That number is the fraction of a step variation you might see from one step to another for an unloaded motor. Yes, it is due to magnetic inhomogeneities, and could be quite irregular around the full circle. Note that since a full circle add up to exactly 360 degrees and (usually) 200 full steps, for every step that is too big, there have to be small steps to make it all add up still. They can't all be 102%, since the number of steps per full circle is exact and constant.

Note that I use this principle to calibrate ultra-high precision x-ray diffractometry systems. With no external standards, and a highly repeatable (bot not accurate) angular scale, one can use 'circle closure', which is this property of cancelling errors, to define angular scales of truly extraordinary accuracy.

See, for example, https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4911639/
which is one of the papers I have published on this technique. The technique has been used since the 1800's (!).

Just in case someone on this thread missed the link from the original thread (linked at the very top of this thread), here is a paper I wrote on the topic of measuring stepper errors and encoder errors.

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4911639/

It may be of significant interest. This link is to the non-paywalled pubmedcentral source. The original (paywalled) article is in Metrologia (the official journal of the Bureau Internationale des Poids et Mesures, which oversees the metric system worldwide).

Also, here is a second paper, which discusses periodic errors in interpolated encoders. However, I don't think any of the discussions above refer to encoders that interpolate between their reference marks. The long, ugly token at the end of the link de-paywalls it. (Note that this is legal; it is an official U.S. Gov't publication, and free of copyright, at least in the USA). (Changed link... de-paywalling wasn't really working). It seems that the PDF link on Google Scholar may de-paywall this correctly. Try this:

https://scholar.google.com/scholar?hl=en&as_sdt=0%2C21&q=An+algorithm+for+the+compensation+of+short-period+errors+in+optical+encoders&btnG=

and use the PDF link

@Corexy The advantage of the Pt sensors over thermistors for wide temperature ranges is that the temperature coefficient is very well defined, and fully standardized across all the sensors. Thermistors have varying beta values, and when used over a wide temperature range can give significantly different results between two nominally identical units. In my day job, I work in a ver highly temperature-controlled lab with 0.01C regulation, and logging to 0.001C. This is a US Government standards lab. For this, we use calibrated thermistors because of their very high sensitivity. They are perfect for narrow-range applications. However, to cover a few hundred C or more, they are far from ideal. Although a Pt sensor is less sensitive (0.3%/C at room temp vs. typically 6%/C for a thermistor), they are very linear and interchangeable. A thermistor has too big a coefficient for wide ranges; a 100k thermistor at 25C is < 100 ohms at 280C. That's a huge dynamic range to cover. One the other hand, a Pt1000 is 1k at 0C and 2k at 273C. This is an easy range to digitize, and the resistance is high enough that modest-length wires don't affect the value too much.
The Pt100 sensors are well liked for heavy industrial and high precision applications because they are fairly robust, and the very low impedance makes them relatively noise resistant. On the other hand, the signal levels are low, and you must use a four-wire Kelvin connection unless the leads are very short, since the wiring resistance will be a big contribution to the total resistance. For high-precision work you can't even correct for the wiring resistance in a 2-wire connection, since you don't know the temperature of the wires.

@elvisprestley
The VIN voltage at the terminal block fluctuates from 24v - 9.5v. The voltage at the bed heater terminal block is constant at 9.5 V.
Your power supply has a big problem. Are you sure it doesn't have a 120/240 volt switch, set to 240 volts, and you are running on 120. This results in a power supply that typically fades in and out. Your Vin should vary at most a couple percent.
If you don't have the input voltage set wrong, the supply probably is defective.

@ignacmc Yes, a PT1000 sensor will have far better absolute temperature accuracy than a thermistor, if you don't have a precise way to calibrate the thermistors.

Thermistors have very high resolution, and can be easily calibrated over a narrow temperature range. I make much of my scientific living working with system controlled to absolute temperatures within 0.01C. Thermistors are great for this, if you only need a 10 degree span and have access to a calibration lab. However, without calibration, tiny errors in the Hart-Steinhart coefficients add up to very large temperature errors when used over a wide span.

Starting with something very close to linear in the first place, and with a temperature coefficient which is set by the properties of a (nearly) pure element, such as platinum, results in a a sensor which can be used over a very wide range with no calibration. A PT100 or PT1000 sensor has lower resolution than a thermistor (it's very hard to read to 0.01C), but a much wider reliable span of readout. It should be within 1C over the entire temperature range from room temp to 300C or higher.

You should get a decent quality calibration resistor (0.1% accuracy) of about 2000 ohms, to check that the duet readback is working right in PT1000 mode. If it works out right, you will be in great shape. The reason I bring this up is that, for example, my duet2 board (1.02 revision) seems to have a significant charge injection problem on the scanning ADC. Putting the PT1000 on channel zero shows a significant (5C) offset at room temp, but putting it on channel 1 is fine. This is likely due to residual charge on the sample/hold capacitor left over from whatever port the ADC scanned before reading channel 0. I haven't looked into the software to see in detail, but it is a classical scanning A/D problem.

My experience with PETG is that it likes the bed quite hot, to get good adhesion. I have an Ultrabase, which has 3mm glass on the aluminum base. The temperature is measured at the aluminum layer. A rough estimate of the heat flux gives me about 10 degrees lower at the surface of the glass than at the thermistor. If I set the thermistor to 90C, so the glass is about 80C, PETG sticks quite nicely. Much lower than that, and its adhesion isn't too good. One characteristic of PETG is that you don't want the nozzle too close to the bed on the first layer. If the nozzle is close, the PETG pulls itself along off the bed. It likes a bit of a drop height, as opposed to most filaments which like a lot of squish.

Also, I print PETG at a fairly high nozzle temperature, 250C. I am using a PT1000 sensor, so I am fairly confident of this number. The viscosity is fairly low when it is this hot, so one can print fairly fast (240um layers at 90mm/sec with a Hemera extruder and 0.4mm nozzle).

One could apply a statistical hack if one really knows the problem is every 20 samples, and either the first or last sample in a batch. One can just replace the (known) bad point with the average of the point before and after. This doesn't change the power spectrum significantly. This is equivalent to adding a random Dirac comb of small amplitude (the difference between the correct, missing point and the average) to the data, which has only a very weak effect on the spectrum. The noise floor at frequencies which are harmonics of (sampling rate / 40) will be slightly raised.

@amit-bandarwad I would go HTTP; you already have the network available, avoid extra wires, and (as mentioned elsewhere) ground loops. There is also a lot better handling of non-determinism in HTTP (well, in TCP really) that makes such communications very reliable. Communications hiccups are 'someone else's problem' in that they are handled by the TCP stack. USB/Serial you have to make sure you never get any surprises, such as cable jiggles causing disconnects, or extra characters due to diagnostic messages, etc. The HTTP protocol guarantees exactly what to expect.

@mrehorstdmd I think they were magnetized by a capacitor discharge, with the flux going through an armature which could be pushed out at the same time the real rotor was inserted, so the flux path never got a chance to open open. AlNiCo was sensitive to this. High-strength AlNiCo magnets required 'keepers' (flux shorts) to not lose strength when stored.

It's worth realizing just how much the performance of permanent-magnet motors has improved in 30 or 40 years, due to rare-earth magnets. They were really wimpy before, even if not accidentally demagnetized.

@jay_s_uk You and I said the same thing, about the negative temperature coefficient. I said resistance is higher at lower temperatures; you corrected to lower at higher temperatures.

However, your statement about the value for a thermistor being specified at zero degrees is wrong. Most thermistors are standardized at 25C. Pt100/Pt1000 are, indeed, standardized at 0C. But it is still correct that the 100000 is the right number to have put in the file.

It would be interesting to put a small load (10k resistor, e.g.) across the fan, and re-measure that voltage. Maybe the board has a leaky FET.

Also, it is possible that the fan draws very little current at low voltage. That may be low enough that nothing is biased on until the voltage is much higher. In that case, you may just be charging some tiny input capacitance, and a small current might create a significant voltage. The load resistor would tell more about this.

@gnydick yeek! There is something funny with your meter.

I agree, it shows an mV label when on that range, but I have no idea what it is doing. Have you tried putting it on an appropriate manual range and seeing if it still does this?

I do have one idea. Is the "H" at the top 'Hold" mode. I have seen meters sometimes in hold that hold the number, but not the range info. Could it have captured that number in the mV range, and then switched to a volts range while still holding the display?

@gnydick Is it possible your meter had autoranged to a millivolt range, and you were reading 3987 mV, or about 4 volts, due to leakage currents?

@dc42 A quick solution would be to at least sort the leads into sets, so any one package has all identical leads. That way you can continue to buy the bulk leads, but any single user doesn't have to deal with the variation.

@jay_s_uk You and I said the same thing, about the negative temperature coefficient. I said resistance is higher at lower temperatures; you corrected to lower at higher temperatures.

However, your statement about the value for a thermistor being specified at zero degrees is wrong. Most thermistors are standardized at 25C. Pt100/Pt1000 are, indeed, standardized at 0C. But it is still correct that the 100000 is the right number to have put in the file.

@foesi
"but I have put 84000 there which is the resistance I measured at around 18°C"

That's a really unlikely resistance for a 100k thermistor at 18C. It should be well above 100k, close to 150k, at that temperature. These thermistors are specified at 25C, and have a negative temperature coefficient, which means the resistance is higher at lower temperatures.

Is it possible you used your fingers to hold the meter leads on the thermistor, and got a reduced reading due to leakage through your skin?

Anyways, use the nominal 100k value in your calibration. It is probably very close to correct.

Although an IR sensor may make a useful remote diagnostic for general conditions, I doubt it will work too well for the hot end control. IR sensors are very sensitive to surface conditions. A clean, shiny nozzle will have a low emissivity, and read cold. As soon as it gets a little dirty, the emissivity will rise, and it will read hotter.
I see a lot of people on numerous forums who have tried to 'calibrate' their thermistor (or other readout) temperature against an IR thermometer, and somehow, the assumption is made that the IR thermometer is the correct value. This is almost certainly wrong, in most cases. There are way too many optical factors that go into these to make them really useful. Expensive, commercial, multi-band sensors can be good, because they can make a reasonable assumption about the emissivity, but basic single band ones are only useful for general surveys of temperature differences across a uniform surface.
On the other hand, as a general diagnostic, it might be interesting to watch how the surface of the sample cools at different fan speeds, print speeds, etc., and use this to develop better printing conditions. Let us know what you learn.

@fcwilt OK, good to know you found both. The 5.18 is the much simpler (and cheaper) one. I have seen exact ones, like the 5.00, but they are more expensive. I think it requires a couple of stages to get 5 exactly, or a lot of teeth on the gears.

A couple of comments on this thread:

@fcwilt Are you sure the 'exact' 5:1 planetaries are really that? It's a hard number to get out of a planetary stage.

@mrehorstdmd The planetary drives that come with most steppers have rather large backlash, almost certainly worse than a belt system. The reason belts work so well in printers (2d and 3d0 is that they have been engineered to have miraculously low backlash. The planetary reduction drives work fine to give high torque in a single-direction driven systems. They also work well as extruder drives, since you are always pushing, and when you retract you get to remove the backlash when you un-retract. They are never really doing anything when running backwards.

@secretasianman7 It's really hard to get good enough thermal contact to get closer than 20 degrees, unless the probe is really clamped in a well, the way the thermistor is. This is close enough that it probably means your hot end is fine.

I had a thought about the extruder motor. Try the following: with no filament in it, send it a command that makes it run for a good long time (5-10 minutes). It doesn't need filament, since with a current-regulated drive, the heating of a stepper is pretty much independent of its load; it is just I^2 R. Multiple short runs, back to back, are fine, too. Now, put your hand on the motor. My criterion for how hard I like to push a stepper (if necessary) is that at this point it is fairly hot. Not so hot that it burns, but hot enough that it is very uncomfortable to hold your hand on for an extended period. This puts the outside of the motor in the 50C-60C range, which is way inside the safe range. If your motor is much cooler than this, you can certainly raise the drive current without any risk.