The Smell of Molten Projects in the Morning

Ed Nisley's Blog: Shop notes, electronics, firmware, machinery, 3D printing, laser cuttery, and curiosities. Contents: 100% human thinking, 0% AI slop.

Category: Science

If you measure something often enough, it becomes science

  • Marlin Firmware: Stepper Interrupt Timing

    Based on the discussion attached to the post on Z axis numbers, I wanted to take a look at the points where Marlin switches from one step per interrupt to two, then to four, just to see what the timing looks like. The RAMBo board has neatly labeled test points, to which I tack-soldered a pin for the scope probe poked through one of the ventilation slots, and an unused power connector on the left edge of the PCB that provided a ground point (admittedly, much too far away for good RF grounding, but it suffices for CMOS logic signals). The Tek Hall-effect current probe leaning in from the top right captures the current in one of the X axis windings:

    X axis Step and Current probes
    X axis Step and Current probes

    I’ve reset the Marlin constants based on first principles, per the notes on distance, speed, and acceleration, so they’re not representative of the as-shipped M2 firmware. Recapping the XY settings:

    • Distance: 88.89 step/mm
    • Speed: 450 mm/s = 27000 mm/min
    • Acceleration: 5000 mm/s2, with the overall limit at 10 m/s2

    The maximum interrupt frequency is about 10 kHz and the handler can issue zero, one, two, or four steps per axis per interrupt as required by the speed along each axis, up to a maximum of step rate of 40 kHz. There are complexities involved which I do not profess to understand.

    The maximum 10 kHz step rate for one-step-per-interrupt motion corresponds to a speed of:

    112.5 mm/s = (10000 step/s) / (88.89 step/mm)

    The maximum 40 kHz step rate produces, naturally enough, four times that speed:

    450 mm/s = (40000 step/s) / (88.89 step/mm)

    Assuming constant acceleration, the distance required to reach a given speed from a standing start or to decelerate from that speed to a complete stop is:
    x = v2 / (2 * a)

    The time required to reach that speed is:
    t = v/a

    Accelerating at 5000 mm/s2:

    • 112.5 mm/s = 6700 mm/min → 1.27 mm, 22.5 ms
    • 150 mm/s = 9000 mm/min → 2.25 mm, 30 ms
    • 450 mm/s = 27000 mm/min → 20.3 mm and 90 ms

    An overview of a complete 6 mm move at 150 mm/s shows the acceleration and deceleration at each end, with a constant-speed section in the middle:

    X Axis 150 mm-s 6 mm - overview
    X Axis 150 mm-s 6 mm – overview

    The bizarre patterns in the traces come from hp2xx‘s desperate attempts to discern the meaning of the scope’s HPGL graphic data where the trace forms a solid block of color; take it as given that there’s no information in the pattern. I described the trace conversion process there.

    The upper trace shows the X axis motor winding current at a scale of 500 mA/div, with far more hash than one would expect. The RAMBo drivers evidently produce much more current noise than the brick drivers I intend to use.

    The lower trace is the X axis step signal produced by the Arduino microcontroller. You can barely make out the individual step signals at each end, but there’s not enough horizontal resolution to show them when the motor moves at a reasonable pace.

    In round numbers, the acceleration and deceleration should require about 30 ms each. The overall move takes 63 ms, so the constant-speed section in the middle must be about 3 ms long. That’s probably not right…

    Here’s a closer look at the step pulses as the motion starts from zero on the way to 150 mm/s:

    X Axis 150 mm-s 6 mm - 1 ms-div 0 ms dly
    X Axis 150 mm-s 6 mm – 1 ms-div 0 ms dly

    Over on the right, the 5 kHz step rate after 8.5 ms suggests a speed of 56 mm/s and counting 28 pulses says it moved 0.32 mm. Plugging those numbers into the equations:

    • a = v/t = 6600 mm/s2
    • a = (2 * x)/t2 = 8900 mm/s2

    It’s not clear (to me, anyway) whether:

    • The firmware accelerates faster than the alleged 5000 mm/s2 limit
    • It’s accelerating near the overall limit of 10000 mm/s2
    • The acceleration isn’t constant: starts high, then declines
    • The measurement accuracy doesn’t support any conclusions
    • I understand what’s happening

    In order to see the double- and quad-step outputs, here’s a 50 mm move at 450 mm/s, with a 19 ms delay to the point where the interrupt handler transitions from single-step to double-step output:

    X Axis 450 mm-s 50 mm - 200 us-div 19 ms dly
    X Axis 450 mm-s 50 mm – 200 us-div 19 ms dly

    The interrupt frequency drops from just under 10 kHz to a bit under 5 kHz, with the doubled pulses about 16 μs apart. At the transition, the axis speed is 112.5 mm/s, pretty much as predicted.

    If that’s the case, the overall acceleration to the transition works out to:

    5800 mm/s2 = (113 mm/s) / (19.5 ms)

    Delaying the traces to 41.9 ms after the motion starts shows the double-to-quad step transition:

    X Axis 450 mm-s 50 mm - 100 us-div 41.9 ms dly
    X Axis 450 mm-s 50 mm – 100 us-div 41.9 ms dly

    Once again, the pulse frequency drops from 10 kHz down to 5 kHz. The speed is now 225 mm/s, half the maximum possible speed, which also makes sense: at top speed, the pulses will be essentially continuous at 40 kHz.

    The average acceleration from the start of the motion:

    5300 mm/s2 = (225 mm/s) / (42.1 ms)

    That implies the initial acceleration starts higher than the limit, but it evens out on the way to the commanded speed.

    Those scope shots come from moving only the X axis. Moving both the X and Y axes, with Trace 1 now showing the Y axis output, for 50 mm at 450 mm/s, produces similar results; the Y axis output lags the X axis by a few microseconds:

    XY 450 mm-s 50 mm - 100 us-div 19.5 ms dly
    XY 450 mm-s 50 mm – 100 us-div 19.5 ms dly

    Once again, that’s at the single- to double-step transition at 19+ ms. The overall timing doesn’t depend on how many axes are moving, as long as they can accelerate at the same pace; otherwise, the firmware must adjust the accelerations to make both axes track the intended path.

    None of this is too surprising.

    For a motor running at a constant speed just beyond the single-to-double step transition at 112.5 mm/s or the double-to-quad transition at 225 mm/s, the rotor motion should have a 5 kHz perturbation around its nominal position: it coasts for nearly the entire period, then a pair of steps kicks it toward the proper position. At those transitions, the rotor turns at:

    3.2 rev/s = (10000 step/s) / (3200 step/rev)
    6.4 rev/s = (20000 step/s) / (3200 step/rev)

    The perturbation should look like a 5 kHz oscillation (not exactly sinusoidal, maybe triangular?) superimposed on the nominal position, which is changing more-or-less parabolically as a function of time. I expect that the overall inertia damps it out pretty well, but I’d like to attach a rotary encoder to the motor shaft (or a linear encoder to the axis) to show the actual outcome, but I don’t have the machinery for that.

    In any event, LinuxCNC’s step outputs should behave better, which is why I’m doing this whole thing in the first place…

  • Monthly Science: Basement Safe Humidity

    A plot of the temperature and humidity inside the basement safe over the last year-and-a-half:

    Basement Safe
    Basement Safe

    The tray of silica gel (or whatever those granules might be) holds the humidity firmly at 14 to 15 %, at least with a simple masking tape seal around the door opening that dates back to early 2012. Less water vapor gets through the door during the winter, due to the lower basement humidity when it’s cold outside, but it looks like four regenerations per year with just under a kilogram of desiccant in the tray.

    Ordinarily, it’d be time for those granules to endure another oven session, but I just picked up a bunch of real silica gel beads and must conjure up some porous bags.

    The Bash / Gnuplot script that cleaned the CSV files and produced the plot:

    #!/bin/sh
#-- overhead
export GDFONTPATH="/usr/share/fonts/truetype/"
base="${1%.*}"
echo Base name: ${base}
ofile=${base}.png
tfile=$(tempfile)
echo Input file: $1
echo Temporary file: ${tfile}
echo Output file: ${ofile}
#-- prepare csv Hobo logger file
sed 's/^\"/#&/' "$1" | sed 's/^.*Logged/#&/' | sed 's/ ,/,/' | sed 's/\/\([0-9][0-9]\) /\/20\1 /' > ${tfile}
#-- do it
gnuplot << EOF
#set term x11
set term png font "arialbd.ttf" 18 size 950,600
set output "${ofile}"
set title "${base}"
set key noautotitles
unset mouse
set bmargin 4
set grid xtics ytics
set timefmt "%m/%d/%Y %H:%M:%S"
set xdata time
set xlabel "Date"
set format x "%y-%m"
#set xrange [1.8:2.2]
set xtics font "arial,12"
#set mxtics 2
#set logscale y
set ytics nomirror autofreq
set ylabel "Temperature - F"
set format y "%3.0f"
set yrange [40:90]
set mytics 2
set y2label "Relative Humidity - %"
set y2tics nomirror autofreq
set format y2 "%3.0f"
set y2range [10:60]
#set y2tics 32
#set rmargin 9
set datafile separator ","
#set label 1 "label text" at 2.100,110 right font "arialbd,18"
#set arrow from 2.100,110 to 2.105,103 lt 1 lw 2 lc 0
plot    \
    "${tfile}" using 2:3 axes x1y1 with lines lt 3 title "Temperature",\
    "${tfile}" using 2:4 axes x1y2 with lines lt 4 title "Humidity"
EOF

  • LED Output vs. Current: Efficiency Loss

    Some data points from that circuit produced this graph:

    LED Output vs Current
    LED Output vs Current

    Relative to the output at 5 mA, the efficiency drops off pretty much linearly:

    LED Efficiency vs Current
    LED Efficiency vs Current

    That’s computed as the ratio of the actual light output to the output at 5 mA scaled by the current ratio.

    So putting the screws to the LEDs does produce more light, but not quite as much as you’d expect. Above maybe 40 mA, it’s not worth the effort.

    Now we know…

     

  • LED Driver + Zero-bias Photodiode Amplifier

    This may come in handy for something, like measuring LED output:

    LED Output Tester - Schematic
    LED Output Tester – Schematic

    The LM324 converts the input voltage to an LED drive current, scaled by the sense resistor and the gain of IC2B to 25 mA/V. The feedback loop closes through the MOSFET and C6 rolls off the response, so there’s a nasty overshoot on the leading edge of input pulses where the current increases faster than the op amp can tamp it down:

    Red LED - 25 mA 14 uA
    Red LED – 25 mA 14 uA

    The LM356 acts as a transimpedance amplifer to convert the photodiode current to voltage. The PIN-10AP specs say it should operate in photovoltaic mode with zero bias and that more than -3V of bias will kill the photodiode; the LM356 should hold its inverting input at virtual ground, but the two 1N5819 Schottky diodes enforce that limit. There being zero volts across the diodes, they don’t leak in either direction, so it’s all good.

    The circuit is an embarrassing hairball on solderless breadboard, so use your imagination…

    You could mash this together with the LED Curve Tracer, although you’d want better low-current resolution from the Arduino output.

  • LED + Photodiode: Verifying Linearity

    Given that test fixture, the obvious question is whether the PIN-10AP photodiode’s output current varies linearly with light intensity, just like the specs would lead you to believe. I excavated the sheet of 2-stop neutral density filter gel from the Parts Warehouse Wing and cut some 30 mm disks:

    LED Photodiode test fixture - ND filter disks
    LED Photodiode test fixture – ND filter disks

    A single filter layer should reduce the light intensity by 2 f/stops = a factor of 4. Each successive layer reduces the intensity by another factor of 4. They’re all at least reasonably clean and free of defects, but they’re definitely not optical lens quality.

    Running the LED with a 100 mA pulse at 20% duty cycle and stacking the disks in the fixture, one by one, between the LED and photodiode, produces this data:

    Layers Attenuation Scale V I – uA Ratio
    0 1 1.0000 8.7 87  
    1 4 0.2500 1.9 19 4.58
    2 16 0.0625 0.43 4.3 4.42
    3 64 0.0156 0.097 0.97 4.43
    4 256 0.0039 0.022 0.22 4.41

    The Ratio column divides successive pairs of current values. The first step, from “no filter” to “one filter”, came out a bit larger than the rest, probably because the gel sheet isn’t anti-reflective and some light bounces off the top.

    After that, though, it looks just like I’m cheating, doesn’t it?

    The ratios should be 4.0, but the actual 4.4 means it’s a 2.1 stop filter. Close enough, methinks.

  • Makergear M2: Extruder Thermistor Recalibration

    Those measurements suggested that my initial correction to the Table 1 values weren’t quite correct, but a similar correction might work as long as I didn’t change the insulating wrap. This graph includes a linear fit to the Nozzle TC data, based on the original M2 firmware’s Table 1 thermistor data and cotton insulation:

    M2 Extruder Thermistor Recal - Table 1 Insulated - Nozzle TC linear fit
    M2 Extruder Thermistor Recal – Table 1 Insulated – Nozzle TC linear fit

    Applying that equation to Table 1 produces this thermistor lookup table:

    #if (THERMISTORHEATER_0 == 8) || (THERMISTORHEATER_1 == 8) || (THERMISTORHEATER_2 == 8) || (THERMISTORBED == 8) // M2 thermistors on RAMBO
const short temptable_8[][2] PROGMEM = {
	{23*OVERSAMPLENR, 243},
	{25*OVERSAMPLENR, 239},
	{27*OVERSAMPLENR, 235},
	{28*OVERSAMPLENR, 231},
	{31*OVERSAMPLENR, 227},
	{33*OVERSAMPLENR, 223},
	{35*OVERSAMPLENR, 219},
	{38*OVERSAMPLENR, 215},
	{41*OVERSAMPLENR, 211},
	{44*OVERSAMPLENR, 207},
	{48*OVERSAMPLENR, 203},
	{52*OVERSAMPLENR, 199},
	{56*OVERSAMPLENR, 195},
	{61*OVERSAMPLENR, 191},
	{66*OVERSAMPLENR, 187},
	{71*OVERSAMPLENR, 183},
	{78*OVERSAMPLENR, 179},
	{84*OVERSAMPLENR, 175},
	{92*OVERSAMPLENR, 171},
	{100*OVERSAMPLENR, 167},
	{109*OVERSAMPLENR, 163},
	{120*OVERSAMPLENR, 159},
	{131*OVERSAMPLENR, 155},
	{143*OVERSAMPLENR, 151},
	{156*OVERSAMPLENR, 147},
	{171*OVERSAMPLENR, 143},
	{187*OVERSAMPLENR, 139},
	{205*OVERSAMPLENR, 135},
	{224*OVERSAMPLENR, 131},
	{245*OVERSAMPLENR, 127},
	{268*OVERSAMPLENR, 123},
	{293*OVERSAMPLENR, 119},
	{320*OVERSAMPLENR, 115},
	{348*OVERSAMPLENR, 111},
	{379*OVERSAMPLENR, 107},
	{411*OVERSAMPLENR, 103},
	{445*OVERSAMPLENR, 99},
	{480*OVERSAMPLENR, 95},
	{516*OVERSAMPLENR, 91},
	{553*OVERSAMPLENR, 87},
	{591*OVERSAMPLENR, 83},
	{628*OVERSAMPLENR, 79},
	{665*OVERSAMPLENR, 75},
	{702*OVERSAMPLENR, 71},
	{737*OVERSAMPLENR, 67},
	{770*OVERSAMPLENR, 63},
	{801*OVERSAMPLENR, 59},
	{830*OVERSAMPLENR, 55},
	{857*OVERSAMPLENR, 51},
	{881*OVERSAMPLENR, 47},
	{903*OVERSAMPLENR, 43},
	{922*OVERSAMPLENR, 39},
	{939*OVERSAMPLENR, 35},
	{954*OVERSAMPLENR, 31},
	{966*OVERSAMPLENR, 27},
	{977*OVERSAMPLENR, 23},
	{985*OVERSAMPLENR, 19},
	{993*OVERSAMPLENR, 15},
	{999*OVERSAMPLENR, 11},
	{1004*OVERSAMPLENR, 7},
	{1008*OVERSAMPLENR, 3},
	{1011*OVERSAMPLENR, 0}
};
#endif

    I extrapolated the last entry from the previous two, because if the table doesn’t include an entry for 0 °C, then when you turn the heater off, the setpoint winds up being the lowest temperature greater than zero. Doesn’t make any difference, I think, but looks odd.

    Load that table, run the temperature up, record more data:

    M2 Extruder Thermistor Recal - slope-offset fit from Table 1
    M2 Extruder Thermistor Recal – slope-offset fit from Table 1

    The error isn’t particularly pretty, being off by +4 °C at the high end. You could hand-tweak the linear fit equation to push the error down at normal operating temperatures, but it’s close enough for my purposes.

    Although I don’t have any numbers, one benefit of tighter thermal coupling to the extruder nozzle is greatly reduced overshoot during heating.

  • Makergear M2: Hot End Temperature Profiles

    Knowing that all the thermocouples and amps and meters report more-or-less the same values, I tucked several of them around the hot end:

    M2 Hot End Temperature Profile - Insulated
    M2 Hot End Temperature Profile – Insulated

    Their IDs and placement:

    • Nozzle TM – Makergear thermistor epoxied to nozzle
    • Nozzle TC – thermocouple epoxied to nozzle
    • Heater – thermocouple at heater, under insulating sleeve
    • Sleeve – thermocouple at heater, outside insulating sleeve
    • Surface – thermocouple taped to outside of cotton insulation

    Although I intended to put the Heater thermocouple bead  on the ceramic heater itself, I have no way of knowing exactly where it was, nor whether it actually made good contact with the heater body, because it’s tucked inside the fiberglass + silicone insulating sleeve. That sleeve will, perforce, be somewhat cooler than the heater, and that will certainly affect the results.

    The sensors are stacked more-or-less radially outward from the center, which may or may not make any difference.

    The upper fan (which runs constantly) does not blow directly on the leads, but air flow over the leads does change the reported temperatures: I haven’t taken that into account, even though it’s certainly significant, but the leads and fan remain in (approximately) the same position for the tests.

    In the stock M2, the lower fan blows directly on the uninsulated hot end, the thermistor, and the nozzle; the G-Code controls when it’s turned on, so whatever effects it has are not constant. It was always off for these tests, but that’s certainly not the case while printing an object.

    The cotton insulation wrap isn’t the same as I used earlier; it was easier to use a new length of cloth than to remove the Kapton tape from the old insulation. The new insulation was slightly thicker, as well, and did a better job of reducing heat loss. I took the Insulated measurements first, then removed the cloth for the Bare measurements. Although I tried to keep the thermocouples in the same positions, I certainly nudged the wires while peeling off the cloth:

    M2 Hot End Temperature Profile - Bare
    M2 Hot End Temperature Profile – Bare

    The Marlin firmware in the M2 normally uses thermistor Table 1. I adjusted those values to create Table 8, which exactly corrected the mismatch, at least with the earlier, thinner insulation.

    After each temperature step, I waited until the temperature plot in the Pronterface graph had settled to a single pixel line for one minute. That didn’t mean the temperature was exactly at the setpoint, but it wasn’t changing very much at all, which is all I needed for this dataset.

    Keeping all that in mind…

    Graph 1 — Thermistor Table 1, bare (the as-shipped M2 configuration):

    Hot End Temperature Profile Graph - Table 1 - Bare
    Hot End Temperature Profile Graph – Table 1 – Bare

    Graph 2 — Thermistor Table 1, with insulation:

    Hot End Temperature Profile Graph - Table 1 - Insulated
    Hot End Temperature Profile Graph – Table 1 – Insulated

    Graph 3 — Thermistor Table 8, bare:

    Hot End Temperature Profile Graph - Table 8 - Bare
    Hot End Temperature Profile Graph – Table 8 – Bare

    Graph 4 — Thermistor Table 8, with insulation:

    Hot End Temperature Profile Graph - Table 8 - Insulated
    Hot End Temperature Profile Graph – Table 8 – Insulated

    The data in Graph 4 clearly show that the correction factor I used to create Table 8 doesn’t apply with a different insulation wrap around the hot end. Although the Nozzle TM and Nozzle TC lines are quite close, they aren’t the exact match I saw before.

    When you compare Graph 1 with Graph 3, then Graph 2 with Graph 4, you’ll see that the thermocouple data remains consistent: the temperature differences at a specific temperature are the same, regardless of what the Nozzle TM indicates. For example, at the upper-right corner of Graph 1, when the Nozzle TM reports 175 °C, Nozzle TC is at 145 °C and the Heater is at 124 °C (use the Y axis values): Nozzle TC is 21 °C higher than the Heater. Looking in Graph 3 to the point where the Heater is 124 °C, the Heater is once again 21 °C hotter (again, using the Y axis values).

    Although it seems odd, having the thermocouple on the bare Heater run cooler than the Nozzle TC is entirely possible, because the Heater thermocouple is in contact with the relatively thin sleeve, which is cooling the outside of the heater core. The Nozzle TC has a direct metallic + epoxy connection to the inside of the heater core, which will be hotter than its exterior surface.

    Conversely, Graph 2 shows the insulated Heater running hotter than the Nozzle TM. That also makes sense: with less heat loss through the Sleeve, the exterior of the heater gets hotter than the threaded brass cylinder in the middle, which is losing heat at both ends.

    Those correlations suggest the various thermocouples do indicate the actual temperatures and the nozzle thermistor doesn’t.

    I believe bonding the thermistor to the nozzle with epoxy doesn’t affect that conclusion. It does make the results less subject to random changes due to the thermistor bead’s exact position and contact with the nozzle, though, and certainly makes the temperatures I record quite different from those found in other M2 hot ends. The fundamental rule here is that when you want to measure the temperature of something, the probe must make solid contact with the something, not dangle in mid-air somewhere nearby.

    Based on some earlier (and rather crude) measurements, I proposed that the thermistor was gaining heat through its leads, because they pass over the heater core. That’s definitely not true, as the Nozzle TM and Nozzle TC have the same temperature difference between the bare and insulated cases: compare Graph 1 with Graph 2, then Graph 3 with Graph 4. If the thermistor gained heat, it would be relatively hotter than the thermocouple in the case with additional insulation, because the Heater would then run hotter and pipe more heat into the thermistor leads.

    That’s why you make measurements…

    Along those lines, I’ve asked several people I trust to measure their M2 hot ends [You know who you are. Thanks!] and the results are unequivocal: nobody sees any significant variation between the thermistor and a thermocouple tucked beside it. The only difference in the setups seems to be the solid connection between my sensors and the nozzle. I can’t explain it, either, and I’ve shot down several of my own proposals.