S-Curve/ sinusoidal , Jerk +acceleration

dc42

That picture doesn't illustrate S-curve acceleration.

stewwy

Is this what is trying to be achieved?

alt text

If so, do we also need to think about the timing ? As it effectively moves the area under graph in a positive way which is going to lead to an overrun. or am I over-thinking this?

Apologies if this has already been discussed, I didn't notice it on a quick re-read of the thread.

dc42

The problem with changing the profile like that is that it makes the total acceleration and deceleration times longer, which slows the print down. You could keep the trapezoidal profile but reduce acceleration and deceleration to lengthen the acceleration and deceleration phases instead, and that too would typically reduce ringing.

To get an accurate comparison, you need to use a higher peak acceleration in the S-curve profile than you do in the trapezoidal profile, so that the total acceleration time is the the same in both cases. Similarly for deceleration.

markdashabout

Did you say higher pint speeds?

stewwy

@dc42 makes sense, heading towards the classic bell shaped curve, if you had unlimited speed and limited acceleration that is where you would want to be anyway.

JoergS5

just for info: I saw the TMC5161 uses S-Shaped motion. I'll test whether it reduces vibrations at the extruder.

Neonode

I am using printer with ball screws and I can say that for me S-curve is really important. While belt motion got some elasticity ball screw got 0. This is really cool as I have no ringing at all and really smooth print but I need to live with very low Jerk and acceleration settings like 200 Jerk and 300 acceleration. If I got faster the ball screws start producing noise like hammering during direction change. Current jerk implementation is just stupid. It is okay to change the speed with jerk but it is not okay to change the direction with half of the jerk speed. So I am really waiting for S-curve to come as it really will make my system to perform really well and to be silent.

Catalin_RO

@neonode What size of ball screws are you using (length, diameter and pitch) and what size of stepper (NEMA* and the torque)?

Edgars Batna

@dc42 said in S-Curve/ sinusoidal , Jerk +acceleration:

Unfortunately, in 3D printing we have a much worse problem, which is that curves are approximated by straight lines. This unfortunately forces us into making the first derivative of position discontinuous, to avoid dropping the speed to zero at every boundary between line segments in a curve. As long as we are forced to do this, there is very little point in worrying about the discontinuity of the second derivative.

If we ever reach the situation where the model files we slice represent curves properly, and the slicers that generate gcode from them generate Bezier curves, cubic splines or some other representation of curves, then implementing smooth changes in acceleration may be worth looking into.

Yes, but that would also mean whole new generation of modelling tools, gcode, slicers - generally the whole toolset. Can't we have a feature which approximates segmented movement using curves? Supporting curves way down the pipeline in the firmware is a thing that can be reused once the slicers are up to par.

The thing about curves is that nothing is a 100% curve. The 3d models are meshes or a mix of corners and curves that would otherwise need to be approximated somewhere, be it in firmware (if hardware permits) or PC application software as a pre-processing step.

Urban

@neonode I agree!! The line segment jumps can be handled with filtering in the servo driver even if that is not a perfect solution.

gnydick

I agree with trying out s-curve. My printer is turning out great, and I want higher speed printing.

These ripples are more visible than they are palpable, but the corner ringing is detectable to the touch.

https://dyzedesign.com/2016/10/printing-300-mm-s-part-1-basics-hardware/

https://www.controleng.ca/servosoft/SSHelp1033/source/MotionProfile.htm

I'm making another post with the photo with a different topic, keep an eye out

dc42

Have you looked at the dynamic acceleration control feature in RRF 2.02RC6? It may help you to control the ringing. See https://duet3d.dozuki.com/Wiki/Gcode?revisionid=HEAD#Section_M593_Configure_Dynamic_Acceleration_Adjustment.

gnydick

@dc42 worth a try. Still would like s-curve. I'm not too worried about being slightly slower, my printer is printing cleanly at 150mm/sec, probably could go faster if I had a more powerful system of drivers and motors.

Twigz

Good morning

I've run into a problem that may or may not need a s curve.

I'm driving the x and y gantry with a brushless/ encoder + lead screw setup and am able to get speeds up to 1mtr/s.

The whole hotend assembly is rather hefty at 0.5 kg. At quick direction changes (corners of Infill at 45 degrees in a cube) it shakes uncomfortably much and I have to reduce to 500mm/s^2. At this acceleration it would take 1.5 seconds and approximately 500mm to get to its maximum speed.

I did some tests and when printing a corner in a radius of 75mm an acceleration of 10.000mm/S^2 even seems reasonable
My thought would be that the slower ramping up is what is causing this improvement. (as the direction turns from x to y the y gantry has to move exponentially faster)

At 10.000mm/s^2 it only takes 0.07 second and 25mm to get to its maximum.
If we interpolate between the two that gives 0.75 seconds and 262mm to obtain maximum speed. (in reality this would only be 25% quicker) this could decrease the overall print time on long complicated prints by quite a lot.

I think printers with either a high capability of speed or a heavy hotend assembly will greatly benefit from a ramping acceleration/deceleration.

I don't know if this is easier to setup than a s curve but perhaps it would be an idea to multiply the acceleration by time and by a factor in time to reach the max acceleration.
In this case we could ramp up to 10.000mm/s^2 in 1 second and it would look like this:

Acceleration = (acceleration*((t/factor) ^2))

After 0.1 seconds:
Acceleration= (10.000*((0.1/1) ^2)=100mm/s^2

After 0.5 seconds:
Acceleration=(10.000*((0.5/1) ^2)=2500mm/s^2

After 0.75 seconds:
Acceleration=(10.000*((0.75/1) ^2)=5625mm/s^2

After 1.0 seconds:
Acceleration=(10.000*((1.0/1) ^2)=10.000mm/s^2

Ramping up to 5000mm/s2 in 3 seconds:

After 1 seconds:
Acceleration= (5000*((1/3) ^2)=555mm/s^2

After 2 seconds:
Acceleration=(5000*((2/3) ^2)=2222mm/s^2

After 2.5 seconds:
Acceleration =(5000*((2.5/3)^2)=3472mm/s^2

After 3 seconds:
Acceleration=(5000*((3/3) ^2)=5000mm/s^2

Applying the same formula to the extruder would also ramp the extruder to not create under or over extrution during the ramping up.

I've never heard of issues caused by the jerk between acceleration and max speed so this may or may not be a problem.

Keeping acceleration and deceleration seperate would lead to even more tuneability as acceleration tends to be able to be a little bit higher.

Jeff

Twigz

After some more calculations and thinking i figured the reverse might be beneficial as a replacement for jerk. To stop extreme shaking and ringing the best would be to get to a full stop before changing direction.
In this case reversing the above formula to jerk=jerk*(SQRT(T/Factor)) would start from a stop with a high acceleration where the acceleration increases exponentionally less.

You could then finetune the jerk for sharp corners and direction changes after which you can tune the acceleration to the max your printer is capable off.

I made some Ghraps to show what i mean in the hopes of it making things more clear in my explanation.

EDIT: When the jerk speed has been reached it would continue using acceleration instead.

jeff

dc42

What I am looking to do at the same time as implementing S-curve acceleration is to replace jerk by junction deviation, but for the deviation to be planned instead of mythical. This will make it possible to eliminate attempts to change the speed of the motor instantaneously. In fact i see little point in implementing S-curve acceleration without tackling jerk (i.e. commands to change motor speed instantaneously) at the same time, because instantaneous speed change is much worse than instantaneous acceleration change.

When implementing S-curve acceleration, you can either keep the peak acceleration constant (which lengthens the acceleration time, and hence printing time), or you can increase the peak acceleration so as to keep the acceleration time constant. Lengthening the acceleration term in itself reduces ringing in most cases. So where S-curve acceleration has been reported to improve print quality, it may actually be the increased acceleration time that is making the difference. Also, the Bezier curve implementation of S-curve acceleration in Marlin has the side effect of reducing average acceleration when the acceleration takes place over several short segments, for example when printing curves.

I do expect S-curve acceleration to improve the sound of the printer when cornering; although I think there are probably easier ways to do that.

Edgars Batna

@dc42 said in S-Curve/ sinusoidal , Jerk +acceleration:

Have you looked at the dynamic acceleration control feature in RRF 2.02RC6? It may help you to control the ringing. See https://duet3d.dozuki.com/Wiki/Gcode?revisionid=HEAD#Section_M593_Configure_Dynamic_Acceleration_Adjustment.

I'm using it and I can see an improvement in ringing on some corners. Overall ringing is less, but it is predictably now more inconsistent over multiple layers. Also, it depends on a well calibrated single ringing frequency, but here I've got X, Y ringing to actually take into account. On CoreXY ringing is different for both axes, plus things like tool changing means we need to sort of recalibrate each time. I assume E and Z are not directly affected, but I think they do need to have their own ringing controls.

Sphyloid

@dc42 I know this is an old topic but your post here is 100% wrong, it is not entirely about ringing. It is instead about how stepper motors work. As you get higher RPM the motor loses torque exponentially. With a proper S curve and a rigid machine it may be possible to cut print time in half without losing steps or quality as you can use every bit of available torque at any given RPM with no fear of step-loss. Gone is the need for max speeds and conservative accelerations as you are only limited by the motor. Instead of the motor at the highest RPM in your desired speed range. There is no fear of going "too fast", setting a max speed is not necessary beyond a software limitation to catch errors in calculation.

Personally I am searching for a feature that dynamically allows the user to define their own curve biased on the torque curve of the steppers. Marlin has already done this, it is not impossible. Though I do not believe they allow this to be user customizable.

Not sure how this slipped past you guys.

deckingman

@Sphyloid Whilst I accept what you say may be true as a general statement, it only applies to situations where motor torque is a limiting factor, and with the light weight tool heads that 3D printers use, achieving the desired torque is easily done by selecting an appropriate motor. For 3D printers the overal print speed is limited by how fast you can melt and extrude filament, not by how fast you can move the hot end in X or Y directions. So I have to disagree that any form of fancy acceleration control is going to reduce print time at all, let alone cut it in half.

Whilst I accept that there may be some benefit in using S curve acceleration with CNC tool heads that have mechanical cutters, I fail to see how one could coax the filament being forced through a tiny hole to faithfully follow an S curve acceleration profile in the same way that the hot end carriage might. Smooth linear acceleration of molten filament is difficult enough to achieve, due to the severe damping effects and time lags involved with melting filament and forcing that viscous fluid through a tiny hole.

Sphyloid

Did the math out and found something very intriguing.

Say your moving mass is 200 grams. With the pitch diameter we can find the force exerted by the motor on the print head, lets say a GT2 12 groove has a pitch diameter of 7.65mm. With a circumference of ~24mm you would get 0.06mm steps out of a 0.9* stepper. Also lets get some RPM numbers at 20mm/s it would be turning 50rpm, 60mm/s would be 150rpm, and 150mm/s 375rpm.

Now that we have our numbers, lets use MS17HA6P4150 running at 24V 1.5A which would make a minimum of 0.385nm from 0-20mm/s, 0.3105nm from 20-60mm/s, 0.16nm from 60-150mm/s. Bear in mind that is only if the driver is outputting 24V 1.5A, at lower supplied voltages the drop is far more aggressive. 12v for example the 60mm/s number being ~30% lower and the 150mm/s number being ~50% lower.

In this config the motor would be able to exert ~100N at 20mm/s, ~80N at 60mm/s, ~40N at 150mm/s. From F=MA we know that the maximum acceleration at 20mm/s is ~500m/s^2, 60mm/s is ~500m/s^2, 150mm/s is 200m/s^2. Then why are numbers for real 3D printers so low? There are several possibilities

-The bottleneck is the extruder
-The weight is higher in real life
-The achievable torque is much lower

We already know that in i3 style printers using current firmware all three are true. Having movements made of many straight lines instead of curves makes mathematically calculating accelerations very difficult. The stress we are putting on the motors is not immediately obvious. Also lets face it, 3D printers supply their motors with much lower voltages and use far weaker motors. Though I am not familiar with the output voltages of the duet 2, I doubt you can output 12V let alone 24V from that driver chip. Perhaps what is left on the table is more on the hardware side than the software side. With this information I would change my argument to an increase of driver output voltage is better than anything possible on the software side, which is what I believe you have done with duet 3. At which point the increase in vibrations/ringing from an extruder that can keep up may have a greater impact. Increasing printer quality is more complicated than I may have given it credit. Similar to how people think having steel bones would make them much stronger when pound per pound having bigger bones would be stronger.

Perhaps using step files in place of STL would yield better quality and less stress on the motors but would it be an appreciable difference? My opinion has shifted. I now think a duet and an e3d hemera are the best upgrades you can make to any 3d printer. Except on the machine I am engineering. Net moving mass is about 5kg, Hbot linear motion, internal volume is 0.36 cubic meters up to 200C heated enclosure, 220C heated bed, 500C hotend. At this scale, there is appreciable acceleration left on the table. The motion system is very interesting. While the way I designed it for my application is quite overkill, I believe it will yield the cheapest printers for a given stiffness. The designs will be released early 2021 and you will see me at 3d printing events later this year.