3D Printer Mechanics: Belt Tension and Resonance
ฝัง
- เผยแพร่เมื่อ 28 พ.ค. 2024
- Today I'm going to review some data I gathered from an accelerometer on my CoreXY 3d printer. This was made possible by a resonance tuning test created by Dmitri:
github.com/KevinOConnor/klipp...
Here's the accelerometer I used:
amzn.to/3k6pbz1
I hope you enjoy! - วิทยาศาสตร์และเทคโนโลยี
![Klipper Resonance Compensation Overview - [input_shaper]](http://i.ytimg.com/vi/pH-1RWdC75E/mqdefault.jpg)
![Klipper Resonance Compensation Overview - [input_shaper]](/img/tr.png)
Started watching this while procrastinating on studying for my uni exams, ended up being exactly one of the topics I needed to study! I love it when I can combine awesome topics like 3d printing with more dry subjects.
Usually in control theory, a dampening ratio of 0.707 is preffered as it has a insignificant overshoot and a significant faster response time than 1.
0.707? Thats the RMS ratio for voltage on a sine wave.
@@TerryGilsenan Correct. It's 1/sqrt(2).
Both loose belt and tight belt have disadvantages. You have already explained the drawbacks of loose belt but a tight belt will increase the inertia load on motor and also increases the load motor bearings ( only if force with radial load of motor bearings). In short the torque on motor will increase with increasing belt tension. I have done a lot of motion simulation before coming up with this conclusion. It is important to note that the stepper motor itself produces some resonance depending on the full step of motor and microstepping in driver. There is a very interesting correlation between belt pretension, motor load and stroke length or traversing distance. Great work by the way, thank you.
Thank you for the insight on that! There’s a lot of factors for sure and some I haven’t covered 😄. Maybe someone will continue the analysis and teach us more!
So interesting, looking forward to your next measurements and conclusions 👍
this was extremely useful, thanks!
this is a unique channel going through the dynamic equations of 3D printing. Just signed on in my lunch break. Bravo!
Ive been watch a few videos on this subject with reguards to input shaper, and is very intersting to see what is causing this in 3d prints. but i also watched a video, not sure who it was but it had to do with vibrations introduced by the extruder motor that travels through the filament and into the print object. It was a very intersting video also. Would love to see more on this in the future from you. Edit* I would also be interested to see if the different types of Rail systems (V wheel, Linear tube bearings, and linear MGN12) has a effect on the vibrations.
Very nice. I wish more people would address this. I currently do not have the ability to do any testing. So I greatly appreciate your effort.
There is a sweet spot for belt tension I am sure but that sweet spot does not address the fundamental resonance issue.
Is belt tension the only major contributor?
I am just listing a few brainstorming ideas
1. Does resonance change for the X axis based on carriage position.
2. Same as above for Y
3. If the sensor is place on the carriage at different points (middle and ends) is there a difference in the amplitude and or frequency shift
4. If belt tension affects frequency of the system resonance , can it be assumed that the belts themselves are the primary source of the resonance?
Assuming that belts are the source of the resonance. The frequency would shift based on the position of the head and bridge due to the belt lengths changing. However as one belt shortens another increases in length. Does this shift where the resonance is seen and or the amplified. If the location of resonance is shifting I wonder if locating the sensor independent of the head would yield different results.
These are all really great questions! I haven't continued work on this recently, but I had tried to understand the factors driving this. One calculation was to try to estimate the natural frequency of the toolhead assuming that a corexy toolhead could be modeled as a mass suspended by 4 "springs", two on each side, constrained by the drive pulleys. I calculated the variation in natural frequency as the toolhead moved around the XY plane and saw that there was some variation as the different "springs" were longer or shorter based on toolhead position, which affected the spring "k" value. Unfortunately, the natural frequencies I calculated were pretty significantly higher than what I've seen from accelerometer data. I assume that's due to the fact that the belt isn't really a spring constrained to move in a single direction--it's flexible and can vibrate/move independently of stretching along the belt.
With the latest accelerometer code in Klipper, you can run tests at various X, Y, Z positions--and the resonance response does change some. Also, if you place the accelerometer out at the front of the toolhead vs. close to the belt mounting/carriage mount location, the accelerometer will show some additional vibration--the trick really is to try to understand what position is best. My current hypothesis is that it's best to tune the system with the accelerometer close to the belt/carriage mounts to remove toolhead movement, and then once that data looks good, add the additional variability from toolhead wobble. It's actually a pretty fascinating diagnostic tool--there has been a few times where someone's resonance data looks strange and after a lot of diagnosis, a loose or missing screw was found to be the culprit.
There's so much more work that could be done here! It's really quite fascinating :)
I was able to dig up some data from that analysis I did a few months ago--I posted it here: twitter.com/eddietheengr/status/1363176259405111301?s=20
as belt tension increases, the head will couple more directly to the frame because the belt becomes rigid. This is clearly visible in the graphs, you can see the peaks converging as tension increases.
At lower tension the belt will act as a dampener because it is made from rubber, once the tension is raised to the point that the load is being carried by the fiberglass or metal core, it will act less as a dampener, and more like a coupler. This is also clearly visible in the graphs as the peaks are wider at low tension, and narrow rapidly above a certain tension.
The real issue here is not resonant frequency, it is the *amplitude* of the resonant frequency. Until the Maker Sphere decides that rigidity is important, fixes like Input Shaping are nothing more than a software band aide over the real problem.
Great job
I thought I knew what the double peak was on your y-axis. I figured the x-axis was just the toolhead banging back and forth so just one resonance peak, while when the Y-axis was moving, the second resonance was from the extrusion flexing from the weight of the HEAVY toolhead in the middle of it. The funny thing is, when I just ran the input shaper, my X-axis was the one with the double peak, and my Y-axis was a single peak. I have zero clue what's going on there. Sort of strange to me that different belt tensions would give the double/single peak behavior, since the corexy belts have to be tensioned in unison.
Great work!
Nice video. With a looser belt will you not be sacrificing some positional accuracy as there will be more give in the belt? You may reduce ringing but end up with less dimensional accuracy. Would be interesting to see some test prints.
Agreed! It will be interesting to see the results
Good content! Subscribed.
Awesome!
Thanks mate
Really interesting stuff. I wondered how the belt resonant frequency might correlate to the axis resonant frequency. I think this could be measured with an FFT app on a phone reasonably well. I wonder whether damping can be included in the belt tensioner assembly also.
Also thinking about using an analogue accelerometer and monitoring resonant frequencies with a scope while the printer is running.
The problem is that without directly measuring the resonance at the head, you do not know how to map it to belt resonance. So no matter what, you will need to take the direct measurement. Once mapped though, you should be able to do a quick verification of tension using a phone app. The good news is that the accelerometer is dirt cheap (cheaper than the wire connecters in fact).
Interesting idea about using an analog sensor. The RFI from stepper motors is pretty bad and easily interfere with the digital stream from the sensor when doing live monitoring when a direct drive feeder is used. This will have an even bigger impact on an analog stream, but it might be possible to filter, or use balanced signal wires to remove it altogether.
@@joshua43214 Yes, really only worth using an analogue sensor if the measurement bandwidth is higher than a digital one, and a differential output would indeed help with the motor noise.
Also quite convenient/intuitive to see a live trace on the scope.
I was presuming that as the belt is under some tension, that this would be responsible for the resonance effect and the mass of the print head would add damping.
This can be done but you will to collect the data independently, which isn't hard to do.
Can be done with either a microphone or accelerometer.
For the belt, hookup a microphone and record, pluck the belt, perform FFT, natural frequency and mode sof belt will be at peaks.
Take a measurement of the system sitting still by tapping your printer with a hammer (gently) in the direction of travel, you may been to use an accelerometer instead of a mic, perform FFT and boom you have your natural frequency of the printer frame.
Confirm your results
Use accelerometer to collect nat. Freq from system while in motion. Sum the FFT data from individual tests and compare the FFT collected from the system in motion. Hopefully the FFTs will look similar
Subscribed! Excellent work.
But it begs the question of whether belts are really the right choice for moving the axes.
That’s an interesting point! Do you have another recommendation of something you think would be better?
Super interesting video. Wondering if we could have a servo controlled active tensioner with a closed feedback loop linked to an accelerometer on the toolhead. With some algorithm you could optimise the tension dynamically to reach the less possible oscillation on your moving systems (bed, gantry...), even if your resonance is not uniform throughout your print volume. That would be really the next step in printing faster without artifacts. It would also allow to automate the resonance compensation. Think about it as some sort of 4D bed leveling. Such a system could be easily adapted on a cartesians or coreX/Y with 2 belts for the gantry. Z axe could be left untouched as I doubt that resonance would matter for it. Who says this would be over engineering ;-)
I had a similar thought in passing when I had to keep going to the printer to tweak the tension slightly! Definitely not over engineering :)
@@eddietheengineer I have started looking around for a candidate for a motor... Not sure what the requirements would be in terms of torque and type of motor, but the way the tensioners are placed on a Voron make it a feasible concept I believe. You may have to change your name to eddietheoverengineer ;-)
Great idea! It definitely not an over engineering but smart engineering.
Very interesting, just one thought, how to be sure that the two belt are equally tensioned? I was playing with the idea of using accelerometer to do the resonance test but moving the head on a diagonal 45 degree pattern so that only 1 of the bed will be activated, visually or eventually from the data generated by the tool will be possible to precise determine the frequency at which the specific belt resonate. Doing this on both the 45 degree diagonal should give a precise way of tuning the belt to the same tension. And this should give a better ground for the search of the correct or best tension otherwise slight difference of the tension between the two belt can influence a lot how the head will move and the structure resonate
Yes! You can use Klipper and the ADXL345 sensor and run the toolhead diagonally-if both belts aren’t tensioned the same, the hypothesis is that the peaks from one diagonal vs the other will be at different frequencies. I haven’t dug a lot into it recently. You can find information here: github.com/Klipper3d/klipper/blob/master/docs/Measuring_Resonances.md#testing-custom-axes
Have you got any updates to this in the past year or so?
You mention that the printer not being rigid enough and that with a stiffer frame you can reduce the resonant frequency, but there another aspect which can play a major role in this too, that most people seem to miss, the table that the printer is on. The table is most likely going to less rigid than the actual printer so when the printer moves around the table is also going to be vibrating as well.
I haven't looked at it recently, but I'd like to revisit this! I hear that there have been some cool new accelerometer features integrated into Klipper that should make testing a bit easier.
Belt tension needs to be set according to the manufacturer specs!
I wonder if x has a single peak because the blocks are in compression on the cross beam, but in Y they are free to move so the bar and the belts become active.
yep, most likely one hump is the an artifact caused by the stiction release of the beam, and the other is the actual resonance while in motion.
What changes did you have to do because of the swapped X and Z axis? I cannot find anything in the Klipper documentation.
I did not have to do anything with the swapped X and Z axis--I believe Input Shaper takes the sum of the resonances now instead of just the one axis. Check the link here though--you can see that you can "map" the axes to the correct orientation if you wish! github.com/KevinOConnor/klipper/blob/master/docs/Config_Reference.md#adxl345
Addressing resonance. ... if the structural members like the gantry contribute more to resonance, then would mechanical dampening help? Or different material selection such as the much debated carbon fiber?
The one issue that I do not know exists in material selection is the expansion coefficients of the materials.
If carbon fiber is used I think the difference between it and aluminum are 20:1 on the high end and 10:1 on the low.
So if the bridge expands less the frame in the same X direction of heated, the rails holding the bridge would move further out and the bridge relatively stays stationary. This would put pressure on the rails and probably other parts in the system. So the resonance would change again.
Another great question! It would be interesting to replace all the gantry components with metal and see if that helps or hurts. Potentially a combination of metal for rigidity with some ABS for a bit of damping?
The thermal expansion is also a huge topic that I assume I'll go down in the future. I think e3D had used a carbon fiber X axis for their tool changer originally before switching back to aluminum due to the thermal expansion causing issues? There's so much going on with thermal expansion--it's a small enough factor that it can fly under the radar, but still significant enough that it can mess up your first layer. That's one of the tricky parts with probe accuracy that I'd like to dig into more--how much of the variation in probe performance vs. ambient condition is actually driven by the probe sense distance shift vs. temperature, and how much is driven by frame expansion driving slight shifts in Z height?
Adding stiffness with carbon fiber would increase the resonant frequency, but other materials might be better due to thier natural damping. Cast iron is used a lot in the machining world for its damping effect, but I believe adding kevlar to a carbon fiber composite also increases damping significantly, at least I heard that is the case for Dyneema, which as far as I can tell is very similar to kevlar. So perhaps a carbon fiber + kevlar composite is far better suited.
@@FranseFrikandel I come from a machinist family background and whole heartedly agree. Cast iron mass is great but heavy. Of course in cutting steal you are fighting deflection vibration and in 3D printing you deal more with vibration from the machine itself.
Iron combined with steel shot in cavities of the iron help absorb vibration. Also granite ways help with thermal stability, accuracy, and vibration. But all to heavy.
I like your idea about the Kevlar material. But I am still curious as to how much carbon fiber alone compares. My understanding is that it dampens vibrations as it resists resonating. But the weight savings alone with the rigidity seems too enticing.
@@eddietheengineer E3D switch ! I thought the same thing and I think is correct based on an interview.
My guess is that carbon fiber was harder to form into a shape that is compatible In the installation and operation of the printer. Also a simple beam might only be rigid in one direction more so. Combined with cost and fabrication, thermal expansion difference etc. it would be cheaper to machine a hunk of aluminum in a couple minutes. The aluminum would solve expansion differences, customized multi axis rigidity tuning , and almost plug and play. All based on machine and tooling. Milling webbing to reduce weight and keep rigidity while also machining in all the mounting points is way easier that’s carbon fiber.
I've been thinking recently about damping. Why don't we add friction to the moving parts to effectively damp the motion ? I see lots of people saying "we need to remove as much friction as possible to remove ringing" and I don't understand why.
Fuck, I need an accelerometer to test this out.
If someone here tries, please be sure that the component creating friction can't have play (or less than the amplitude of the ringing) else it won't matter
too much friction and motor will need to work very hard, at high speed you can loose steps, BTW belt tension will also add more friction.
7:50 - This is intuitive, but this is not true. Guitar string has transverse vibrations which IS depends on the tension, while ptrint head-timeing belt should vibrate in longitudinal direction, which IS NOT DEPENDS on the tension, it depends on mass and systen Young's modulus only.
And you can definitely see on your graphs that your resonanse frequency tends to 50 Hz frequency, overwise (if it was dependent on the tension - it would proportionally goes higher in frequency).