# When to use an anti-backlash bolt for a Z drive gear?

I am building an HEVO printer with a 300x300 build plate and the project includes two T8 lead screws, lead 8 mm ("Tr8x8(p2)").

I read that such long lead may worsen backlash issues, so anti-backlash bolts are often used. They however increase the torque required to drive the build platform (quite important, since 8 mm lead involves using microstepping for fine adjustments) and they also reduce the usable vertical travel.

Since the build plate has already a significant weight (2020 frame, 2x 2 mm aluminium plates, 4 mm borosilicate bed, 8 linear bearings, heater), I wonder what is an approximate weight threshold to decide for using the anti-backlash or to skip it.

• I have exactly the same machine (using Tr8x4(p2)), I installed POM backlash nuts, but I'm using the native steps for Z movement. – 0scar Jun 8 '20 at 8:43
• The weight of the bed already provides anti-backlash. I don't think using anti-backlash nuts would provide any further improvement. – Tom van der Zanden Jun 8 '20 at 9:42
• @TomvanderZanden I thought so, but I wondered whether a general rule is available. – FarO Jun 8 '20 at 9:49
• I'd just use a lower lead... – Trish Jun 8 '20 at 11:59

First of all, let's look at the geometry: We have a static XY and changing Z on our build plate. This mitigates several problems we might have faced in a different setup, mainly that our lead screw has loads changing from one face to the other: all loads always go into $$-Z$$, so the lower surface of the Trapezoidal threads in the brass nut of the bed carrier and the upper surface of the screw will always rub against each other.

However, let's talk about your lead. Tr8x8(p2) is not a Metric ISO-Trapezoidal pattern that is commonly recognized - the only 8 mm diameter one in that standard is Tr8x1.5, very flat and very well suited for putting high loads onto it because there are several engagement surfaces in the nut and a low pitch angle - the thread only has about a 5° (+-1°)to the horizontal. Assuming a 15 mm nut, that's 10 times the projected engagement surface for a total area of about 214 mm².

A Tr8x8 is a very common oddball as in, it's not in the metric tables but available everywhere. It is considerably steeper, and with a 16 mm nut (for easier calculation) would result in 2 times the projected surfaceof a single engagement per thread. But that's only a projected area of 42.8 mm² per thread - about 1/5th of the Tr8x1.5, which correlates directly into that much less friction, because the friction is linear with the surface, which is linear to the length of the nut.

Taking an "intermediary" TR8x4 gets us about 1/2.5th of the Tr8.1.5's holding power per thread at the cost of half of the speed. From a physical standpoint, I'd take this one, also increasing the precision of the Z-movement by a factor of 2 in comparison to the Tr8x8.

Generally speaking, we have a tradeoff here:

• Pitch is proportional to the movement speed
• double the pitch and you move twice as fast
• Pitch is anti-proportional to holding power/torque and Z-position accuracy
• half the pitch gives twice the torque and the Z-position error is in average reduced by half
• holding power is proportional to the diameter of the rod and the number of threads engaging with the nut
• Z-position accuracy is anti-proportional to the effective step-size of the motor
• Z-position accuracy can be increased by using a reduction gearset: a 2:1 reduction gear halves the step-size and doubles the torque at the price of halving the movement speed. However, it can and will introduce slop and backlash.

Due to the geometry, the slop in the nut should not be an issue, as the relevant engagement surfaces never change. Further, the heavier the bed, the fewer problems you'll have with fast movements, as gravity will prevent the bed from going "airborne" at the end of travel towards the printhead. Travel away from the printhead, as it will do during printing, should never experience such.

• Well with bed mesh leveling movement is in both directions, but never fast. But if the only issue is going "airborne", then I can reduce the weight of the bed using a pulley and a counterweight to quite low values, before backlash becomes an issue? This would reduce the torque required to move the bed in position, and also allow higher microstepping (which is an issue if you need a lot of torque, which I would avoid). – FarO Jun 8 '20 at 15:26
• @FarO actually reducing the weight increases the chance of going airborne, so keep it high, then the weight force will ensure contact. Only if you go really fast you even get the chance to go airborne. But yes, reducing the weight does reduce the torque needed. – Trish Jun 8 '20 at 15:48
• Do you know how to calculate, roughly, the torque required to lift a defined weight with different lead screws? of course assuming reasonable lubrication. This way, the weight could be kept lower than what the motor can hold, but also high enough to avoid loss of contact. – FarO Jun 8 '20 at 17:39
• But does the weight even matter to calculate loss of contact ("going airborne")? shouldn't it depend only on the downward vertical acceleration of the bed? which can be easily controlled using the print/machine settings. – FarO Jun 8 '20 at 17:43
• The airborne state is extremely unlikely to appear in normal operation unless you regularly hit your printer from below, that's why I said it is unelectable. For the other... we had that somewhere... – Trish Jun 8 '20 at 18:12