Pro-Tip : Just buy a z-axis. It’s likely not worth the hassle, unless you don’t value your time. Or if this really and truly a hobby and you enjoy doing and redoing things.
That said I built a z-axis! I bought a bundle of parts off ebay and used that as a ground floor for measuring and designing. Having parts on hand provided a good starting point for scale and feasibility in Fusion 360.
From there it was quite a few iterations to draw up what would become the axis. During this process I learned a LOT about fusion, as I wanted all the movements to work so I could watch for clearance issues etc. Saunders Machine Works’ youTube channel was a huge help. The final drawing (looks like 42 edits) looked something like this.
Mounting the stepper that way was a little more work, but it keeps it from sticking out the top, and counter-balances the weight a little bit. Here is a zip file with the fusion model if you want to use it.
I started doing the manufacturing of the backplate the manual way. Lobbed off a piece of 3/4″ aluminum stock and started drilling, tapping, and cutting. Fusion allows you to print out 1:1 sized prints which worked super well. I just sprayed on contact adhesive and glued the template to the stock. It was a lot of holes, and a lot of tapping.
The studious observer may notice the two pockets where the bearing-blocks for the lead screw attach. Those I didn’t get done in my garage. At the high school they have a old cnc Haas mill that we have access to for working on the robotics team. They were kind enough to let me run the pocket operations I needed on that mill. Thank goodness! It would have been nice to mill the whole piece there, including the drill holes but I didn’t want to overstay my welcome.
Quick gratuitous Video of chips flying: