This is the all-quad geometry which the bevel modifier is having a problem with!
There are two meshes in this picture. The outer mesh has bad topology and N-gons everywhere but the bevel modifier gives a decent result. On the other hand, the inner mesh (all quad) looks very distorted with the bevel modifier applied.
I do not understand why bevel modifier cannot properly handle such a simple mesh. I have fixed the geometry so that my mesh has all quad. I also applied Scale and Rotation in Ctrl+A menu. I have also tried different bevel method like Angle, Weight and Vertex Group. All of these methods give the same terrible result as you can see above.
Without knowing the intricacies of blender but having seen similar artefacts when writing my own bevel tool I would suggest that there's something wrong with the mesh. Assuming you don't have duplicate edges and that everything is welded properly you probably need to reinitialise the mesh and clear out any transforms or history.
In maya you'd combine it with a fresh mesh to do that - no idea what you'd do in blender
From the first picture it looks like it might be a flipped normals issue. Can you try pressing Shift+N in edit mode please? If it fails please provide the file and I will have a look
From the first picture it looks like it might be a flipped normals issue. Can you try pressing Shift+N in edit mode please? If it fails please provide the file and I will have a look
That was exactly the issue. Thank you for pointing out.
I'm glad that worked out. Also I just noticed you're on 2.79 so the info I gave you was slightly incorrect - in 2.79 'Flip Normals' is Ctrl+N, whereas in 2.8 it's Shift+N. If you ever feel like something is off and it might be the normals I recommend changing matcaps or turning off backfaces as it's very hard to see flipped normals on this specific white matcap.
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Assuming you don't have duplicate edges and that everything is welded properly you probably need to reinitialise the mesh and clear out any transforms or history.
In maya you'd combine it with a fresh mesh to do that - no idea what you'd do in blender