2.00thesis

Design and Prototyping Methods for Brushless Motors and Motor Control

Actually you should read James Mevey's thesis instead.

LEAF Motor: Spin-Up

The Less Epic Axial Flux motor, a thought exercise a bit over five weeks ago, is now a spinning physical prototype. (Okay, I cheated a little since the rotor disks were already made for the original Epic Axial Flux motor.) Most of what remained to be fabricated was the new coreless stator. Although the entire motor did get a bit of a redesign. Here is the exploded view of the latest design:

Click for full-res.

And, the collapsed version:

  Click for full-res.

The only new thing since last post is the "outrunner outrigger." It connects the mounting structure to one side of the motor shaft, which is not rotating. This completes a structural loop, giving the shaft more stiffness than if it were just connected to the central stator structure. The extra weight it adds is offset by the ability to take significantly more abuse from the chain load on that side of the rotor. This is a minor design change, though. What about the windings?

There's the first six, done in about three hours.

Compared to the ones in the scooter motors, these windings are a breeze to make, for a number of reasons. First, the flat magnet wire is absolutely wonderful. It packs nicely and stays where you put it. But, it only really works because I can remove individual winding inserts and wind in free space. This means instead of looping wire through slots, I simply spin the entire insert, spooling wire onto it under tension. It's not trivial, but it's not very hard either. I would place that in the "win" category for this motor.

All the windings, a two-day job.

With all 12 windings in place, and plenty of room in the center of the stator for interconnections, the job is easily finished. I decided to connect all four winding sets (12 divided by 3-phase) in parallel, and to wire the parallel sets in delta. This will give the lowest-voltage, highest-current motor possible with these windings. Before you yell at me for that being the most inefficient configuration: To first order, it can produce the same power per unit dissipation in the copper. And even in this lowest-voltage configuration, the motor still takes about 50V to get to 3,000RPM. When I get a controller that can handle more than 48V, I'll re-wire it. For now, I'm eager to get on with testing, so I put it together:

Kit Bot FTW. I'll replace the outrigger later.

It's not set up for sensored control yet, so I needed to borrow a high-current sensorless controller. Luckily, I know exactly where to find one. Cold Arbor, a combat robot with a brushless cold saw, happens to live nearby and also happened to have pre-cut and stripped wires courtesy of a particularly violent match. So, with a kick-start to get the sensorless controller going, it spins up:

This test went to 1,500rpm. (Not 3,000 as the tachometer seems to say.) That's at 22V using BLDC (square wave) control. This falls right into the expected range for the delta-wound, 40-turn, 4-in-parallel winding set. It seems to draw a good deal of no-load current at this speed (15A). I think it's too early to say whether this is a function of circulating current in the delta winding, eddy currents, bearing losses (and in what proportions). The next step will be to set it up on my sinusoidal controller with rotor position sensors and see how it fares then. Since this is the target control scheme anyway, I will defer judgment for now and move on to smaller and better things...

LEAF Motor: Assembly Box of Doom + Back EMF

If you're just tuning in, the LEAF (Less Epic Axial Flux) Motor is the end result of a long and unnecessarily complicated process that started when I decided I would buy a set of 16 neodymium iron boron wedge magnets for $74, figuring I would make a motor out of them some day.

Well now I have two sets of 16 magnets, and I want to put them together with less than 3/4" between them. This translates to roughly 500lbs of force trying to smash them, and anything between them, together. This calls for the fabrication of a very strong box from which to make a giant motor puller. Here's the bottom of the box:


It's only purpose in this world is to hold the lower rotor disk securely. The top of the box is much more interesting:

This is the "puller," with three 5/16"-18 threaded rods that screw into the top rotor hub. The rods in tension do the work of lifting or holding against the axial force, sending it to the side of the box in compression. All together, it looks something like this:

The motor puller box is designed with about a 3x safety factor on all the forces, but along with the box, there are some rules. Rule Number One is never put appendages between the disks. They are always separated by the puller and then the entire top of the box is removed by lifting from the sides before any work is done on either disk. Rule Number Two: whenever the disks are separated, a block of wood between them acts as a failsafe in case the box or rotor disk breaks.


So that takes care of one of the things over which I was losing sleep. The other, winding, turns out to be not that hard at all with the flat magnet wire I picked up from Alpha-Core. Now all I need is a few solid free hours in which to do it. (Actually, probably like a full free day.) But anyway, I managed to do a single winding. I basically half-ass the 40-turn winding, then force it to be the right shape with my winding press:

Patent Pending.

Okay, I will put a little more effort into the real winding. But for now I just wanted to get to the magical single-winding back EMF test that I have so many times claimed is actually a useful thing to do. This time, I'm sure it's legit. With a coreless motor, there is no incomplete magnetic circuit to worry about. The no-load B-field between the disk looks the same with or without the windings. So with one winding's measured back EMF, I can extrapolate the performance of the entire motor. (You probably still don't believe me...I don't blame you.)

Anyway, I put the winding in the stator and put the stator in the box:

(Notice the nice new countersunk non-magnetic stainless screws?)

And stupidly I did not take any pictures of the whole thing together. But to my great relief it actually spins, the magnets no longer grind against the screws, it is centered, and the gap is...well it's not very uniform. It sort-of favors one side. I think it might need a little persuasion toward the other side. But it doesn't seem like the 1/r^2 problem...the dual bearings on each rotor disk seem to take care of that. But anyway mechanical stuff can be poked and shimmed and squeezed into compliance. What about the fundamental premise that this thing can actually transform power?

This time, I didn't need the go-kart to spin it up. (No cogging torque, and no violent shaking of the entire test bench.) I used a smaller but equally unorthodox prime mover: a cordless drill with a hole saw attached to it. The hole saw dug into the rotor hub nicely and got it up to about 600rpm, plenty fast enough to capture a back EMF waveform on the scope:

Oooooooooo...shiny.

That is much more sinusoidal compared to the steel core version. Why? It's still a concentrated winding with non-skewed magnets. Well, probably a few reasons: The magnetic interaction is more distributed, not focused to the edges of the stator teeth by steel. It's also interacting with field that is relatively far away from the magnets, where it starts to blend together smoothly from North to South instead of having sharp transitions.

As for the fundamental motor constant, the amplitude of the back EMF as a function of frequency (speed), I get about 9.5V(rms) per 1,000RPM. Since four of these windings would be in parallel, that is essentially the phase voltage of the motor. That's a fairly nice number, since in the practical speed range for a home-built motor (3,000RPM?) it falls into the 72V battery category. Through the magic of power conservation, I can come up with a torque constant for the motor as well: 0.27Nm/A(rms). This is...well it's all pretty much dead on with the predictions. (Wow, even the shape of the back EMF is correct...)

Lastly, I measured the winding resistance for a single 40-turn winding to be 0.127Ω. Since there would be four in parallel, the phase resistance is actually one quarter of that, or 0.032Ω. This starts to give me a feel for the thermal performance of the motor. Altogether, the motor constant and resistance are fairly similar to the array of small EV motors (Etek, Mars PMAC, PERM, etc.). The LEAF, which is the only coreless motor in this lot, will likely have a slightly higher torque constant, but also a higher resistance and lower thermal mass for heat sinking. So we'll see how it compares in continuous and peak ratings. As always, it will depend a lot on the cooling solution.

More winding ahead!

LEAF Motor Blitz: Everything but the Windings.

One of the most important lessons I've learned in the last six years of engineering study is how to slow down, organize, and carefully execute a big project.

But screw it, sometimes you just have to put the gas down.

Since my Feb 4 post, I've been blitzing the LEAF motor project, refining the design and building all the new components in two weeks. Everything but the windings. Here's the latest design:

It's gone through significant refinement from the Feb 4 concept mostly as I realized the particular characteristics of a coreless stator that made the design more flexible. The most obvious change is in the mounting and loading: One benefit of the coreless design that I didn't mention in the last post is that, at least in open-circuit, there are no axial forces between the rotor and stator. In fact, in open-circuit, there are no magnetic forces at all between the rotor and the stator. No cogging. The only forces paths are between the two rotor disks.

There is still a tremendous axial force, almost 500lbf, trying to squeeze the two disks together (and crush your fingers in the process) but the coreless version doesn't suffer from the air gap instability I mentioned here, where one rotor disk or the other would rather snap to the stator than maintain an equal air gap thanks to the 1/r^2 law. There's also a very large torque holding the two magnet disks in alignment, much larger than the torque the motor itself is usually producing. All this means that the outer can is, in fact, optional. It does provide a degree of stiffness, but with 1/4" steel-backed magnets, rotor stiffness is the least of our problems.

Ditching the outer can opens up a whole new range of possibilities. For one, wire entry no longer has to be accomplished through the shaft itself, as it would in a hub motor. In fact, the shaft doesn't have to be the mounting point, either. Hence, the blade-like design you see above with a hollow mounting tab that allows wire entry through the side. It's not hard to imagine forcing air through the side as well, for cooling. Here's what it looks like IRL:

The shaft is actually integrated with two machined aluminum hubs. The structure is essentially a sandwich of ABS plastic winding inserts (the black triangles) in 1/32" carbon fiber, with a bit of aluminum thrown in outside the magnet area where extra stiffness is required, such as at the mounting points. The inside thickness of the sandwich is 1/2".

Myth: Carbon fiber is difficult to machine. Actually, it's difficult to make. But if you buy plates of it and just need to drill a few holes, it's actually very easy to do. I didn't even need a mill: I made a nice aluminum template and rotated it around to locate all the holes:

And for the 1-1/2" center hole:

Yep, a wood-cutting spade drill. (Wood is made of carbon too, right?) The pointy edges cut through the thin carbon fiber sheet very nicely just before the flat spot hits the surface.

The result is a remarkably stiff stator sandwich that weighs about 750g and looks really cool. The windings will add another 1.25kg or so to the stator mass, but more about those later.

Even though the rotor disks are no longer attracted to the stator, they still suffer from the 1/r^2 problem with each other. Meaning, they would potentially tend to close the air gap on one side of the circumference while opening it wider on the other side, rather than sharing it evenly all the way around. Furthermore, there will be large forces and torques on the rotor disks from the load as well, coming in through the chain and sprocket. All this suggests that the single conical bearing, even magnetically preloaded, is not at all sufficient to hold the air gap. Without an outer can linking the structural loop, they are under-constrained.

So I did what I should have done before anyway and modified the rotor halves to each be completely supported. Meaning, they each have their own thrust bearing and radial bearing, separated by a large enough distance to well-constrain the rotor disk on the stator shaft. This required an array of new round parts...


...which fit together as in the exploded view above. Also in the category of things I should have done before anyway, the sprocket spacers now have centering features that capture the sprocket. The bolts are no longer used for alignment, they simply hold things together. The sprockets are captured between the two bearings, providing a well-supported reaction to the chain loads. Minus the bolts, it looks like this:

And it spins quite nicely. There will be sprockets on both sides, mostly for symmetry, but it could potentially drive a split axle. I'd like to believe it would behave like a limited-slip differential, but honestly don't know what this would do.

So that leaves the winding. And here I have one last trick: flat magnet wire!


Processed by Alpha-Core, this stuff is rectangular cross-section enamel-coated magnet wire. While it may actually be more difficult to wrap a normal motor with this wire, because it can't twist, it's significantly easier in this case. I can take off an individual winding insert, spin it around while pulling some wire off the spool, put a bit of epoxy to hold it in place, and then screw the insert back in place. (Okay, that makes it sound easy... It's still a time consuming process, which is why I haven't actually done it yet.) The result is a relatively tightly-packed winding that also has a thinner cross-section, cutting down on eddy current loss.

The best part is that I can wind the whole motor. Meaning, it can actually run. It won't be the 30kW monster that this project originally targeted, but it will still fall into the high-single-digit horsepower category, and weighing in at just about 25lbs. It should get pretty good efficiency numbers as well. Testing to begin soon!

Thought Exercise: The LEAF Motor

Okay, I've been playing with SolidWorks a little too much.

Here's the thought: Since I already have awesome rotors with conical bearings for my axial flux motor, maybe I can get something up and running quickly while I debate what to do about the problems with the full ("epic") version. Specifically, the cost in both dollars and hours of finishing the stator, the difficulty of assembly and testing, and the lack of a real use for it anymore are limiting my desire to push hard on the segmented stator core version, thus far the focus of the project.

Talking to some solar car types got me thinking about coreless motors. A coreless motor is a motor that has no steel core, just windings. In fact, for the first time this year M.E. sophomores at MIT got to make coreless DC motors as part of Mechanical Engineering Tools. They have some obvious benefits, such as lighter weight, no cogging torque, and high efficiency due to the elimination of core losses.

But aren't they, like, way underpowered? It's true that the steel core helps focus current from lots more windings up into a tiny air gap with very high fields. Coreless motors, by contrast, tend to have lower field strengths and less space for windings, both of which limit the maximum torque output of the motor. So this will not be the Epic Axial Motor. Instead, it's been named the

Less Epic Axial Flux Motor

or, for short

LEAF Motor

And I have no less than four ways of estimating the performance of such a motor as is pictured above, which would have a total thickness of 1.7" when collapsed. You know, like a leaf. First, a little more detail about this semi-arbitrarily-chosen test case:

Rotor: Same as before. These magnets on two low carbon steel backings. Not ideal for a coreless motor, but they already exist which gives them +1,000 points by my score keeping.

Stator: 14AWG magnet wire, 28 turns per coil, 12 coils in the following winding pattern: ABCABCABCABC. For once, I'm not using a crazy fractional-slot configuration because cogging doesn't matter. As a reference value, I am using 20A as a reasonable amount of current to put through this wire, which equates to about 10A/mm^2, or 200 circular mil per amp. This is not conservative, but not insane.

Gap: The gap between magnets is 0.7". This means the peak flux density is about 0.5T, with these magnets. This is significantly lower than the 1T field density in the air gap of the steel-core motor. This, plus the fact that 0.7" is not a whole lot of space for copper, is what will make this motor less powerful.

So, what about those four methods?

Method #1: Nibbler

My favorite method, because everyone understands it. Or at least, everyone who has taken high school physics knows the formula for the force acting on a current-carrying wire in a magnetic field:

Just an example.

The force acting on the wire is just: F=IBL (fibble), and it obeys the right-hand rule. In a motor, there are many lengths of wire all carrying current, so we multiply in the total number of active wires, N. Also, to get to torque, we use a radius, R. That gives T=NIBLR (nibbler). In this motor, N=448, I=24.5A, B=0.5T, L=2in, and R=3in. (All roughly speaking...I can justify those numbers but it would take another page of maths.) This gives a torque of 21.2Nm (at this value for current, which gives the same power dissipation as 20A continuous in each wire...don't ask).

Method #2: FEMM Static

The trick I've been using for axial motors in FEMM is to unwrap them around the average radii of action. So, the magnets span from 2in to 4in. I unwrap the motor at the 3in radii, literally unrolling it into a straight line. This has worked pretty well for me so far, but it's a little trickier with a coreless motor, I think.

Anyway, FEMM allows you to set material properties, magnet orientation, turn counts, current, etc. It then can predict electromagnetic forces. It is inherently a statics program, meaning it will give you a force, but won't simulate motion or back EMFs without some coding (see below). Anyway, all I really care about for now is a ballpark torque estimate. So, I put the model into FEMM and put 24.5A into a coil sitting right between two magnets (max torque). It created a force on the coil of 32.6N. If 8 of 12 coils were generating this force, at a 3in center of action, it would create a torque of 19.9Nm.

Method #3: FEMM Dynamic

Here's where it gets ugly. My recent adventures in sinusodial, field-oriented control have got me thinking about better ways to characterize motors. The NIBLR and FEMM Static methods give you torque as a function of current, which is like a DC motor torque constant. This is a pretty good approximation, but it leaves out the important details of the shape of the back EMF, which is related to the shape of the magnets and coils. This is especially true in a coreless motor, where the focusing effect of steel stator segments is not present. So, I've also played around with scripting FEMM to generate a back EMF plot. I won't go into details, but the basic steps are:

1. Import geometry. Group coils so that they can be selected as one block.
2. Loop through a set of angular displacements for the coils, moving the block between each one. Run static analysis each time and record flux linked by the circuit.
3. You now have a graph of flux vs. electrical angle. Take the derivative [Wb/rad] and multiply by electrical frequency in rad/s. [Wb/rad x rad/s = Wb/s = V]
4. That's back EMF.

The more points you take, the less noisy it will be.

How do you get from back EMF to torque though? Thanks to The Best Motor Reference Ever, I finally understand this link. The idea is simple: Take the back EMF and drive a current into it. That's power. On the other side, you get torque and speed. Speed is already set by the electrical frequency you choose in step 3 above (1,000RPM in the case of this example). So just...solve for torque. This all works very nicely when you assume that both the back EMF and the current driven are sinusoidal. You can then use RMS values to get power.

Doing this quick math for the FEMM dynamic back EMF nets a torque of 18.4Nm for 20A RMS.

Method #4: What the FluxCutter?

Ok this isn't a real method. I just made it up. But it might have some appeal to the mechanically-inclined out there, since it's a very geometric method involving CAD. The problem I was trying to solve was: FEMM is 2D. It can't account for the strange shape of the coil, which occupies a different fraction of the circle at the inner radius than it does at the outer radius. How, then, to get a fourth method (there must be four, now that I said it) without switching to a 3D magnetics package?

Well, I can use a 3D CAD package...like SolidWorks. First, I made a visual representation of the flux density one might see in this motor. I made it sinusoidal, but really I guess you could make it whatever you want. FEMM suggests it might be sinusoidal in the middle, and closer to trapezoidal near the magnet faces. Anyway, a sinusoid seems like a decent place to start. I wrapped that around a cylinder with the correct inner and outer radius, in inches. Then, I scaled the z-axis features such that 1 inch was equal to 1 T. Thus, 1in^3 is really 1Tin^2 which can be converted to flux in Webers!

All that's left was to make the FluxCutter, an extruded cut with the profile of an individual turn of wire, that cuts volume off the bulk shape. By measuring this change in volume, I got the flux. The rest was the same as Method #3. Oh, except I could also account for the slight offset as coils get wrapped in multiple layers. I assume FEMM does this for spread-out coils, but not in 3D.

With a chunk of flux cut out.

I will admit this is just plain silliness. You get more accuracy in the shape of the coils, but less accuracy in the shape of the field. (Unless you can model the 3D field more accurately than a sine wave...which if you can do that you probably already have a 3D magnetics simulator.) But it was fun and did yield a result. The torque predicted by this method was 15.8Nm at 20A RMS.

In summary, the four methods I use predicted reasonable torque values between 15.8Nm and 21.2Nm for 20A through 14AWG wire. I would call that pretty consistent. This says nothing about the operating voltage and current of the motor; that would depend on whether the coils are connected in series or parallel. (Probably, all four would be in parallel, giving an 80A motor...but the torque is the same.) Depending on the achievable speed, this is decent power (1.7-2.2kW per 1,000RPM). And this is not really a peak rating.

What about dissipation? Well, a quick estimate of the resistance of such a winding suggests that at 20A the motor would be dissipating a bit under 200W due to copper losses. So it has a chance to break into the mid-90% efficiency range by 2,000RPM, and even earlier at lower currents. Although I think with the existing bearings it won't.

So, not quite as epic as the full version, but probably worth a try. It's definitely easier to make, and might in fact make a very practical motor.

EAM: Single-Winding Back EMF Test

I finished up the sheet metal can of axial motor fluxage:

It's four layers thick, squeezed down from 12" ID to 9" ID by painstakingly tightening the hose clamps, flexing the can a bit to get it to slip, then tightening again, for about three hours. That's after I used up an entire cutoff wheel to cut it out of the large roll. Don't worry, I cut the ends of the clamps off before I ran it. This isn't part of the real motor, it's just a hack to get a more realistic result from the single-winding test. See this post for a better explanation.

Now, I'll admit, I kinda over-hyped this experiment. Although I still wouldn't want to be anywhere near it, this was a low-power test...no real load is being applied to either motor. So, although it looks "terrifyingly epic," the kart motor had no trouble at all getting it up to speed with just a bit of throttle. In "low gear," that means roughly 1,500 RPM. The vibration was just about as bad as I expected. (Remember, it only has one stator segment in place...) But, nothing broke. Here's a video. If you look carefully, you can actually see the entire test rig flexing.

But it's clearly generating a trapezoidal back EMF, and it got above the minimum speed I set for a valid result (1,000RPM). This is more so that the kinetic energy of the rotor overwhelms the push-pull of the magnetic forces, giving a smooth speed. Smooth here is a relative term.


The peak of the trapezoidal back EMF is proportional to motor speed, and the constant of proportionality in this case turns out to be 5.7 Volts per 1,000 RPM. Without the flux jacket, it is 5.2 Volts per 1,000 RPM. I expected a bigger difference, but maybe there are return paths I don't know about that are doing the job of the flux jacket already.

More importantly, how does this compare to the prediction? Well...the shape is right. And it's within a factor of two, so I probably didn't really mess up the calculations. But, plain-old math assuming a 1 Tesla airgap magnetic field predicts 9.7 Volts per 1,000RPM with this geometry and number of turns. A linearized simulation with FEMM predicts 9.6 Volts per 1,000RPM.

I have no idea if adding in the rest of the segments will make up the 40% difference, or some of it. Let's say it didn't, for now. Since back EMF tells you most of what you need to know about a motor, these results are very useful. Extrapolating these results, which are for a single winding on a single segment, to the whole motor gives the following as a rough performance estimate:

Operating Voltage: 96V-144V
Top Speed: 4,000RPM @ 144V
Torque Constant: 0.33Nm/A
Peak Torque: 66Nm @ 200A
Peak Power (3-minute): 20kW @ 3,000RPM and 200A
Continuous Power: 10kW @ 3,000RPM and 100A

That puts it squarely in the category of "small EV motor." It's the next step up from the kart motor, I guess. It could run well on inexpensive Kelly brushless controllers. Doubled-up, it would make a nice rear axle motor set, although I'd wind it for direct drive: lower speed, more torque. The catch: you have to build it! And in low quantities, the stator segments are still pretty expensive to produce. Please somebody steal this design, fix it up a bit if you like, and make one like it in large enough quantities to be under $2,000. I'll buy it! Seriously. Let me know when you do. Until then I'll be figuring out how the heck I might assemble the whole thing...

Epic Axial Motor - IAProgress

It's been quite a while since I've done a post on the axial motor. In the last post, things were just starting to get built and the big question was how to validate the performance of the motor without actually building the whole thing. "Performance" meaning...? The predicted torque/speed curve, the thermal characteristics, the efficiency, or even just does it shred itself into tiny little pieces? I'll get back to that. First, build updates:

"Master of the EZ Trak" Mike N. put together two beautiful rotor halves worth of aluminum and steel. The magnets, as scary as they look, were actually very easy to put in. Only problem is that in the process of gluing them, the magnet O.D. changed enough that the wonderfully-machined inner surface of the magnet retaining ring didn't slip on anymore. I came up with a quick fix, but I don't think Mike will like it:

Sorry Mike. :(

I am fairly certain that this piece will need to be replaced in the next version anyway, for reasons I will get to in a bit. This first build is really meant to be a learning experience, with the possibility also of collecting some data on the back EMF. By learning the voltage generated by a single stator segment and winding, the torque/speed curve of the whole motor can be extrapolated (to a degree). Which is good, because I only have enough material and time to build one stator segment.

One problem I avoided for as long as possible but finally had to deal with is getting the conical bearings to be properly loaded, even with a single stator segment. The axial forces in a motor like this are tremendous and the imbalance of having just one steel segment makes it very difficult to line up the rotor halves and load the bearings instead of just having one half slam down on the face of the stator segment. The "solution" I pursued was one of undersized axial spacers that, when they go into tension, pull on the rotor halves with more force than the magnetic attraction of the single segment. Like this:

The problem was that we didn't design the rotor back-iron to screw into the spacers from the side. And I had already put the magnets in... Time for some very careful drilling.

On the plus side, it is self-fixturing and has built-in chip collection.

Not wanting to cut too much on the first try, I left them a little long. As expected, it was impossible to get an air gap on both sides of the stator segment. One or the other rotor half would just slam down:

In the end, I wound up making the spacers a good 0.020" undersized. This sounds huge, and I expect some of it is actually being taken up by the rotor back iron flexing. But whatever, it got the job done:

Air gap on both sides!

I'm not thrilled with this solution. Mostly because I don't think it's stiff enough to last. I am fairly convinced that what's really needed is a no-nonsense 1/2"-thick solid aluminum can that goes around the whole thing. It would do the job of both the magnet retaining rings and the spacers. I will look into this option. But for now, I need a steel can. Here's why:

(Warning: Science Content)
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I learned in freshman physics (the hardest class I took at MIT?) that if something looks symmetric, it probably is. The full axial motor certainly looks symmetric. But this version with one tooth...certainly not. Well, how to trick it into thinking it's symmetric? Mostly, I care about the magnetic circuit formed between the rotor disks, stator segments, and permanent magnets. In the case of symmetry, there's no telling which rotor half is which. They should therefore be at the same magnetic potential.

With just one stator segment, though, there is no clear return path for magnetic flux and the rotor halves will rapidly shift from "N" to "S" as the motor rotates, shooting off field lines into space for lack of a better place to put them. Not good. Solution: connect them with a giant steel can. This will force them to be at the same magnetic potential, just as a wire forces two nodes to have the same voltage. This is probably a close approximation to the symmetric case with all stator segments in place.
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So, I need to make a giant steel can, preferably not out of one solid piece of steel since it would be very hard to make. On radial motors, this might be called a flux jacket. Cue the giant role of sheet stock:

Don't worry, it's not a solid roll. It's only about 3/16" thick.

The dotted line is where I will be attacking it with a cutoff disk. The enormous hose clamps are to keep it rolled up. (It's under an incredible amount of tension.) They might also be useful for squeezing it down to the correct diameter. I'm sort-of winging this part, since it isn't part of the real motor, so don't expect much...

I also need a way to spin the motor so that I can measure the back EMF of the single stator winding. Chain drive seems like a good option, for reasons that will become clear momentarily. I made some quick disconnect hubs...

...which I lost for an hour in MITERS. Turns out after cutting them off I, without noticing, put them on the lathe tool holder post and then put the regular tool holder back on top of them:

No wonder I couldn't find them. Anyway, they provide a quick mounting solution for sprockets of various sizes and tooth counts. Altogether, the motor (minus its forthcoming flux jacket) looks like this now:

So all that's left is to find a suitable test rig. Normally when I test a motor, I just stick it in a drill and hook up the leads to a scope. But this is...bigger. The test rig will need enough torque to overcome the large cogging force of the single, unbalanced stator segment. And it will need to get up to a high enough speed that the rotor inertia damps out the speed ripple created by this cogging. I only have access to one machine with enough power to pull this off:

You might be surprised, but this is only the second most dangerous thing ever to be driven by the kart motor. (The kart itself is the third and last.) The first...well I don't talk about that anymore.

Actually, I'm not that worried. The biggest problem will be vibrations. It's going to vibrate like crazy with just one stator segment. I predict I will only get about 10-30 seconds of useful data collection time per run before something breaks. My money is on the spacers. When your experiment is almost guaranteed to end in catastrophic failure, you can't be disappointed. And you take appropriate safety precautions such as not being near it when it does. Everything will be recorded on high-speed video, including a scope channel with the back EMF, while I stand...somewhere else.

As for the future of this project...well, if the back EMF test fails miserably that's easy. If it actually works, well then it may or may not continue. I don't really have a use for this motor, nor does anyone else around here, really. It's meant to be cheap, easy to build, and easy to test. But for me, with my resources, it is none of those. I'm pretty sure somebody else with more skill and access to better equipment could build this motor or a better one in much less time. It's still fun, though, and a good learning experience. So, I'd like to finish it, but no guarantees.

For now, insane, one-shot, near-certain-destruction testing awaits!

"The problem with your blog is, I can't understand any of it." -Ken Colton

Happy New Year! Time for my first post of twenty-oh-ten. My New Year's resolution is to work on my blog post explanations a little, if for no other reason that so that my brother (who made my awesome site banner^^^) can follow along when not reinventing the internet. Shouldn't be that hard...I just need to stop talking about software, right?

I'm back in Cambridge and back to work, getting ready for another fun-filled year of 2.007: Design and Manufacturing I (OpenCourseWare from last year for those of you working on your FREE MIT education). Although the stardard box of raw metal and plastic stock is pretty much unchanged, we have some new and exciting additions to the kit this year. For one, everyone gets there very own small fireworks Lithium Polymer battery and charger thanks to dirt cheap overseas manufacturing. There's a whole new line of servos and gearmotors this year, too, which means that I may finally be free of the curse of the Tamiya 72001 Planetary Gearbox Kit.

DO NOT WANT!!!

How about Project Updates?

Well I must admit I've been spending most of my project-time on making this microcontroller do impossible things that it wasn't designed for, like simultaneous field-oriented control of two motors. You might think I'm wasting my time, but allow me to motivate this with a scenario:

You're stranded on an island after a plane crash, but after hours of walking the shore you find a boat. This boat happens to be powered by two brushless motors, and it happens to come with all the batteries, power electronics, and maps and charts you'd need to make it home by dinner.

Motivated now?

But there's just one problem. Your boat is missing a controller. Your laptop, cell phone, and iPod were all destroyed in the crash. But wait, in your back pocket:

Yes, a TI-83.

That's the type of controller we're talking about here. A graphing calculator. Not even a new one. That's roughly the processing power equivalent of the MSP430F2274. But hey, it's all you got. At least it's better than an Arduino. Oh, and also, it isn't sufficient to control one motor, because clearly the boat will go in circles. So now you see why this is important. And if you're already putting in the effort, you might as well make it quiet.

Well if I was stranded on an island, I would have starved to death, because I've been working on the software for this thing for two weeks now (not including the holiday break). Software, though, is a thankless job that produces literally no tangible evidence of progress, which is part of the reason why my recent blog posts have degraded to pretty much indecipherable gibberish (that I assure you is cleverly-constructed and efficient code) .....

BUT NO MORE. Next, I will show an actual, measurable result. And it's more than just that the motor runs more quietly...that's a nice bonus, but it's not the ultimate goal of the upgrade. Look for a post by the end of the week.

And how about the other projects? Well, I plan to do some serious work on the axial motor this month. Even if it's doomed to failure, I'd like to get there quickly. First step is to make some combination hub adapters / bearing retaining plates. Then, spacers that will give the rotors at least some small chance of being aligned to each other. Then, assembly and the single-tooth test, which is about the most boring way to test a motor ever but gives me all the information I will need and costs nothing to do.

Those are the two big ones. Might throw in a brand new mini-project along the way...depending on how things go. 2010 begins.

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.