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uncle_bob
In the world of printers, we (hopefully) smoothly accelerate and decelerate the stepper. That means we have a varying frequency sine wave that's the drive in the high speed case that this all came out of. The discussion is revolving around a high rpm rather than a low RPM use case. In the low RPM case you do get steps in the current, but you are in what we are calling an "ohms law" region.
Who is "we" that is calling for an "ohms law" region, and does that imply there is another region that is "outside ohms law"?
Just to sum up how i see things about "ohms law" region issue i am going to take some liberty and express in a direct way like this:
- its ok to say things like: "we dont care for ohms law", or "it doesnt bother us", or "we can ignore it". Or any expression along the lines, but without essentially denying ohms law. It could be true in some context for some level. Its not the best thing to say because it leaves open to interpretations such as next part.
- its *not* ok to say things like: "does not apply" or "steppers work inside ohms law region and outside ohms law region" or "ohms law does not apply for steppers at all". Anything along these lines just doesnt fly. Makes no sense, to me at least.
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uncle_bob
We very much do generate a sinusoidal current to drive a stepper motor.
You keep on saying the driver ic outpus a sinusoidal current, and i say stepper ic outputs square voltage. Now, lets take a good look at the output stage of the driver ic. That is a h-bridge made with fets which are operated like switches, and supplied with the input voltage. If you think about this more, i think you will see the light. I wasnt able to change your pov this far, even tho i tried, so perhaps you can do that instead, sometime in the future. For the time being i will keep to my pov and say it outputs the voltage, and it switches it, so its kind of a switched voltage, hence some kind of square voltage. Well maybe rectangles instead of equal sides square, but angles are squared at least.
And then i will say the current grows in inductor as a result of voltage being applied to it. Now somebody will get picky and will say it doesnt grow there. It grows somewhere else. That would be true. Ofc the current needs the entire loop, and current is exact same in entire loop. So if it grows in inductor it also grows in the Rsense, grows in the high side and low side fets, etc, just grows across the entire loop. But while all other parts of loop have other element laws, e.g. rsense resistor element law is just straight line and fets can be modeled for this as ron as switches, then the inductor gives the essential element law, the dominant one, thats what is actually responsible for the current shape. So while one could say current grows somewhere else, even grows in the pcb tracks, well i guess that would be also true, just none of those places is interesting. So, saying it grows in inductor makes more sense because thats the element resposible, the dominant one, and coz i need to put the finger on that place. Its habbit to say current "grows/falls in inductor", although ofc in fact, it does grow/falls the same everywhere in the entire loop - always. Just a matter of words. So i will say "current grows in inductor" and its an expression, and afaik quite in use this way.
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uncle_bob
The stepper is being operated as s synchronous AC motor when it's in micro stepping mode. The data sheets for the stepper chips show this very clearly.
In vfd (variable frequency drive), the ac frequency directly gives rpm. If that would be true for stepper, it would mean that when stepper holds position then switching frequency=0 ?
Now, this is some
practical variable frequency driver, its supplied by mains ac (essentially its a cycloconverter) the size of ~ half desktop pc and cheapest costs 200 eur. This does output a sinusoid e.g. those ones say 0.5-1000hz, and that directly relates to rpm. The motor positions are continuous.
And this is our
practical stepper driver supplied with low voltage dc (essentially its a dc switch mode) the size of a big thumbnail and cheapest costs less than 10$. This outputs a square voltage, not a sinusoid, the switching frequency measures in tens of Khz range, and this switching frequency is *not* proportional to rpm. In fact switching is also that high even when motor stays still. And the motor positions are discrete, and e.g. distinct and individual, sort of separate to each other. Just in extreme case we would want to output a sine while having a dc for input, that would be called an inverter - but this one is not.
*The ok part*
The datasheet does show something that looks like a current sinusoid, thats true. This sinusoid also represent the coil current levels for different step positions, and look like a sinusoid as the motor moves from one position to the next. And it is related to rpm, because it shows how motor moves from one position to another, rpm-wise this sinusoid is like an acordeon: increase rmp and its narrower, and vice-versa, lower the rpm and its spaced out. This far i think we agree.
*The other part*
But! it does not mean the driver actually outputs a sinusoid current and applies it to the coils. And this sinusoid is just something we observe, or an abstraction of what we see. As the motor moves from one full position to the next. Because it has to go from one coil state to the other. Incidentally, sinusoid is exactly that, a smooth transition from one state (=1) to its reverse (=-1). So the sinusoid shape is incidental to the fact the motor needs to change the level of coils current in order to move from one point to the next. And it can not change these levels randomly or chaotically, it needs to have some logic, so it needs to change it proportional to the incremental change in position. So this is why it does end up looking like a sinusoid. However what driver outputs is not current, nor sinusoid. And that is quite normal, e.g. to put in something and get totally different output. On the other hand, if we have an input and would get same thing for output, then we would know we are in trouble, because we did nothing or just did too little to the input. Sort of speaking.
Also, this sinusoid is made out by abstracting current levels to some average value hence constant levels, hence being depicted as lines. But are not actually constant if we zoom in enough. These average levels are in turn made by rise and fall edges - anything but constant. And each rise/fall edge means something that is, i believe more or less related to all this discussion(s).
Zoom 1: Looking more carefull at the sinusoid, it appears its made out of straight lines, so its not quite a "pure" sinusoid, but has straight lines. These lines correspond to the level required for a position. And are also an abstraction for their value showing up as constant: they are shown as straight lines even if they are not.
Zoom 2: Zooming on a previous straight line: its not straight anymore. The previous straight line was meant as abstraction of an average or peak level or something like that. But now that line is made of somewhat looking triangle curved shapes. Like a sawtooth wave, or triangle, except the sides are not lines, but curves, because those are rise and fall shapes. This is how actually current looks like. It rises and falls, and keeps doing that all the time. Restless, just goes like crazy. When i think of switching frequency, this is it showing up. Not that sinusoid. That sinusoid is at least one abstraction level above fs.
Zoom 3: Zooming in on just one triangle like that. Left side the current is growing, current can only grow if the voltage is on so it corresponds to on time. It is bent upwards. Lets call this rise edge. The right side part is decreasing, it can only do that if the voltage is off, so it somewhat corresponds to off time. Its also curved and bent downwards. Lets call this fall edge. For both the general function of current by time is Fcurrent(time)= initial*e^-time/tau + final*(1-e^-time/tau), this just how we model generic rise or fall edges. For the rise edge the initial value = 0 idealy, so just last part counts and that final is =V/R. For fall edge should decrease to zero, then only first half counts, where the initial =where the current rise was previously interrupted, aka current setting point in driver. So ok, this is ideal, perhaps simplistic, but thats it. In practice perhaps things get messed up, perhaps fall times will get different because of recirculation or perhaps the rise time doesnt have enough time to reach set peak. Perhaps in certain conditions the average gets to be too low. Perhaps some drivers deal with frequency and peaks in different way when cant fit everyting perfectly. However i think this is still a good explanation for this place here, at least can show some points.
Some points then. That V/R is ohms law, and its right there, its the final value where the current would settle if not getting interrupted every time. It is part of formula that describes exactly the current as function of time, from current=zero up to current=peak where it gets interrupted. This does not depend on that sinusoid, nor of rpm - its just there always. The second part is why we may not care for ohms law, because the driver always interrupts the current when it reaches that peak level. But however saying that we dont care for it, does *n0t* meat it does not exist or that it does not apply. It does apply - we may not care for ohms law, but ohms law doesnt care for us either- so ohms law still applies and again, its even more than just a law, without ohms law we dont have resistance as a concept, we dont have time constants, we dont have anything without it. So i believe the above shows quite how ohms law applies in this context. Also we can say that the switching frequency is unrelated to rpm and unrelated to that sinusoid. And this switching does exist also when the motor stays still. And we could also make crazy leap forward and force the semantics a little. Because positions are discrete not continiuos, that means movements are simply made by motor "standing still" at this postion for very little time, and then "standing still" at next position also briefly, etc. So incredibly, but rotating through discrete positions can also be interpreted like it just it stays still at different places, but just changes the places fast. Again, thats because positions are sequencial, but still discrete and not continuous. So the sinusoid that shows its a consequence, something we see as a result. And again, its not the sinusoid current wave that the driver outputs to be put into the coil. So this sinusoid is not an input, nor shows the switching frequency. Its perhaps an output that agregates itself to that aspect of sinusoid. At least thats how i see it, and i guess everyone has some liberty to make intepretations, but not to the point to say things like "ohms law does not apply" or "we are in ohms law region" as if there is a place outside ohms law - well things like that and also other things i quoted are just simply stretched out too far. I think are just result of bits of knowledge taken from different parts and although they dont fit together they are forced in a stiching that makes no sense anymore. We cant have so many "kodak moments" like that. I generally post rarely and only if i think its worth saying, and this is reason why i posted this. Because this is imo best place to intervene to make a plus change. Oh my defense, i did put some effort into it, even if i dont have methodics. What i have however is a talent to get deflected, so this is also why i post rarely. For example it took some effort to put all this up, imo i do deserve a cookie, but i am pretty sure i aint gonna get one, probably not going to change anything, so its sort of futile (if thats the right word for it).
