The Halbach Disc Motor Ebike Project

[safe]

Enhanced



What if you could discover some clever way to boost the yield of your magnets? The big magnets can achieve 0.7 Teslas, but the small ones can only achieve 0.4 Teslas in a standard configuration. Are there tricks to increase performance?

It looks like there is a way...

By spacing the magnets out more and then adding an extra cube outside of the focal point of the pole you "enhance" performance. The net result is ABOVE 0.7 Telsas with wimpy little 0.25" blocks. The total gap is 0.375" so it's slightly more narrow than the 0.5" gap of the bigger blocks, but it's pretty darn good.

Enhanced 2H 3P 0.375 cross section.gif (4.57 KB) Viewed 932 times

Enhanced 2H 3P 0.375 image.gif (34.42 KB) Viewed 931 times

Enhanced 2H 3P 0.375 speed and frequency.gif (4.08 KB) Viewed 933 times

...the basic concept here is that the only block that matters is the "pole block" and it needs to have a fully supported containment field around it. By having the extra block outside and the Halbach blocks to the sides it creates a containment field so that very little leakage occurs. It's as though you are focusing the lens of magnetic force and cramming it through the pole block.

[safe]

What Are The Metrics?

Now that I have about fifty simulations to evaluate how do I decide which are good and which are bad? Highest Tesla values? What about power density, how many blocks are "active" as poles compared to those being used for magnetic field focusing? (Halbach, doubling)

One way to look at it is to take the power expended (watts) and set up a ratio with the force created (Newtons) and then you will have a ratio for comparisons. The less energy (watts) per force (Newton) created the better because that means it's more efficient.

Here's a list of a bunch I just went through starting with your plain vanilla Steel backed non-Halbach setup:

Steel 1P Flat 676 watts 57 N = 11.86 watts per N
Steel 2P Flat 1014 watts 99 N = 10.24 watts per N

Halbach 1P 1H 2030 watts 212 N = 9.58 watts per N
Halbach 1P 2H 1014 watts 116 N = 8.74 watts per N

Enhanced 2P 3H 1352 watts 170 N = 7.95 watts per N
Enhanced 2P 2H 1014 watts 136 N = 7.46 watts per N

...the last one looks like this:

Enhanced 2P 2H image.gif (33.49 KB) Viewed 923 times

...all the data assumes the same 1/4" cubes being arranged differently while maintaining a gap of 0.375" (3/8").

The fully Enhanced version loses 37% less energy compared to the Steel flat single block option. But in the final analysis if we are talking about a 10% loss for the Steel case (for example) then maybe we might instead get a 6% loss in the Enhanced Halbach case. There is a point of diminishing returns because the Steel option is already pretty good.

Still... you might as well shoot for perfection. (can't hurt)

[safe]

Torque

If it takes 7.46 watts to create a Newton of force then it should be possible to figure the torque that can be created by a 1000 watt input. This might give some validation that the numbers are making some sense.

7.46 Watts / Newton = 0.134 Newton / Watt

1000 Watts * 0.134 Newton / Watt = 134 Newtons (total force)

Torque = Force * Radius (0.11 meter for the size of the disc)

134 Newtons * 0.11m = 15 Nm (at the hub itself)

------------------------------

If you look at first gear on my old bike and assume that you are only using 1000 watts of power then you would get 10 Nm of rear hub torque. So this is better than that by 50%.

PWM kind of scrambles the comparisions because it allows more than the rated current at low duty cycles, so if you look at the "actual" low end torque I've been running for 7,500 miles it's more like 80 Nm but that was with 2000 watts of input. Using equal current comparisons the Halbach does well. (the efficiency is good anyway) It's a little like comparing Armature Current Limiting verses Battery Current Limiting, the powerbands are radically different.

It's hard to know for sure...

[safe]

Litz Wire Matters

There are typically two things that people building Halbach axial flux motors will talk about. The first is the Halbach magnet configuration because it eliminates losses due to steel and reduces weight. The second thing that is talked about is the use of Litz Wire. It's really only when you get deep into the math of the performance that the reason that Litz Wire is useful stands out.

Litz Wire.gif (52.49 KB) Viewed 895 times

The "bottom line" on copper losses is that the more current you have flowing through the wire the more losses you get. So if you use a single wire and try to flow a lot of current through it you get a lot of losses, but also a lot of magnetic force. Split the coil up into multiple "winds" and you reduce the current through each coil and that cuts losses. (I learned this before with my rewinding projects) Changing wire thickness is another dimension to consider.

So in my case I started with a simulation that used one coil and it had 30 turns of wire and that produced an efficiency of 7.58 Watts per Newton of force. When I switch to three coils of 10 turns each I get an improved efficiency of 2.5 Watts per Newton of force.

That's a proportional 2/3 reduction of losses.

30 Turns, 1 Coil - 100 amps - 1015 watts - 134 N - 7.58 w/N

10 Turns, 3 Coils - 33 amps each - 110 watts - 44 N - 2.5 w/N

...but you can also see that you lose peak power this way. So in order to compensate you need lots and lots of Litz Wire to create more peak force. Given the fact that the gap between magnets arrays is limited you only have so much room for this increased amount of copper.

This performance improvement "dwarfs" the Halbach enhancement, but they work in tandem, so you can do both.

Hub torque goes from 15 Nm to 45 Nm for 1000 watts assuming you can use enough wire to actually achieve 1000 watts.

[safe]

The More You Know...

There are so many ways to do this project and so many of the options will produce marginal results while others can be excellent. I tried a direct comparison of the "stock" Halbach using a standard one wavelength gap size with one of my most recent "Enhanced" configurations and the difference is impressive.

Halbach vs Enhanced.gif (6.06 KB) Viewed 879 times

...this is about double the peak magnetic force (0.9 Teslas) which should mean that I get more force for less current and that means less losses. (will need to buy some 1/8" end magnets)

0.9 Tesla.jpg (128.74 KB) Viewed 881 times

What is amazing is that these little N40 blocks only produce 0.375 Teslas when they are on their own. So if you just placed them onto a steel disc (non-Halbach) you're not going to get any more than that. To be able to scale up from 0.375 Teslas to 0.90 Teslas is impressive.

Single Block N40.gif (3.49 KB) Viewed 873 times

Note also that the stock Halbach increases the magnetic field from 0.375 Teslas to about 0.45 Teslas.

[safe]

The Speed (Mph) vs Frequency (Hz) of the setup in the previous posting looks like:

Mph vs Hz 32 Poles 16 Pairs 24 Wheel.gif (7.19 KB) Viewed 858 times

...this means that the Inductance will need to be very low in order to be able to get up to 60 mph without the backEMF preventing higher speeds. This is fine since the narrow gap isn't going to allow a lot of room for coils. The main worry is whether the RC ESC is able to be reliable all the way up to 200 Hz. A benefit is that it only takes 3 mph before the frequency is up to 10 Hz which is generally considered the point at which things settle down with the controller. (at least that's how it is with Induction motors)

Power with these motors is incredibly linear. This means that when you make tradeoffs as far as number of turns or wire thickness it will have a direct relationship with the ramping up of power (horsepower) and the eventual no load speed. The only problem is that I'm still not at a point of having any certainty about how much power will actually be produced. I'm still in the dark in some areas.

Ideally the no load speed will be at about 60 mph... (and not way past or way below)

Efficiency on these motors is also linear and is related to current. So unlike with the regular motors with iron cores there is less of a "powerband" shape to worry about. If you used Armature Current Limiting (phase wires) you could be assured of very high efficiency across the entire spectrum and not have to worry about overheating, but you would sacrifice low end torque. Since I'm in a quest to achieve a perfect 1000 watts across the entire powerband the effect would be to have less efficiency down low and higher up high.... so in the end it will be more similiar than one might think.

[safe]

Trusting the Simulation

The FEMM Simulation program produces all kinds of data about the things you create. It has the ability to oscillate the current at a specified frequency and that can tell you how much backEMF you are creating with your simulation... or at least that's the assumption I'm making. Actually figuring out the correct back EMF requires a solid understanding of the Inductance (which is actually pretty easy because the simulation gives you that) and also the magnetic field that the wire is passing through and the rate of current change. Maybe someday I'll try to go through the math manually, but for now I'm just plotting several data points coming off the simulation.

I assume 28 volts at peak and then "fudge" differing current values to approximate the backEMF. The result is that each phase gives simulation results about it's voltage drop and once you exceed the 28 volts then you would be past the motors ability.

From what I can tell the motors capabilities will look like the chart and this means that if I'm shooting for a "flat" powerband of 1000 watts that I can current limit most of the way. Being able to current limit means that you have better efficiency with a lot less heat. The moment you stop being able to current limit is when the backEMF is dominant and that doesn't appear to happen until 52 mph.

So this is more or less a simulation driven "guess" about the motors actual behavior:

Speed, Power and Current.gif (4.47 KB) Viewed 820 times

...this appears to fulfill my requirements if it's accurate.

If I want to double the top end power I can reconfigure the coils from series (the way I'm simulating now) to parallel and that will shift everything to the right much like Wye to Delta switching would do. However, doing that is the same as going from 32 poles to 16 poles in the disc and my goal here has been to have a low inductance motor with strong low end torque. It's also possible to switch the wires from the battery from 20 cell NiCads to 40 cell NiCads and get up to 56 volts, but then I couldn't use those cheap RC motor ESC's.

Efficiency is supposed to be in the 95% range, but that's just based on the Halbach formulas. CSIRO manages to do it and I'm just hoping that I can too. (no reason not to think it's possible) As long as nothing dramatically wrong happens the input and output power limits should be close to the same. (so the chart is both an input and output power chart +/- 5%)

To be honest I just don't know what will happen.

On the positive side the entire motor will weigh about 3 lbs which is more in the scale that it should be for ebikes.

[safe]

Not Satisfied

I want to gain more precision in my predictive abilities with the motor constant for this project. The problem with using the alternating current frequencies in the simulation is that the coils aren't moving relative to the magnetic field. With a Halbach motor there is no "back reaction" caused by iron because there is no iron. Without iron the backEMF is entirely defined by the coils inductance multiplied by the rate of change of the current "demanded" by the changing magnetic field. Using a simple sine wave as an approximation isn't that good because the shape of the magnetic field is more like a sawtooth.

0.9 Tesla Sawtooth Waveform.gif (3.5 KB) Viewed 817 times

So what I'm thinking is to export the data of the sawtooth magnetic field waveform and armed with the knowledge of the coils inductance I should be able to take the first derivative of the waveform and then be able to calculate for things like pole count and speed and come up with the true backEMF. (a true motor constant)



This might take some fiddling...

[safe]

Too Good To Believe?

I looked up the Aurora solar car specs and noticed that they have a 0.91T peak magnetic field and that eases my mind a little bit that I'm on the right track. Also, they publish their efficiency chart and lot's of data so it gives me a little more confidence in the numbers I'm looking at.

Aurora Specs.gif (10.17 KB) Viewed 792 times

Aurora Efficiency.gif (10.42 KB) Viewed 796 times

http://www.askmar.com/Magnets/Halbach%2 ... 0Motor.pdf

In other pdf file that talks about Halbach Motors they say:

"In this ironless system, and for all feasible values of the
winding currents, there is no “back reaction” between the
stator windings and the inducing magnetic field. There is,
of course, an effect of the winding inductance on the output
voltage as well as the usual resistive drop. However, since
the system is ironless, inductances are low, and with good
design, the resistive drops are also low. As will be shown,
not only is the power output very high, but the effciency
is also typically much higher than that of an iron core
machine of comparable physical size."

...the numbers for "Motional Back EMF" that I'm finding are so small that it suggests that you can more or less ignore any sort of cogging behavior ("back reaction" doesn't exist just like they say) and just focus on the electrical inductance of the coils. It might be in a sense "so simple" that I can't see it with any confidence. (or I'm totally missing something)

I'm left with simply making sure there is enough copper to prevent overheating for 1000 watts of power.

[safe]

Oooops!

Glad I caught this now... (before building it)

For all the simulations I've been running I had been using the default layer depth of 1". That's wrong because the magnets are only 1/4" x 1/4" square facing from the top, but also only 1/4" in depth.

So all my numbers are off by a factor of four when it comes to power output. This means if I built it as envisioned so far it would be really underpowered. Time to go back over it all and redo it.

[safe]

Back EMF

Apparently it's a "known issue" that the FEMM simulation doesn't really have the ability to calculate a motors back EMF directly. There are some tricks out there to do it, but they are kind of awkward. Without the ability to know the back EMF you can't know the motor constant and without that you have very little ability to know how the motor will behave.

So I decided to figure it out using manual means (doing the math) and came up with a small spreadsheet that I call "kvCalc" that does nothing but accept the parameters of an axial flux motor like you would create in a FEMM simulation and then produces an estimation of the "Rpm per Volt" constant.

kvCalc.gif (6.91 KB) Viewed 762 times

...what had been tripping me up for a long time was that the angular velocity (w) normally described for radial motors needs to be rethought for a FEMM simulation because you are dealing with a "Flat" perspective. By switching from polar coordinates to cartesian coordinates it becomes possible to simply look at the length (period) between north pole magnets to figure out the value you need in order to know the speed.

Now I can start to get a handle on how the simulations will really behave in real life because I can know the motor constant. Try it out, it only takes six parameters to arrive at the motor constant.

[safe]

CSIRO Motor

Eager to validate that the kvCalc actually works and produces reasonable results, I plugged in the best numbers I could find for the CSIRO motor which is the motor I've been trying to imitate. (imitation is the highest form of flattery)

CSIRO Motor kv.gif (4.67 KB) Viewed 753 times

...they are able to use only 4 turns of wire because of the large magnets they use. My "guess" is that the magnets are about 2" square and they are very powerful. The result is a very low kv value of about 25. They actually list their constant in terms of Volts per Radians per Second, so there was a conversion added for that.

[safe]

The Problem With Math...

Math can't give you an answer just because you want it to.

After running the numbers on the designs I have so far the math says that the motor is underpowered. The problem is that as I increase the number of coils of wire it requires more space and that added width decreases the magnetic field within the gap. The CSIRO motor uses huge magnets that create intense fields and so you can use less copper inside to achieve a good result.

What I'm finding is that there isn't enough room for the copper to achieve the efficiency I want. (a recurring problem in these motors it seems) As a result the motor ends up with a Kv up in the 100 range which is fine for a motor with gearing, but wrong for a disc motor. The Kv needs to be down in the 25 rpm per volt range and the resistance needs to be low to accomplish high efficiency.

The backEMF "awareness" is so important in designing the motor that if you exclude it in your design process you will likely not produce anything of value. I'm glad I learned this now rather than later.

[safe]

Tritium Boosted Nuclear Weapons

http://en.wikipedia.org/wiki/Nuclear_weapon_design



One thing scientists discovered when developing nuclear weapons is that the addition of a material called Tritium at the core significantly increased the yield you get with the bomb.

-------------------------

In my situation with the dual Halbach arrays I've spent a lot of time figuring out how to maximize the Halbach side, but never thought about improving the core. The longer you stretch out the gap between the Halbach arrays the more the magnetic strength "sags" in the middle. The coils magnetic strength (in air) is small compared to the magnets, so if you add an iron core you can bring back the strength in the middle and complete the magnetic circuit. Magnetic strength needs to be in a circle and the weakest link defines the overall strength... a wider gaps weakest link is in the middle of the gap, so the idea is to correct what is "wrong" and keep what is "right". I tested the concept at 200 Hz in the simulation and the eddy current losses are small, in the neighborhood of a watt or two, so the benefits far outweigh the losses. The new "yield" is double what you get without the core and with the now nearly unlimited width I can add all the coils I need.

Adding a Core 40A 120 Turns Image.gif (33.41 KB) Viewed 713 times

Adding a Core 40A 120 Turns.gif (4.62 KB) Viewed 721 times

...so it seems the project isn't dead yet. With the addition of a small core in the coils the yield is going to be good enough to achieve some significant power.

Gap width is no longer a problem.

[safe]

Doing The Math...

I have been creating another spreadsheet that applies all the normal formulas for electric motors. This spreadsheet includes the quadratic equation solution so that you can simulate the controller. (something I learned a couple of years ago) But what is really new is that I've modeled the Halbach disc component parts like the magnets and the dimensions so that I can interactively test out different motor designs. Most of the designs produce terrible results, so it's not easy to find the right combination by just guessing at it. I use the FEMM simulation now as a confirmation step to make sure there is agreement on two platforms.

Later I'll post the spreadsheet when I'm completely finished expermenting, but for now here is one example that uses my existing 300 magnets in such a way as to be able to only require a total of three coils... one for each phase. The coils will be large, but the design I've switched to (will discuss later) uses a new configuration. Here are the estimated results for a 1K limited motor and a 2K limited motor which is the way I see the racing classes evolving:

42 Pole 0.25 N40 1K Racing.gif (6.28 KB) Viewed 897 times

42 Pole 0.25 N40 2K Racing.gif (6.35 KB) Viewed 898 times

...my confidence level is beginning to climb as I begin to understand how all the pieces fit together. This does seem to be something that "should" work as intended.