Running directly on the 2020 frame (e.g. with pulleys or teflon blocks or something) would likely be quite a good option. The z axis doesn't see a lot of cycles or speed, so you can worry less about wear than the x and y.

It's a bit of a conundrum this bed stiffness thing. Four corner rails, with double bearings on each corner (plenty of distance between the pairs, maybe even more than pirvan has there) - or something equivalent with bearings on the frame - and a z motor on either side would probably get you as close as you need. It's a fair bit of hardware though, which is probably why commercial / budget printers don't go there - they figure the bed stiffness is probably not as important as the cost.

My printer 2.0 is looking like 4 corner rails and some experimentation with spectra line and pulleys to positively restrain everything!

For monk and claghorn- do you really think any type of wheels on rails system would be strong enough for a Z axis?  I kinda feel that this needs a bearing on hardened rod solution.  Keep in mind all the forces that are transmitted when you have to scrape a print off the bed.  Got any examples of a successful Z axis using wheels?

People build CNC machines with the openbuilds v-slot rails and wheels that probably experience much greater forces than bed scraping causes.

You'll probably want to do a dual motor/screw Z axis, with the screws cross-corner from each other and smooth shapft on the other corners, like this:

I'm not quite sure I like this design.  First, it only has two linear rods.  If I did my idea and moved the linear rods to the left and right, I can have 4 rods and 2 lead screws.  With only 2 rods, and assuming the lead screws are not supported at the top, you are putting some serious stresses on those two rods every time you do something like take a scraper to the build plate to remove a print.  I'm just not convinced it is sufficiently rigid.

My main question at this point is if I have to use two lead screws if I go to a 4 linear rod system and support them on the front/ back or left/ right.

So the main issue that I am hung up on now is that the Z axis is just too flimsy as built.  A bump on the table sends the whole build plate wobbling and there is visible bending on the bed holder.  This is only from the weight of the parts themselves, I have been very careful to not apply any forces to it.  The bending is not really surprising due to the fact that the table is only supported in the back with no braces.  Apparently just because that bed holder worked for ultimaker does not mean it will work for me.

So I am looking to redesign the Z axis.  I like using the 12mm rods and the M8 screw will do for now, but I'm convinced a bed holder of this size simply cannot be cantilevered and must be supported from two sides.  I see a couple options:

1.  Get more 12mm rods and M8 threaded rods and another Z motor and move the entire Z axis assembly to the left and right sides of the machine.  This presents a potential conflict with the moving X motor.  Potential resolution:

• The bed would have to be mounted on quite long M4 screws and springs to reach the hot end (which could lead to bed wobble).

• Or I have to find a way to hang my hot end much lower, which would be an entire redesign of the X carriage (a lot of work).

• Or I could cut a hole in the bed holder for the X motor to slide thru (which leads to a weaker bed holder)

2.  Get more components and add additional 12mm rods for support in the front of the machine.  This eliminates the conflict with the X motor.  However, I can't really do a dual Z motor configuration like this without putting the motor shaft/ M8 rod right up the front and center of my printer.  This is clearly unacceptable from an aesthetics and functionality aspect, but I'm not sure if 1 threaded rod will be enough to drive this relatively large and heavy bed holder.  If it is only being driven on one side, I think it might cause binding.  What do you think?

Both options require fabrication of a large bed holder with tight tolerances.  I can design it in openSCAD and leave oval shaped screw holes in one side in case it needs slight adjustments.  I could make this bed holder out of wood, but that does not offer as good as a strength to weight ratio of metal.  I'm thinking 1/8" aluminum might be a good choice and I could look into getting it cut on a CNC or water jet aluminum cutting, although I have no idea what either of those would cost.

If none of the above results in a sufficiently rigid Z axis, my "nuclear option" is to abandon the solidoodle carriages and go to an ultimaker style gantry, eliminating the X motor conflict and moving the Z axis components to the left and right.  I was originally inspired by this: http://www.thingiverse.com/thing:666549 so I know it can be done.  This would also leave me the option to eventually change this printer into a coreXY design too, if I'm ever feeling that ambitious.  The downside of the ultimaker design is that I loose my ability to print ninjaflex with the bowden extruder.  But I understand everything is a compromise.

Any thoughts on how I can make this Z axis better or move this build forward are much appreciated.  Thanks.