Show us your wireframes? Likely has to do with the two intersecting cylinders segments not lining up. If even if they are an even amount perfectly and are welded/lined up, the curvature of the cylinder could ruined the moment you move/weld things out of place, giving you those shading artifacts.
Yeah, judging from the wireframe: * too many edges * edges/cylinder segments on the inare not evenly spaced, ruining the curvature already * edges are not lining up with the perpendicular cylinder edges Depending what this mesh is used for (offline rendering? game art? highpoly/sub-d model to be baked down?), just start…