cold arbor

First, I would like to say that I finished Ninjabridge.

It looks like this:

Yup. Back to a relay.

Ninjabridge worked briefly after extensive noise-reduction and ground loop prevention surgery. Sadly enough, it suffered a gate drive failure and subsequent Epic Shoot-Through at almost full saw speed. Nothing was particularly happy.

And so with the sun rising yet again, I pitched together this 12v SPDT relay assembly. It’s triggered by the previously mentioned R/C switch.

At least the saw works. Some more drive testing confirmed that my fears about the saw’s startup and running current pulling down the entire system were unfounded. Here’s a video of Arbor nibbling on some wood.

And a “pre-event” picture (not that D*C is a destructive enough event to warrant it, but hey.)

Überclocker

After putting all the screws on Arbor, I turned my attention back to Clocker to address one last detail that hasn’t proven fatal, but isn’t very healthy to ignore.

The bot’s drive chains have been getting increasingly looser as matches passed. The left side, in fact, has become so loose that the chain hits the ground on the bottom side of the frame. This is just begging to get snagged on something, or to make the chain walk right off the sprocket.

I’ve been meaning to put a chain tensioner on the drive since I built the bot, but never got around to it until now. The tensioner is just some simple bits of milled Delrin that has holes for perpendicularly tapped screws. I freehanded the vertical holes with a cordless drill, which brought back memories of before I was saved from a life of meager tools and hand fabrication. It was a heartwarming moment.

With the tensioners, the drive is substantially quieter. I would also venture as far as to say the bot is a little more responsive, too, since before the tensioners, the front wheels could spin 30 or more degrees before engaging.

If the chains ever get looser (Robot Jesus forbid) the Delrin sections can be milled more to compensate.

So now it’s time for a Clocker photo – I cheated a bit here, and actually took the picture before adding the tensioners.

And an everyone shot:

boxxy

No, not that boxxy.

This year, I’m going to be shipping down the bots ahead of time – which really explains why I’m working on them now and not, say, next weekend. Last year, taking Überclocker and support equipment as baggage cost me a cool $90 or so for overweight, oversize, over-the-top baggage fees. For essentially the same price, courier services will ground-ship an excessively large “package” from here to Atlanta in about 3 to 4 days.

Now, I’m defining “package” as “giant 2-foot wooden cube weighing 135 pounds and loaded with two (and a tenth) deathbots”, which might be stretching the definition some. But here’s the wooden box.

It’s made of some cheap Home Depot plywood (the same plywood, in fact, that Arbor was nibbling on. That panel became the bottom.

This time, I have enough overhead such that I’m actually bringing SPARE PARTS.

The bots go out in several hours and will hopefully arrive Thursday…

They’re done!

Well, one of the new drive motors for Überclocker is, anyway. The bot edges closer to being reassembled and rewired. I’m going to devote this week to getting Clocker running, and bringing Arbor as close to it as possible. The next week, which is essentially the last one, will go to finishing Arbor as well as packing the robots up for shipping to Atlanta. That’s right – I can’t bring 2 full robots and all their support equipment with me on the plane. It’s not a TSA issue, and never has been – I’ve been flying with robots since the 2006 RFL Nationals. Instead, it’s a matter of Airtran billing me up to the sky for very excess baggage. Clocker by itself last year ate up to the second category of oversize and the first category of overweight baggage, which cost me a pretty $95 or so. Add to that a second robot and I might be forced to shove them on air cargo. Instead, I can build two small shipping crates and load them up to 50 or 60 pounds, then send it all UPS ground.

What this means is that I have to physically send away the robots several days early, lest they not make it in time for D*C. We’ll see how this goes.

In the mean time, a lathe chuck.

…holding one of the gearbox end plates. No matter how many times I complain about it, I always end up coming back to the square chuck. It’s simply the quickest way to turn out revolute-symmetric parts on noncircular substrates. This is the motor mounting end.

And this is the gear holding end. The needle bearing assembly from yesterpost presses into the bottom-most bore.

The ring gears press in like so.

The original second stage shifter ring gear gets pressed all the way to the bottom of the cavity, at the second shoulder from the top. The trimmed first stage ring sits at the first shoulder level. All of these are \m/etalfits, which is a variant of the Beast Fit, which is an extension of the 20-ton-hydraulic-press-fit.

In the above picture, I have also installed the needle bearing. I took more care on this bore because compressed bearings reduce to the degenerate case of a solid chunk of metal.

I dropped the DeWalt gears in to confirm axial spacings and diameters. Result: splendid.

The first stage gears actually sit about 1/8″ below the surface of the gearcase. This is by nature of the DeWalt motors, and is something I just compensated for with a 1/8″ tall boss on the motor mounting side (visible in the first picture).

Repeat ad nauseam and add in a bit of mill time, and here are the gearcases with drilled holes. Because these parts were again square and rotationally symmetric by 90 degrees, I was able to pull off the Pop-Lock-Flip-It-and-Reverse-It to great effect. Who needs to move machine axes when you can just move the part around?

Now with more tapped holes!

Something disturbing that I noticed on Überclocker during its Motorama showing was that the DeWalt motors were starting to come apart at their crimped seams. These motors were designed with ease of manufacturing in mind, and feature rolled-crimped-and-folded sheet metal everything. The face plates in a motor are normally retained by bolts or are one-piece constructions, integrated with the can itself. But these are crimped together – or rather, were, since the mounts I used only held them by the faceplate.

Solution: tack weld! I dropped a small bead in 4 locations midway between the crimps. This ought to hold them…

The big moment!

Because I replaced (forcibly, and irreversibly) the pinion on Clocker’s 14.4v DeWalt motors with a HF drill pinion, I actually had to break out my two stock 18v motors to use on these gearboxes.  The combination of lower gearing but higher voltage motor will actually cause Clocker’s top speed to remain roughly the same.

To my relief, everything fits. There’s about a millimeter of axial slop in the gearset if I loosen the retaining ring and just let all the internals slide. I find this slop to be totally acceptable, since even if I engineered it to be spot on, after the first match it will be off by a millimeter anyway.

Finally, the new drives mounted in the robot.

The increase in length by about 1/8″ means that the endcap of the DeWalt motor is now tangentially contacting the supports in the back.

What’s left to do on Überclocker? Surprisingly little. I need to make one more hollow gear carrier for the other side, but that’s it. All of the other work on the drivetrain is just putting it back together. However, I might make some hubs for the McMasterBots wheels that are compatible with the existing hub structure.

I ripped all the wiring out of Clocker such that I can’t effectively put it back together the same way, so the robot will be rewired from scratch. It’s better this way, because I felt like I could have routed quite a few connections better than the first time around.

Arbor is currently hanging in limbo as I wait for parts to get cut, but depending on how many drill gears I can salvage, I might not actually make a replacement DeWalt drivetrain for it. Arbor never had a gearbox stripping issue at Motorama – in fact, I harvested a working gearbox from it to fix Clocker up.

TO DRAGON*CON!

The robots are slightly less skullfucked.

Only marginally, though. What physical work have I performed in the past week or so to bring them back to competition spec? Relatively little. Shipping lead times and oh god i need to finish these scale CityCar wheel modules has mostly kept me away from the robots.  However, during this “productive downtime”, I’ve made steps into testing part fabrication and designing system upgrades such that they will amount to less work than building one whole robot from scratch.

Now, depending on which side of my projects you know the best, that’s either an imperial asston of work to be blitzed all in one week, or just an hour on the waterjet and 11 on Facebook.

Überclocker Remix

In the last Überclocker episode, I presented this crude representation of the new drive gearmotor layout:

The trickiest operation involved in manufacturing this design is the process of turning a deep internal part, the 2nd stage carrier / 3rd stage sun gear, into an output shaft mount. This would be relatively simple if I had more advanced tools such as a broach (or the patience to hunt them down), but in MITERS, the set screw, “elastic compensation”, and Loctite reign supreme. In this case, I decided to go for the press fit.

The 3rd stage sun gear in a DeWalt gearbox can support a center bore of about 12 millimeters. The pinion itself can be shaved down to a 14mm shaft relatively easily, so that’s the route I took.

Before that, though, I decided to finish the easy operation of turning down the clutch flange on the first stage ring gear, so the overall diameter is under 1.75 inches. Here is where I discovered the quality of metal sintering on DeWalt gearboxes as compared to the cheap import drills.

Harbor Freight (and co.) drill gears make steel powder when machined. These gearbox parts made curls. The amount of pressure needed to get steel particles to fuse together into a ductile solid is pretty incredible.

While I was jiggling the machine levers, I started to think about how to fixture the 2nd stage carrier such that I could perform concentric operations on both sides. The problem is that I needed to turn down both the outside diameter of the gear and the inside diameter. While I could have made a chuck spacer such that the 3-jawed chuck could grab the thin flange portion of the carrier effectively, I wasn’t as confident in how concentric the 3-jaw chuck ran. It is, after all, a shady eBay chuck.

The solution was remembering a trick I was shown once called pressure turning. Essentially, pressure turning amounts to pinning the workpiece against the spindle so hard that friction alone is enough to transmit the cutting forces. To do this, you need a live center with real lubricated rolling bearings. Luckily, we had one. I mounted the carrier in a loose-fitting collet that just acted as a buffer space for the planet gear pins. The collet was not tightened or closed. Then, I rolled in the live center and cranked down on the tailstock quill. Hard.

This is where you get to find out whether or not the lathe headstock has good thrust bearings. The Old Mercedes started making an ugly crunching noise, which was luckily silenced by a few liberal squirts of spindle oil into the semi-exposed thrust bearing race.

One side benefit of this turning method is that the piece always stays with the live center, so it mitigates workholding wobble that might otherwise be present.

A few passes later, all the gear teeth are gone. It is not shown in this picture, but I added a new retaining ring groove in the same setup.

I turned down the former pinion to 14 millimeters dead on – enough to snugly fit a needle roller bearing onto. As 14mm is a hair under 9/16″, I flipped the piece around and locked it in a 9/16″ collet. Now the center bore was accessible (no blockage by the tailstock), and I bored it to a hair under 12mm diameter.

Here’s the hollowed and turned shaft, with needle bearing, retaining ring, and some shims. I got a bag of 0.1mm shims from McFaster-Carr to take up any axial error resulting from inconsistent retaining ring groove cutting.

It’s been a long time since I’ve made such a mechanical and machining oriented post. I must say it’s very refreshing to just mince metal again. Here’s the insert stub shaft undergoing the one operation it actually needs, which is flat-milling. I bought some 12mm precision-ground O1 steel rod, which seems to go for 5 eggs and half of a slice of cheese per 6 feet on McMaster. Because I could finally be confident in the shaft diameter, I could just end-tap it and then put the flats of cheap waterjet gear retainment (+9000) on it.

After the flat cutting, the stub shaft was Beast-Fitted (an advanced cousin of the press fit involving beastly strength) into the hollow former pinion.

And suddenly, I turned a planetary gear carrier into an output shaft.

That’s all the work Überclocker for now. I was mostly concerned with how the pressure turning process would actually work, and how tightly the single needle bearing output could be made by someone with my level of machine patience. Overall, I’m confident the single bearing output can work – there wasn’t a good ball bearing or doubled ball bearing selection for the shaft sizes that could be made from the output gear.

Left to do on these “FrankenWalts” is making the aluminum gearbox case and shoving everything inside. After that, Clocker should be running again.

Cold Arbor

Arbor is currently well-strewn about my robot table at MITERS. Much of the work on it in the past week has been inspecting the parts and designing the upgrades. Last time, I was investigating how to make the “structural loop” of the saw arm wider for more stability:

The dark red and blue are the positions which I hope to extend the anchor and hinge points to, such that they use the entirety of the robot frame for support. I’ve made alot of progress towards that, as well as  redesigning the claw actuators to fit their new home in the robot’s anterior. Here’s the rundown:

In short: The saw actuator is now hinged at the rear, and the claw actuator is slung underneath the original saw actuator hinge point and drives the claws themselves through a slightly ass-backward inverted crank linkage. See if you can visualize how the claws move:

It took a while of stuffing and alot of happy hardcore to get that design through. The claw’s grabbing capacity (grabacity? grabass-ity?) remains the same – from frames about 6″ tall to those about 1.5″ tall. I have to recut the claws themselves to conform to the new angular displacement range, but that’s easy.

An overview of the new situation. The claws are now driven together by a single rigid crossbar instead of two roughly independent-but-sort-of-coupled-still-you-know-just-friends ball links. This should constrain the whole leadscrew nut assembly from just rotating itself to a point where seizing friction causes difficult letting go.

I originally spec’d a 1/2″ diameter carbon fiber tube to replace the 7″ or so of steel Acme leadscrew that wasn’t being used for its Acme-ness, but decided that saving 6 ounces was not enough to justify buying 3 feet of CF tubing at a price of around $50 – just to use a few inches.

An overhead view better shows the claw linkage crossbar as well as the FrankenWalts dropped into position. For Clocker’s gearboxes, I only have to make face-mount holes, but for Arbor, I need to make side-mount holes.

Now here’s the exciting part – the replacement for Deathrunner. I’ve elected to change out to the Mini-EV-alike motor with one caveat: that it be “pre-geared” to drive the worm gearbox. The motor rotates at 18-24,000 RPM no load, unlike Deathrunner, which barely hits 4 or 5 thousand on a good day. Driving the wormbox at 5-digit revs is just going to turn most of the power into heat.

As luck would have it, I have most of the wreckage of a Banebots 48:1 P80 gearbox. The 4:1 stages of this gearbox have identical sun and planet gear tooth counts, so I have gears left over to bore out as a motor pinion (since I can’t find the original motor pinion).  I intend to use 1 stage as a 4:1 pre-ducer. In the above image, the MEV-alike and the preducer gearbox have been modeled in more detail.

In total, the gear reduction from the motor to the saw will be 120:1. That’s  higher than most lifter gearboxes. With the self-managing torque characteristics of the DC motor, I really hope Cold Arbor will rip some serious shit at D*C.

With all of the replacement parts designed out (oh, minus that front frame assembly, which will be addressed), I’ve ordered parts and intend to get all this fabbed soon.

It’s August! That means the end of the summer build season, MIT’s Freshman Orientation, and most importantly, Dragon*Con, are all coming up soon.

In other words,

AAAAAAAAAAAAHHHHHHHHHHHHHHHH

D*C’s Robot Battles has been my annual robot party since 2002 when I first began spectating (and 2003 when I began competing). I’ve tried to go every year possible – 2007 was the big exception because my very own freshman orientation trapped me on campus then. I’ve always enjoyed the atmosphere of the event moreso than most other competitions just because it’s so not serious business. It’s a primarily sumo and show-off event because of the limited audience protection, at least for the 12 and 30lb class events – even more tame than the NERC Sportsman class I entered Überclocker and Cold Arbor in for Motorama. The event is seriously almost as old as I am, and it’s always been like that.

So now… speaking of Clocker and Arbor, how are they doing?

Yeah… about them robots

That doesn’t look too good. The bots have all been sitting, piled on top of my cart of miscellany, since February. They’re relatively undamaged as far as active combat robots go, but Moto took its toll on the drivetrains. I went through 4 and a half gearboxes at Moto, running through all of my spare 24:1 drill gears. After Arbor was eliminated from the competition, I harvested its gearbox parts to keep Überclocker running…but not for too much longer.

Long story short, Arbor has 1 semi-working drive side and Clocker has zero.

cold arbor

Here’s Arbor after retrieval from the cart skydeck. Past the drivetrain (or lack thereof), it’s also been the subject of parts harvesting. I think I’ve stolen the two Dimension controllers (which were briefly used to run Segfault), the Spektrum receiver, and the 5 volt BEC out of the electronics bay – those are all scattered about MITERS and so need to be retrieved or replaced.

One of the issues I intend to address is the front frame assembly. First off, it’s physically bent about a degree and a half. Not much, but several of the braze joints in the bend region have failed and some of the sheet metal has become twisted. This was probably just a result of battle, but either way it’s unsatisfactory.

Much of this front assembly was designed using 5AM Joltgineering™, therefore structurally unsound. I want to do a better job making it stiffer, so the plates may be recut and rebrazed.

Gearbox issues aside, I’m otherwise satisfied with the drivetrain. The oversquare wheelbase and central mass location means that Arbor actually handles very well. The drive is fast, but the super-soft McMasterBots wheels were grippy enough to avoid uncontrollable sliding. I’m also satisfied with how the Delrin hubs have endured in the front half of the drive.

Comparatively, ‘clocker handles like a total brick since all of its mass is in the rear 33% of the robot.

But I’m extremly dissatisfied with how the whole swinging saw assembly is mounted. If you call, several months ago in the last Arbor update before the Motorama update I never wrote, I said:

However, this was the first time that I discovered that Arbor would never work as I anticipated in its currrent configuration.

I was referring to this. In what must be yet another symptom of 5AM Joltgineering™, I somehow made the entire 14 pound swinging saw pivot off the front sheet metal assembly. As in, everything. All moment loads, all bending, and all shocks were transmitted through the beefy 3/8″ aluminum saw pivot mount…. right into the 1/8″ aluminum plate in the front. The above picture shows the “load triangle” pretty well.  One point of the triangle is located at the left side by the actuator trunion screw, and the other two are effectively shared by the two cap screws from the right side (front) and the screws on the top and bottom, which… happen to be missing, and probably were all through Moto.

From a Course II standpoint, this assembly is one giant piece of unwanted flex. It became very clear during Moto (and during testing) that the entire saw was prone to pulling itself into the material (or opponent) and becoming stuck hard simply because the whole frame twisted several degrees due to the torque of the worm gear drive.

My plan for redressing this problem is to make the saw’s structural loop much larger. Effectively this means swapping actuator positions – placing the saw actuator at the back end of the robot and the claw actuator where the current saw actuator is.

The light red, green, and blue lines indicate where the current structural loop of the saw lies, and the dark shades show where it should lie after modifications. The bigger the loop, the more the structure can resist torque about the orthogonal axis (in this case, the direction of saw rotation). But because I’m keeping the green line a constant length, I should have the same “swing” of the saw available.

As long as I’m wailing on the saw assembly, I might as well talk about Deathrunner. It’s been shiny, menacing, powerful, and reliable, but Deathrunner is going to be replaced with something else for D*C.

But why? Well, Deathrunner weighs 4 and a half pounds, was wound somewhat hackishly (the number of turns and wire fill percentage is a total waste of the stator), and hangs awkwardly off the saw arm. Even worse, it’s sensorless. Now, I could very well add sensors, but then I run into the problem again of not having a sensored controller powerful enough to feed it – no amount of DEC modules will drive this thing. I noticed that the sensorless controller had problems keeping up with sudden changes in the motor speed, such as those caused by the saw biting something.

Overall, the weight could be better used by a short Magmotor (!) or something similar. It’s much easier for me to control a DC motor, and I don’t have to worry about its transient response.

For now, the candidate motor is a big DC brush motor about the size of the classic Mini-EV. It otherwise seem to share all the MEV’s charactistics, such as being fast and obnoxious. Since it IS a fast motor, I might put one stage of “pre-gearing” on it by harvesting parts from one of several junked industrial planetary drives I have in the cruft pile.

überclocker remix

Poor Überclocker.

Being 1 event older than Arbor, it’s more beat up. A few things are bent, screws are missing, and there are little saw nicks all over the place from Freakin’ Enforcer, but fortuntely the major structural components are still sound.

Again, the number 1 issue is the drivetrain. More precisely, it’s the lack of one. A combination of “DeWalt motor into Harbor Freight drill gearbox” and battle impacts destroyed both gearboxes. At the event, I pulled parts from Arbor to keep them running, but ultimately Clocker lost out of the tournament by virtue of not being mobile enough to attack anything.

Besides the gearbox, the external portions of the drive have been flawless.

Well, most of it. This right side has apparently been gimpy since fight #2 at Moto because the internal binding screw backed out, so the standoff went all over the place. In the grand scheme of things, an easy fix.

I have about this much space if I want to switch to a stock solution like the Magnum 775 motors (which actually seem to be a bit too long). If I want to keep the current drill gears arrangement, I’d have to return to 550 motors because I’m out of 15-tooth pinions for 24:1 drill gearboxen. That would be a pretty stiff power and thermal mass sacrifice that I don’t feel like making.

Or I could keep fucking around with drill parts. A while ago, I posted some information about the 3 speed DeWalt (read: legit) drill gearboxes to Delphi Robotland, including a gear ratio count and pictures of all the stages.

With some crafty adaptation of the 2nd stage gear carrier’s sun gear, I could use the first two stages as a 17:1 planetary gearbox that has bigger and meatier and more gears than the comparable import-class drill. I started thinking about it, and hopped into Inventor to model some of the major components.

Here’s a preliminary layout showing some of the changes to be made to the parts. The sun gear will be turned down to a 14mm stub shaft, which will ride in a 14x20x12mm needle roller bearing. Its center is bored out to 12mm.

The first stage ring gear with the weird wavy flange remains as the first stage ring, but I intend to machine off the weird wavy flange to save on diameter. The second stage ring gear (the one with the dog clutch teeth that are unmodeled above) will remain the same.

All the ring gears will be heat-shrink-fitted into a custom aluminum casing…

…which looks the same as the current Clockerbox, and is made from the same 2″ square aluminum.The difference is that now the motor mounting plate is actually a plate instead of, say, the entire back half of the gearbox. It makes things a bit easier to manufacture.

The output gear will be the same one on the robot now, and will ride on a short chunk of 12mm drill rod shoved into the bore of the former sun gear, and with a Double-D profile machined into one end to simulate the old Clockerbox output shaft.

Dropped in place…

This new assembly is about 0.1″ longer than the current motors, which is an acceptable change.

I might switch Clocker over to the same kind of McMasterBots wheels that Arbor currently uses. It doesn’t hurt to have more traction on the D*C stage, especially since going from 24:1 to 17:1 is going to boost the robot’s top speed even more.

Here’s where I get to find out if my robot driving skills have faded any from the 2003 Test Bot 2.0 days.

While I have the gearboxes designed, I’m debating whether or not it’s worth just going with the 775 gearboxes because they are a stock solution – that is, I don’t have to build them. It’s mostly a matter of cost versus time spent – I could buy the 4 gearboxes (assuming Arbor also needs a pair) for $400 or so, or build two FrankenWalts for virtually free, and if necessary, two more for about $100.

It comes down to do I think I can get them done in under approximately 32 hours because my time is apparently worth about that much this summer.

In the last Überclocker-related post, I said

this conversion ought to go quickly since I’ve already drilled the new mounting holes to accommodate them.

By this I meant ”

this conversion ought to go quickly since I’ve already drilled the new mounting holes but am swamped with classes, other duties, and a lack of motivation to do anything robot-related so Überclocker has been sitting on a table at MITERS taking up work space for two months

But that’s over now. I charged the Mental Capacitor of Project Motivating (+1) enough to go take apart the drivetrain to stuff the DeWalt motors in. The whole operation actually took about 30 minutes total, by the way, it’s just that the time constant of the MCPM is a semester or so.

Here’s a picture of the robot.

I excavated the carcass of Test Bot SP1 to use as a chew toy for testing ‘clocker. There’s no test video, unfortunately.

I can’t exactly describe the new drivetrain as “Fast”. In fact, I think the HTI motors resulted in an overall higher speed, but not by much. Calculations put the anticipated top speed around 8 to 9 miles per hour. The bot isn’t slow by any means, but it was almost too controllable. I like a bit of unpredictability in robot handling.

For future events, I might consider recutting the intermediate drive gears to act as a speed increaser. 8MPH is nice for small arenas and stages like Dragon*Con, but in a larger arena it is a handicap.

Here’s an overall picture of the robot internals, now featuring DeWalt drill motors mated to undoubtedly overdriven Harbor Freight drill gearbox parts.

Segfault

Alright, so I’m pretty damn sure the project is moving forward now, considering I just dropped big Benjamins on aluminum plates. The project has actually been limbo for a while because I’ve been slammed with everything else that does not pertain to building. As the assignments-and-papers season winds down and OH-GOD-EXAMS-AND-FINAL-PROJECTS season begins, there’s an occasional moment where I can… you know, do other stuff.

I’m also in luck because I have no classes this term which have final exams.

In the last SEGFAULT episode, we left off with a picture of two wheels.

Like before, not exciting at all. Through some more excavation of the archaeological site that is MITERS, I sequestered these 180 watt DC scooter motors, which seemed to have been paired with the wheels at one point in time. They have matching pulley pitches.

The pulleys gave a speed reduction of roughly 6 to 1. Through some crafty mathematics, I backsolved the specs of the motors so I can actually play some numbers games.

The manufacturer, Unite Motor, was kind enough to give some measurements of torque and current for these motors. Real measured numbers are better than theoretical ones, and leaps better than bullshit such as “TURNS” and “WINDS”.  The rated torque (Tr) and rated current (Ir) were 0.7 N-m and 10.6 A, respectively.

This was nice because if you have torque and amps, you can immediately get a critical constant of the DC motor, the torque constant (Kt). The Kt of this motor , Tr/Ir,  is 0.66 Nm / A.

This alone doesn’t tell me much, because I don’t know what the maximum torque of the motor is if I don’t know how many amps it can ultimately pull if stalled. This is not provided by Unite Motor, shame on them.

But fortunately, they also gave a rated speed specification, which occurs (I hope to Robot Jesus on a stick, anyway) at the same point they rated Tr and Ir. This rotational velocity ω at the rated input voltage Vin of 24 volts is 2,600 RPM, or 272.3 radians (rad) per second.

In an ideal motor, power in equals power out. Power is torque (T) * speed(ω) AND also volts (V)* amps(I). Therefore, the crafty relation T/I = ω/V occurs.

Hey, this is convenient, because what it’s saying is that in SI units, torque per amp IS speed per volt. The motor back-EMF constant, Kv, is equal to Kt. So this motor as an ideal model gets 0.66V / rad / s. This is to say that if you turned the motor at 1 radian per second, it would generate 0.66 volts for you. Conversely, running the motor at 0.66 volts will make it turn 1 radian per second. Kv = Kt only works in metricland, by the way.

But real motors aren’t ideal transducers. They have resistance in the windings that turns input power into heat. A real motor can be modeled as a resistor in series with the ideal motor. The resistor drops some voltage across it while the motor is under load, so the ideal motor sees some value below your input voltage.

Luckily, I know that the motor is rated for 24 volts Vin while turning 2,600 RPM or 272.3 rad/s and having a BEMF contstant of 0.66 V/rad/s. This means the voltage the motor is generating by virtue of turning, Vbemf = 272.3 rad/s * 0.66 V/rad/s = 17.97v.

Even better is that this is known to happen while Ir amps are flowing through the windings.  When you have the differential voltage across a resistance and the current flowing through it, you know the resistance R through Ohm’s Law.

So the motor resistance Rm is simple (Vin – Vbemf) / Ir = 0.56Ω.

Now the stall characteristics of the motor can be calculated. When the motor is stalled balls to the wall, Vbemf = 0 because there is no rotation. Rm dissipates all the power you put into the motor, and the only current flowing is therefore Istall.  Through Istall = Vin/Rm I know that the motor will pull a maximum of 42 amps. Then smoke. At 42 amps, the motor can make about 2.75 N-m of torque.

The no-load speed of the motor ideally occurs when the input current approaches 0. In practice this never happens because of Rm, but the NL speed is something that has to be measured. I can only conjecture on how fast the motor will turn with no load by ωnl = Vin * Kv, and assume the motor current to be something small. This usually gets you within 10% or something. The guessed no load speed of these motors is around 345 rad/s, or about 3300 RPM.

Okay, enough DC motor theory.  So now I wanted to find out what the limit is in terms of speed and tilt angle if I used these motors and their matching wheels.

Here’s a (really, really) rough model of me on a balancing vehicle. Segway-type vehicles are a variant of the inverted pendulum, a classical problem in control theory and physics. The actual equations of motion for such a system are a bit convoluted, though rest assured I have been forced at chalkpoint to derive them step by step.

I just want a ballpark number for how fast I can go, so I can gauge the type of helmet I need to prevent too much brain splatter when I fall over. This can be easily approximated in the above system, where you have a point mass approximation of me, tilted out in front of the vehicle by an angle Φ, and away from the center of rotation by a distance d. d is the distance that my center of mass is above the vehicle platform. In a typical human, the CoM / CoG occurs a bit above the hips. I assumed this was 1 meter for sake of argument, since I’m not that tall and this is not very scientific. The vehicle itself is assumed to have no mass yet. This is a very bad thing to assume, and strictly limits this to guessing “steady state” characteristics – i.e. no acceleration of any kind is allowed.

In classic 8.01 fashion, the goal is to keep me-in-a-black-hole from acclerating. That means all forces and torques have to be balanced.

Φ is referenced from the vertical, so the Condensed Matter Charles Equivalent Force Diagram™ is thus. N is provided by the ground – we are assuming I’m on solid ground here, not flying, so the vehicle doesn’t have to generate lift. This may also be bad assumption.

That leaves just F and mg sin Φ to fight it out.  The latter is provided by me existing and also tilting the vehicle forward or backwards. F comes from the torque of the motor and the radius of the wheels: F = T/r. Therefore, mg sin Φ = T/r.

The uber-ballparked approximate steady state model of the vehicle is then given by Φ = arcsin ( T / mgr ). If I have a torque figure, I can estimate the maximum angle of tilt that the motors can sustain while moving at constant velocity. That means if I run over a pebble, it’s all over.

To avoid this scenario, I want to size T to be under half the stall torque of the motors. The reason is that Tω = VI maxes out at one half of any of the input variables. This is the point which the motors make maximum power. If I’m crusing at maximum power, there is no recovery if the unstable system deviates further from the vertical because the motors can’t exert any more torque without slowing down. Which of course will only make the situation worse.

I decided that 33% peak torque was the “safe point”. This gives me some leeway such that the motors can exert a momentary, more powerful shove to counteract my attempts at crossing the critical Φ. The real Segway does something like this – if you try to go too fast, it will start tilting back to save your ass (/face).

33% of stall torque for my two motors driving a 6:1 reduction  on 4″ radius ( 0.1m) wheels is  (2 * 2.75 N-m * 0.33 * 6) = 10.89 N-m. So that gives Φ = arcsin ( T / mgr ) of 9.6 degrees or so.

Decently smooth. 10 degrees is pretty steep for a lean angle during travel, but I was concerned with the peak torque (/force) limiting how quickly the platform could react to a sudden input like me jumping on it. If this is limited, then the whole vehicle will feel sloshy and risk not being able to recover from a sudden disturbance, like hitting a small child.

Okay, so I’m not designing to target small children (honestly!), but things like bumps in the ground, terrain changes, sidewalk seams, door and hallway thresholds, etc. all represent sources of external disturbances.

Having these numbers, I put the motors into the parts bin (i.e. LOLrioKart) and began working on vehicle design.

This is a kewl motor.

I wasn’t able to design for too long before another intrepid MITERer mentioned that he crufted some motors out of a lab cleanup.

The deal with lab cleaups here is that the proper response as an engineering student is, as soon as you receive an email containing the words “LAB CLEANUP” or similar, drop everything you are doing and immediately report to the scene to claim cool stuff. Sadly, I don’t make it to many of them, but a surprising majority of cool Reuse stuff goes to MITERS because there are so many of us that at least one person is on guard.

These are Kollmorgen Servodisc motors, renowned in the industry for being flat and pancakey…as well as being extremely power-dense. They are coreless motors. That means there is no big iron thing in the rotor to accelerate, and such motors can reach extremely high angular accelerations. That means they respond to commands fast.

Fast is good. Also, Kollmorgen, being a legit motor manufacturer for legit industries, completely chracterized their motors in the datasheet. Even handily providing me with armature inertia if I care to include that in the system dynamics (hint: No.)

These type U9D-E motors are attached to 10:1 precision spur gearboxen. Convenience in motor form – so I borrowed them on good faith that they won’t be baked or damaged. I sincerely hope this will remain true, because I sure as hell can’t possibly afford these motors in real life.

Running the numbers, I got that the vehicle could achieve almost 30 degrees of forward tilt. This just shot the error margin into low earth orbit, so the ‘morgs win the motor race. When the vehicle is 30 degrees off kilter, shit has gone down anyway. Or is about to go down. Hard.

With these, even if I was completely wrong on the physical modeling, I’d have enough torque capacity to tune the final system to taste.

What to do with kewl moters? Digitize them!

I like motors that are flat colors and prismatic.

Hey, it’s a circle.

I’ve recently taken a liking to the truncated circle profile. This is clearly visible on my 2.007 robot. It’s alot less boring than just plain square sides.

SEGFAULT is built around a 24 inch diameter circle. Having an actual 2 foot circle as a baseplate is excessive, so the ends will be clipped off.

Underside, showing the motor carriers.

The circle is cut where the motor modules end. The overall length is now around 17 inches.

…Okay, just a LITTLE LEAP OF FAITH THERE.  What the hell is that?

I skipped over more screenshots of the CAD work because it was essentially done in one night. That means it sucks and is riddled with flaws. I’m putting this here because it will probably represent the overall shape of the thing, even if details change.

The frame is all 1/4″ and 3/8″ aluminum appropriately waterjetted and T-nutted together. I’m currently on a mission to reduce the sheer amount of metal used in construction. While the whole thing (including stick AND both drive motors!) only weighs 36 pounds, it needs alot of metal. And it’s a waste of the metal, because the plates are totally trussed out and hollow.

What was that I said about it sucking and being done in one night?

The difference between this frame and essentially all the other DIY balancing vehicles is that it has tiny-ass wheels. I mostly chose this route because i already had said wheels. In order to fit components, then, I had to make an “middle deck” above the motors, where most DIYers will just put parts between the motors and under the top platform. A bit convoluted, but I don’t want to go back and redesign everything. Batteries go in the middle deck, along with most controls.

There’s nothing on the stick yet, because I haven’t gotten around to it. At most, there will be a simple panel dashboard showing battery voltage and probably speed, along with a main power switch. And handlebars.

Steering will be performed by tilting the stick left and right, so there’s no conventional grip throttle like on the first generation Segways.

Alright, enough is enough. Time to start on something – pay attention to this space. And I promise that SEGFAULT will get its own page soon!