Interesting reading - Presure in advance
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I found very interesting the fact that acceleration limitation is not mechanical (inertia)... Great blog post!
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@deckingman said in Interesting reading - Presure in advance:
For me, on my machine, the critical acceleration rate is 1000mm/sec^2 and no higher.
1000mm per second per second? So, assuming a brisk print speed of 100mm/sec, you reach full speed in 1/10th of a second from a full stop?
I've seen the videos of your machine and I'm surprised that the mass of your "print head" (with it's diamond hot end, 3-5 extruders and stepper motors) would be able to accelerate that fast.
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@garyd9 said in Interesting reading - Presure in advance:
@deckingman said in Interesting reading - Presure in advance:
For me, on my machine, the critical acceleration rate is 1000mm/sec^2 and no higher.
1000mm per second per second? So, assuming a brisk print speed of 100mm/sec, you reach full speed in 1/10th of a second from a full stop?
I've seen the videos of your machine and I'm surprised that the mass of your "print head" (with it's diamond hot end, 3-5 extruders and stepper motors) would be able to accelerate that fast.
Yes that's exactly right. In fact, doing the maths on the motor specs, and taking one carriage mass of around 2Kgs, I could (and have) run at twice that acceleration). Also, the maths assumes a single motor so because on a CoreXY, each motor contributes to motion when doing pure X or pure Y moves, I could double those accelerations again and likely achieve 4,000 mm/sec^2. However, for 45 degree moves, only a single motor is used. But then again, the geometry of a CoreXY is such that for such moves the belts move around 1.4X the distance that the gantry travels, giving a leverage effect. So the maximum acceleration for that mass, with those motors (Nema 17, 59N.cm) is about 1.4 x 2,000 - say 2,800 mm/sec^2.
I do of course have the extruder mass as well making the total mass moving in the Y direction in tad over 4Kgs but the extruder gantry is a separate XY gantry with it's own motors, so for pure X or pure Y, 4 motors are employed and for 45 degree infill, 2 motors are used.
Once in motion, things get a little better still because instead of starting from a standstill, it starts from the instantaneous speed threshold (jerk) which in my case is set to 20mm/sec.
If you read my latest blog post, you'll see that I was printing at up to 300mm/sec with "jerk" set to 20mm/sec. So a speed change of 280mm/sec at 1,000 mm/sec^2 would take 0.28 seconds during which time the head would travel 39.2mm. Meaning that the acceleration and deceleration distance would be around 78 mm which for a 100mm long move means that the print head would only be at 300mm/sec for 22mm. If acceleration was set to less than 784 mm/sec^2 then it would never reach 3000mm/sec during a 100mm long move.
If you want to see it in action, watch the video that accompanies that blog post from about 9 minutes onwards. Here is a link https://www.youtube.com/watch?v=rUV5IZxfAxU
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then I ... print without problems, at a speed, grab the chair, of ... 50 mm / s or 60 mm / s.
How do you stay? HE ...
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@peirof There is nothing wrong with that. Most people print at 50 to 60mm/sec and usually that's fine. You start the print going, then go away and do something else and come back when it's finished so it doesn't really matter how long it takes.
The advantage of being able to print fast really comes into it's own when you have a big printer and want to print big items. That can often take several days. Personally I would never feel comfortable about leaving the house with the printer running. The same applies to washing machines. I'm comfortable with them running over night as I have smoke and fire alarms etc, but if I had to go out, I'd either turn the washing machine off or wait until it finished. That's not an option with my printer as the heated bed would cool down and the part would likely fall off. So it can come down to a choice between not leaving the house for 3 or 4 days, or print at 5 to 6 times the speed and have the job finished overnight. Or if you make things commercially where the adage "time is money" counts.
But I agree, for the majority of hobbyists, printing fast doesn't really matter. -
It is also nice to be able to print fast when prototyping, making several iterations to tune dimensions. I go up to 120-150mm/s, with 1 perimeter, 10% infill, so small parts take less that 15 minutes to print.
As you, I don't print with nobody at home!
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@fma said in Interesting reading - Presure in advance:
It is also nice to be able to print fast when prototyping, making several iterations to tune dimensions. I go up to 120-150mm/s, with 1 perimeter, 10% infill, so small parts take less that 15 minutes to print.
As you, I don't print with nobody at home!
Yes I do that a lot too. That's why I print on removable glass and why I have 3 sheets of it - so that I can slide one out when a print finishes, slide a new one in and be printing again, in less than 2 minutes.
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The irony here is that I checked my direct drive delta kit's printer settings and found my accel and "jerk" are also 1000mm/s^2 and 20mm/s:
M201 X1000 Y1000 Z1000 E8000 ; /sec, not /min
M566 X1200 Y1200 Z1200 E1600 ; /min, not /secI never realized that they were this high, but I never had problems so never tinkered with them. On the other hand, I've never even tried a print speed of 300mm/s. (I've done 120mm/s successfully, but prefer to stay around 80mm/s max print.)
So, I owe you a "thank you" for making me look at my configuration and realizing something I hadn't paid attention to.
(I wouldn't even dream of running my duet converted FFCP at these speeds. For that printer, I start to see quality losses at 50mm/sec.)
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@garyd9 Spooky how you happen to have the same values.
Actually, in the grand scheme of things, 1,000 mm/sec^2 is nothing much. Acceleration due to gravity is 9.81metres/sec^2 so we are are only talking 1/10th G.
In a previous life I did a lot of stuff with internal combustion engines. You probably know that a typical road car engine can do 6,000 rpm plus. For the sake of keeping the maths simple, the stroke might be 100 mm, and every piston has to start at the top, travel 100mm, reverse direction and travel back up to the top. So have you considered that at 6,000 rpm, it does that 100 times per second. Or 5ms for a complete up-down-up cycle or 2.5ms to go from rest, travel 100mm and slow down to a stop, before reversing direction and repeating. And that's nothing special either. F1 engines are now limited to (I think) 12,000 rpm but 18,000 rpm has been rumoured to be true in the days of 1.5 litre turbo engines. That's 2 to 3 times faster still. So in the world I used to inhabit, 1,000 mm/sec^2 is bu**er all.
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@deckingman ahh, but how much acceleration does your printer actually see during a corner jerk? Hmm
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@rcarlyle said in Interesting reading - Presure in advance:
@deckingman ahh, but how much acceleration does your printer actually see during a corner jerk? Hmm
Nobody likes a smart are*e
All jesting apart, I have mulled this over from time to time. It won't be infinitely high acceleration - that's impossible. All else being equal, I guess it depends on what "gives" (and something must). When a ball is struck by a foot or a club, the ball itself deforms at the moment of impact, then it accelerates until the force is no longer applied.
As an aside but interesting none the less, is that my (now deceased) father-in-law used to make arrows for traditional long bows. He was somewhat of an expert in his field and wrote a book on it. What is interesting is that, when an arrow is "loosed", it bends as it accelerates forwards. The optimum "bend rate" for accurate shooting is such that the arrow does 1 1/2 deflections before it leaves the bow. I won't go into the details but it's called "the archers paradox". The stiffness of the arrow is called the "spine" and a matched set of arrows will all not only have the same weight, thickness, taper and length, but also have the same "spine", and that "spine" will be matched to the draw weight of the bow. Surprising how much science there is in a simple thing like an arrow.....
So maybe the optimum "jerk" (I hate that term) for a 3D printer is one that matches the printer equivalent of an arrows "spine".
Another thing I wondered about (and you will know the answer to this better than I) is does motor rotor inertia play a part? I'm just thinking along the lines that the motors (on a CoreXY) will be spinning in one direction, then when there is a corner jerk, they will have to reverse direction, which can't happen instantly because of the inertia of the rotor. My gut feel is that the rotor inertia would be insignificant in comparison to the inertia of all the other moving mass but do you know differently?
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@deckingman said in Interesting reading - Presure in advance:
My gut feel is that the rotor inertia would be insignificant in comparison to the inertia of all the other moving mass but do you know differently?
If I remember correctly, the resulting torque is moment of inertia (kg·m²) x angular acceleration (rad.s⁻²).
Moment of inertia of the rotor is: mass (kg) x radius² (m²), where radius is taken at center of gravity of the section of the half rotor (R/2 for a plain cylinder).
Correct me if I'm wrong...
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http://www.softschools.com/formulas/physics/torque_formula/59
A quick check shows that the torque due to moment of inertia is 3 or 4 orders of magnitude lower...
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@fma Yes (and no). I wasn't thinking about torque, just inertia. i.e. when changing motor direction, does the inertia of the rotor play any significant part in how fast that change of direction can take place? Given that the motor is coupled to the gantry I suspect not, as the inertia of the gantry will be significantly higher.
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Mmm, for me, what prevents direction change is the needed torque due to inertia... same as linear accelerations, where you have a resulting force, which in turn gives a torque...
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If the drivetrain is designed properly, the load angular inertia seen at the motor (“reflected inertia”) should be between 1x and perhaps 10x the rotor inertia. If you’re outside that range, your motor is either too big or too small. (The rule of thumb for servos is 1-5x but they have closed-loop feedback stability issues to worry about which open-loop steppers do not.) * You get maximum possible low-speed acceleration capacity when the reflected inertia equals the rotor inertia. * If the rotor inertia is greater, it’s putting too much energy into accelerating its own rotor and not enough into the load. If the reflected inertia is greater, a different gearbox / belt / screw ratio would allow the motor to accelerate the load faster.
In practice, we don’t like to add gearboxes due to parts count and backlash, so the reflected inertia will be a lot larger than the rotor inertia. If it’s more than about 10x larger and you don’t want to change the drivetrain ratios, your motor is probably undersized, but that’s just a loose guideline.
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Thanks for the explanation. So, in Ian's config, the load inertia is (if I do the maths correctly):
m x r² = 4 x 0.01² = 4.10⁻⁴ kg.m² (where r is the radius of the pulley)
I previously estimated the rotor inertia to 4,5.10⁻⁵ kg.m². So we are about 1:10 ratio, which is good?
