# steppers with lots of Amp... + M906 command

• rotor-inertia given in g cm^2 -> "J" for ratio

To calculate that you need the radius of whatever is attached to the motor shaft and then in insert it into the formula a bit further above (and I think it also is on that page you linked with all these formulas).

But what if there is a small pulley going from the motor to a "main"-shaft that has a ratio? -> What pulley then? Say 25,465mm r(-motor) to 14,006 r(-mainshaft) (gear-ratio of 1,818) -> Pick the one where the load is driven from?

Something doesn't add up here. First you say a small pulley in to motor and then in your example the small pulley is the larger one. Anyway, radius or diameter is not the base of gear-ratio (even though in most cases it comes close) but interacting number of teeth of the different gears. Then again the gear ratio on my calculator expects rotation on the motor : rotation on the load. I will fix this later.
In your example this would mean your gear ratio is 1:1.818 since one rotation of the motor shaft leads to 1.818 rotations of the load shaft as far as I can tell from your description.

do not make the same mistake as I did: If there is a reduction/adduction (gear-ratio) of the motor involved the NM of the Motor is (de-)amped by the amount also...

I don't think I can follow you here. Why would adding gearing reduce or increase the motor torque? It will of course affect the torque that is applied on the load but the motor does not change. What am I missing?

• First: Thanks for coming back on this!

rotor-inertia given in g cm^2 -> "J" for ratio

To calculate that you need the radius of whatever is attached to the motor shaft and then in insert it into the formula a bit further above (and I think it also is on that page you linked with all these formulas).

-> Thanks! So this is exactly that point where we "add" the wheel attached to the motor to the rotor inertia? Canยดt we just sum up the motor-inertia + the attached wheel-inertia for that? For what do we need the rotor-mass in Kg?

But what if there is a small pulley going from the motor to a "main"-shaft that has a ratio? -> What pulley then? Say 25,465mm r(-motor) to 14,006 r(-mainshaft) (gear-ratio of 1,818) -> Pick the one where the load is driven from?

Something doesn't add up here. First you say a small pulley in to motor and then in your example the small pulley is the larger one. Anyway, radius or diameter is not the base of gear-ratio (even though in most cases it comes close) but interacting number of teeth of the different gears. Then again the gear ratio on my calculator expects rotation on the motor : rotation on the load. I will fix this later.
In your example this would mean your gear ratio is 1:1.818 since one rotation of the motor shaft leads to 1.818 rotations of the load shaft as far as I can tell from your description.

-> These were just examples, will pick one example for this post to ease communication... You understood the "last" example perfect, will stick to it

do not make the same mistake as I did: If there is a reduction/adduction (gear-ratio) of the motor involved the NM of the Motor is (de-)amped by the amount also...

I don't think I can follow you here. Why would adding gearing reduce or increase the motor torque? It will of course affect the torque that is applied on the load but the motor does not change. What am I missing?

-> Exactly! Of course the motor-torque is not magically de-/increasing, but the applied torque AFTER the drive-ratio is scaling with the drive-ratio, sorry for my "wald & wiesen denglish" here Just wanted to point out that I forgot to include this trade of speed<-to->applied-torque in my calc. Anyway was just going through my mind...

• -> Thanks! So this is exactly that point where we "add" the wheel attached to the motor to the rotor inertia? Canยดt we just sum up the motor-inertia + the attached wheel-inertia for that? For what do we need the rotor-mass in Kg?

This is an artificial mass that is added to the mass of the load to be moved. So if for example the load to be moved of an axis is, say, 1kg and the rotor inertia is 68g.cmยฒ on a 16 tooth GT2 pulley (`r=0.51cm`), this will add about 260g of additional mass for the motor to move.
And since `acceleration = force / mass` where force is given in `N` and mass in `kg` this is converted to kg (although this results in `m/sยฒ` and I multiply the result by 1,000 to get the more common `mm/sยฒ`)

-> Exactly! Of course the motor-torque is not magically de-/increasing, but the applied torque AFTER the drive-ratio is scaling with the drive-ratio, sorry for my "wald & wiesen denglish" here Just wanted to point out that I forgot to include this trade of speed<-to->applied-torque in my clac. Anyway was just going through my mind...

Two Germans writing in English about complex mechanical physics... what could possibly go wrong?

Also my calculator ignores speed constraints. It is solely about possible acceleration - if you can achieve high speeds with it is another topic.

• -> Thanks! So this is exactly that point where we "add" the wheel attached to the motor to the rotor inertia? Canยดt we just sum up the motor-inertia + the attached wheel-inertia for that? For what do we need the rotor-mass in Kg?

This is an artificial mass that is added to the mass of the load to be moved. So if for example the load to be moved of an axis is, say, 1kg and the rotor inertia is 68g.cmยฒ on a 16 tooth GT2 pulley (`r=0.51cm`), this will add about 260g of additional mass for the motor to move.
And since `acceleration = force / mass` where force is given in `N` and mass in `kg` this is converted to kg (although this results in `m/sยฒ` and I multiply the result by 1,000 to get the more common `mm/sยฒ`)

Ah! So but in my case I have 2 synchro-belts per Axis = 4 in total, 2m long, 9mm wide, guess I have to add that mass also since that will not be neglectable in perspective to the rest mass

-> Exactly! Of course the motor-torque is not magically de-/increasing, but the applied torque AFTER the drive-ratio is scaling with the drive-ratio, sorry for my "wald & wiesen denglish" here Just wanted to point out that I forgot to include this trade of speed<-to->applied-torque in my clac. Anyway was just going through my mind...

Two Germans writing in English about complex mechanical physics... what could possibly go wrong?

Also my calculator ignores speed constraints. It is solely about possible acceleration - if you can achieve high speeds with it is another topic.

Yeah but this forum is great & thanks for helping me out anyway in whatever language - "math & physics are some sort of universal language" they told me

• Ah! So but in my case I have 2 synchro-belts per Axis = 4 in total, 2m long, 9mm wide, guess I have to add that mass also since that will not be neglectable in perspective to the rest mass

If you want to use the calculator just add it to the axis mass input field.
But seriously, have you weight them? How much could this be? 50g? These are all very lightweight objects.

Yeah but this forum is great

I say that on every occasion. I learn something new every day here.

• Ah! So but in my case I have 2 synchro-belts per Axis = 4 in total, 2m long, 9mm wide, guess I have to add that mass also since that will not be neglectable in perspective to the rest mass

If you want to use the calculator just add it to the axis mass input field.
But seriously, have you weight them? How much could this be? 50g? These are all very lightweight objects.

...but 4 of them will be already - 200gr? - then, yeah will put some additional mass into that field... (confirmed in this "big" build it will be another ca. 150-200gr)

Yeah but this forum is great

I say that on every occasion. I learn something new every day here.

I think I will stop posting here and open a new post solely on "inertia" & "inertia-match" and all the calculation involved.

• @lb By 50g I meant the total weight of all 4 belts... I have no clue if that is anywhere close to being realistic - I never had the idea of weighing my belts and pulleys.

• @danal From what the OP added as resources via links this was actually the inertia added by the mass of the pulley and belts themselves. Those 10 to 50 grams.

Agreed, highly variable.

My comment was really in response to (paraphrased): "This can be calculated with just pully diameter". 6mm vs 9mm vs ??? comes into it as well.

So the input might need to be pulley weight & radius, belt width and length... maybe more...

• @dc42
"stupid" (maybe) question, while digging up new motor-alternatives: Those 2,4A, are they "per phase"? Or in total? I assume per phase.

Because: Letยดs say I pick a motor that has 2,12A (1phase), what would be fine... then this motor will have 2 * 2,12A * 1/sqrt(2) -> = ca. 3A then on every two-phase step in total (with only 1,5A on each single phase of course).

• Just because I have everything within arms reach (don't ask), here are the weights:
2m of 6mm Width GT2 belt: 16.11g
16T 6mm W, 5mm ID Aluminum Pulley: 2.92g
20T 6mm W, CR10 stock pulley: 6.10g
All of the above measured with an uncalibrated cheap Chinese scale, so just useful to get an idea.

• @dc42
"stupid" (maybe) question, while digging up new motor-alternatives: Those 2,4A, are they "per phase"? Or in total? I assume per phase.

Because: Letยดs say I pick a motor that has 2,12A (1phase), what would be fine... then this motor will have 2 * 2,12A * 1/sqrt(2) -> = ca. 3A then on every two-phase step in total (with only 1,5A on each single phase of course).

The 2.4A is the peak per-phase current. When using microstepping, only one phase gets the peak current at a time. When full stepping is selected, both phases get the peak current all the time.

• @dc42
Thanks so much! That helps me so much to better understand the whole stepper-stuff!

So for learning/understanding:
Even the trinamic-driver in full-step-mode do not scale down to sin(45) = 0,707... * A + cos(45) = 0,707... * A in a two-phase position and have at this time 1.414... times A but with 2 * 1A = 2A in total in a single-phase position
-> That does no user any help because we all have to design our systems for the weakest point then and that is single-phase-on... which means in 2-phase-fullstep with 1*A in each winding I actually have more torque and heat and power consumed then I need because I designed everything in a way it can deal with this less torque in single-phase-on-position that cannot be avoided by any means when using microsteps... (though of course we can think of an always 2-phase full-step-mode)?

Another question design-related:
If I have 3,8rps (=225rpm) in my system with 16times micro-stepping I need 3,75 * 16 * 200=12000pulses per second -> Judging on the 300KHz stated here "https://forum.duet3d.com/topic/3493/maximum-stepper-speed/2" I do not run into any problems, even if in total 3 axis-stepper are mounted + 2 printhead-stepper, because that 300KHz is not limited by the amount of steppers connected?

• The 300kHz was measured with just one stepper motor moving; the figure with 3 motors moving simultaneously was 120kHz. When using external drivers, the maximum rate will be less because of the need to lengthen the step pulses.

• @dc42 Not to hijack the thread, but this makes me curious what the step rate of the Duet 3 will be with a CPU that appears to be about 3x faster. And as a knock on from that, would it be possible to run in native 256x microstepping mode for all axis?

• @dc42 Not to hijack the thread, but this makes me curious what the step rate of the Duet 3 will be with a CPU that appears to be about 3x faster. And as a knock on from that, would it be possible to run in native 256x microstepping mode for all axis?

Although the SAME70 that we use on the prototype Duet 3 can do 300MHz, we currently run it at 240MHz because it makes it easier to sync the expansion boards with the main board. This is twice the clock rate of the SAM4E on the Duet 2. Performance doesn't scale with CPU speed because higher speeds need a larger number of flash wait states to be used, although the SAME70 has a cache that helps with this.

I doubt that it will be possible to run with native x256 microstepping on deltas even with Duet 3. However, the stepper drivers support interpolation to x256 from any microstepping, so you would be able to use e.g. x64 interpolated to x256.

• pulleyRadius? -> Of which pulley, the "main" pulley?

The pulley fixed to the motor shaft.

Thought about it after working for weeks on the hardware, sorry for coming back so late: In a direct-drive-system: yes the pulley attached to the motor, but in a system where the "gear" is realized also with a pulley this could be confusing, so for me I understand you here: In a load/mass-finally-driven-by-pulley-system the "diameter" (pitch) "neutrale Fase" of that "final" pulley moving/attached to the main-mass/toolhead? Am I going way off road here or is that a good assumption?

• To summarize things up:
In the end, the all-integrated-closed-loop JMC-stepper where the bottle neck because instead of T2.5 what was printed in their datasheet they had to be minimum T3.2, slowing things down...

I can see now the benefit of an all integrated solution Cannot wait to see what the duet3 will be capable off!

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