The smooth rod is to maintain the proper X and Y position of the Z carriage. The threaded rod is to move it up and down. The distance between the two doesn't matter, except if the threaded rod is working against the smooth rod. If this happens you will get some sort of X and/or Y position issue (ripples or ridges).
As it is difficult to maintain perfect alignment between the two and the threaded rod may not be particularly straight, the vertical position system is designed so the threaded rod can "float" and not affect the positioning held by the smooth rod. This float is accomplished by the flexible coupling on the motor end and by not constraining the other end of the threaded rod.
In the case of my Anet A8, there were a number of problems that were causing X and Y printing issues.
1 The flex couplers came installed on the motors, and I installed the motors without checking them. It turns out that the couplers were install far too deeply onto the motor shaft, effectively eliminating any flex in the coupling. Both the motor shaft and the threaded rod should only penetrate the coupling far enough for the set screws to properly secure the rods.
2. The motor was mis-aligned enough that the threaded rod was pushing into the side of the guide hole at the top of the shaft. This was fixed by moving the Z to home, loosening the motor mounting screws and shifting the motor until the top of the threaded rod was about in the center of the hole. It may be necessary to "slot out" some mounting holes to do this. After this is done, run the Z to the top position and verify that the threaded rod never touches the side of the hole. It may be necessary to increase the hole size or find a straighter threaded rod. If the threaded rod touches the sides of the hole at any point in travel, it will cause the X and/or Y to be forced out of position and cause printing problems.
3. The smooth rods were loose in their mounting holes. The smooth rods are what holds the carriage in the proper X and Y position, if it can move, it will allow the X and Y to shift depending on the drag from the hot end. To fix this I shimmed the smooth rods to be tight in the mounting holes, top and bottom. The Y carriage rods should also be tight, or you may have issues show up in X positioning.
All this should be done on both Z axes, of course.
I hope this helps with your issues.
-Brian
