It’s the tale of a sphere that had a difference boolean modifier with 5 tores and two small spheres.
Everything runs fine in flat shading but there is a like a distorsion around the intersection with the small spheres while turning to smooth shading.
The normals are OK.
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Edge split modifier, changing angle value to suit or turn angle off ans select edges and Ctrl+E / mark sharp
Also please ALWAYS show screenshots and importantly attach or post a link to your blend file. Only you can currently see your scene, everyone else has to use their imagination, the result of which differs from person to person.
It’s probably because when you use the boolean modifier it tends to put lots of edges going in to one vertex. This makes faces with very small angles, all concentrated at one point. Not good for a smooth model. If you apply a subdivision to it, you’ll see the problem even more.
Best advice is to retopologise. Delete the edges and faces connecting the hole and the surface of the sphere and start building up faces which are a bit more spread out. You’ll probably need to use loop cutting to make sure you get a nice distribution.
I am getting a good result when smoothing the big sphere before applying boolean modifiers with the small ones.
I am also getting a buggy situation when increasing the resolution of the big sphere when applying the boolean modifier with the last tore.