Sunday, November 8, 2009

Epic Axial Motor: Epic Axial Update

I don't exactly know what an axial update is, but at least it's an epic update. Dare I say the turning-point. (Every project has one...on the Cap Kart, for example, it was the complete revision of the power circuit at the last minute that made everything simpler and, well, possible.) If I know something can work, sometimes I don't work out the details until I need to. And now I need to.

Detail #1: The rotor. Okay I gave this one to Mike N, master of things that spin dangerously fast. He came up with an awesome design that looks even better in real life than it does in CAD. Something about the aluminum, nickel-plated magnets, and the ground steel back-iron makes it look bad-ass. This does not do it justice at all:

It looks like it should be in outer space somewhere.

Simply epic. The bearings, which neither of us have bothered to model in, are tapered roller bearings that can handle the high thrust load of the magnets. All the parts are fabricated and right now we are assembling the stator and rotor independently. The total width of the assembled motor will be 3-5/8", not including a bearing retainer plate and any sprocket/encoder packages we add. The diameter will be 9". And the total weight is on track to be under 40lbs.

Detail #2: How to get the wires in. This motor will be handling up to 200A of current, so it needs some massive wires. Remember the shaft is stationary, so the wires all come in through its hollow center (ID=0.5"). Turns out the largest three-phase set of wires you can fit in that diameter is 8-gauge, which would be enough to carry about 100A. I opted instead of two sets of 10-gauge fiberglass-insulated wire (McMaster PN 8209K21). It's a smaller diameter conductor than the 8-gauge, but it's rated for high-temperature use up to 100A. The fiberglass will also protect it from sharp edges. The problem is after traveling through the shaft, it has to make a tight turn to come out of the hub in the center of the stator. I thought about this for a while and decided to split the shaft and leave the center of the hub open to give the wires more turning radius room:

Two sets of wires enter through the hub.

The aluminum hub has a much higher Ixx and Izz than the steel shaft anyway. And both common sense and FEA show that the center of the motor does not take much torsional or bending load. It all gets transfered out close to the side plates. This was an easy modification that doesn't require any fancy machining. And to my amazement, all six wires actually fit without much persuasion:

Something that was easier to make than I expected, for once.

What you see there is the current state of the stator. We only have two sets of stator tooth laminations right now, to test windings and maybe back EMF. (I'm starting to doubt whether the backEMF test will give a useful result, since there is a large part of the total magnetic circuit missing.) But anyway we will at least get to see how things physically go together.

Detail #3: How to wind it. The original plan was a strip of copper just a bit under 2" wide and 0.016" thick. It would be covered with Kapton tape and wound in a nested fasion around itself, six layers per tooth. I gave this a try:

Test winding of one stator tooth.

The good news is that it was very easy to wind. I did one layer of Kapton tape to cover the steel, then wrapped the copper/Kapton strip with only hand-tension. Having the tooth out in free space to wind is one of the biggest advantages of this type of motor, in my opinion, and it definitely showed here. I was able to wind a tooth is less than 10 minutes. The 0.016" copper is soft enough to wind without a jig. After compressing the layers with a clamp, it was within the space allowed in the design. The end turns stick out a bit further, because of the sharp radius, but they go out into free radial space, another nice aspect of this design.

The bad news is that after winding this one, I realized how difficult it would be to get to the innermost layer. I knew this would be a problem, but seeing it physically convinced me that any of the potential solutions I had thought of so far would not be clean. So I asked around and thought for a while before coming up with a new idea: Instead of one 2" wide winding, having two 1" wide windings such that the winding starts and ends on the outside. A picture is worth 1,000 words:

Two nested windings.

The two windings are connected to each other at the inner-most layer. This might be hard to visualize, so imagine taking a piece of paper that starts out looking like this...

...and folding it away from you on the dotted lines, then continuing to wrap the strips around something so that they overlap each other. That's how the winding would be created. Except instead of paper, it would be copper. The nice thing about it is that the start and the end of the winding are on the outermost layer, offset from each other axially. No need to make tabs. The interconnections become very easy:


The end of one tooth's winding lines up with the start of the next tooth's winding. You could just solder the ends together, for the most part. I had to think about this for a while, but I'm 99% convinced it would work out. Here's how half of the motor would be connected:


Reference for the winding layout for a 16-pole, 18-slot motor:
Jae-Woo Jung; Jung-Pyo Hong; Young-Kyoun Kim, "Characteristic Analysis and Comparison of IPMSM for HEV According to Pole and Slot Combination," Vehicle Power and Propulsion Conference, 2007. VPPC 2007. IEEE , vol., no., pp.778-783, 9-12 Sept. 2007.

Notice that with the exception of a single jump wire, all of the connections are edge-to-edge and could be done with a quick solder joint. This should make final assembly very straighforward.

But there was one huge problem with all this. That is, now every tooth has 12 turns, and the copper is half its original width. If this was wired up according to the original plan, which was to have all six teeth of a given phase (18/3) in series, it would create a motor with twice the operating voltage for a given speed. Sure, this would be more efficient, and maybe it's something we want to do down the road. But for now, we had been planning to test it as a low-voltage, high current motor, hence the low turns count and massively wide conductor.

The solution to this was actually obvious, although it took me some hours of thinking. Since the motor has 16 slots and 18 poles, the magnet/tooth cycle repeats itself once. (The GCF is two.) To get more current in, I had already put two sets of three input wires. Instead of connecting the two phase-A wires together and then routing the combined current to all six phase-A teeth in series, all I have to do now is connect each of the phase-A wires to it's group of three teeth on one side of the motor. The two phase-A windings will be in parallel. Ditto phase-B and phase-C. This will create two parallel windings, each seeing the same amount of flux (and thus the same voltage) as the original design. And it can carry the same amount of current, split between the two halves of the motor. Problem easily solved. Of course, I still didn't quite trust the analysis so I re-did the FEMM simulation with two parallel windings:


I used circuits {A, B, C, U, V, W} and set IA=IU, IB=IV, and IC=IW. The total current for the parallel set of A and U, therefore, is twice the current of either. What I got was that at IB=IV=-100A and IC=IW =100, the torque produced was 63N-m. The total current for the parallel phases would be 200A. This gives a torque constant of about 0.32N-m/A, very similar to the one I calculated with 6 turns per tooth and all teeth in series.

Side note: The reason the FEMM model looks nothing like the real motor is because FEMM can't do 3D simulation. So, I unwrapped the motor into a semi-infinite linear motor. I can then simulate for x-axis force and use the effective radius at the centeroid of the magnets and stator teeth to caculate the torque. I'm pretty sure this checks out.

Detail #4: What is the continuous power rating of the motor? I can do the thermal capacity calculation that says "I have this much copper mass and it is generating this much dissipated power. How long can this stay under this many degrees, given no heat transfer capability?" (No heat transfer meaning either it is completely insulated, or the time of the event is much shorter than the thermal time constant of the motor.) In fact I did do this and came up with something like a peak torque rating of 120N-m fo 60 seconds, starting from room temperature...

But this is a stupid way to calcuate torque/power. You want to run the motor continuously for some time longer than one minute, and ultimately the limit is how quickly you can get heat out of it. Heat comes out at the surface of the windings. (Yes, some goes into the stator core as well, but since that's going to be generating a good amount of heat itself, and since the path from there out of the motor is much harder, I assume most of the real cooling will occur at the outside of the windings.) Disclaimer: heat transfer and fluid mechanics is not my thing. But I did go back into my notes to find the forced convection equations, before stumbling on this nice efunda calculator. Here are the numbers I put in:


This is for a single side of the outside layer of the copper strip. What this says is that with 5m/s air flow (corresponding to about 200cfm through the entire motor), the copper can transfer out 2.34W per 2" of strip in the airstream. With 18 teeth, 2 sides per tooth, and 2 strips per side, this means it can get rid of about 168W continuously with a winding temperature rise of 50C. Well...that's not very much, now, is it? Let's say we do an insanely good job with the motor and it is 95% efficient. That means that the continuous rating would be just 3.2kW :( This seems to defy my intuition of how much current you can push through something this size. There are obvious analytical ways to improve this. It could run at a higher temperature. If the windings were allowed to go to 125C, the heat transfer would roughly double, allowing a 6.4kW continuous rating. If the air speed is increased by a factor of two, the cooling goes up by 2^0.5 (something about the Nusselt number and the square root of the Reynolds number...). But still, it's not looking good for continuous power rating. Even with the windings allowed to run to 125C and 400cfm air flow, and 95% efficiency, it's only ~10kW continuous as predicted by this method.

Well.... Here is where my analysis is going to stop. I could go do a fluid flow simulation and see what the actual numbers are. My intuition says you can dissipate more than 168W with 5m/s over this geometry and a 50C rise. Also, if you go by even the conservative rating for magnet wire, 5A/mm^2, you get a higher continuous power rating. And I would imagine that Kapton/copper sandwich is better at conducting heat to the surface than a magnet wire winding. (Actually, I don't have to imagine. I did this calculation and it's true.) So something is wrong here. Maybe there is conduction and radiation to add in too? Maybe there is also heat transferred out of the sides of the teeth? Maybe some really does go out through the shaft? Maybe I just don't know anything about heat transfer. But I do know how to pass large amount of current through something and measure its temperature rise over time, so I think I'll do that instead and report back the results!

Things are getting real.

12 comments:

  1. For now, something like 72-144V. I know that's a huge range, but I've been worrying a lot about the core losses at high speed. I'm working on a more thorough thermal model of the stator that includes both copper losses and core losses, as well as speed-dependent cooling. But like I said, heat transfer and fluid mechanics is not my strength.

    The copper losses are a little easier to predict, so I can say more confidently that it can probably run at 125A continuous current and 300A peak for three minutes, starting from 50C with 38C ambient temperature.

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  2. Where did you get the rotor Laminations made?
    Thanks JC

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  3. These were made by Proto Laminations: http://www.protolam.com.

    They are laser-cut M19 steel, 0.025" thick.

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  4. How much problem does the bolt cause? wouldn't it short the lamination's or cause any hysteresis heating?

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  5. I think the eddy currents want to flow in a path that the bolt does not short-circuit, but I'm not sure. The bolts themselves will see internal Eddy current and hysteresis loss, though.

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  6. Hello, I have a question about the magnet arrangement. How would arranging the magnets in a halbach array affect the LEAF motors performance? At one time, I had wanted to try an create a motor like this but in a much smaller foot print for use in rc vehicles. Unfortunately I have neither the skill or aptitude for this sort of thing.

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  7. hello. i have some doubts about core saturation and losses related - you seem to use neodymium magnets , and those give out enough field to saturate any type of steel core i am aware of.

    would it not be better to use no cores, flat coils, and increase number of poles (and magnets) - perhaps also increasing diameter of the motor ?

    this way magnets put on two sides of the design will be more close , and magnetic field inbetween their north and south poles will be stronger - creating less magnetic reluctance.

    also, motor will be more 'flat' which makes it better heat radiator.

    p.s. i try to design such motor myself, for use in electric bicycle - so low loss one (incl. low free spinning loss) - but i lack machining workshop and skills.

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  8. I later went on to make a coreless motor that was flatter as you describe. That would definitely be a better choice for an electric bike, since it would have zero cogging torque and the potential for lower eddy current loss, if the windings are done properly.

    NdFeB magnets have a remanent flux density of about 1.3T, and accounting for some leakage and the reluctance of the air gap, the average flux density in the air gap might be close to 1.0T. Silicon steel saturates at about 2.0T, so to not saturate the core, it would have to have at least half the area of the magnet disk at its narrowest point.

    Many motors run parts of the stator core saturated or near-saturated and still achieve high efficiency. Saturation does not necessarily mean loss. One benefit of the steel core is that it can focus a lot of flux through a long axial distance of windings.

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  9. notice SmCo magnets have higher flux density.
    also, your calculations about saturation seem correct... except you assume there is no current flow in the coils, contributing to the field.

    in practice yes, near-saturated motors work efficiently - at high rpm and low torque (and practice confirms this).

    but then they are not really efficient at stall or low torque/high slip , with efficiencies dropping to as low as 10% in such conditions.
    for direct drive application like hub motor this sounds bad.
    also rotational speed variance isn't that great, i.e. in high rpm mode eddy current losses contribute to efficiency losses and too long windings (high inductance) limit upper rpm of motor.

    given high frequency PWM (with freq's like 1Mhz for 100A which was not possible (so cheap) in 60-70's) is available to drive modern electric motors i do not see much point into increasing axial distance of windings (and their impedance).

    instead more of them can be ran in parallel , and more poles can be used.
    the axial design of the motor, with two magnet plates perpendicular to eachother allow strong focus of magnetic field - and i think it is what axial motor is all about.

    few theoretical questions remain, like what is optimal number of poles and what speed range and stall torque it offers. it will ofcourse depend on motor diameter aswell.

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