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Re: Calculating motor torque required

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Not even manufacturers make torque numbers like that, i think what they give is mostly tested empirically instead. But methodology can differ, some manufacturers will say torque graph is from constant current (like driving the motors with resistors e.g. not our case) or some manufacturers will give a voltage and freq (e.g. which closer resembles chopping which is our case). First method would ofc give a sort of inflated torque number because current never grows or falls - hard to say, but that is sort of a marketing hint perhaps. So one conclusion, those numbers are the kind which have to be interpreted only being aware of the method used to display them. Therefore sometimes should not even compare those numbers between different manufactures which used different methods to give those numbers.

Now about the methodology am not sure i understand what you mean so i will rather start over. A voltage falls across inductor and current grows in inductor, reaching the I(trip) in t(trip) time. When current reaches I(trip), the voltage shuts down then afterwards at some point cycle starts over. One conclusion, t(trip) is not known, its not always a fixed duty cycle because it mostly depends on I(trip) being reached. And I(trip) is a maximum, a "peak", where the current "trips" or gets interrupted. But to get something that relates to power we need an time average current which would be proportional to average flux. Such average is not easy to make because it depends on a ton of things. To start, just because we know the max, does not mean we know the average. Because we dont know how and in how much time it reached that peak. You can find out the t(trip) out with e^(-t/tau) formula applied to current growth, particular for variables of L and R, voltage and I(trip). And this has multiple cases, e.g. when the motor is able to reach I(trip) which is what is should be like, then frequency is to be deducted as a result. When it does not have time to reach I(trip) like in the case of 12v motor with 30ohm coil and setting I(trip) to 1A which obviously cannot be ever reached, that will probably fall back to driver freq, and have to fall back to max ohms law which is 12/30=0.4a, but this is more of a corner case. Sort of speaking the current can grow enough to be chopped, or may not grow fast enough (or may not grow at all) to reach the chopping point, so it may not even get chopped. So we have to break down cases and solve this part. Anyway, assuming the rise part is done (current growth, which corresponds to voltage on), that is only half of story, because the current cannot grow all the time, it needs time to decrease, to fall down, e.g. to "decay". And this part is bit more opaque, because of synchronous rectification or external diodes or etc. And the decay mode (fast,slow,mixed) and offtime approach depends on driver, and perhaps has settings for it or not, but even if it has a setting it would be an analogue one and hence bit harder to model. The offtime also differ, there are drivers with fixed offtime (~allegro), other with variable offtime, and finally some with adaptive and "random" offtime (see trinamic datasheets). And in cases like digital stepper drivers and some which employ dsp and stuff like that, schematics are not open, programming neither, so largely datasheets are opaque with very few clues for fall time part. So about the second part of the current behaviour we can generally say it should be lower than the rise time, and sometimes we know and set the offtime, but otherwise i would say this part is largely unknown. Just in the reverse from rise time case, in fall time even in the peculiar case where we know the exact offtime, does not mean we know the average either: again, it could have current only in its first part, or it could have current till the end even have some after ending. So we dont know how this contribute to average. Bottom line, we can model the rise time part but only for specific terms, like specific motor, voltage, driver settings of I(peak) and so on. The fall part depends on first part and also more on driver design choice for this. In other words, from the above, we do not really have a good clue about an universal way to average current, its not that easy, too many variables have to be set in place, too many different driver settings and different approaches of the fall time part. My opinion ofc.

In the time being, easy fix to cover all the unknowns above, is the pot on driver, which is specifically meant to help with all this: set the current to a setting that works for the hardware, and be efficient to this, e.g. avoid setting too big currents which would not be otherwise needed, because extra current would just grow the consumption without any additional benefit (imo). This works as decreasing the current by half produces a power reduction to 1/4. Just like an observation the pot works on the peak not the average, but that is good enough anyway and that is the better control point.

Now what i find interesting for the rise time part, if you compute that for 3-4 reprap motors and 12v supply, you would get a rise time for say 0.7A setting, and would be surprised that it assumes a frequency lower than expectation (expectation would be lets say higher than 30kHz). I think that is something interesting to see and think about.

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