a 4 mm thick structure with the connections on the outside
of the flat circular coils. Make a mould, put in all your coils, add epoxy et viola, there you have your coil plate.

[Alan B]

Use hollow copper material to pump cooling water through. Then it won't mind being embedded in epoxy. Otherwise heat fail.

[Kingfish]

Lots of good comments! Thanks Gents

For the record, I am working on the assumption that the operation limit is set to 120°C which keeps us in the game for good strong commercial magnets.

The way I went about calculating the stator was to approach the problem with the following in mind:

• Maximize the average radius to reduce the required Force (F) which in turn reduces the required current (A).
• Calculate the Length of conductor for a single stator.
• Maximize the length of the magnet.
• Calculate the number of Turns per Tooth.
• Using the Inner-Trace limitations and clamping the rise to 15°C, figure the thickest & width of the trace for the current with the acceptable maximum temperature rise.
  
  
  Conclusion: The trace will never fit.
• Add a matching layer and recalculate with layers in parallel. This eventually winds up being a very fat pcb. Using FEMM, the thickness proved counterproductive by reducing the flux density between the rotors.
  
  
  Solution: Add another stator/rotor of the same parameters and twiddle. The overall current drops per stator and the traces can be reduced further. I followed this development path all the way to 5 stators. (Shall we say ‘Money no object’?)

That’s where I was at about a month ago. I had a long commute into Seattle and there was time to kanoodle with different ideas… that’s when I thought about breaking form and going with more turns in series rather than parallel turns. Using that methodology I was able to save a layer for each stator, reduce the number of stators, and drop the current substantially with FEMM affirming the results both modeled statically and with the LUA scripts provided by Biff.

However – I don’t think these stators can be built. It would require vias between layers and how do you plate that? I’m a pretty clever guy; perhaps once I get into doing the design layout it might become self-evident, though it would be a challenge. To be certain I really need to speak to some quality pcb manufacturers to determine the limitations of manufacturing. The problem is that I am not convinced that FR4 will be the final production material.

• Specifically, what is the thickest copper cladding possible for inner layers, and at what cost?
• Dimensionally, most pcb houses can craft a board the size I need; that’s not a problem.
• What is the thinnest possible lamination? We’re talking voltages less than 200, so I know the dielectric can withstand whatever we throw at it.
• What other types of laminate can be used?

I’m open to other ways of constructing a stator – it’s just that the pcb or laminated-process has a great appeal in terms of unitizing manufacturing: Tooling-wise I think it would be less expensive and laborious.

Would someone care to take a stab at my original question about electric steel material candidates?

Most appreciative, KF

[Thud]

KF,
ellectrical (high silicon steel) is better suited to stator laminations & IIRC your using it as backng the magnets & keeping the flux in the general vacinity.

standard low carbon steel would be an advantage in that senario from my muddied mind.

Now, if you find a source that will cut me 100#s of .008"t ellectrical steel into 6"x 6" squares, I can get rolling on another project.

Glad to see you working in this thread again.
the penut gallery has spoken.

[Kingfish]

Hey Thud, howyadoin?

Electrical Steel:
Actually I’m using the term as a pseudonym because what I really need is back iron for the flux ring. I have tried various materials in FEMM, although the non-descript "iron" returns the best concentration. Perhaps the question would be better stated as

"What the heck are yous guys using for flux ring material?"

Glad to see you working in this thread again.

Heheh ~ I took a break for summer; had a little trip I wanted to take, just me and the bike. Now with winter approaching, time to return to the pipe dream <stuffing the pipe… just kidding> For a brief time I was thinking about Cheech y Chong Sister Mary Elephant wanting to explain "What I did on my Summer Vacation".

Yeah, time to get cracking and carve up some metal this winter; it’s practically all I think about now ~ a purpose-built wheel that could make even Luke smile (e.g. wheelie-capable).

Let’s make some fun!
Happy Friday, KF

[Kingfish]

So I have been pouring over my books again and for the type of motor that I’m building – coreless stator – it says that the magnetic flux ring, or yoke as they call it, can be CRS 1018; common low carbon cold-rolled steel. I find no examples of saturation above 2T except for the completely ironless Halbach solution where obviously it doesn’t apply. Hmmm…

The one good thing the book does discuss is that they are claiming multilayer printed ink boards (why don’t they just call it PCB?) are superior in performance over Litz and monofilament/ribbon winding, and two-layer PCBs as well owing that the multilayers act as parallel strands (Eric, take a bow).

Q: How can I model parallel layers within the stator using FEMM? Does each layer of the same phase become like A0, A1, A2… An? How can that be scripted?

Confuzzled, KF

[liveforphysics]

The one good thing the book does discuss is that they are claiming multilayer printed ink boards (why don’t they just call it PCB?) are superior in performance over Litz and monofilament/ribbon winding, and two-layer PCBs as well owing that the multilayers act as parallel strands (Eric, take a bow).

It's impossible for PCB traces to function as well as a ribbon coil. You're understanding the book wrong, or the book was written by some worthless college professor somewhere.

This becomes pretty self-evident if you just think about what portion of your desired coil area can be copper with a properly laid out ribbon coil (like Miles diagram'd for us years ago when we went through my first coreless axial-flux motor design thread, which first started out suggesting using stacks alternating PCB stators with magnet plates).

[Kingfish]

Luke, anything is possible under the sun of inspiration friend.

When we talk about using PBC layering or printed inks, my mind goes well beyond what most have seen in this world because the first job I had as a lowly Jr. Engineer was designing custom tooling for semiconductor microlithography. I personally have designed machines that could print on all sorts of oddly substrates, and I know firsthand what can be accomplished through UV and X-Ray spectrums, positive and negative photoresists, thick and thin films, various natural and chemical atmospheres and pressures, and depositions. I know how to design a dense circuit; just provide to me the practical limits of technology.

What I need to understand, and perhaps I should make this a priority next Monday, is the limitations of typical PCB manufacturing cos that is the least-expensive route to large layered circuits, and not a bad way to prototype a proof-of-concept.

Have faith, KF

[liveforphysics]

But... if you've got layers, it's impossible to match a ribbon. A ribbon is traces without layers of dead space.

[Kingfish]

At various times in the past few weeks during the dark winter days I have been studying several minor points of interest. One that has captured my attention is the effects of Back Iron materials and thicknesses relative to Current and Torque. The model of study is described as follows:

1. Beginning at the centerline, imagine a single stator, ironless, coils of copper bound within a rigid substrate, current flowing at a modest frequency.
2. Moving outward, airgap is next.
3. The line of magnets follows, N-S-N-S… unending.
4. Back Iron, thickness and material TBD.
5. Structural hub cover wall, also TBD.

I ran a few tests with FEMM and began with Aluminum 6061 for the hub cover, and 3mm of regular Iron for the Back Iron material, then a LUA script which methodically records the torque produced when Frequency is set to Zero, ramping circuits A, B, and C through current settings in increments starting at Zero. The results were pushed into a spreadsheet. I’m off to a good start.

What happens if we change the Back Iron thickness? I set that to 2 mm and rerun the script: No change. That’s odd. Changed the Back Iron to M-15: no change. This can’t be right. I decide to record the Flux Density across a segment of the stator beginning with the original criteria and note the level of Magnetic Flux Density verses Electric Field Intensity. Changed materials and thicknesses, and recorded the values in the spreadsheet. Clearly there is an expected relationship, although the results provoke more introspection than satisfaction.

The function of the Back Iron is to complete the magnetic circuit between the two opposing rotors more effectively than if by air alone, and in doing so – concentrates the flux in-between and allowing for better conversion of electric field strength into mechanical energy – torque. Weak field = poor conversion, and vice-versa. The focus of this study is to sort out the best solution given mass and effectiveness. Obviously the choice of Back Iron, and even the hub cover affect both Saturation, Density and Intensity. But why does it not affect Torque, at least as far as FEMM is concerned?

Perhaps I should state the obvious: There’s a bug in the LUA script. This is entirely possible and needs review. However there is another strange artifact of FEMM that requires identification when the Back Iron saturates at high levels. For the following, Circuits A, B, and C are at 10 Amps and the Rotor Frequency = 0. For measuring, I picked the same airgap having average density consistently.

Case 1: Back Iron material set to high permanence M-15 and adjusted the thickness until the saturation is about 2T. The airgap registers about 0.6T.
Case 2: Back Iron thickness reduced, saturation is about 3.5T. Airgap registers little change.
Case 3: Back Iron material changed out to Iron and the saturation climbs to 5.5T. Airgap now registers close to 0.7T.
Case 4: Reduce the thickness so that the saturation measures 8T. Airgap measure 0.75T.
Case 5: Push the model until saturation is about 10T. Airgap measure 0.8T.

The results were not expected: I would have presumed the airgap flux density to rise by lowering saturation and not the other way around. From observation, it appears that the Back Iron plays a role similar to a resistor by raising the potential between the two rotors, though more to the point: What is the maximum acceptable saturation of Back Iron?

The second observation is that the finer details of Back Iron appear lost once the rotor frequency rises above Zero. Perhaps this is the artifact that manifests in the LUA script results.

Curious, KF

[bearing]

Case 1: Back Iron material set to high permanence M-15 and adjusted the thickness until the saturation is about 2T. The airgap registers about 0.6T.
Case 2: Back Iron thickness reduced, saturation is about 3.5T. Airgap registers little change.
Case 3: Back Iron material changed out to Iron and the saturation climbs to 5.5T. Airgap now registers close to 0.7T.
Case 4: Reduce the thickness so that the saturation measures 8T. Airgap measure 0.75T.
Case 5: Push the model until saturation is about 10T. Airgap measure 0.8T.

Something has got to be wrong with your model. Maybe the properties of the iron materials are wrong. Seems like it never saturates. When the backing iron starts to saturate, the airgap flux should get weaker.

I have never seen something this strange in FEMM. It has always been close to what you would expect from theory.

Did you define boundary conditions? How much air is there around the motor?

[Kingfish]

Hi Bearing

I finally had some time to review the script. There is plenty of air space; that's not the issue. Instead, I focused upon the maths... from the script:

Code: Select all

  -- compute the force   
  mo_groupselectblock(1);
  Lorentz = mo_blockintegral(11);
  Force = mo_blockintegral(18);


... and this is measurement is repeated per each step through a full cycle of a circuit.

My Conductors are in Group 1. According to the help manual on Page 93, mo_blockintegral(11) = "x (or r) part of steady-state Lorentz force", and mo_blockintegral(18) = "x (or r) part of steady-state weighted stress tensor force".

Should I be looking at other integrals?

I am still looking for a good answer on calculating material saturation; it's like this big secret - deathly silence when asked.

Thanks, KF

[rhitee05]

KF,

I think you're running into a couple of issues here, some of which I've been dealing with as I'm simulating Miles' motor. All of them are pretty deep in the weeds, little land mines waiting for the unwary.

Something has got to be wrong with your model. Maybe the properties of the iron materials are wrong. Seems like it never saturates. When the backing iron starts to saturate, the airgap flux should get weaker.

I am still looking for a good answer on calculating material saturation; it's like this big secret - deathly silence when asked.

#1 - Saturation. I think you've fallen into a bit of a hidden trap here which FEMM has laid. I posted a note regarding this over on Miles' thread, which I'll repeat here. Most of the materials in the FEMM library, at least the magnetic ones, are defined via a list of points on the nonlinear B-H curve. This is a good way to model them, but the catch is that these models are only valid within the range where they're defined. FEMM extrapolates the models linearly outside this range, which results in non-physical behavior such as the relative permeability of iron not going to one for infinite H (it will instead stay constant at the value for the last two points defined). This lets you push B in the material way higher than it would ever go. You would never get 10 T in a real material. Most steels will saturate around 2 T or so for reasonable (achievable) values of H. The solution to this is quite simply to stay within the bounds of the model, or find material data to extend the model where you need it to be. If you get values of B greater than the maximum entry in the material B-H curve, you're in dangerous territory. All the B-H curves for "soft" materials I've looked at in FEMM have data well into saturation. For example, the model for 1006 steel has data to 2.3 T, which is well into saturation and past anything you'd really want to see in a motor.

According to the help manual on Page 93, mo_blockintegral(11) = "x (or r) part of steady-state Lorentz force", and mo_blockintegral(18) = "x (or r) part of steady-state weighted stress tensor force".
Should I be looking at other integrals?

#2 - Force. I've had iffy results from using the Maxwell stress tensor in FEMM. I'm deriving my force results from the magnetic coenergy instead. I'm not claiming that the stress tensor method is wrong, or that FEMM is implementing it wrong, but I've been getting much more believable results using coenergy. Perhaps I should try and find a reference case where experimental data are available for comparison and validation, that would be something good to do when I have time. I believe the FEMM documentation describes the coenergy method; if not I can help you. The other issue I had using the tensor method is that I had to use a very fine mesh size in order to get the results to converge, which was taking way too much computation time. No matter which method you use, you should be wary of convergence. That is, you should get basically the same answer if you make the mesh slightly smaller or larger. Numerical methods are notorious for this and it's another trap for the unwary. Also, you don't want to use the Lorentz calculation unless you're modeling an iron-less stator. Even then, the coenergy calculation is valid for all cases so I would suggest using it over Lorentz.

Did you define boundary conditions? How much air is there around the motor?

#3 - Regarding boundary conditions, I experimented with several. I ended up using a Dirichlet condition ("Prescribed A") on the outer edges of the back iron with all components set to zero. This basically forces all flux to stay within the iron (keeps flux lines parallel to the boundary), which is valid so long as you pay attention to #1 and don't drive the iron way into saturation where a lot of field wants to leak out the back. On the left and right edges of my linear array, I left the boundary undefined, which in FEMM means a Neumann condition. This allows flux to pass through the boundary at 90 degrees. If you place the boundary halfway to where the next pole should be, the fields end up being almost identical to those without the boundary. I would still allow at least one extra pole pair, just to keep the boundary a little further away from the area you care about. Using these boundary conditions let you avoid using a whole bunch of extra air space in the model but still get valid results.

[Kingfish]

Thanks Eric

I know from our previous conversations to be wary of B > 2T. In review, I have done as you suggested and looked at the B-H curves: Very enlightening! I cannot source 1006 Steel, although 1018 is available at my local and have been using it instead (stock sizes begin at ¼ inch/6.35mm). With that, my back iron is below saturation for the ironless-stator AF model. I suppose I should stay with that material; the only thing better is pure iron... although I prefer the strength of steel.

Went ahead and manually evaluated magnetic coengery over one single conductor and came up with ~0.7 Joules. Modified one of my scripts to measure coenergy across a full cycle of one circuit and the coenergy remained constant within < 2% - so I take that as a positive sign that the force is more or less constant with a slight ripple. Here – I’ve imported the results into Excel and made a pretty chart.



Looks constant. I take it you would apply this as a replacement for the torque measurement, yes?

Best, KF

[Kingfish]

Something else has cropped up: I was curious and decided to increase the current in the script by 50% to see what would happen to the model. The Force goes up proportionally (as expected) however CoEnergy increased by only +1 and that doesn’t make any sense. I doubled the back iron thickness and expanded the air around the model but these changes are insignificant on the outcome. I am beginning to think that FEMM is useful for crude modeling, though MathCAD might be the better tool.

<sigh> KF

[rhitee05]

The torque is derived from coenergy by the derivative of position. The concept is similar to gravitational potential energy - the potential energy of an object at height y is m*g*y. Take the partial derivative w.r.t. y and you get F = m*g, which is the expected result for gravitational force (although here you need a negative sign).

This is implemented in FEMM by measuring the coenergy once, and then "perturbing" the portion of the model on which you want to calculate forces slightly in the desired direction, then measure coenergy again. The derivative is then approximated by a simple finite difference, F = (W(x+delta)-W(x))/delta. There are more sophisticated ways to approximate the derivative more accurately if needed, but the simple difference works well most of the time.

[Kingfish]

OK, I now have a better understanding of CoEnergy and how it effects the model:

I spent some time crafting variations of the latest version of the ironless AF model developed back in November, which by itself is the summation of weeks-long tweaking. Of this, I changed only the width of the winding, the number of turns, and the current applied, with all other aspects unchanged. Changing current didn’t seem to affect CoEnergy very much, nor the amount of windings. I found this most surprising and decided jack with the physicality of the windings based on a previous artifact.

• If the winding is narrowed, the gap between magnets is less, flux density (B) becomes stronger, and less current is required to achieve the target torque and force, however resistance (is futile… ) increases. We expect that. I noted CoEnergy at this time, and pegged it at the lowest value, and not entirely sure how it is involved with the modeling. One thing to note is that my back iron was fully saturated according to FEMM; it was at the material limit of the B-H curve ~ 2.38 T.
• For the next test, I increased the width of the windings by nearly 2 mm. The back iron saturation dropped to 2.1 T, as did flux density from 0.8 to 0.69, and so did resistance. The output of Force and Torque using the old method of measurement also dropped proportionally. Strangely though, CoEnergy increased in proportion to the new winding width.
• The last test had the winding at slightly more than twice the original width. Like before, saturation dropped from 2.1 to 1.8 T, and flux density to 0.58. The good news was that my resistance was way low, but then so was the force and torque – about ½ of the starting model. But hey, my back iron is happy, the model produces far less waste heat, and though B was less than 0.6T – that’s still a great showing for cheap stock magnets. But what of the CoEnergy? The LUA script completes and the results say it’s more than twice the starting value.

When I run the LUA scripts, Force and Torque are not measured correctly; I know that, I can see it with my own eyes the sawtooth graph line that something is not right when running through a full cycle; the lines should be more or less level. At the same time, CoEnergy appears to favor winding width, or perhaps winding mass. I changed the number of turns, but that had no effect. I changed the current, no effect. When I changed the material to form a denser pack and lengthened the width – that’s when the magic began to happen.

As it is right now though, I cannot trust the output of FEMM for ironless AF because the resultant force and torque numbers are not tracking relative to the rotation of the axle… and let me restate:

AF models are not round; they are laid out flat and studied like MagLev, looking at the top, down. The one characteristic I can say about torque and force is that as the model (the windings) move away from the center (0,0), the value of both drop in a linear fashion. Maybe that’s something worth chewing on.
In the meantime, I believe that CoEnergy is tied to Lorentz force in some way; it has to be cos the width of the coil is expanding and creating a larger physical effect.

Anyways, I need to study my model just a bit more to evaluate why I see the sawtooth line. I am certain it’s a modeling flaw.

Hacking away at the brambles, KF

[Kingfish]

Greetings FEMM’ters

I worked late into the evening buffing and polishing and tweaking and listening to ancient Bob Dylan, thinking thinking thinking of emotos…

The scripted output of Force and Torque by FEMM has always troubled me, particularly the sawtooth shape. The model I have used looks like a drag strip in the sense that all the magnets are lined up in a straight line, and I have a group of windings that are going to race past them albeit incrementally. The track is twice as long as I need for the group to move the distance of one complete 360° phase cycle.

Normally I have the group of windings near the beginning/left-side when the script starts to churn. At the end, there is still quite a bit of length to reach the end. It dawned on me that the jaggy edge of the sawtooth could be generated by having the group too close to the edge. To remove the possibility, the group was set in the center of the length; equidistant. If the edge had any effect, the output should change. It didn’t.

Time for a long review of the script. Three phases are defined and their associated angles are set to -180 -60 60. Something so obvious, staring right in front of me – and I missed it. I spent the night working out the answer: Many moons ago I was lucky to have some help and got the scripts rolling to automate reporting of output. The graphs produced reflected this trail-and-error progress. Here’s an example of studies conducted last year. From Left to Right, let’s name them A through D.

• Figure A – Chaotic sawtooth. This is what happens when the gaps between the magnets of the same plane are too wide and the windings too narrow or too wide. There is disharmony in the design, and it is destined to create heat and frustration. But we are optimistic and it’s a good start.
• Figure B – A small buff levels the output a bit. The airgap was reduced and flux density (B) increased. Beyond that – physical geometry remained impractical.
• Figure C – Tightened up the gaps between the magnets. Much better output, and yet the strange sawtooth graph resolves from the haze. I should have spotted the problem here, but missed it.
• Figure D – Increase the magnet strength; always a good idea, right? The line levels out somewhat. For the moment, I accept my fate and settle in for the winter.

Round 2, fresh to try again, a second set of tests are ordered up. I had an idea that the phases were out of sync with the physical model. (I know, I’m as dumb as a stump sometimes… ok, maybe more often than that…). This next series twiddles with dialing this into sync. From Left to Right, let’s call them E through I.

• Figure E – A, B, C Phases were previously -180 -60 60; they are now -90 -330 -210. I tried positive numbers but the model would have ripped itself apart; I am glad this is all a virtual study! The new numbers reversed the sawtooth and that was encouraging. I also realized that I had the phases out of order.
• Figure F – Harmony? Hmmm, maybe resonance. Phases were set to -105 -15 -255. At first I thought it was good, but then I realized I wouldn’t want the motor pulsing like that. Besides, the average output was less than Figure E, however the peaks were higher. Optimism flowed.
• Figure G – Definite improvement! Phases set to -115 -5 -235. Best average output yet.
• Figure H – Almost spot on level! Phases set to -120 0 -240. The average output was incrementally higher than Figure G and without the ripple. What happens if we push another 5°?
• Figure I – Nope, we’re back to inducing ripple. Phases were set to -125 5 -245 although I put them back inline with Figure H.

This is Basic stuff. It's worth it to pay attention to detail. Unfortunately the physical nature of the AF model does not always lend itself to finding the TDC-equivalent for the Distributor. This misfire has been resolved. Took me long enough…

Now about those output numbers…
Happy Friday, KF