Introduction to axial-flux machines

Chances are, you have seen some bold claims regarding axial-flux machines in the recent years. They are supposed to be more powerful, have a higher torque density, and be ideal for electric vehicles, among other things.

But how much of this is actually true, and how much simply marketing speech (with maybe a grain of special-case truth blown up into all-around generality)?

Well, you won’t find many absolute answers to that here. But, you will find some tools and the beginnings of the theoretical foundation to make an educated guess of your own.

Note: for a very good* intro to axial flux machines, see Asko Parviainen’s thesis.
* Although I think I found one error; the magnitude of flux density missing from a torque equation.

But first, let’s begin with the basics – what are axial flux machines.

Structure of axial flux machines

Indeed, even something as fundamental as the definition of ‘axial flux’ can get debatable, at least when more exotic machine topologies are concerned. For simplicity, I usually like to think that the name comes from the (strongest components of the) airgap flux density.

Thus, axial flux machines have an airgap perpendicular to their axis (shaft), with the flux crossing it along the axial direction. Correspondingly, radial flux machines have their gap wrapped around their axis, with the flux crossing it radially (away from or towards the axis).

Of course, the flux isn’t axial everywhere – it has to loop back at some point after all! Most commonly, it does this circumferentially – turning along the direction of rotation – before again coming back axially to the opposite direction. However, some special or prototype machine may instead have the return path oriented radially – away from or towards the shaft.

Different topology options for axial-flux machines. From Parviainen’s thesis with corresponding copyright.

Winding structure

Correspondinly, the winding structure is different too.

In radial-flux machines, the ‘active’ part of the winding is oriented axially, usually inside the machine core. This way, the winding is perpendicular to the direction of rotation (circumferential) and the airgap field (radial). This also corresponds to the right-hand rule of the Lorentz force law: a current in magnetic field experiences a force perpendicular to both.

Sidenote: In reality, the Lorentz force does not generate much torque. This is because the flux mainly flows inside the iron core, rather than the winding. However, the Lorentz force approach is good for understanding, andoften yields good results thanks to some mathematics.

The end-winding, then, is often oriented roughly circumferentially outside the core.

By contrast, axial flux motors have their active conductors oriented radially – away from or towards the shaft. Again, this direction is perpendicular to the movement, and again results in a force in the direction of the rotation when combined with the axial airgap field. The end-winding is again circumferential, normally placed outside the outer and inner periphery of the stator core.

Sidenote: There’s been some talk about the ‘uselessness’ of the end-winding, usually in the marketing context. I am not a fan of this. As we so far haven’t figured out how to teleport current, the end-winding simply has to be there, and is thus useful by definition. Now, if one wants to split hairs around more esoteric motor topologies and determine which part of the winding is active and which is end-winding, here’s my approach: Find out where the individual conductors are tangential to (= aligned with) the induced electric field. That’s your active part, and the rest is there simply to connect them to each other.

Number of rotors and stators

Owing to their structure, axial flux machines often have more than one stators or rotors. This is born of opportunity as well as necessity.

Opportunity, because it’s simple to have let’s say two stators sandwiching a rotor. They can be mirror images of each other, after all. By contrast, designing an in-out-inrunner radial flux machine would be much more complex.

Necessity, because having only one stator and one rotor would result in a very strong attractive force between them. This would require very careful mechanical design and manufacture, to avoid vibrations and failures.

Skipping on cores

Similarly to having multiple components, axial-flux machines can often have yokeless or even ironless stators and rotors.

For instance, in the famous YASA topology, the stator is sandwiched between two rotors. As the flux simply passes through axially, there is no need for stator yoke, just teeth. As a result, more space is freed for the stator winding, which can increase performance and reduce the weight compared to a yoked version.

YASA topology on the left (source).

Similarly, a stator-in-between topology can facilitate a coreless stator design*. Meaning, the stator consists only of the winding and support structures. This, by definition, removes the cogging torque (originating from the interaction of rotor flux and stator iron) and can reduce weight. On the minus side, the torque capacity often takes a hit and eddy-current losses in the winding are often increased.

*For a really cool student project, check out this post on OhmNinja.

Finally, the same tricks – removing yokes and/or teeth – can of course applied to the rotor, too, by placing it between two stators. However, this approach is somewhat less advantageous compared to the previous one. Indeed, removing stator iron also removes the associated iron losses, while removing rotor iron (carrying essentially DC-flux) does pretty much nothing.

Scaling laws

You may know that the torque of a radial flux machine is roughly proportional to its volume. Roughly, because the torque tends to grow faster than quadratically when the diameter is increases. And as the volume grows quadratically, torque per volume is somewhat increased.

To understand why this happens, let’s use perhaps the most simple torque formula of them all:

T = r lBNI Q.

It basically says that the torque is the Lorentz force from one slot (BNIl) times the number of slots (Q) times the moment arm (r = airgap radius). (To understand why we can use the Lorentz force formula, see the simple airgap model here.)

Now, as the motor diameter grows, the area of each slot and thus the mmf NI grows quadratically with it. With the increased moment arm r, this would imply cubic increase in torque. However, more Ampere-turns means more heat generated as Ohmic losses – heat that has to go somewhere. For that reason, larger machines usually utilize lower current densities, and therefore the torque grows only slightly super-quadratically with the diameter. But I digress.

The torque of axial flux machines also grows cubically with the diameter. Re-using the earlier notation, this happens because

  • The mmf (NI) grows linearly as the slots get wider
  • The moment arm r grows
  • The active length l, now oriented radially, grows too.

On a quick glance, this cubic increase looks like a huge win for axial-flux motors. After all, the volume would grow only quadratically with the diameter, suggesting an improvement in the torque density proportional to the diameter.

Unfortunately, this is not the case. The entire flux of a half-pole, proportional to the airpag area hence diameter squared, has to fit through the rotor and/or stator yoke. Meaning, whenever the diameter is increased, the yoke thickness and therefore the length of the motor must grow with it.

As a result, the torque of an axial-flux motor scales very much like a radial-flux one – proportional to the volume.

But whaddaboud poles…?

Now, you might be thinking to increase the number of poles with the diameter, to keep the yoke height and motor length at a constant level.

All the associated problems (like increased electric frequencies) aside, this would work. However, the same approach would also work for a radial-flux machine.

Let me expand on that. A large-diameter axial-flux machine with numerous poles is very much like a disc. In some applications, it’s a nice shape to have.

On the other hand, a large-diameter radial-flux machine with many poles is an empty cylindrical shell. And in other applications, that is a nice shape to have. You might fit stuff inside it: cooling, power electronics, gearbox, propeller, you name it.

Which brings us to the…

Conclusion

We covered the basics of axial flux machines. Based on what we’ve seen so far, a lot seems to depend on the application and space envelope.

Next time, we’ll go through some calculations of maximum torque, to see when axial does actually (pronounce: axially) rule.


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Axial-Flux Machines – Part 1

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