Chibi-Everything, Part II: Copter

chorl

Poor Chibicopter.

So I’m proud to announce that I’ve found a solution to the XBee over-the-air code uploading problem. The only catch is that…


…it involves chopping an FTDI cable header onto the board.

Yeah, not groundbreaking or world-changing. But, at least I’ve gotten over my software-induced project fear stage and now have a workable, if slightly convoluted, procedure for uploading code and debugging! The hookup for the FTDI is essentially that of the Sparkfun Pro Mini, but instead of DTR I have RTS from the standard FTDI cable going into my reset isolation capacitor thing.

I really should have just done this like two weeks ago.

Anyways, here’s a picture of me triple wielding XBees in order to get this thing to work. The current signalling protocol is:

  • The Xbee connected to my transmitter (in bypass mode) is address 2, the XBee on Chibicopter is address 1, and my debugging/base station is address 0
  • XBee 2 only transmits to Xbee 1 (ATDL = 1 ATMY = 2)
  • Xbee 1 only transmits to Xbee 0 (ATDL = 0 ATMY = 1)
  • Xbee 0 transmits to the nonexistent XBee #3 (ATDL = 3 ATMY = 0) in order for its serial transmissions to not appear on the others
  • Therefore, my radio transmits commands to Chibicopter, which in turn transmits debugging data to the base station where it appears on my screen.

To reprogram Chibicopter, I remove the Xbee from Chibicopter, disengage the base station XBee adapter and jam the FTDI cable onto Chibicopter. I have to take the XBee onboard out first because there is no selection/domination circuitry which allows both XBee and FTDI cable to use the serial lines at the same time.

It’s quite an overloaded process, but it has at least gotten me to the point of…

…being able to finally read the pulsewidths from my radio. All four of the ones I care about. The Serial buffer reading code needed a bit of tweaking – I had to flush the serial receive buffer after every read or else it would desynchronize because more packets appear as the procedure was executing.

Sadly enough, there is no more Serial.flush() in Arduino 1.0, the functionality having been removed. I wondered why briefly before just writing a dumb serial buffer clearing loop.

Anyways, the good news is that I transferred enough core functionality over from tinycopter such that Chibicopter’s props respond properly to suddenly orientation changes! That means it’s just some tuning of gains away from actually flying.

The bad news is that through some irony of fate, two of the tiny 1S-lithium motor controllers have ceased to function. Just in time, right? I’m uncertain as to why they failed. One possible reason is that since the board has absolutely no logic power supply at all (everything running off the 3.something volt battery) that 5 volts from the FTDI cable was enough to destroy the weaker ones.

Now, I’m also wondering why it is that there is an option for 3.3v-compatible logic but with 5 volt VCC (power supply). If the point is to use it with a 3.3v system safely, isn’t this undesirable?

No matter – I have more spares on the way, but they’ll still take a few days to arrive. In the mean time, I might make a little pass-through board or something which down-regulates the 5v USB power to 3.3v.

…and then it will fly I swear guys

 

 

Chibi-Everything, part I: Kart

chorl3 Comments

A double-update from the term of smaller and cute projects! First, I’ve discovered to little surprise that Chibikart will have no torque whatsoever. And second, I’ve finally gotten over my fear of XBees to mine Chibicopter back out from the pit of paused project despair in order to… attach an FTDI header to it. Oh, the backpedaling.

First, why Chibikart will be a super laid-back performer.

Last time, in testing the mostly-36-turn motor, I found out that my back-EMF (/torque) constant was a dismal 0.126 Nm/A. This was off from the predicted 0.19 Nm/A and even down from the single-winding guessed 0.16 Nm/A. There were probably two major factors involved. First, I could not stuff 36 turns onto all of the windings at all. Not even close. Besides A-phase, the rest of the phases more realistically have about 30 turns per tooth. Just this small (16%) reduction isn’t enough to explain the drop from 0.19 to 0.126, though. I’m also suspecting that the 3 little toothlets on each tooth increase my apparent air gap (since only parts of them are at the design airgap) and the rest are about 0.75mm inwards – the airgap in that area is about 1.25mm.

The depressions and raised tooth areas each occupy about half the area of the tooth, so the average airgap would be 0.875mm for one tooth.  The maximum theoretical flux density at this average surface is therefore (1.2 tesla for N42 grade magnets) * (2mm thickness / (2mm thickness + 0.875mm airgap)) = 0.83T. If the airgap were evenly 0.5mm throughout (which is the design gap), then the average flux density rises to 0.96T. The 13.5% loss of the field strength from 0.96 to 0.83 coupled with the 16% loss of winding turns means that (0.19 Nm/A) * (0.865) * (0.83) = approximately 0.136.

Plus or minus some second-order effects and nonidealities, and I think the lesson is clear – real life sucks. That, and I need to find a better stator.

The second motor was even worse.

Through more test winding, I found that 27 turns was what I could reliably wind on one tooth. Meaning very little “cancerous bunching” as seen in the first motor winding picture, and which could be completed reasonably fast without being messy. It turns (!) out that keeping the wire under high tension the whole time improved packing alot – go figure – and I added another zip tie to my winding jig as a result.

Unfortunately, 27 turns is even worse than 30 turns. The above scope capture is the lathe-o-mometer signature of the second Chibikart motor. The calculated BEMF constant is an even more depressing 0.11 Nm/A. While consistent with an incremental (27/30) decrease in the turn count, it’s still…. so soul-crushing.

By this time, I was seriously questioning if the first generation skate motors which these things are based off of ever reached their design 0.26 Nm/A. It seemed impossible given my above results. The skatemotors were true 36 turn (but single 24 gauge winding), so based on the results I got with the first motor, I should see a realistic Kt of 0.15 Nm/A.

How did I find out? Well, I had to temporarily put the left RazErBlade on blocks to find out – I removed the motor and shoved it on Tinylathe. Another problem was that in this design, the wires ran out through the center of the motor, meaning Tinylathe couldn’t grab onto it at all.

Fortunately, a DeWalt 18v drill in high gear saved the day.

This motor’s waveform is a bit more erratic, but the average voltage magnitude is about 4.5 volts at 62 Hz. This gives a Kt of…. 0.08 Nm/A? Did I wire up this motor backwards?!

Something wasn’t right. I decided to declare this test bogus and just try running the motors using an ESC. I used Melon-scooter propped up on a table as a test jig – it has a 500w type Jasontroller right now, which is very representative of what the final control solution will be, so what better basis for comparison? A laser tachometer was used to record the no-load speed of the motors, and I used a 15 amp power supply set to 33 volts with maxed out current – the no load test shouldn’t result in such high currents anyway.

These results were telling.

  • Chibikart motor 1, ~30 turns, achieved a no-load speed of 2671 (Oh the irony) RPM on 33.0v for a RPM/V (classical “Kv” rating) of 81, and a calculated Kt of 0.118.
  • Chibikart motor 2, ~27 turns, achieved a no-load speed of 3036 RPM for a RPM/V of 92; Kt of 0.103. This is almost exactly the ratio of 30/27. Universe still makes sense: “Kv” is essentially the inverse of Kt, so a higher RPM/V is less Nm/A.
  • Skatemotor, ~36 turns, hit 2078 RPM for a RPM/V of 63 and Kt of 0.151. Well hey.

The ratio of turns alone, 36/30, does not account entirely for the discrepancy – it alone would calculate a Kv of 68 RPM/V using Chibikart motor 1 as a basis. While the difference of 5 RPM/V is certainly within the realm of “bah, close enough”, I think the shape of the tooth and arms is a major higher-order effect that linear models like “T = k*NBLR” doesn’t capture. The original skatemotor stators did not have those stupid toothy things.

Now, why is Kt (calculated) different from Kt (measured-with-oscilloscope-and-lathe)? I should probably mention that Kt changes with the type of drive input (sinusoidal, 120 degree trapezoidal which is the standard, 180 degree trapezoid…) and the phase of the drive input (advanced, retarded, etc.). This is something I kind of sweep under the carpet when explaining How Moter to someone because it’s very mathematical in nature, so for your amusement, here is how moter for real and how2controlmoter.

If I can hold 27 turns on each motor from here on out and maintain 0.11 Nm/A, then Chibikart will have a maximum launch force at 20 amps of 4 * (20 A * 0.11 Nm/A) / 0.05m wheel radius, or 176N at-ground linear force. I chose 20 amps as a reasonably burst rating because not only is it roughly what a stock 350W-type Jasontroller outputs without modification, but to heat up a roughly 80 gram (estimate of the total winding weight*) copper chunk from 20C to 200C, the maximum temperature rating of the magnet wire I used, at 20 amps will take about 30 seconds. The actual math: (0.384 Joules/(gram-Kelvin) for copper [1] * 180K thermal differential * 80 grams) / (20 amps ^2 * 0.37 ohms resistance of the 27-turn motor line-to-line) yields about 37s.

Why 30 seconds? Because I have to put a definition down somewhere. This is why “burst vs. continuous” ratings are bullshit if no time period of overload is given. I could reasonably pump 40 or even 50 amps into these motors for a quick launch, but they’d heat up reeeeeeeeeeeal fast if I tried to push that current continously. 30s is a generous estimate, since my magnets would be long-gone at 200C… even 80C will be enough. (However, the magnets are not in direct thermal contact with the copper, so I can certainly flame out the windings with overcurrent before any other damage is suffered)

So the bottom line is don’t expect Chibikart to behave like tinykart. With ~180N of maximum launch force, I’ll get a maximum acceleration of about 2 m/s^2. Which I guess isn’t that bad, but yeah. It will also not be happy at all going up the de-facto vehicle proving ground.

There’s so much random math in this post that it must be of some use to someone, so I’ll lob this under “Reference Posts” too.

* Each turn on a tooth is assumed to have an average dimension of 21mm length and 10mm width, for a total perimeter of 62mm per turn. There are 27 turns of 6 strands of parallel wire, so on each tooth is 10.04 meters of wire. There are 12 teeth, so the total length of wire in a motor is about 121 meters. In feet, that is 395 feet. #28 gauge magnet wire is 2028 ft/lb so the total mass of copper in each motor is .19 lb – or 3.11 ounces, or about 87 grams.