Acceleration as a function of speed
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@vp:
…....................The change in acceleration does not matter at all in real life.
Try it next time you are driving your car. Rather than accelerating evenly, pump the accelerator up and down. Or conversely slow down by pumping the brake peddle instead of applying gentle even pressure. The jerk you will encounter is the result of altering the rate of change of acceleration (and it does matter in real life as well as in 3d printing).
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@fma:
That's not true, because we use constant current stepper drivers. Torque is proportional to current, so torque is maintained as RPM increases up to the point at which the back emf due to inductance + back emf due to rotation + voltage drop due to resistance exceed the driver supply voltage, and the driver can no longer supply enough voltage to achieve the desired peak current.
It would be true using constant-voltage drivers though.
Are you sure of that? I never saw a torque vs speed curve with a flat part, then a falling part; they always start to fall as soon as rpm>0 (more or less quickly, depending on the supply voltage, for the rasons you mentioned). And I never saw constant voltage drivers (except diy ones)…
The curve you are talking about is for the case of constant driving voltage (nominal voltage applied to the DC motor). I think David is right as duet's drivers are constant current ones.
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That's right, torque vs. speed curves are only relevant to constant voltage operation. If you wanted to publish a torque vs. speed curve for constant current operation, you would have to specify the actual RMS or peak used and the driver supply voltage, because both of those affect the point at which the torque starts to drop off.
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At work, we use Nema 34 Slo-Syn steppers, and curves given by the manufacturer (sorry, I only have them on paper, and as I'm on holidays, I can't scan them) do specify driver supply voltage; I guess they give them for nominal current of the motor. And they usually show 2 or 3 curves, for different supply voltages (24V, 48V and 70V, if I remember correctly).
As I have these documentations for more than 20 years, and as we always used constant current drivers, I assumed constant voltage drivers were abandoned long ago…
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Dear all,
i know very well what constant current vs constant voltage means, i am a CNC guy and in the very old past there was only constant voltage with all limitations.
Please do me a favour and just google –> https://www.google.at/search?q=stepper+torque+curve and check the pictures. I don´t understand why that is a secret here ?!?Because of back EMF as mentioned already several times the torque starts to drop at about 0-10 rps (revs per second, depending on supply voltage). The constant current ONLY applies in the low speed region, because afterwards (at higher speeds) the coil limits the current. The reason to use higher supply voltage is because of this effect. At 12V it starts at nearby 0 rps, at 24V before 5 and with high voltage (48 V and above) the constant current torque maybe gets to 10 rps.
5 rps means with a 16 GT2 pulley 5162 = 160 mm/s !!!!! I don´t know why a 3D printer should not operate in higher speed regions? At 12 V torque drops from "zero speed".
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please do me a favor and e.g. check the following link: http://www.electrocraft.com/products/stepper/TPP23/ and go to the tab "speed/torque curves", there is nothing more to say
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Well, so, there is a constant torque phase, but it is very small; at work, we operate far beyond that zone.
But as you showed, for a 3D printer, it is possible to operate at constant torque, using at least a 24V supply voltage…
Are Allegro or Ti chip constant current drivers? Or are they constant voltage ones?
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The speed/torque curves that vp linked to are indeed specified for different supply voltages and a particular current, so they are applicable to constant current drivers.
I don't think vp has said which particular motor he has chosen, so I can't comment on his calculation that suggests he is limited to 160mm/sec before there is a significant torque reduction, or whether he has chosen the most appropriate motor from the range. But here are some points to note:
1. In 3D printers we normally run the motors well below their maximum current, because at maximum current the motors get very hot. At reduced current, the back emf due to inductance is lower, so the (reduced) torque is maintained to higher speeds. For example, if you halve the current, then the torque at low speeds will be half what is shown on the torque/speed curves and will be almost flat until it intercepts the torque/speed curve shown for the same motor and same driver voltage at full current.
2. Because we want precise motion during printing, we use 1/16 or greater microstepping, and to get position accuracy this means that the motors need to have far more holding torque than is needed to produce the acceleration demanded, so that we can maintain a position accuracy of around one 1/16 microstep. But high-speed travel moves don't need this accuracy during the high speed part of the motion, it's only the end of the move that needs to be accurate. So quite a large loss of torque is acceptable during the middle part of a travel move. If you know the mass of the print head or bed or whatever the motor is moving, you can work out the torque needed to produce the desired acceleration, and you just need to make sure the motor can provide this torque with a sufficient safety margin e.g. 2x.
3. If you are building a CNC machine and need motors with seriously high torque, you should use external drivers.
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Thanks for the explanations!
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I did choose WANTAI 42BYGHW811, in my setup, they should be able to achieve nearly 1g close to about 1500mm/s, without losing 1/16 micro step with a light direct driven extruder/hot end. I don´t have a "problem" at 160mm/s, this is just an example to show that if the torque drop starts with 12 V at "0" rps, this problem is existing in the normal operating range of 3D printer, just check the curves.
1. In 3D printers we normally run the motors well below their maximum current, because at maximum current the motors get very hot. At reduced current, the back emf due to inductance is lower, so the (reduced) torque is maintained to higher speeds. For example, if you halve the current, then the torque at low speeds will be half what is shown on the torque/speed curves and will be almost flat until it intercepts the torque/speed curve shown for the same motor and same driver voltage at full current.
This is not special for 3d printing, it is a good rule of thumb for every stepper application to use at max about 80 % of the specified amps. The steppers itself are normally rated to > 100°C surface temperature, I operate my steppers at about 80 % of the rated current and they get at max about 50 °C (also NEMA32s), which is at least for me no problem. Because P = IIR it is for sure sensitive to the chosen current - but it is also no trick to cool them and in the long term i will use mine at maybe > 100 % current.
Who operates his steppers at half of the design current? This 50 % comparison is completely misleading and even at 50 % and 12 V there is also before 5rps a torque drop. If somebody operates at 50 % i would suggest him to go for different (smaller and faster) steppers. But do these people buy a premium product like the Duet Wifi ?
2. Because we want precise motion during printing, we use 1/16 or greater microstepping, and to get position accuracy this means that the motors need to have far more holding torque than is needed to produce the acceleration demanded, so that we can maintain a position accuracy of around one 1/16 microstep. But high-speed travel moves don't need this accuracy during the high speed part of the motion, it's only the end of the move that needs to be accurate. So quite a large loss of torque is acceptable during the middle part of a travel move. If you know the mass of the print head or bed or whatever the motor is moving, you can work out the torque needed to produce the desired acceleration, and you just need to make sure the motor can provide this torque with a sufficient safety margin e.g. 2x.
Yes, that is one reason for the firmware change request, now we get back on track.
But i would say we don´t use 16 microsteps for finer resolution (with a 16 T GT2 pulley 16th means in theory 0.01 mm), because this fine steps never happen with this accuracy (e.g. stepper nonlinearities and all other mechanical errors of a 3D printer are much bigger) we just do it because it runs smoother and less noisy - and because it doesn´t cost anything. Maybe it can reduce some fancy patterns on deltas, but there only relative accuracy is needed. On xyz printers 16th stepping doesn´t improve accuracy at all.
I have to show more clearly what this request is for because it still seems to be not clear:
1. Many speed as well quality problems are extrusion related. Often people claim their E3D v6 cannot go above e.g. 50 mm/s because then under extrusion and so on is happening. They say the extrusion capacity is not enough - which is wrong. The problem is, that the hot end print speed varies and by that the extrusion rate. Unfortunately, molten plastics have a viscoelastic material law which brings the time factor in play. So any change in extrusion rate/speed is going to make problems - but this is not the root cause. The root cause is the varying printing speed. The root cause for the varying printing speed is a lack of useable acceleration which is limited by the mass/stiffness of the system and the stepper torque which is a function of speed .
Especially at lower layer heights and small nozzles or with e.g. a volcano, the extrusion capacity is enough for speeds far above 100 mm/s. But as soon as the speed drops the extrusion problems will occur. On youtube are enough videos showing damn fast prints - with a miserable print quality. I want fast prints with good quality - this is not possible without the maximum acceleration.
2. Many problems are retraction related. Why do we need retraction at all ? Because too much plastic would ooze out. The smartest way I know to overcome this problem is to give the oozing process no time. Half the time and you half the amount which could ooze out. If you print flexible material that is the only way to go. If you don´t need to retract (or less), problems of 1. are also reduced. Solve the problem by just increasing the speed of travel moves.
3. Think the other way round. With a Duet Wifi capable of acceleration as a function of speed, one could use smaller (faster) and cheaper steppers. This could mean one uses NEMA14 for normal printers or NEMA 17 instead of NEMA23 for big size printers.
4. printing time
Many prints need excessive amounts of travel moves. Normally most travel moves are short distance moves. Using a histogram to show the distribution of travel move length, it would be very heavy on the left side (much more short than long moves). What does short distance mean ? With 2g it takes 25 mm to reach 1000 mm/s, with 5g 10 mm. The problem is, that long travel moves need more time and increasing max travel speed would reduce the time significant. To increase max travel speed, i would have to reduce the max torque - also in the low speed region were most of the moves happen. Increasing max travel speed ends up to give no benefit, if the max torque on the low side has to be decreased.A higher acceleration in the low-speed region (printing) means a higher average printing speed and again a reduction of printing time.
5. Jerk. Jerk was introduces to get away from blobs on every corner (bleeding edges) and to decrease printing time. Unfortunately jerk is the most brutal way and is mostly based on backlash and low stiffness. In the old days both was existing at much higher levels than nowadays. Using too much jerk shows ringing/resonance artifacts in the print (as well as too high accelerations). Using 2 g it takes 0.0xyz mm to get to e.g. 20 mm/s. But it is much more gentle and gives by that less artifacts - or at same amount of artifacts much more printing speed. Jerk could be reduced to nearby 0 and substituted by "soft" acceleration. Doing so would be like a poor mans s-curve acceleration in the very low speed region.
6. Future developments like s-curve acceleration/moves. Although some people thinks it is too CPU intensive, for me it is clear that in future we will use something like s-curve like moves. This gives much more possible printing speed at same artifact level. But using s-curve like moves reduces at the same max acceleration the average acceleration - so in total the benefit is much smaller as it cold be. To overcome this problem, acceleration has to be really maximized - according speed.
Finally:
I don´t care at all, what people are doing now, i question for what is possible, i want to push the limits - and premium products like the Duet are bought because the "normal" stuff is not as good as it could be. It is not true that printing speed is limited by extrusion rate to e.g. 100 mm/s. It is limited by too much varying printing speed, caused by too low acceleration settings.
Why should we bottleneck our printers? Why should we waste resources?
I don´t care if I am able to use 5g in the low-speed region (<= 1000 mm/s) already now if I can get 8g…. or travel with 2000 mm/s instead of 1000 mm/s.BTW: On travel moves, the deflection of the printer parts doesn´t matter (nearby). When printing they become very significant at higher accelerations (e.g. > 1g), and more stiffness (a stiffer system means more mass) doesn´t help more. So finally the firmware will also have to address this problem because there is a mechanical material limit where engineering cannot increase the stiffness vs weight ratio anymore (see 6.).
[Edit: i added 5 and 6]
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@vp:
On youtube are enough videos showing damn fast prints - with a miserable print quality. I want fast prints with good quality - this is not possible without the maximum acceleration.
Maybe you should take a look at this little video I did. It's to evaluate the effect of using pressure but it demonstrates high speed printing with good quality. https://www.youtube.com/watch?v=lnYYNfVoxmQ. Speeds up to 250mm/sec. Nice smooth acceleration with no jerk cause by any step change in the acceleration setting. This is all with a moving mass of around 4kgs, std Nema 17s.
Have you actually done any calculations on the time and distance it takes to travel X amount at Y acceleration? I think if you do you'll find that what you are requesting is simply a waste of time.
Edit…..........Oh, never mind.
2nd Edit. Here are some calcs pertinent to the video I linked to. Acceleration was set to 1200mm/sec^2. This was derived from the available torque of the motor (assuming all sorts of worse case scenarios) and the mass to be moved. The speed reached was 250 mm/sec. So the time to reach that speed is t=(Vf-Vi)/a = 0.208 seconds. The distance travelled during that acceleration phase was (1/2at^2) = 26.042 mm. Let's assume we used double the acceleration which is theoretically possible now that I am using two motors. So acceleration becomes 2400mm/sec^2. At that rate, the time to reach 250mm/sec is 0.104 seconds and the distance travelled during the acceleration phase is 13.021 mm. So your desire to use increased acceleration at low speeds will have an almost negligible effect on the overall print time (but if you change the acceleration rate mid move, it will lead to jerk and poor quality prints).
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Thanks for your comments.
please correct me if i am wrong. Are most (and there are many) postings regarding pressure advance problems made by you - i would say yes? I don´t need something which does maybe work under certain circumstances. Pressure advance doesn´t solve the root cause, it tries to heal the wounds. It will never work perfectly, it just tries to improve the situation. Solve the root cause and you don´t have these problems. If somebody drills a hole in his knee, he will go to the doctor. My approach is not to drill in my knee.
Have you actually done any calculations on the time and distance it takes to travel X amount at Y acceleration? I think if you do you'll find that what you are requesting is simply a waste of time.
Yes for sure, but i don´t talk about max 250 mm/s and 2500 mm/sec^2, take both by a factor of 10 ( i know at 2500 mm/s it will be hard to produce the pulses in time, but to show you the direction). If you are able to use high accelerations you can increase max travel (and with a stiff system also printing) speed a lot, this is missing in your calculation. Besides this, decreased printing time is not the only benefit.
Better than calculating some straight lines is to simulate e.g. a 3D benchy in total and compare it (–> http://www.gcodeanalyser.com/).
I don´t understand this way of thinking. I guess when jerk was introduced, some people also said - why do we need this **** - it is working fine the way it is…. it will just ruin the print.
It is a software change, it doesn´t cost any money. See how much other gimmicks are available. If it gives only 20 % improvement for some users, why not take +20%. Technical development was always going step by step. With the above kind of thinking we would still live in caves. As for many other features it is easy to implement an on/off switch - like pressure advance. I don´t use pressure advance, so the switch is off (by that i don´t say it is bad in general).
but if you change the acceleration rate mid move, it will lead to jerk and poor quality prints.
1. It depends on how you change it.
2. You seem to have no problems with jerk (because you use it) - but have a problem with changing acceleration - how does this come together ? Crashing a car is ok, but gentle touching it not ?
3. This is exactly what is happening already now at every move. 1 phase accelerate, 2 phase constant speed, 3. phase decelerate. Most moves never reach the constant speed phase, so skip step 2 and what comes out is the worst case, the acceleration changes from + to - instantly. Does this work or not ? I would say yes - because it happens all the time it is proofed that it seems to be not a problem. For sure stepwise changing acceleration means a stepwise change of forces. With a mass > 0 and a stiffness < infinity it leads to unwanted changes of the position - and it still works in real life. That is the reason why i have written more above, that this "doesn´t matter at all" - if at the same time, jerk is accepted and no problem.But again, thanks for your valuable comments. You have a very unique printer and i guess you have found your way, but i think there is also another way.
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The vast majority of moves do have a constant speed phase. The ones that don't are short travel moves, the first few in a sequence of extremely short printing moves in a curve where the head accelerates from rest after a travel move, and similarly the last few moves at the end of a curve that is followed by a travel move.
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I am not sure if i understand what you want to say.
Maybe i should have written instead of "Most moves never reach the constant speed phase" " Many….". This was just to show that a change in acceleration won´t harm more than jerk, because the acceleration changes already now at least 1 or 2 times per move, that is nothing new.It doesn´t change anything about "acceleration as a function of speed". In short terms: with a stiff system the print quality is improved and the travel time is reduced. So in total you gain more quality at the same printing time.
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I agree that changing acceleration in the middle of a move is unlikely to cause any particular problems, because as you say the acceleration is changing frequently anyway.
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I agree that changing acceleration in the middle of a move is unlikely to cause any particular problems, because as you say the acceleration is changing frequently anyway.
Seriously? Velocity changes during a move but the last time I looked, I have only one acceleration value per axis and extruder. My understanding is that for any given given move, the acceleration is derived from whichever axis or extruder has the lowest value and that the same acceleration rate will be applied until the maximum speed is reached or it is time to decelerate (but at the same rate). I say again that the first derivative of position with respect to time is velocity, the second derivate (the rate of change of velocity) is acceleration and the third derivative (the rate of change of the the rate of change of velocity) is referred to as jerk because it results in a near instantaneous change of velocity.
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@vp:
Thanks for your comments.
please correct me if i am wrong. Are most (and there are many) postings regarding pressure advance problems made by you - i would say yes? I don´t need something which does maybe work under certain circumstances. Pressure advance doesn´t solve the root cause, it tries to heal the wounds. It will never work perfectly, it just tries to improve the situation. Solve the root cause and you don´t have these problems. If somebody drills a hole in his knee, he will go to the doctor. My approach is not to drill in my knee.
OK then. You propose that you can have higher accelerations at low speeds. This means that you will also be accelerating the extruder and thus the filament entering the melt chamber at higher speed. This will lead to a build up of pressure in the hot end which is known phenomenon under "normal" circumstances (but which would be exacerbated using higher acceleration), and one that pressure advance compensation aims to eliminate. The only way to reduce pressure build up is to print more slowly yet you seem to be advocating that you can print faster by using high acceleration at low speed. How do you reconcile those two differences.
Have you actually done any calculations on the time and distance it takes to travel X amount at Y acceleration? I think if you do you'll find that what you are requesting is simply a waste of time.
Yes for sure, but i don´t talk about max 250 mm/s and 2500 mm/sec^2, take both by a factor of 10 ( i know at 2500 mm/s it will be hard to produce the pulses in time, but to show you the direction). If you are able to use high accelerations you can increase max travel (and with a stiff system also printing) speed a lot, this is missing in your calculation. Besides this, decreased printing time is not the only benefit.
Better than calculating some straight lines is to simulate e.g. a 3D benchy in total and compare it (–> http://www.gcodeanalyser.com/).
Ah OK. Lets look a this. So 250 mm/sec print speed x 10 would be 2,500 mm/sec and acceleration of 2500 mm/sec x 10 would be 25,000 mm/sec. So the time to reach 2500 mm/sec would be 0.1 seconds and in that time, the print head will move 125mm. But what if our 3D Benchy doesn't have any moves that are 125mm. Let's say it has a move of 5mm. So, at 25000 mm/sec^2 after 5mm it will only reach 500mm/sec speed and take 0.02 seconds to accomplish. So even at that massively high acceleration, you'll only get a fraction of the speed. Oh and by the way, assuming you could ever build a printer rigid enough, doing 5mm moves at 0.02 seconds would mean that the print head would be moving back and forth at 50 times per second - don't view it under fluorescent lights because it would appear statonary)
I don´t understand this way of thinking. I guess when jerk was introduced, some people also said - why do we need this **** - it is working fine the way it is…. it will just ruin the print.
It is a software change, it doesn´t cost any money. See how much other gimmicks are available. If it gives only 20 % improvement for some users, why not take +20%. Technical development was always going step by step. With the above kind of thinking we would still live in caves. As for many other features it is easy to implement an on/off switch - like pressure advance. I don´t use pressure advance, so the switch is off (by that i don´t say it is bad in general).
but if you change the acceleration rate mid move, it will lead to jerk and poor quality prints.
1. It depends on how you change it.
No it doesn't. I say yet again that the first derivative of position with respect to time is velocity, the second (the rate of change of velocity) is acceleration, and the third (the rate of change of the rate of change) is jerk, so named because implementing it results in a near instantaneous change of velocity. You cannot change the rate of acceleration without introducing jerky motion.2. You seem to have no problems with jerk (because you use it) - but have a problem with changing acceleration - how does this come together ? Crashing a car is ok, but gentle touching it not ?
Simple. Jerk as used by 3d printers is an instantaneous speed change when there is a change of direction and is not the same as Jerk in the physics sense caused by a change in acceleration. Jerk in 3D printers is to prevent the print head having to come to a complete stop at the end of a move when a change of direction for both axes is present (i,e greater than 90 degrees). It is NOT a change in acceleration and is NEVER applied to moves which start or end at zero speed in any axis. Using your car analogy, it enables me to turn a corner without coming to a complete stop. In 3D printer terms, driving up to a corner would be one move, going around the corner would be a series of short segmented moves, and driving away from the corner would be another move. Without the instantaneous speed change threshold, I'd have to stop at the corner, do a series of short start stop moves, then drive away. It's nothing like crashing car whilst altering the rate of change of acceleration (Jerk in the physics sense) is exactly like a car crash!
3. This is exactly what is happening already now at every move. 1 phase accelerate, 2 phase constant speed, 3. phase decelerate. Most moves never reach the constant speed phase, so skip step 2 and what comes out is the worst case, the acceleration changes from + to - instantly. Does this work or not ? I would say yes - because it happens all the time it is proofed that it seems to be not a problem. For sure stepwise changing acceleration means a stepwise change of forces. With a mass > 0 and a stiffness < infinity it leads to unwanted changes of the position - and it still works in real life. That is the reason why i have written more above, that this "doesn´t matter at all" - if at the same time, jerk is accepted and no problem.But the rate of change of velocity is the same and constant regardless of whether it is increasing or decreasing. So it's the "direction" of the rate of change which alters between acceleration and deceleration.
But again, thanks for your valuable comments. You have a very unique printer and i guess you have found your way, but i think there is also another way.
This biggest thing in all of this is how do you propose to get the filament to follow the behaviour of the print head? Given that it starts as a semi rigid filament, which then has to be melted and turned into a viscous liquid, then forced through a tiny hole. How are you going to melt is fast enough for the speeds you propose and how are you going to accelerate and decelerate it at the speed you propose?
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I agree that changing acceleration in the middle of a move is unlikely to cause any particular problems, because as you say the acceleration is changing frequently anyway.
Seriously? Velocity changes during a move but the last time I looked, I have only one acceleration value per axis and extruder. My understanding is that for any given given move, the acceleration is derived from whichever axis or extruder has the lowest value and that the same acceleration rate will be applied until the maximum speed is reached or it is time to decelerate (but at the same rate). I say again that the first derivative of position with respect to time is velocity, the second derivate (the rate of change of velocity) is acceleration and the third derivative (the rate of change of the the rate of change of velocity) is referred to as jerk because it results in a near instantaneous change of velocity.
What I mean is that the acceleration within some moves already changes abruptly from positive maximum configured, to zero, to negative maximum configured - for example when doing rectilinear infill. I doubt whether making the transition from maximum allowed acceleration to zero via an intermediate acceleration (and vice versa) would make anything worse.
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I can't seem to get my point across so we'll have to agree to disagree then.
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I can't seem to get my point across so we'll have to agree to disagree then.
I should also have said that I only see this feature being useful (if at all) during fast travel moves. So the extruder behaviour to the extra acceleration change would not matter, because it would only be used in non-extruding moves.
