Thank you, looks good!

]]>On this topic, I stumbled upon this short note by Soong, which I like a lot:

https://www.scribd.com/document/60016511/Soong-Sizing-of-Electrical-Machines-2008

]]>You have a point there! There are probably use cases where the reverse is true (Python being more compact than Matlab), but MY typical line of code might read like

solution(n_free) = (P’ * S * P) \ (P’*F);

In Python, having to do the multiplications with the .dot(–) method would indeed bloat the expression.

]]>Michael, how can you wrap a rotor with surface mounted permanent magnets and not violate Tecla’s patent?

Curious as we are having to figure a new way of securing surface mounted magnets at high speed with as little eddy current as possible.

]]>I stand corrected. Someone (me) was wrong on the Internet!

]]>Thanks for the question! While it’s possible I have made a mistake (happens all the time), I don’t think you get the multiplication by two. You can think of the problem by first imagining a single-rotor single-stator AFM, and writing down the torque production equations for that.

Now, if you now remove the back-iron from the stator and replace that by another rotor, the flux linkage in the stator coils stays constant, as does the number of Ampere-turns. Thus, the torque should stay the same.

Now, some torque calculation approaches have some form of the airgap surface area appearing in the equations. The one based on surface current density, or linear current density is probably the most well-known one. In this case, the Ampere-turns in the coils get divided between the two airgaps, so the surface current density is actually halved, cancelling the doubled airgap area.

* This is not to say that there are no benefits. First of all, we just got rid of the stator yoke, and its mass and losses. Secondly, a halved surface current density translates to halved reaction field from the stator, meaning we can double the Ampere-turns before we are at the same level of saturation and demagnetization risk as the single-sided machine.

]]>If we consider an AFM with one stator and two rotor disks at each end, shouldn’t the torque be twice the previous value, given that the magnetic flux density in the tooth stays constant?

That would give the following comparison:

* AFM (1 rotor disk): 50%

* AFM (2 rotor disks): 100% (reference)

* Radial Flux: 77%

So that would result in a ≈ 20% advantage for that configuration.

]]>These (BLDC) are absolutely synchronous machines. Consider the fundamental (Fourier decomposition) of the applied current distribution and associated flux (in space). This component is what interacts with the fundamental component of the rotor flux to produce useful torque (in steady-state) when it rotates in time, most all of the other components contribute to heating. And in the case of concentrated windings, it is a harmonic (in space) of the winding/current distribution function that synchronizes with the rotor (e.g. the 9 stator slot, 8 pole rotor 3 phase BLDC motor is actually a two-pole three-phase winding that has a very strong fourth harmonic which then rotates synchronously with the fundamental 8 pole rotor field).

]]>To understand the providence of “Brushless DC” one must first understand that this term does more to describe what this motor does not have with respect to the motors that it replaced (and had similar performance characteristics. The (brushed) “DC” motor ran from a DC source and the commutation occurred by mechanical switches turning on and off rotor circuits energized via the brushes. The rotor contained the mechanically commutating armature, while the field was fed by DC current from the same voltage source (series vs shunt windings notwithstanding).

Starting with that machine topology, then 1) replace the stator field coils with PMs 2) allow the PM field to rotate whilst holding the armature stationary 3) since the armature is stationary the brushes are no longer necessary, but rotary position sensors and electronic switches are now used to provide the commutation… at the operational/system level the motor behavior can be fairly similar with the biggest difference being that the motor no longer requires brushes that wear (with variable contact resistance and arcing) and must be replaced. One should be able to see with that heritage how the common jargon of “brushless” DC motor came about as the operating principles are very much in common with the DC motor rather than the more ubiquitous ac induction motor (at least at the time of inception).

Common in industrial motion control applications, “BLDC” is referred to the PM machine commutated from a regulated or unregulated DC source (the current is regulated to a fixed value, although ultimately still alternating) where the switching occurs at fixed positions (typically using hall effect sensors) in contrast to a “BLAC, Brushless AC” which is a PM machine where the current is regulated against a sine-wave (typically through pulse width modulation, sine-triangle with hysteresis band or space vector with field oriented control is common)… but the regulation of the current is to a sinusoidal waveform. BLDC vs. BLAC is absolutely about the drive not the motor, however because of these differences and the applications selected for each type of motor-drive system the motor has features/design details that are common in one type than the other.

]]>Sometimes, we would need to consider additional constraints related to temperature transient. Following your method for the optimization problem can easily include them. As you already mentionned it, the optimal point relies on how accurate is the model. ]]>

I don’t really have experience on Spice, so I can’t really comment on that. Could work, though.

]]>Nice, I can imagine!

]]>what is your opinion on generating a net list and using a program like spice for solving?

Thanks,

Alexander

]]>Happy to be of service!!

Norbert

]]>Ah, good question! The terms ‘boundary’ and ‘line’ actually, now that I think of it, only apply to 3D analysis. Consider a single-loop coil, made of thin wire. Then, the ‘surface’ in question would be some surface with the coil-wire as its boundary. The exact shape does not matter – it could be plane, or a colossal bubble – the flux linkage would still be the same, thanks to the fact that the magnetic field lines always for closed loops.

The line integral would then be along the wire itself.

Now, in 2D analysis, the coil would be assumed to be infinitely long in the z-direction, and the field to lie in the xy-plane only (Bz=0 everywhere). Here, the surface inside the coil would be seen as a line in the 2D plane. And the line integral along the wire would be reduced into a point evaluation multiplied by the length of the problem in the z-direction.

]]>First of all, congratulations for your posts! You make them very interesting, clear and rich of good information.

When you said to “replaced the surface integral by a line integral, across the surface boundary”.

Which boundary we must consider for this line integral?

Kobayashi

We have developed a machine for wrapping rotors of this sort. Have to be carefull because of Tesla patent. We find that provided you can wrap under very high tension with very thin wrap a simple surface mounted design can compete directly with the Testla style of IPM look. Once you are up around 20,000 RPM the SPM design outperforms IPM in our opinion provided you can execute the wrapping under high tension.

Contact me if you want more information.

Michael Durack

Thank you, means a lot!

]]>Hello,

Not really, I’m afraid! Perhaps you could try asking companies who do make CF sleeves (e.g. Cygnet Texkimp) about where they get their machines. They might not be very forthcoming, but it’s still a better place to start than nothing.

Hope you do find something!

Antti

Very interesting report !

I am responsible for R&D at one of Japanese car manufacturer.

Do you have any information about the machine for wrapping rotors with carbon fiber?

Which company is manufacturing such an interesting machine ?

just stumbled (with 1 month or so of delay) on this video from Munro where they show the actual rotor turn down, and indeed there are no bridges at all, all the containment task of the rotor in on the “shoulders” of the fiber wrapping…

https://youtu.be/4lGVimLK58g?t=860

Thank you! And yes, many news pieces indeed leave me (and many others) scratching my head. I can only imagine how bad it is for other fields like medicine or health sciences.

]]>Carbon sleeved high speed rotors have need around for over 20 years. I have used them for that long (Motorsolver) as has Calnetix , Carpenter, Windings Inc, MTS and others. These carbon composite sleeves replaced Inconel 718 and Titanium about 20 or so years ago. The near zero thermal coef of expansion is a very helpful advantage along with its very low elongation as compared to inconel an Titanium.

]]>Hey Sven, and thanks for the question! My guess would be that the holes are there mostly for reducing the rotor mass without compromising mechanical strength. They MIGHT also help with cooling, although often the rotor is clamped between end-plates so there wouldn’t be any cooling air flow.

They will of course slightly increase the reluctance of the flux path on the rotor side, but the effect will most likely be very small.

]]>Great article, thanks for sharing your thoughts! Looking at the Plaid rotor picture, there are these big triangle holes in between the rotor magnets. I would assume that they would interfere with the flux path in between the two magnets. Having said that, there must be a good reason why the Tesla engineers designed it this way. I was wondering what your thoughts are on the matter.

]]>Great article, many thanks for sharing your thoughts. I’m an hobby motor designer & builder myself and I was wondering if you could explain the big triangle holes in between the rotor magnets. Wouldn’t they negatively impact the flux path in the rotor? Since the are in the middle of the flux path between the two magnets and greatly reduce the iron area?

]]>Good points both of them! Regarding the peak torque, I’m not at all sure if I’m correct or not, just some quick musings 🙂

]]>Thank you, very good points!

]]>As the picture shows, there’s indeed at least one IPM motor in the S Plaid.

Tesla has used both motors types in the same car in the past, so maybe the S Plaid has a front IPM motor, and Induction motors in the back.

That would explain why Musk talked about containing the expansion of copper in the rotor, due to centrifucal forces.

Sandy Munro & Associates will buy a S Plaid soon, so we’ll have more details when they’re done analysing it.

Cheers.

]]>Great discussion and reasoning on this ‘Carbon-sleeved/wrapped rotor’ topic.

Two points I’d like to make,

1. For induction motor case, you gave a good comparison for two rotor bar design at full load condition. But for EV application, at high speed up to ~20,000rpm, you probably won’t have peak torque capability. So if there is any benefit to quantify at those speed range, you probably need to have to look at some other operating points/conditions.

2. For the IPM case, referring to your discussion here ‘if we can increase the airgap AND keep the saliency ratio (Lq/Ld) the same, we can actually increase the peak reluctance torque achievable’.

Are you implying increasing peak reluctance torque as a result of increased airgap? This would be counter-intuitive, just take a syn-reluctance machine as example, this machine doesn’t prefer large airgap at all.

I’ve never studied that topic personally, but I’m sure there’s some good material around.

]]>Some composites are quite decent nowadays (way better than the old ones saturating at 1 T), but still fall short of laminated steel. Plus, actually getting the properties promised in the datasheet often seems like gambling to me.

]]>Can’t really remember anymore what I was thinking while I wrote this, but it was probably indeed compared to SRMs.

At least, more material needs to be cut off from a SynRM rotor. If laser-cutting for small batch production, this means a longer time spent cutting each sheet. In series production, a more complex cutting tool needs to be manufactured. But, these are just guesses of mine – detailed production economics is beyond me.

]]>Thank you! That’s exactly what it means; 3D analysis also accounts for the end-winding flux, while 2D analysis is by definition confined to the 2D-plane (as though the problem were infinitely long in the z-direction).

The d- and q-axes, on the other hand, are more related to circuit analysis. The flux linkages are first computed for each phase, using e.g. the method in this post. So nothing special in this step.

Then, the three phase quantities are transformed with a linear transformation, into the d- and q-axis components and optionally a third 0-component.The transformation is defined so that a balanced sinusoidal 3-phase system gets transformed into constant d- and q-axis components. Furthermore, the d-axis is typically selected to coincide with the permanent magnet flux (or easy magnetization axis in case of synchronous reluctance machines).

Why we do this is due to two reasons at least. First of all, salient-pole machines are easier to analyze in the dq-frame, as we’re dealing with (almost) constant quantities. The second reason is related to the first: controllers are easier to implement in the dq-frame, as we’re controlling a DC-quantity rather than a constantly-changing sinusoid.

]]>Also a sort of related question. In my FEM software, I am able to plot the “d-axis” and “q-axis” flux linkage for a motor. What is the physical meaning of this, i.e. does one count flux lines (in arbitrary units) in the d and q directions?

]]>LencLaw is too small. Generator work with out atraction. I revind one washmashine motor and attach PMrotor ]]>

Hello Anthony, and thanks for your words!

The dynamic hysteresis thingy is a very interesting topic! I know the loop gets wider at higher frequencies, and suspect it is indeed largely due to in-lamination eddies. But I haven’t had any time to look deeper into it.

For the macroscopic H, I THINK the Lagrange multiplier directly corresponds to the average field strength, times -1. I’ll update the example so that the instantaneous (B,H) points are plotted; it seems to work correctly based on some simple tests at least.

]]>I very much like what you have done here. And even more the fact that you make the code available. I see that you have some code to get the result for non linear material as well.

I am trying to use it to get the “macroscopic” B and H. Basically the B and H that you would mesure outside of the specimen if this was an experiment in the real world. B is easy to get. H seems a little more tricky. Then I would like to try to change the excitation wave form.

The ultimate goal is to draw some “dynamic hysteresis” loops and compare it (or try to fit it) to some measured data. I am hoping for some useful results.

There is a threshold in the understanding of the FEM and the code that I have not quite overcome yet though.

]]>Thank you! I think I remember LL saying that the cores are (at least partially) made from laminated material, so there’s probably some compromise to be made about that. It might be possible to keep the stator yoke flux paths almost radial-flux-like by extending the axial-flux rotors a little further out and using cleverly-designed tooth pieces, but that’s just speculation on my part.

Good point about the VFD!

]]>The “no-VFC” claim, for me, means the machine doesn’t need a sinusoidal feed. I think it’s obvious it will need to at least switch the coils on and off (“trapezoidal” control) or like a switched reluctance machine. Nevertheless, power electronics will be needed to drive this machine with variable speed. ]]>

Thank you!

]]>Thank you! And your approach sounds interesting; I think I may have read about it somewhere.

]]>In the last years, I introduced Poynting vector concept in a unitary and efficient method in electrical machines design(transformers,synchronous machines,etc),an alternative at classical Arnold-Esson method; It will be interesting to change some ideas

Best regards ]]>

Thanks Olli! Yes, I now realize the poles-turns-flux example was perhaps a little too simplified, in many respects. Especially in the case of field-windings in salient-pole generators, the relationship is likely very much nonlinear.

Likewise, my use of ‘turns’ was perhaps unclear. Ultimately, what it boils down to is more or less the electric loading, i.e. the number of Ampere-turns per unit airgap circumference.

So, for two pole-pairs, the number of total (Ampere-)turns would almost certainly be higher compared to one pole-pair, but the number of turns per pole might be lower. I write ‘might’, because the space constraint might not be that significant for such low pole counts (if we’re still speaking about field-windings). However, if we were to consider say 16 pole-pairs, there the space limit would really start to count.

]]>One question regarding this statement: “The flux per pole gets halved, but this is immediately compensated by the fact that we have more of them in series. As each pole is now smaller, we can only fit half as many turns in each of them.”

Does e.g. splitting the pole in two smaller ones really limit the space for pole windings in the same ratio? So if we use same size field winding conductors could we not use more effective turns in two poles that what would be fitted on one pole?

Thanks for your writing again and hope to see more to come.

-Olli

Well, there’s something of a sliding scale there. After all, even the planes we have today utilize electric actuators in ever-increasing degree.

However, I guess for a plane to be ‘truly electric’, a significant portion of the effective thrust would have to be produced electrically.

]]>Thanks! I think already on LinkedIn, but in any case let’s see if I can spool something simple up in the near future!

]]>Looking for performance comparison..specially at low voltage, high current, high speed machines..typically used in aerospace and automotive domains widely..

]]>Yeah, I think that’s exactly the story behind the term. Calling them just PMSMs would be good, or maybe calling the entire package a ‘BLDC drive’ when appropriate.

]]>Thanks! 🙂

]]>Hi Chengliu, and congrats on your assistant prof. position! Sure, I have used a sliced model myself, although haven’t published one yet. So it shouldn’t be any problem at all. We can discuss the details by email.

]]>I remember the FEA kitten, it’s adorable!

And don’t worry, magnetics doesn’t get any easier with further study. “Opposites attract” is pretty much as good as it gets.

]]>This is what I love about your work Antti – the fun! Well… I don’t understand much more in all honesty – I finished magnetics in my primary school I think. All I know is that “Opposites Attract” (https://www.youtube.com/watch?v=xweiQukBM_k)!

]]>Haha, I guess that’s a very common feeling when moving outside one’s own specialty! 😀

]]>This is insane how you solve problems I don’t really understand 🙂

Great work… I guess 🙂

]]>Thanks on my behalf! 🙂

]]>Ravi, you can have a look at this paper:

M. Aubertin et al. “Periodic and Anti-Periodic Boundary Conditions With the Lagrange Multipliers in the FEM”, IEEE Trans. Magn., v. 46, no. 8

They describe the use of Lagrange multiplier approach to periodic boundary conditions quite detailed.

]]>Hi Ravi, periodicity conditions can indeed also be enforced with Lagrange multipliers.

And yes, P will indeed be a matrix if the nodes on the two boundaries won’t match 1-on-1. Or, to be precise, it will be a matrix in any case – but with matching nodes it will simply be a permuted identity matrix with zero columns. It’s probably easiest to understand with Matlab notation:

Let n_periodic_1 and n_periodic_2 be the indices of the nodes on the two periodic boundaries (ordered so that they match 1-on-1), and n = numel(n_periodic_1), and N = number of total nodes. Then, following the notation in the Sliding interface paragrap, the matrices are as follows:

I = sparse(1:n, n_periodic_1, ones(1, n), n, N)

P = sparse(1:n, n_periodic_2, periodicity_coeff*ones(1,n), n, N)

Now, in case the nodes don’t match, I will still be the same, but P will be a more complex interpolation or mortar matrix.

Hope that clarified something 😀

]]> Interesting post. I am curious is it the same way periodic boundary conditions can be enforced.

For eg. In machines antiperiodic boundary conditions are let say a1=p* a2 . Here for anti periodicity p=-1. (provided node positions are similar). However in case of a random mesh at boundaries it can p will be some matrix. Will it be used as langrange multiplier?

Indeed!

]]>Speed up!! 😁 ]]>

Hi! The color scale is the absolute magnitude (or norm, if you like) of the flux density vector B.

The flux lines, on the other hand, are such lines that at any point on the line, the line is tangential to B. So the lines are illustrating how the flux flows in the machine. Furthermore, between any two lines, the total amount of flux stays constant.

]]>Thanks! Core losses might not be very accurate, at least if first-order elements are used. And by “accurate”, I mean “compared to what would be obtained with a very dense mesh, using the same model”. The accuracy of the loss model itself is whole another story, again.

Winding losses are also complicated, but in another way. Cage and damper windings can be treated easily enough, but any other kind (be it stranded or form-wound) usually requires quite a dense mesh due to the sheer number of conductors alone. Well, that’s why I spent four years writing a thesis about them 🙂

]]>