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I tried to model something like a cog. I created one tenth of the cog, mirror modified on 2 axes and added a circular array modifier to get the final result, using the merge option.

When I import the final model in Substance Painter, it looks as if the normals were off on the big flat surface. At least that's how I interpret it:

enter image description here

Any ideas what could be wrong here?

I checked, and all of the selected vertices below are on the exact same Z. Not their median, but the individual values.

enter image description here

If I simply create a circle mesh and fill it, I get a perfectly flat mirror surface:

enter image description here

enter image description here

EDIT:

Shading entirely smooth or flat doesn't seem to influence this issue:

enter image description here

enter image description here

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    $\begingroup$ Is the shading set to smooth (of the problem faces)? $\endgroup$ – Mr Zak Aug 18 '15 at 16:10
  • $\begingroup$ @MrZak Should be flat. I added two images to my question. Once is shaded entirely flat, the other smooth. The artifacts are visible on both. $\endgroup$ – Jawap Aug 18 '15 at 16:30
  • $\begingroup$ Try selecting all vertices and removing doubles ( W --> Remove doubles ). Seems to me you might have created quite a few doubles by modeling with the array modifier. $\endgroup$ – TLousky Aug 18 '15 at 16:48
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It seems to be an UV issue. I mapped identical parts of the cog to identical areas on the UV map. Substance Painter doesn't seem to like that. Unreal Engine doesn't seem to have this issue. I now applied all modifiers and smart UV unwrapped and I'm finally having no artifacts.

enter image description here

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Based on the other answer I created a Blender add-on for this exact purpose called TiNA which allows you to more easily transfer normals between objects. TiNA basically turns the somewhat overwhelming Data Transfer Modifier into a set of more comprehensible operations.
There's a special branch for those using Blender 2.80 beta.

TiNA|

 Hotkey           | Operation 
------------------|-------------------------------------------------------------------
 Alt+N            | Transfer Normals from selection to active object
 Shift+Alt+N      | Transfer Normals from active object to all other selected objects
 Ctrl+Shift+Alt+N | Clear Custom Normals data for entire selection
 Alt+W            | Wrap Normals

You can selectively transfer normals from a source object (possibly just a plane) by selecting both objects, and - with the target object as your active one - hitting Alt+N. You can then select a vertex group to limit the effect.

Example results

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