Finest z-axis leadscrew solution with zero backlash

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macpod
I'm working on building an SLA printer

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cnc dick
I have been trying to explain this to the reprap community for a while now. The linear bearing and rail and frame that it's attached to has to be extremely strong as far as the screw being bowed doesn't matter as it turns it will straighten itself out without flexing the linear rail and bearing system. This is the way you design systems the Z axis has to be rigid enough that any push from the screws side to side does not affect it. I do not see too many printers that have anywhere near adequate Z linear systems that is why some people with printers use little teeny quarter inch or 5 mm diameter threaded rods because they straighten themself out really easy and don't deflect the Z axis bearing system very much. But the real root of the problem is the z-axis linear system is just nowhere near strong enough. I've built a lot of systems with ballscrews and Acme screws thing is you really should never use regular threaded rod it's really not made for that purpose. Thread pitch doesn't really matter as much as you think if you make a good bearing system or purchase a ballscrew bearing mount you can run a belt and pulley system to the screw and use a belt reduction from motor to the screw. Here is a picture of a small milling machine I made yours doesn't obviously have to be this strong but it shows the motor pulley system driving the screw for the Z

s1333.photobucket.com

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A2
DLP-SLA or SL Laser?

Suitable resin chemistries
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3D DLP Printer, 14″ of travel
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nicholas.seward
Backlash is only a problem for an axis that switches directions. With a z that will continually raise in one direction, the backlash can almost be as big as you want assuming you don't have anything vibrating your system. I would highly suggest an ACME screw with a normal flange nut. I would cry to see a ballscrew or an anti-backlash nut wasted on a slow moving unidirectional axis. Even if you switch directions, you will move so slow that gravity will push you down to the lower extreme of your play.

Try to avoid gearing to increase your precision. In theory you will be fine but it will increase cost and complexity. With the 12TPI a traditional full step will be 10 microns which should be all the precision you need.

I agree with cnc_dick. You need to make sure you have a well supported z. That is easy enough to do. Resist the urge to mount both sides of your screw. Your screw should be coupled to your stepper and then you should remove any end play the stepper might have by using some thread clamps (dumptercnc) to sandwich two bearings against a rigid frame element. I usually do this close to the coupler and then the other end of the screw hangs loose after it goes through the lead nut. This will make alignment less of a headache and will keep the screw from exerting sideways forces on your z axis.

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macpod
Z-axis travel will occur in both directions every layer. In addition a "knock" will occur for every layer. These are why I'm looking for a zero backlash solution.

12tpi may give you a theoretical 10 microns but that is assuming the leadscrew threading does not vary. I'm looking for finer in an effort to:
1. Avoid gearing/belts if I can.
2. Try some "oversample"-esque experiments.

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cnc dick
This plenty of belts to choose from here in the US as far as tension goes not that critical with steal reinforced belts you just have the motor be able to slide. But you had mentioned Nema 17 motor you have plenty of room and it is not going to move the motor I definitely would go with a Nema 23 motor much more power for same amperage

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nicholas.seward

I assume that after you burn your layer in you will move up and then back down. In that case you still don't need a anti-backlash solution because you will always be approaching the positions that matter from the same direction.

What resolutions do you need? The error from the threading won't go away if you gear down the screw. The only reason you would want to gear the screw down would be if you were going to map the error of the thread and get the firmware to use this info to do adjustments on the micron level.

Keep in mind that your lead screw will be +/- 250microns over 300mm according to McMaster-Carr. You can do better than that by calculating the actual pitch of the screw you get instead of trusting the nominal number. After that, you are left with local variations in the thread form that will vary from manufacturer to manufacturer. I suspect that you will be able get the resolution/accuracy you want by that point.

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nicholas.seward

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macpod
Z-axis travel will occur in both directions every layer. In addition a "knock" will occur for every layer. These are why I'm looking for a zero backlash solution.

12tpi may give you a theoretical 10 microns but that is assuming the leadscrew threading does not vary. I'm looking for finer in an effort to:
1. Avoid gearing/belts if I can.
2. Try some "oversample"-esque experiments.

I assume that after you burn your layer in you will move up and then back down. In that case you still don't need a anti-backlash solution because you will always be approaching the positions that matter from the same direction.

What resolutions do you need? The error from the threading won't go away if you gear down the screw. The only reason you would want to gear the screw down would be if you were going to map the error of the thread and get the firmware to use this info to do adjustments on the micron level.

Keep in mind that your lead screw will be +/- 250microns over 300mm according to McMaster-Carr. You can do better than that by calculating the actual pitch of the screw you get instead of trusting the nominal number. After that, you are left with local variations in the thread form that will vary from manufacturer to manufacturer. I suspect that you will be able get the resolution/accuracy you want by that point.

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A2
Calc Torque required to lift 5 lbs at the nut:
Ok, so now lets calculate the torque required of your stepper motor to lift 5 lbs with friction at the nut/shoulder pivot.
A max system weight = 15 lbs for this analysis.

Note: If the motor doesn’t have the necessary torque (plus start up friction) then you need to use a bigger motor or reduce the lead/pitch.
As you decrease the lead (axial travel / revolution) you decrease the torque required to lift a load, i.e. your mechanical advantage will increase.

There are different types of thread angles, and thread terms have been interchanged by unwitting groups.
So if you try to compare functions from different pieces of literature it can get confusing.

Note: There are 3 types of angles associated with a thread:
Lead angle (measured from the axis-plane to the thread profile) .
Helix angle (measured from the axis-center to the thread profile.
Thread angle (the included angle, between thread profiles, (2 x lead angle)).

There is also an angle taken from the normal (direction that the force is being applied), I forget what this angle is called?,
but it's the same as the lead angle (this does not apply to a square thread).

Roton Dia 1.00” x 1.00” lead:
Pitch (multi start thread) = 1.00”.
Thread starts = 5.
Lead of a multi start thread = No of thread starts x pitch
Lead = 5.00”.
Lead angle = arctan(lead / pi x dia of helix):
Lead angle @ pitch dia = arctan(5.00” / 3.1415 x 0.812”): = 63.00 degrees.
Helix angle = 90 degrees – 17.66 degree lead angle = 72.34 degrees.
Circumference = pi x d, or 2 x pi x r = 3.1415”

Terms:
p: pitch.
dm: pitch diameter.
u: coefficient of dry friction.
lambda: helix angle of the thread.
F: The screw is loaded by an axial compressive force.
N is the normal force.
Ff = u N: Friction force equation.
l: lead = No of thread starts x pitch
Tr: torque required to overcome the thread friction and to raise the load.
To : The torque required only to raise the load when the friction is zero.
a : alpha, lead angle.

Torque required for an Acme-threaded power screw, pg7:
Tr = (((F/cos a) x dm) / 2) x ( (l + pi x u x dm x sec a) / (pi x dm – u x l x sec a) ):

Variables:
F = 5 lbs
a = 63.00 deg
dm = 0.812”
l = 5.00”
u = 0.08

Tr = (((5 lbs/cos 63 deg) x 0.812”) / 2) x ( (5.00” + 3.1415 x 0.08 x 0.812” x sec 63 deg) / (3.1415 x 0.812” – 0.08 x 5.00” x sec 63 deg) ):

Tr = 4.4715 x ( 5.4495 / (2.551 – .8811) )
Tr = 4.4715 x ( 5.2142 / 1.6699 )
Tr = 4.4715 x 3.1225
Tr = 13.96 lb-in

Summary:
The stepper motor can deliver 26.75 lb-in, and we require 13.96 lb-in to move 5 lbs per stepper motor, or 5 lbs x 3 motors = 15 lbs.
You have about ~48% more torque than is required.
But if you derate the motor by half then you will stall the motor, which I think you said you plan to do?

So we can't work with a total system weight of 15 lbs, it would be OK to have a max system weight of ~7 lbs given this stepper motor.

Note: the max weight has to include the weight of the arms, bearings, extruder, etc.
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