Ed Nisley's Blog: Shop notes, electronics, firmware, machinery, 3D printing, laser cuttery, and curiosities. Contents: 100% human thinking, 0% AI slop.
Here’s a howling 1200 Hz mechanical resonance excited by a full-step drive at 290 rpm, with the resonance running at 5 cycles for every 4 full steps.:
1 Step Res 240 Hz
[Update: top trace is voltage from big stepper-as-generator, bottom is small stepper winding current = 1 A/div.]
Switching to 1/2 microstepping at the same rotational speed pretty well tamps it down:
Half Step Res 240 Hz
However, here’s the same resonance excited by 1/2 microstepping at half the rotational speed, oscillating at 9 irregular cycles for every 8 half-steps:
Half res 120 Hz
The resonance was strong enough to back the setscrew completely out of the generator end of the shaft, leaving me wondering why the output was dead when the motor was obviously running. Yes, several times…
Conventional wisdom has it that stepper motor torque decreases as the number of microsteps per full step increases. One reasonably careful measurement trumps a kilo-opinion, so here’s a chart (clicky for bigger) of measurements to mull over:
Microstepping Mode vs Speed – 17PM-J034
Each group of like-colored dots marks the results for full, 1/2, 1/4, 1/8, and 1/16 microstepping with the same load resistance. The caret marks the full-step data point within each group. The load resistances range from a dead short (about 1 Ω due to winding resistance) on the left to 50 Ω on the right.
While I’ll grant the existence of the occasional data-collection error, it’s pretty obvious that:
Torque is reasonably constant regardless of microstepping mode
Full-step mode doesn’t produce more torque and, indeed, produces considerably less under heavy loads
Now, one can argue that the A4988 doesn’t operate in real full-step mode, because it energizes both windings at 1/√2 of the maximum current setting for each full step rather than energizing a single winding at the maximum current. That may be true, but conventional wisdom seems to not bother with such details when opining about torque, either…
As nearly as I can tell, 1/8 microstepping gives as much torque as you’re likely to get from the motor, while having reasonably smooth motion that avoids exciting mechanical resonances.
That chart (or one remarkably like it) will appear in an upcoming Circuit Cellar column. The tonnage of data supporting those dots suggests building an automated dynamometer would be a Good Idea …
Just to see what happened, I reversed the stepper dynamometer and drove the larger (480-ish mN·m) stepper in 1/8 step mode while recording the short-circuit current from the smaller (anonymous) stepper. Slowly cranking the step frequency upward produced this trace when the stepper stalled:
48 mm motor – pullout – 30 rps
The bottom trace shows 30.4 rev/s = 191 rad/s = 1824 rev/min: a pretty good speed for a loaded stepper! The rotor began slowing just before the last sync pulse, but hadn’t lost any appreciable speed.
The current scale is 0.5 A/div (set on the Tek probe amp), which makes the winding current (500 mA/div × 10.4 mVpk / 10 mV/div) = 520 mApk. The scope’s computed rms value includes the waveform after the stall, which isn’t helpful.
The small stepper has a 2.1 Ω winding resistance, so a short-circuit load dissipates (0.52 A)2 × 2.1 Ω = 567 mWpk in each winding. The rms equivalent is half of that, so the total rms power is about half a watt, essentially all internal to the motor.
The pull-out torque depends on the peak torque load, not the rms and not the sum of the two windings, so it’s 0.6 W / (191 rad/s) = 3 mN·m, which doesn’t sound a lot for a 480 mN·m motor until you consider the screaming 6000 full step/s speed: pretty much off-scale high on most of the torque-vs-speed graphs you’ll see. Not much torque left out at that end of the curve, indeed.
In order to stall the motor at lower speeds, the load stepper must generate enough voltage into the load resistor (here, the winding resistance) to push the power/speed ratio (the torque!) above the drive motor’s ability. That implies the load stepper must always be larger than the drive stepper, which means I must conjure up a bracket for that NEMA 23 motor that’s been holding down a stack of papers on my desk…
Incidentally, the voltage required to produce that load current is 0.52 mA × 2.1 Ω = 1.1 V. The 0.58 v/(rev/s) open-circuit generator constant for the smaller motor predicts 0.58 v/rev/s × 30.4 rev/s = 17.7 V. Obviously, you can’t get from the open-circuit unloaded generator constant to the short-circuit loaded voltage… Lenz’s Law gets in the way.
Having acquired a bunch of cheap batteries from the usual eBay suppliers for my new Canon SX230HS pocket camera, it’d be nice to measure their actual (and undoubtedly pathetic) capacity, which implies the need for a holder to make firm contact with the terminals. Sounds like a 3D printer might come in handy for that, doesn’t it?
The first step: measure the dimensions of actual batteries:
NB-5L Battery Dimensions
The terminals lie on what looks to be hard 1/8 inch centers, which must be pure coincidence. They’re recessed anywhere from 0.75 mm to 1.0 mm, depending on who made the thing, into the battery’s endplate.
The Canon charger has three spring-loaded bent-wire contacts, arranged so the (-) terminal touches first as the battery slides into the holder, then (+), and finally the thermistor (T), with about 0.5 mm between each pair. That spring loading provides enough force to hold the battery in the charger.
FWIW, the thermistor is 7.5 kΩ w.r.t. (-) at room temperature.
The plan so far: use three big old gold-plated terminal pins as contacts, with flexible wires to a PowerPole connector that matches the battery tester. Cross-drill the pins to fit music wire lever springs, because the contact spacing is smaller than the smallest coil springs in the Big Box o’ Little Springs. I only need two terminals, so maybe I can force-fit a pair of small coil springs in there, which would be nice.
As described there, the buttons on the back of my pocket camera stopped working, but the obvious laying-on-of-hands repair (i.e., wiggling the cables) didn’t improve things. I later discovered out that two other buttons on the side that didn’t go through the same flex cable were also dead, which suggested that the common failure was on the CPU board deep inside the camera. I gave it to my Shop Assistant with some handwaving about how she could maybe fix it by delving deep inside, tracing the cables, and doing some jiggling: if she could fix it, she could have it.
The first step was to take both covers off, which required a Philips 00 bit:
EX-Z850 front cover removed
Then the side plate comes off, which requires maneuvering the spring-loaded battery latch out of its recess, at which point the lug for the carry strap will fall out:
EX-Z850 battery latch and carrying lug
En passant, we discovered why the clock dies while changing the battery pack. It seems the miniature rechargeable lithium (?) NiMH (?) cell has rotted out:
EX-Z850 internal battery corrosion
Fortunately, it charges in a cradle, so the main battery can remain in place indefinitely. We’ll replace that thing at some point.
The CPU board has two flex cable connectors on the front surface and two on the back. My Shop Assistant released the clamps, removed the cables, wiped down the contacts with DeoxIT Red, gave it a test run with the covers off, and came bounding up the stairs as happy as I’ve ever seen her: the camera worked perfectly again!
Not being used to these things, though, she managed to crack one of the side latches on the far connector. I’ll admit to doing exactly the same thing, so I knew how to fix it: a dab of acrylic adhesive holds the fragment in place with a bit of springiness to hold the latch down.
EX-Z850 connector repair
The connector in question comes from the flash control board, to which those other two buttons (Ex and Drive mode) connect. The inside of the camera is a maze of connections, so I guess that was the simplest way to get the conductors through the body.
She reassembled the camera and it continued to work; we declared the job a complete success.
Shortly after that, I promoted her from Shop Assistant to Larval Engineer, First Instar, and we installed her in her new socket at college, where that camera should come in handy for something.
I think she’ll ace the Freshman Engineering Practicum, wherein her compadres will learn how to solder components to circuit boards, use multimeters & oscilloscopes & other instruments, and generally survive in a laboratory. Maybe she can wrangle a job as a Lab Assistant?
Before trashing (*) all those caps from the Ampeg, I marched them past a capacitance meter that gives the dissipation factor D. As D = tan δ = ESR / ¦X¦, we know ESR = D*¦X¦ at the meter’s 1 kHz test frequency. We don’t know the magnitude of the total reactance X (the meter doesn’t tell us that) and in this case we can’t assume the ESR will be small with respect to the capacitive reactance Xc = 1/2πfC.
Ampeg capacitors
The smaller green 0.022 µF Cornell-Dubilier caps all came in with D=0.05, so they’re marginal.
The larger green 0.15 µF Cornell-Dubilier caps had D=0.00 and the black 0.1 µF was D=0.01. Those are OK.
The small black caps had D=0.14. Yikes! The larger one and the yellow cap had D= 0.01 or 0.02.
The blue Ducati (!) electrolytics ranged from 0.06 to 0.48. That was without reforming, as the last time Phil turned it on, the finals about melted down: I wasn’t going to risk that again just to find out if you can reform all the electrolytic caps without the tubes in place.
So, yeah, some of the coupling caps were exceedingly bad. If you’d like to rub the values & data against the schematic to find out which one(s) were killing the finals, go ahead.
All of the measured capacitance values were within spitting distance of their nominal values.
[Update: Eks points out that I really should measure the leakage at operating voltage, so as to find the current that would drive the grids off their normal bias points. That’s a project for another day… ]
(*) They’re in the e-waste recycling box, of course.
Now, if that isn’t suspiciously linear, I don’t know what is!
The slope is 0.583 v/(rev/s).
I used the scope’s RMS trace calculator, which smushes out the non-sinusoidal nature of the lower speed waveforms. As expected, there are several nasty mechanical resonances that appear in the output waveform while they’re tormenting my ears:
Stepper Resonance – 4.82 rps
Top trace is the winding output voltage, bottom trace is the drive input current, plus a line of junk I forgot to turn off.
Useful conversions:
Drive waveform frequency / 50 = rev/s
Drive waveform frequency * 6/5 = rev/min
So it works. Now I must figure out how to connect load resistors with something more reliable than crappy alligator clips.
The Smell of Molten Projects in the Morning 