“It appears that undercut can be eliminated in some cases but in most cases, the elimination of undercut, for example by increasing the root fillet radii of a pinion, results in performance problems in the operation with its mate. My question is, when can I eliminate undercut and why is it not possible in most cases?”
Since the macro geometry of bevel gears is directly dependent on the manufacturing process, there are limitations in the combination of pre-machining and hard finishing processes which are related to the geometry of the gaps.