Category: Science

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:

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:

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.

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:

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:

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):

Graph 2 — Thermistor Table 1, with insulation:

Graph 3 — Thermistor Table 8, bare:

Graph 4 — Thermistor Table 8, with insulation:

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.

With the stock thermistor and my added thermocouple epoxied to the M2’s nozzle, I stepped the temperature upward, let it settle, and recorded the temperature from the Pronterface status display and my Fluke thermocouple meter:

Because the firmware servos the temperature through the stock thermistor, that line is dead straight at the exact setpoint values: the reference never disagrees with itself. The thermocouple, however, reads low by about 12%: according to it, the nozzle runs much cooler than the thermistor value.

Huh?

Several explanations come to mind:

• The firmware is using a lookup table that doesn’t match the thermistor
• The Fluke thermocouple meter reports the wrong value
• The thermocouple junction is defective
• Despite the epoxy blob, the two sensors aren’t at the same temperature
• Something else is kaflooie

This obviously calls for more data…