You will need to connect the motor to the leadscrew with a shaft coupling. The shaft coupling allows for a small amount of angular and linear misalignment of the motor shaft and the lead screw. The coupling will also manage the different diameter of the leadscrew (1/2") and the motor output shaft (1/4").
Lovejoy couplers are cost effective. Depending on choice of spider material backlash on the couplings will increase over time due to deformation of the spider. There are a variety of elastomers to choose from - Urethane or Hytrel would be a better choice than the low cost Buna-N Rubber. When you buy the lovejoy couplings you have to buy 2 couplings plus the spider to complete the assembly. Since most stepper motors have a 1/4" shaft and we need to couple to the 1/2" leadscrew, we will select a 1/4" and 1/2" coupling with a urethane spider. The spider also dampens the vibrations from the stepper motor for quieter and smoother operation. Urethane spiders do not dampen vibration as well as the rubber spider, but can handle 1.5 times as much torque.
To order from ENCO www.use-enco.com , the following part numbers are needed. You will need to order 3 sets, one set for each axis. A set consists of a 1/2" hub, a 1/4" hub and a spider.
Hub 1/4" Inner Bore 1.08" OD 1.72" Length
The motors that drive each axis are not designed for axial loads. You need to decouple the thrust of the leadscrew from the motor by using a thrust bearing. This is important. Leaving out the thrust bearing will result in damage to the motor over time. Thrust bearings are cheap, motors not so. Use them. ENCO and McMaster have good prices on needle type thrust bearings. These are preferable to the low-cost ball style thrust bearings as the thrust is distributed over a larger area. The ultra low cost ball style thrust bearings are better than not having a thrust bearing at all though.
Needle style thrust bearings are more suited for heavy duty low friction work.
No matter where you buy your thrust bearings, for a complete bearing you'll need one cage assembly and two washers.
P/N 5909K31 Needel Roller Bearing Cage Assy $2.65 ea
P/N 5909K44 0.032" thick Steel Washer $0.90 ea
P/N #891-4795 Needle Roller Bearing Cage Assy $2.95 ea
P/N #891-4802 0.032" thick steel washer $0.95 ea