Understanding long Lead Screws

I'm currently debating increasing my build height on my 3d printer design, which would require 1400mm lead screws to move my bed along the z-axis. I've been looking at 12mm dia ones and also at the option of just using a belt driven Z-Axis. Now I'm trying to justify using the belts system over the lead screws, but I just don't see the advantages, but maybe I just don't understand how lead screws work and can add to uncertainty/defects in prints. So I did an ANSYS analysis. In my setup, seen here:[openbuilds.com] with 900mm lead screws instead of 1400mm (haven't added the extra height yet), I have the bed constrained on 4 corners with rollers going up the v-grooves of the vertical posts. This should make it as steady as the frame in the x and y axes, so any x/y 'wobble' of the lead screw won't be seen in the print, I don't think. I then ran an Ansys analysis to look at the Z-direction deflection, and with a 10lb load at the top (weight of bed+bedfram), fixing the very bottoms of the 3 lead screws, in a triangular position, and constraining the bed to only being able to move in Z direction (due to v-groove rollers). This shows 1400mm long, 12mm dia lead screws bowing out in the x/y direction a maximum of .00076inches (.019mm), which should not be seen in the print due to rollers, and a z direction deformation of .00005inches (.0013mm). To me this seems well below allowable limits. If this is the case, why are people switching to using belts to move their bed up and down? The lead screw seems to have negligible deflection, very small precise steps compared to using a belt, and when used in the z-direction, I wouldn't think there would be any backlash since gravity should load the bed down onto the threads so only the top sides of the threads will be contacted (whereas when used horizontally, both sides of the thread would be in contact depending on which direction it is going). Am I not understanding something? Is it because people maybe are having issues when using the screws as the sole supports for the bed, instead of using guide rails and thus having the screws just used to positionally move the bed? What do belts have that the lead screws do not have for Z-axis bed movement, other than a fun meteor-like finale when the power is cut?

I have a belt driven z axis it's only 180mm, I have it because it was easy to build, I have two guides (8mm rods and long bearings) mounted opposite the mid points of the long sides of a rectangular bed 300x200. I could add two more guides on the shorter sides but it's not tall enough (or wide enough) to be too flexible and cause a problem.

It has not let me down in terms of accuracy or reliability, I use a 400 steps/rev motor and 16t pulleys at 1/32 stepping so the theoretical resolution 2.5 microns (I know that not all microateps result in motion) is far smaller than any layer height I might want to print eg 100 microns even accounting for accumulating microsteps to get it to move. The bed is heavy so I have a counterweight which also prevents the free fall issue on motor power off.

My experience with leadscrews was on an i3 rework, they were better than m5 rods but they were cheap ones, it took effort to align them, and would be much more effort on my corexy, and I'd have to run belts and pulleys possibly gearing down the motor to have one motor running two or three leadscrews, to prevent them going out of sync unless I try DCs new idea on RRF of having a motor per screw independently controlled. I could buy good leadscrews or ballscrews and do the hard work and be quite satisfied with it but I was going for better not best and achieved it quite affordably in terms of time and money. If I were building a 1400mm z axis I would probably not chose belts, they would have to be very long and therefore more stretchy (or would have to be much thicker, heavier and more expensive belts).

I think the short answer is at a certain scale belt driven z axis is cheaper easier and good enough.

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Simon Khoury

Co-founder of [www.precisionpiezo.co.uk] Accurate, repeatable, versatile Z-Probes
Published:Inventions

I think constraining all four corners of the bed support is likely to end in the mechanism binding at the slightest misalignment. Two bearings should be enough if everything is perfectly inflexible, so three should be plenty in the real world.

Belts vs lead screws is a personal choice. Belts look like a cheaper alternative initially, but when you solve the bed-drop problem, I suspect the cost ends up about the same. Belts do make it pretty easy to build the Z axis to any arbitrary length. In a printer with a very long Z axis belts may be better than screws because they can't produce lateral forces that will create Z wobble in the print. It can be difficult to build a very tall machine rigid enough to withstand the lateral forces that offset motor couplers, etc. can produce in a screw driven system- in that regard a very tall machine is similar to a small, cheapo machine with a rickety frame. In a very tall machine when the bed gets loaded with a massive print (that's why you're making it tall, right?), the screws may bow under the load and that may produce some of those dreaded lateral forces when they rotate. In a belt driven Z axis the belts will stretch a little, but won't create any lateral forces.

Edited 1 time(s). Last edit at 04/19/2017 02:21PM by the_digital_dentist.

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Ultra MegaMax Dominator 3D printer: [drmrehorst.blogspot.com]

Quote
the_digital_dentist
I think constraining all four corners of the bed support is likely to end in the mechanism binding at the slightest misalignment. Two bearings should be enough if everything is perfectly inflexible, so three should be plenty in the real world.

Belts vs lead screws is a personal choice. Belts look like a cheaper alternative initially, but when you solve the bed-drop problem, I suspect the cost ends up about the same. Belts do make it pretty easy to build the Z axis to any arbitrary length. In a printer with a very long Z axis belts may be better than screws because they can't produce lateral forces that will create Z wobble in the print. It can be difficult to build a very tall machine rigid enough to withstand the lateral forces that offset motor couplers, etc. can produce in a screw driven system- in that regard a very tall machine is similar to a small, cheapo machine with a rickety frame. In a very tall machine when the bed gets loaded with a massive print (that's why you're making it tall, right?), the screws may bow under the load and that may produce some of those dreaded lateral forces when they rotate. In a belt driven Z axis the belts will stretch a little, but won't create any lateral forces.

Shouldn't the guides (in my case carriages on linear v-groove rails) prevent any Z wobble though? I just don't get how it would be able to move when constrained like that; also since it doesn't move while X/Y carriages/extruder is typically moving, it shouldn't impart wobble due to z-movement while printing.
As for having it constrained on 4 corners, I may just use the inside wheels for each carriage, instead of inside and outside sets of wheels on each carriage/post. Think that may help with keeping it from binding?

@DJDemon: I do hear you on it being harder to align them, but I'm okay with that. Thanks for your input!

You're assuming the frame is perfectly rigid. If the screws wobble, they'll cause the frame to flex if it isn't super rigid, and that's hard/expensive to achieve with a very tall frame.

Using 4 wheels is still over-constraint. If the frame members aren't perfectly parallel and perfectly rigid, you're asking for trouble.

My latest printer has a 700 mm belt lifted Z axis that lifts the 300x300 mm bed at the middle on two sides, adjacent to two linear guides. The mechanism is very rigid, very simple, and it works beautifully.



There's no visible bounce at the free edges of the bed, and print quality is very high. I have not had to relevel the bed since the initial set-up over a month ago, in spite of transporting the printer in my car laying on its back a couple times.

The printer's frame is 1.4 m tall, made of 40x40 mm t-slot, and I find it less rigid than I want, so I'll be adding some bracing.

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Ultra MegaMax Dominator 3D printer: [drmrehorst.blogspot.com]

Interesting. I'm using all 2040 but may go to the junkyard to find some scrap pieces of metal to use to brace the thing more.
I recalculated the load, and the whole bed/frame assy that will be lifted is about 15 pounds for my design. Do you think I should go with a 9mm wide belt for this instead of 6mm? The belt will be about 2600mm long. Currently my X/Y belts are just a little shorter and are 6mm, but I'm debating upgrading those to 9mm just so cuz of jerking, but i'm hesitant as to if that is even necessary since they aren't supporting any weight and aren't pulling that much; just jerky motions.

Your machine is 1400mm tall but your bed only goes up/down 700mm? That seems like a bit of a waste of space, imo.

Wider belt will stretch less than narrower belt, all other things being equal, so yes, use wider belt. It doesn't cost much more than the narrower stuff. Steel core belt will stretch less than glass core belt, and costs only a little more. I used 10mm wide, steel core, PU HTD-3M belts in my printer and IRIC, 5m of that belt cost $13-15. The moving portion of the Z axis hanging from the belts is 3-4 kg. On this machine the belts stretch about 42 um/kg of load on the bed, measured with the bed at about the mid point of the Z axis. Since stretch is a function of the belt length between the clamp on the bed support and the drive pulley, the stretch will be smallest at the top of the Z axis and greater at the bottom of the Z axis.

The pulleys at to top of the Z axis are just stacked F608zz bearings on shoulder screws threaded into 1/4" aluminum tooling plate holders. The bright green blocks at the bottom are TPU bumpers- I have the same blocks at the top of the Z axis, too, to prevent metal to metal contact if the axis should somehow move beyond its normal range of motion. I installed a Zmax limit switch at the bottom left that stops the motor when the bed gets within about 1 mm of hitting the bumper. The Z=0 switch mounts near the top right side and the screw is mounted on the right side belt clamp. I used a lever and cam to provide a reduction in the screw's effect so that a full turn of the screw moves the bed position by about 100um.

In my printer I started with a long serpentine belt like this:



While it worked OK, the asymmetry bothered me. The weight of the bed/print is ultimately transferred back to the drive pulley through the belt. With the serpentine belt, the length of belt back to the drive pulley from the belt clamp on the left and right sides of the Z axis are not the same- the right side has much longer belt running back to the pulley. That means that when loaded, the belt that goes to the right side will stretch more than the belt clamped to the left side. That means the bed support assembly and bed may start to tilt as the bed gets loaded with a heavy print. I opted for a symmetrical arrangement instead that has matched belt lengths on both sides, so the stretch under load should be equal preventing the bed from tilting.

I designed this machine to be enclosed and heated to allow reliable printing of ABS. Designing for enclosure always bumps up the size. If you don't design to enclose, then decide to do so after the fact, the enclosure ends up being even larger.

Edited 2 time(s). Last edit at 04/20/2017 12:56PM by the_digital_dentist.

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Ultra MegaMax Dominator 3D printer: [drmrehorst.blogspot.com]

So you almost have me convinced on the belt driven z-axis. The biggest problem I see with mine is that my Z-Axis (if I make it taller, which I'm leaning towards doing), will be moving about 1200mm, so 71% bigger. Doing quick calcs, that means .072mm/kg of stretch, position dependent. So while printing small parts would be fine and wouldn't see much stretch, if any at all, larger parts could cause the belts to stretch a good portion of a layer. Now, when printing larger parts I'll be using larger layer settings, which could mitigate these effects. I don't, however have experience to know how this would affect the print and if it would cause more than insignificant errors.
So my options appear to be:
Option 1) Go with lead screws. Pros: very fine, precise adjustment to the height/z-axis of .00012in/step (.003mm/step). would be theoretically possible to print with very fine layer settings. Max Z-axis delta deflection appears to be .00013in (.0033mm). As parts get larger and heavier (negative impact to this), the bed moves down the Z-axis (positive impact to this), so I do not expect this to get worse. I've found this option to be slightly cheaper unless using cheap belts. Cons: Potential .0013in (.033mm) of x/y deflection due to bowing/bending of screws.
Option 2) Go with belt driven. Pros: No Z-wobble what-so-ever. It should look beautiful in this sense. Cons: Not as fine z height steps at .00083in/step (.021mm/step)...this is using a belt from a 16T driving pulley on the motor to a 60T pulley on the shaft with the belts on 16T pulleys. However, in most cases this is probably plenty. Bed could crash down upon power being turned off (i don't really count this since it can be fixed but will add cost to do so). Probably more expensive, esp if having to find an option for the meteor-like bed, unless using cheap belts. Much larger Max z-axis delta deflection as the print is created, which could lead to problems, but negligible for small prints. It could be .0028in/kg (yea i just used in/kg haha) or .072mm/kg of stretch lower towards the top and higher towards the bottom. Could larger create under-extrusion type problems?

Mitigations for Cons: Sanding parts should (i think, right?) get rid of visual effects of z-wobble. I also have an idea that may allow the screws to bend without the bed moving with them but will add additional cost. Sanding may also remove visually ugly stuff from z-axis deflection/stretch of belts. I'm unsure if that's all the problems that this could create though, or even if it would create problems at all, tho i imagine they would.

Pretty much, what of the following is a better scenario? Up to .0013in/.033mm of x/y deflection, negligible z deflection, .003mm/step or twice as large potential Z-axis deflection (but only for larger parts) with negligible x/y deflection and .021mm/step. My brain hurts.

Has anyone ever tried or considered a rail supported z axis which climbs a rack using a pinion gear like a mountain railway? Then it wouldn't matter how tall it is, provided the pinion gears were geared highly enough not to roll back down the rack on power off.

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Simon Khoury

Co-founder of [www.precisionpiezo.co.uk] Accurate, repeatable, versatile Z-Probes
Published:Inventions

The Z motor/bed always moves in the layer thickness you specified in the slicer. Let's say you print a 1 kg print in 1000 layers. In my machine the as the belt stretches, the layers get slightly thicker until the accumulated stretch is 42 um. That 1000 layer print will have 42 um/1000 = 0.042 um error per layer on average. The actual error starts at zero and increases gradually with the mass of the print as the belt stretches. In each layer the amount of stretch induced error is the stretch caused by that layer's mass. How massive is any given layer? Not very. Will it cause any visible effect in the print? Not likely.

Think about it this way: if I made a print that was solid block of PLA (1.25 g/cm^3) in 200 um layers, each layer would have a mass of 22.5 g (300x300x0.2 mm= 18000 mm^3 so that's a mass of 18000 x1.25/1000 = 22.5g). Belt stretch is 42 um/1000g, so the belt stretch in each layer would be 42um/1000gx0.225g= 0.945 um. That much error will be added with each additional layer, but it will be added as each layer is printed (the end of a layer will be 0.945 um thicker than it was at the start). You will never see a discrete step in the error, and the error will accumulate layer by layer until at the 44 th layer the total error will be 42 um.

Step size of 0.021 mm in Z is plenty for a 1.4m tall printer. You're not likely to be printing 1.4m tall objects in 100 um steps because you'll be waiting for weeks for the print to finish. You build a tall machine to print in thick layers. If your intent is to print in 100 um layers, don't make the machine 1.4m tall.

Edited 3 time(s). Last edit at 04/22/2017 08:05AM by the_digital_dentist.

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Ultra MegaMax Dominator 3D printer: [drmrehorst.blogspot.com]

Quote
DjDemonD
Has anyone ever tried or considered a rail supported z axis which climbs a rack using a pinion gear like a mountain railway? Then it wouldn't matter how tall it is, provided the pinion gears were geared highly enough not to roll back down the rack on power off.

Interesting idea. I feel like the lack of available parts is the biggest hindrance, and i'm assuming that alone makes it expensive. Apart from that, it doesn't sound like a bad idea. The gear could induce some slight movement/forces perpendicular to the direction of movement though do to angle of attack of gear teeth.

@Digital_Dentist

The extruder/hotend puts out a specific amount of filament per unit time right? so even though your average stretch per step is 42um/1000, you are still 42um off on your last layer. My equivalent would be 72um. If printing at .1mm, thats 72% further away. Granted with large parts, i'd probably be printing at .3mm layers which would be 24%.I just feel like this could allow the filament to move a little before hitting the previous layer, but you are probably right in that it won't really have noticeable effect tho my gut just tells me it could. You should do a test on your machine; create 2 parts, either one very wide and tall, and one much skinnier and tall (same height, just essentially different weights), and see if there is any noticeable difference with your last layers. Do you happen to have a link still to the belt you used? I'm having a hard time finding inexpensive ones.
Also, while looking up belts and what-not, I took a gander at open builds and saw someone in the midst of a build using lead screws with a counter-weighted bed so there won't be much weight on the screws at all. I'm thinking this is a great idea and may actually be the best of both worlds, what do you think? Getting the weight off will prevent any bowing/deflection of the screws, and even with a 1-2 kg, it shouldn't deflect the screws much, especially since the bed at that point will be pretty far down the screws. the more I think about this, the more I like it.

I corrected a math error in my post. In the example, a 200 um layer, if it were solid plastic covering the bed, would have a 0.945 micron error at the completion of the layer. That's about 0.5%, of the layer thickness and that amount only occurs if the layer is solid plastic covering the entire bed. Prints that do that are pretty rare. The error accumulates slowly, and the z axis mechanism still steps in the specified layer thickness. There will never be a single layer with a 42 um thickness error because there's no filament dense enough to weigh 1kg in a single 200um layer.

A 1kg print will be 42 um taller than designed and a 2 kg print will be 84 um taller. As the kids say, meh.

The flatness of the bed, even tooling plate, will vary by that much, and first layer thickness will vary from the design value depending on how you zero the print bed. Top layer infill is rough and you will get different thickness measurements depending on where you place your caliper. In the end, the error due to belt stretch is on the same order as and is masked by the other errors. If you gotta have um accuracy in the height of a 2 kg print, smooth the top surface with a piece of sandpaper.

Edited 2 time(s). Last edit at 04/22/2017 08:35AM by the_digital_dentist.

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Ultra MegaMax Dominator 3D printer: [drmrehorst.blogspot.com]

Counterweights on the z axis can help with the bed drop problem, but only to compensate for the weight of the bed and support structure. What about the weight of the print? If you use counterweights equal to the mass of the bed and support, you can no longer rely on gravity to prevent backlash in the mechanism. That means you'll need antibacklash nuts. Unless you use counterweights that are more massive than the bed and support. But that just reverses the problem. When power is cut, the bed will go up instead of down, and if there's a print on the bed, it will slam into the extruder. You're better off letting the z axis slam into the bottom of the printer.

Then there's the problem of how to implement counterweights in a way that doesn't look bad. All the counterweighted machines I've seen pictures of look pretty bad. I suppose it doesn't matter as long as it works, but it only sort-of works.

A motor that is geared down so that the weight of the bed plus a print can't cause the motor to turn is the ideal solution for screws or belts. You lose some speed due to the gears, but the z axis doesn't have to go fast anyway. The weight of the bed and print will keep the gears fully meshed so backlash won't be a problem.

I ordered the steel core belts through an ebay vendor in China. Just search for steel core polyurethane belts. I bought a 5m belt for about $15 including shipping, IRIC.
I also got some 2mm pitch steel core belt to try in the xy stage but decided that it was too stiff to use, so I put the glass core belt back on the machine.

Edited 2 time(s). Last edit at 04/22/2017 09:08AM by the_digital_dentist.

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Ultra MegaMax Dominator 3D printer: [drmrehorst.blogspot.com]

Quote
the_digital_dentist
I corrected a math error in my post. In the example, a 200 um layer, if it were solid plastic covering the bed, would have a 0.945 micron error at the completion of the layer. That's about 0.5%, of the layer thickness and that amount only occurs if the layer is solid plastic covering the entire bed. Prints that do that are pretty rare. The error accumulates slowly, and the z axis mechanism still steps in the specified layer thickness. There will never be a single layer with a 42 um thickness error because there's no filament dense enough to weigh 1kg in a single 200um layer.

A 1kg print will be 42 um taller than designed and a 2 kg print will be 84 um taller. As the kids say, meh.

The flatness of the bed, even tooling plate, will vary by that much, and first layer thickness will vary from the design value depending on how you zero the print bed. Top layer infill is rough and you will get different thickness measurements depending on where you place your caliper. In the end, the error due to belt stretch is on the same order as and is masked by the other errors. If you gotta have um accuracy in the height of a 2 kg print, smooth the top surface with a piece of sandpaper.

I understand what your saying, but in the end, the distance from the bed to the extruder will still be 42um further away than the 3d printer thinks it is. Thus, instead of being 100um away from the nozzle (if thats your layer thickness), you will be 142um. I thought the extruder/hotend would still put down a 100um layer, and have a 42um gap where filament could move around a little before hitting the previously laid down layer. Is this how it happens, or would more filament actually come out to fill that 42um gap so that you would actaully be putting down a 142um layer? If I'm wrong and the second is the case, then the rest of my argument definitely becomes moot. Also, realistically, if that's the case and the hotend doesn't put out the exact same amount of filament regardless of the height of the bed from the hotend, then to your point, it would never get to the 42um gap either.

I was worried steel core would be too stiff for X/Y axes too...I'm trying to find some kevlar core belts for that but they are expensive so I currently have it priced out with glass core as well.

For weighted bed, yes you can't completely counterweight. I'd leave probably about 1lb unweighted. This would make the Ansys Output of .021mm X/Y deflection of the screw go to .0013mm, which I believe is definitely negligible and on the outside edges will be far overshadowed by any belt stretch of X/Y belts changing direction. But you are correct, you can't take all of the load off so you can use gravity as anti-backlash. Personally I'm okay with it looking ugly if it works great, so I don't care about the ugliness of it, but I can think of weighs (get it?) to make it look more appeasing. With a corexy fully framed setup, actually doing it would be very easy. Also, as you pointed out, as the print grows, the more the weight of the print will still affect it. With screws, as it grows, the load point is further down the screws which creates a positive impact on the deflection and will counter the weight of the print. With belts, it will still cause just as much stretching as w/o counter weights, so counter-weights on a belt driven z-axis is for a completely different reason (bed-drop) vs using it on lead screw configuration (prevent screw deformation induced wobble).

Edited 1 time(s). Last edit at 04/22/2017 10:12AM by shortyski13.

Steel core belts are good but don't run them around anything smaller than a 20 tooth pulley or 6 months later all the steel cores will fatigue and snap one by one, creating very sharp protruding wires, and 5 pages of forum posts trying to puzzle out why my delta was printing leaning towers but only up to 70mm, after that they were straight!

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Simon Khoury

Co-founder of [www.precisionpiezo.co.uk] Accurate, repeatable, versatile Z-Probes
Published:Inventions

You're still not getting it. In my example, the distance from the nozzle to the bed will never be more than 200.945 um. The error is cumulative and the total error in a 1kg print is 42um. There will never be a layer that's 242 um thick.

Edited 1 time(s). Last edit at 04/22/2017 11:47AM by the_digital_dentist.

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Ultra MegaMax Dominator 3D printer: [drmrehorst.blogspot.com]

Quote
the_digital_dentist
You're still not getting it. In my example, the distance from the nozzle to the bed will never be more than 200.945 um. The error is cumulative and the total error in a 1kg print is 42um. There will never be a layer that's 242 um thick.

I completely understand what you are saying. What I'm asking is: If there is 201um gap between the extruder and the print, and your printer is set to 200um layer heights, will it lay down 201um layer of plastic, or 200um layer of plastic?

I've got some fancy calipers but they don't read to 0.00x mm.

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Simon Khoury

Co-founder of [www.precisionpiezo.co.uk] Accurate, repeatable, versatile Z-Probes
Published:Inventions

The thickness of the plastic is always the distance from the nozzle to the bed or previous layer. If the extruder is squirting out plastic for a 200 um layer and the space is actually 200.945um the layer will be slightly under extruded which will show up as a slightly narrower line.

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Ultra MegaMax Dominator 3D printer: [drmrehorst.blogspot.com]

Quote
the_digital_dentist
I think constraining all four corners of the bed support is likely to end in the mechanism binding at the slightest misalignment. Two bearings should be enough if everything is perfectly inflexible, so three should be plenty in the real world.

Belts vs lead screws is a personal choice. Belts look like a cheaper alternative initially, but when you solve the bed-drop problem, I suspect the cost ends up about the same. Belts do make it pretty easy to build the Z axis to any arbitrary length. In a printer with a very long Z axis belts may be better than screws because they can't produce lateral forces that will create Z wobble in the print. It can be difficult to build a very tall machine rigid enough to withstand the lateral forces that offset motor couplers, etc. can produce in a screw driven system- in that regard a very tall machine is similar to a small, cheapo machine with a rickety frame. In a very tall machine when the bed gets loaded with a massive print (that's why you're making it tall, right?), the screws may bow under the load and that may produce some of those dreaded lateral forces when they rotate. In a belt driven Z axis the belts will stretch a little, but won't create any lateral forces.

What do you mean when you say that the lead screw will bow under the load? I've calculated the column strength of the lead screw and it seems that as long as you fix the ends correctly, 10 or 12mm lead screws should be fine.

In a printer with a screw lifted Z axis, the screw(s) support the weight of the bed assembly and the print. The screw(s) have to attach to the frame at some point, either at the top, or the bottom of the screw(s), or both. If they attach to the frame at the bottom, you have a large weight (the bed assembly) standing at the top of long, skinny screw(s). That weight will cause the screw(s) to flex. I can't tell you how much, and it may not be significant, just pointing out the possibility.

What's more likely to be a real problem than an imagined one is that the longer the lead screws are, the more likely they are going to arrive bent. You will have to make sure the Z axis has solid guidance and the lifting nuts are allowed to move laterally, or the screws will move the bed laterally as they turn, the same way they move the X axis in a cheesy printer kit that uses end support guide rails in the Z axis. If you use fully supported rails in Z it may not be a problem, but I would never consider end support rails for a printer as tall as the one proposed.

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Ultra MegaMax Dominator 3D printer: [drmrehorst.blogspot.com]