The Death of the Motor Design Guide and the Birth of Pablo

    tl;dr: This post is the result of me learning more about electric motors since the last design guide post and coming to the conclusion that a brushless motor design guide no longer satisfies the initial reasons motivating me to create one.  I will still be designing and fabricating brushless motors, but the design process is different than what I thought it should be in previous posts.  The first part of this post is instructional, but my design choices in the latter half are not reviewed as slowly and thoroughly.

-

    Welp I didn't get very far with this one, did I?  I'm not too disappointed because this cancellation is the result of me learning and now I can move on to other things that might prove to be viable.  I should also add that I don't think that I would have made it to this point motor-knowledge-wise so quickly if I hadn't started this project.  So, definitely a positive outcome overall and I think that I will tackle similar projects the same way in the future.

    Alright, now to the part where I tell you where I went wrong.  Basically, the fatal flaw in my logic was assuming that you can always design around torque.  One of the reasons why I became so interested in creating my own electric motors is that I thought I could get around using a gear reduction by altering the parameters of motor and irking out more and more torque by sacrificing other things like operating range or copper.  This is not the case.

To understand why, let's look back on my last post and analyze the beginning of the design process:

"    This is the flow process that I have so far:

• Desired torque -> Estimate a reasonable current for that torque -> Calculate required kT"

    There is nothing immediately wrong with what I have written here.  If you have an output torque from an input current, you can easily relate the two with what is known as the torque constant (kT) of the motor.  The issues arise when trying to guarantee that a kT value remains "true" for desired operating points when other performance constraints come into play.  The pertinent constraint in this scenario is magnetic saturation.  One of the basic principles in electric motor theory is that torque and current have a linear relationship.  Linking these two values can be confusing as the current is not actually what creates the torque.  It would be more accurate to say that it is the magnetic field generated when current flows through the coils of a motor that create torque.  There is a limit to how strong these induced magnetic fields can get because a material can only hold so much flux per unit volume.  (It is important to keep in mind here that flux is not a physical object; flux lines just describe magnetic potential.)  This material property is commonly illustrated with a graph known as a B-H curve:

    This is the B-H curve of a soft magnetic material which is used in magnetic circuits in motors.  The B axis represents the apparent flux density within the material we are analyzing and the H axis represents the strength of an applied external magnetic field.  In a motor, this H field is created both by the permanent magnets and by current in the coils.  When continuously increasing current in the coils of a motor, after a certain point, the magnetic pathways in the motor become saturated (meaning they cannot hold any more flux) and flux generation flatlines as seen above at the pointy ends of the B-H curve.  This also means that torque generation flatlines, essentially hitting a ceiling (which I have tried to illustrate in the figure above with green lines).  It is at the onset of saturation where the linear relationship between current and torque breaks down.

    In the figure below, magnetostatic finite element analysis (FEM) is being done.  The long yellow rectangles are permanent magnets, the blue regions mostly void of lines are air, and everything else is laminated iron like you would find in a motor.  The bright pink sections are parts of the iron that are saturating from the flux from the magnets.  You can see how the flux density increases as the width of the iron decreases.

    This ceiling is only a function of how much flux the magnetic circuit of the motor can support before saturating and doesn't give a crap about you tweaking any of the other parameters of the motor.  This is the realization that had been eluding me until now.  Once you hit the ceiling, there is no way around it, so it must be accounted for in the design.  This sentiment makes a lot of the legwork I was doing unnecessary and greatly lessens the usefulness for a design guide the way I planned it.

    I think that providing one last alternative view of the problem would be helpful in justifying the purging of the guide: A motor of a given diameter only has so much real estate around its circumference and that space has to be split between copper (to act as a medium for current) and a soft magnetic material, commonly referred to as iron (to act as a medium for flux).  Too little copper and you will generate lots of heat and perhaps even electrically saturate your wire.  Too little iron and you hit the flux density ceiling too early and limit the performance of your motor.  You can also describe this ratio of copper to iron in a slotted stator motor as tooth width to tooth pitch.

    Omega is the tooth width and rho the tooth pitch.  A common value for this ratio is 0.5, meaning that the circumference is split evenly between iron laminations and slot space which copper may inhabit.  I am starting off with 0.5 myself and may tinker with the value as needed.

    So, with the constraints that I have laid out, how do we now go about designing a motor that can output more torque?  A common way of doing this is with a transmission, however I plan on using this motor in a scooter as a hub motor where no transmission is employed.  As previously explained, in order to extend the pre-saturation operating region of the magnetic pathways, we can make the pathways larger.  It is easy to see that this requires an increase in diameter or in axial length, both of which lead to an enlarging of the motor.  As it turns out, if you know the type of motor you are dealing with and can generally characterize it, the volume (measured at the airgap) operates as a reliable indication of torque output.  So, according to figures that others have worked out, if I have a decently optimized, surface permanent magnet, brushless motor with a volume of... let's say 645 cm^3, I can expect it to be able to produce just under 13 Nm of torque.  A quick conversion like this is obviously really handy for sizing your motor early in design.

Now, on to the design of my first motor!

Meet Pablo:

Motor Render without End-Caps

    I named Pablo after one of my recent favourite artists, the virtuosic performer/composer for violin, Pablo de Sarasate.  Go listen to Zigeunerweisen if you haven't yet.  Good stuff.

    The volume of Pablo's airgap comes out to around 645 cm^3, which is why I used that as the example figure above, so he should be able to generate 13 Nm peak torque as well.  The diameter of the airgap is about 165 mm and the width of the stator is right around 30 mm.

    A big influence on the design was material acquisition constraints.  I wanted to use neo magnets because their strong fields lead to higher efficiencies, but they are quite expensive.  SuperMagnetMan has some strong magnets at nice sizes and reasonable prices so I determined the magnet size by choosing from their inventory.  I had a general concept of what I wanted the diameter of the motor to be so, with the dimensions of the magnets in hand, I then selected a number of poles and slots that would land me near to my desired diameter and also provide the most sinusoidal BEMF possible because I may implement FOC in the future.  This led me to the 20 poles and 24 slots, a classic pairing.  The number of laminations that made up the 30 mm of my stator thickness were not really a concern for me other than not having too many, thin laminations.  Larger lams mean more eddy current losses, but I want this thing to be assemblable what all is said and done and fewer, larger pieces will be much easier to deal with.

    Now to touch on a bit of interesting mechanical design before going over the basic analysis.  The part of the motor that connects the stator to the shaft (in typical motor construction) is called the spider.  This piece is typically non-magnetic as you usually want to isolate all the fun stuff going on in the stator from the motor shaft and everything that lies beyond and it must be strong enough to be able to support (in this case) high radial loads from a scooter frame and passenger and be able to transmit all of the moments going from the stator to the motor shaft.  I elected to use aluminum as many others have because it is cheap, strong for its weight, and easily machinable which gives an amateur machinist such as myself more room to make errors.  The render below depicts one half of the spider.  The idea is that the spline visible on the outside of the spider (which has a slight draft) will interface with a matching feature on the stator.  Past the spline there is an overhang which will serve to clamp the stator lams on either side.  I'm hoping these two features will make the spider-stator interface rock solid.  The many pockets are to reduce weight and look cool, but they will actually not be visible in the final assembly because they are on the inside of the spider.  Six screw holes on the inner and outer diameter each will keep the two halves together and if I thread the spider they can act as jack bolts to break the assembly apart.  Finally, another cool feature of a split spider is that the motor shaft can be totally captured inside and not have to rely on a press fit.  I also added an interior keyway to prevent relative rotation between shaft and spider.  The halves will be created with subtractive manufacturing in a single work holding on a 3 axis mill and then finished up on a manual lathe.

Spider Render (the surface texture changed from the last render)

    Analysis time!  There are a lot of parameters at play when designing an electric motor and I am not going to go over all of the relationships and attempt some crazy optimization.  I am really only going to estimate some values of parameters that determine if the motor will be practical and fun to stick on a scooter and drive around with.  So, just keep in mind that what follows is really just a surface pass at analysis and validation and would be grossly inadequate in many serious applications.

Magnetic Circuit Analysis in FEMM

    Here are some magnetostatic analysis results from a study I created and solved in FEMM, a very accessible and simple to implement analysis tool.  Increasing flux density is represented in a heat map fashion by increasingly warm colors, with the magenta color representing the highest flux density.  The main purpose of this analysis is to give me some idea of saturation in the stator and in the rotor backiron.  In the left picture, the flux density measured at the center of the stator tooth is nearly 1.933 Tesla.  On the right, the flux density measured at the center of the backiron is around 1.426 Tesla.  The approximate value for maximum acceptable flux density in the teeth of a slotted stator is 1.6 T.  The tooth measurement greatly exceeds that value.  This poor performance can be traced back to an error I made when creating the equation bank in SolidWorks that I used to determine the proportions of the stator.  It should also be noted that this analysis was done with the assumption that the laminations in the stator and backiron were as tightly packed as they would be in your average (well made) industrial motor.  However, I doubt that I will be able to achieve that level of packing and thus the issue would be even worse.  This must be corrected in the design before moving on to fabrication.

    Despite the above error, more valuable analysis can still be done before the redesign.  I want to be able to put Pablo on a scooter and have decent performance, i.e. be able to accelerate the scooter and passenger at a "fun" rate.  Just from the volume, ideal performance should yield 13 Nm max torque.  The current minimum OD, which would be the diameter of the outside of the stator backiron, is 200 mm.  I plan on having the rotor endcaps, which connect the backiron to the bearings so that the rotor may rotate, slide over the OD of the backiron for greater contact and, hopefully, better stability between the parts.  I am also still debating on what to use as the actual wheels or tires after the endcaps go on.  So, lets assume the final diameter of the hub motor assembly to be 250 mm.  With 12.9 Nm assumed torque, that means that the reaction force on the scooter will be about 103.2 N, leading to an acceleration of 1.14 m/s^2 with an assumed payload of 90.7 kg (200 lbm).  This means that the scooter would take right around 4 seconds to accelerate to 4.47 m/s (10 mph) and even less if I am kicking it off from zero speed.  These numbers are adequate if not a bit underwhelming.  SuperMagnetMan offers magnets that are longer than the ones employed currently and have higher remanence (N50 rather than N42) and would almost double the volume (and thus torque) of the motor.  The main downside is that they are more than twice as expensive and I need 20 of them...

    The next steps are to finalize the design, apply for a maker grant (Invention Studio covers part of my bill), and then order materials!  I am already calling around for some quotes, so hopefully material acquisition will go smoothly.

    Damn it took me way to long to publish this in the end.  My general tenacity and school/project balance still need a lot of work.

    I am getting close to a 3 phase controller update but want to spin a motor before I post anything and I have yet to do that.  Stay tuned.