# Dealing with stator magnetic saturation

In my previous experiments demonstrating torque feedback (full rate inverse dynamics, ground truth torque testing), I’ve glossed over the fact that as the stator approaches magnetic saturation, the linear relationship between torque and current breaks down. Now finally I’ll take at least one step towards allowing moteus to accurately work in the torque domain as motors reach saturation.

## Background

The stator in a rotor consists of windings wrapped around usually an iron core. The iron in the core consists of lots of little sub-domains of magnetized material, that normally are randomly oriented resulting in a net zero magnetic field. As current is applied to the windings, those domains line up, greatly magnifying the resulting magnetic field. Eventually most of the sub-domains are aligned, at which point you don’t get any more magnifying effect from the iron core. In this region, the stator is said to be “saturated”. You can read about it in much more depth on wikipedia or with even more detail here. The end result is a curve of magnetic field versus applied current that looks something like this:

To date, moteus assumes that you are operating completely in the “Linear” region, where the torque and current are linearly related.

## Operating in the Rotation Region

To operate in the “rotation” region I ended up using the following formula:

$\tau = K_T * I_c + ts * log2(1 + (I - I_c) * is)$

Where $I$ is the input current, $K_T$ is the motor torque constant, $ts$, $I_c$ and $is$ are three constants that I fit to measured torque data. With some approximations, this can be calculated relatively efficiently on the STM32G4 that drives the moteus controller, adding only a microsecond to the overall loop time to go in both directions.

I then ran a torque sweep with my load-cell fixture from before, and sure enough, the input and output torque match much better now across the entire range of operation, despite the fact that the phase current needs to start growing very rapidly near the top end:

# Testing qdd100 stator windings

My initial design torque for the qdd100 was a little over 17 Nm. However, when I did my first ground truth torque testing, I found that some servos had a lower maximum torque than I had specified. While working to diagnose those, I built a qdd100 that used an alternate stator winding of 105Kv instead of the 135Kv that are in all the beta units. The Kv rating of a stator describes how fast the motor will spin for a given applied voltage. If you assume the same amount of copper mass of wiring, a lower Kv will mean that there are thinner wires that wrap around the stator more turns (or fewer wires in parallel). A higher Kv will have thicker wires with fewer overall turns.

On paper, if you assume a perfect controller, this shouldn’t make much of a difference. The same input power should be required for the same output torque. The only differences should come into play once you have a controller with either a limited maximum voltage or a limited maximum current. The higher Kv motor will be able to go faster given a fixed maximum voltage, and the lower Kv motor will have more torque for a given maximum current.

I wanted to verify that this was true as part of my evaluation to identify the cause of my decreased torque, so I used a slightly upgraded torque testing fixture:

For now, I rigged up the world’s cheapest load cell from amazon to a Nucleo configured to report the load in grams over the serial port. I also wired up my Chroma power supply over USB using the linux USBTMC driver. With those two things hooked up, I was able to run tests that sweeped across torque commands, while recording output torque, phase current, and input power.

At higher torques, the input power was pretty sensitive to the temperature of the windings — hotter windings increased the resistance, which increased the power required to achieve a given phase current, thus my plot isn’t perfect as it was grabbed over several different runs. For the highest power samples I couldn’t use my Chroma, as it is limited to around 600W. Thus those samples don’t record the input power.

Plotting the input power vs output torque on the same chart shows that indeed, modulo some measurement error, they are the same for the two stators:

So, this experiment reaffirmed my understanding of stator magnetics and confirmed that the stator winding was not the cause of my decreased torque.

# moteus servo mk2: Reduced weight test

Because my working environment is otherwise too idyllic and peaceful, I’ve been running the new moteus servo mk2 through its paces.  All day long.  8 hours a day.

This is the same test I ran to verify the controller, only now I’ve done it several times longer to get a better feel for if there are any weak links.  Somewhat surprisingly, the ball doesn’t drop all that often, only once an hour or two.

# Making the reduced weight servo mk2

Earlier I described my design plan for reducing the overall mass of the moteus servo mk2.  Constructing a prototype of this turned out to take many more iterations and time than I had expected!  Along the way I produced and scrapped two front housings, two outer housings and a back housing.

I made one complete prototype which only had the weight reduction applied to some of the parts and lacked a back cover and any provision for a wire cover.  It was the one from the moteus controller r4.1 juggling video:

Because of the multiple tries on the large-for-me front and back housing, I had to make soft-jaws and prepare stock in a more efficient manner.

I also had to get new workholding solutions for the PocketNC in the form of the wcubed vise.

Every one of the pieces got reworked in some manner or designed from scratch for the things that did not exist previously.

Front housing: Here I iterated on how much material to remove from the central cavity.  Initially I removed more, but it gave the primary output bearing problems to be loaded intermittently.  Also, I had adhesion problems with the ring gear when too little material was left there.  I settled on a continuous ring for the output bearing and a decent amount of material for the internal gear.

Back housing: I tweaked the back housing mounting points so that the outer housing could be symmetric.  Also, I added a facility for the wire cover to guard the phase wires entering the controller.

Outer housing: The outer housing was largely unchanged from my initial weight reduced design, although I produced one bad one due to a simple mistake locating the mounting hole, and a second because the stud lengths between the front and back were different in an earlier iteration.

Planet output: The planet output design changed only to add some weight reducing cutouts.  This was the last part for which I was still using mk1 servo spare parts for, so now I actually manufactured a prototype in house.

Planet input: Here there are now weight reducing cutouts, and the mating studs use less material.

Back cover: The back cover design is basically unchanged, I just had to make one for the first time.

Wire cover: The wire cover is a part of the design I had deferred until now.  It bolts to the back housing and shrouds the phase wires.

## Assembly

Here’s some assembly pictures:

# First walking with gearbox chassis

Short recap: After building the quadruped with near-direct drive motors, I discovered that the lateral servos had insufficient position control authority to keep the robot standing up.  Thus I embarked on a now month long quest to design and build an integrated planetary gearbox.  At this point, I have enough gearboxes built for all the lateral servos, so it should be able to walk, right?

And tada!  It can!  Well, at least a little bit.  I’ve only spent a short while with the gearbox based chassis, and have a lot of work left to do.  However, here’s a quick video showing it walking around, slipping on a ruler, and almost falling over a few times.

# Wiring up the gearbox chassis

Now that I had a set of 4 at least minimally working lateral servos, I needed to wire up the chassis so that everything had power and data.  Here are some pictures of that process:

Next up is making it do something!

# Lateral servo gearbox build(s)

After completing one gearbox, I needed to build at least 4 more of them to replace the lateral servos on Super Mega Microbot (2).  So, I got to work.  First, I disassembled 5 more BE8108 motors.

Then, I drilled out the rotors, this time using the mill at AA.

Next I removed the stators from their backing.  This was painful enough last time, that I tried a new technique using the mill to do most of the work.  Unfortunately, one of the stators was critically damaged during my initial experimentation.  So, now down to 4 survivors.

I went and printed 5 copies of all the printed parts:

And turned down some more internal gears:

Then, I started assembling!

# Rebuild of gearbox assembly

After finally getting the darned thing apart, and printing a new outer housing, I went about re-assembling the whole mechanism.  This time, I tried to take care to make the future disassembly less painful.

To start with, I filed down the problematic outer bearing interfaces of the sun gear holder so that the bearings were a slip fit over them.  These two interfaces don’t need to be particularly snug, so that was easy enough, if monotonous, to accomplish.  I also machined out a some pockets around the magnet hole, to make it possible to just hot-glue the position magnet in place and more easily extract it.

Next, I re-installed the sun gear holder back in the rotor.

After that, I pressed the input bearing into the new planet input:

Then I went about installing the shaft output bearing into the planet output, the planet output into the output bearing, the planet shafts into the planet output, the planet bushings into the planets, and the planet bearings into the bushings.

Those got dropped onto the shafts, and the planet input was stuck into place.

After that, the screws were installed in the planet input, and the stator was fit onto the front housing, using a shrink fit again:

At this point, I aligned the rotor and pressed it and the primary shaft into place.

Now I used my paper strip alignment technique to get the rotor properly (or at least functionally) spaced from the stator.

At this point, the rotor still didn’t spin freely.  Because of all the rework I’ve done, and my sloppiness in executing it, bits of the exploded bearings and other detritus had lodged themselves against the rotor and stator.  The problematic pieces were small, sub 5 thousandths, but still plenty enough to cause the rotor to hang when spinning.  These I carefully extracted under a microscope with a pair of tweezers.

At this point, I had a gearbox that spun freely and seemed mostly correct!

# Rotor removal, and complete disassembly

So, last time I had a functioning gear-train, I just needed to disassemble everything in order to replace the outer housing.  As I was putting things together, I realized that several custom fixtures would likely be needed in order to disassemble various parts cleanly.  Here, I made a giant 3D printed cylinder that the front housing and planet output would bolt to, and then the central shaft could be pressed out.

I somewhat skimped on the printing… even at 25% infill it took something like 14 hours, however the shaft should be relatively easy to extract since it is only held via a mild press fit with the output shaft bearing.  Or at least, it would have been had my mild press fit not ended up being tighter than desired, and had retaining compound not seeped over there.

My first attempt at removal just resulted in my carefully constructed fixture delaminating and the entire planet output and output bearing pushing into the assembly.  The shaft didn’t budge at all on the shaft output bearing.  Then, rather than wait for an even longer print, I installed all the washers on each of the bolts to better distribute the load across the fixture.  At that point, removal was accomplished…. kinda.  The fixture didn’t fail this time, but the planet input in the gearbox shredded.  Fortunately, that was enough to remove the rotor.  I could just print a new planet input, and toss the shaft which now appeared very well welded to its bearing.

## Rest of the disassembly

At this point, the rotor was removed from the stator, but there was still a fractional planet input attached to it, with the planet input bearing very securely fastened to the sun gear holder, and the rotor bearing, even more securely fastened to the sun gear holder.

First, I shredded the planet input with a pair of pliers.

Then, I was able to get the input bearing off by cooling down the sun gear holder with the compressed air again.

However, the rotor bearing was too well pressed on to achieve that.  So I ground it off with a cutoff wheel, after trying a few other things first.  At this point, I was finally able to remove the sun gear holder from the rotor, and call my disassembly, as it were, complete!

# Rotor and stator alignment

Last time I covered getting to the point of having the rotor installed into the gearbox.  Here we’ll look at making it actually work in that configuration.

When I first got the rotor in place, it was clearly not centered properly.  Although much closer than in the plastic gearbox, it did interfere with the stator during a portion of a revolution.  The first obvious problem was that the primary shaft wasn’t making it all the way through the front shaft bearing.  That should have been an easy fix, but for two different very annoying reasons.

## Reason 1

When I made the sun gear holder, one of the tweaks I made during my 3d printed iterations was to leave a hole where you could press on the primary shaft.  That was intended to be used to install it all the way into the output bearing.  Unfortunately, that hole is behind the position sensing magnet.  The one that I superglued in place last time overly eagerly.

That magnet has a recess in the sun gear holder which nearly exactly encloses it, with maybe only a few thousandths around it in all directions.  There was no way to grip the magnet at all.  I tried soaking the junction in acetone for some time, I tried using the heat gun, and in the process ruined the 3d printed outer housing, but none of those loosened it up enough to allow another magnet to retrieve it.

Eventually I pressed on the primary shaft from the front of the motor, and used that to pop out the position sensing magnet.

## Reason 2

Now that I had the magnet off, I could press the shaft back into place.  Or at least I should have been able to.  I made it into the output bearing, but then the pressing became inordinately difficult.  I think even more so than in any of my test fits.  This may have had two causes… one is that I was using a dowel for the main shaft which is slightly oversized, and second the retaining compound had seeped around into the interior of the bearing, and fractionally cured.  Those combined made it both really hard to push the shaft in, and as I later discovered, impossible to press out.

## Aligning the rotor and stator

At this point, I had the rotor installed seemingly properly, and it still was interfering with the stator.  After much experimentation, including partially exploding the rotor bearing on the sun gear holder, I arrived at a technique that allowed me to align them properly and simultaneously discovered that my intended mechanism for registering the rotor to the sun gear holder was, at the least, sub-optimal.

The sun gear holder has 4 M3 flat head bolts which fasten it to the rotor.  I had oversized those holes to 3.1mm, and put tapered countersinks on each.  I had planned on the countersinks forcing the rotor to be centered.  However, it didn’t look like that was working as I had expected.  Each time I would loosen up the bolts and re-tighten them, the rotor would interfere with the stator in a different way.  Eventually, I was able to center them by sliding slips of paper all around the stator between it and the rotor, then tightening the bolts down.

Then I spent a few hours, painstakingly under the microscope, picking out grains of steel that had managed to find their way to the rotor, most likely from when I partially exploded the rotor bearing.

## Success?

At this point, the rotor did seem to be aligned properly to the stator, everything moved freely, and the gearbox worked as expected.  I just need to disassemble everything in order to install a new outer housing to replace the one I destroyed while attempting to remove the position sensing magnet.  That is its own story, for next time.