Shaft with rigid coupling between two bearings
What is supporting the vertical shaft in position? Is there a thrust type bearing at the bottom of this shaft to support the hanging weight? Or a fixed bearing at the bottom? Since you are using a solid flange coupling, the shaft "acts" as if it is one solid piece. Expansion and contraction of the shaft with temperature changes might be problematic if the Delta T is enough and the shaft is long enough.
You should have a "fixed" bearing at the top nearest the sheave to support the weight of the shaft and also keep the drive and driven sheave aligned to minimize belt wear and sheave wear. That is, if you do NOT have a fixed or thrust bearing already mounted to the shaft elsewhare. If there is a thrust type bearing or a fixed type bearing mounted on this shaft elsewhere, the bearings on either side of the solid flange coupling can be expansion type. Self aligning bearings in pillow block or flange block type should be used. Flange type are easiest to mount and "center" in a vertical application.