Just a little something I threw together today.
Let me know what you guys think!
I know, on the logo model, it isn’t completely smooth, and I am not quite sure as to why that is, I made this by modeling the geometry using a plane, so that could have something to do with it, I also used the smooth shading. So, if anyone has any ideas on how I can get rid of that, I would be very happy.
Anyway, leave some feedback! Thanks. 
Hi,
To get a smooth model you should use the subdivision surface modifier AND set the crease to 1 for edges you want to keep sharp.
I have the subdivision surface modifier, and I have it set to 3 subdivisions, but I do not see a crease option.
I think you use the subdiv for the blue part of the logo, but not for the yellow part (by counting the edges I would say you used a 32 segment cylinder as a basis).
Be sure you add the modifier to each mesh.
The crease option is in the right panel of the 3D view window, in Edit mode. Just select your edge and change crease from 0 to 1 to get a sharp edge, or play with intermediate values to get something that please you.
They both have a subdivison modifier added, the yellow part started out as a plane for the basis, and a modeled it from that.
You may have problems with subdivision surface if the topology is not good:
You try in edit mode selecting those faces and Split (Y key), or Edge Split modifier.
You also watch your normals: in edit mode Ctrl+N (Make Normals Consistent)
Please post your blend file or a wireframe render if you expect more help, without that it is hard to find where the problem is.
Ok, I found the problem.
You actually used “simple” subdivision modifier instead of “Catmull clark”. “Simple” does the same as the subdivide tool: it creates new vertices on a straight line in the middle of each edges. Catmull clark creates a vertice in the middle of an edge too, but it also makes the topology smoother, which in your case leads to this donnut shape.
What you have to do is switch fro simple to catmull-clark (1), go in edit mode and select the edges you want to make sharp in edge select mode, not vertices select mode. Then you change the crease from 0 to a value close to 1 that create a edge sharp enought to you (2).
You have some topology problems too. There are triangles in you mesh that will lead to shading artifacts and you should get rid of it.
On the image below red circles indicate the major problems and the blue lines indicate some modifications you can do to eliminate these problems. I think your spiral on the left side is not gonna make it.
The base principle here is to use radial lines and to add a edgeloop in your circle.
Modelling this logo fro a cylinder would be easier.
You also have a lot more edge loops than you need. Let the subserf do that. I would start from somewhere around a 16 edge cylinder or circle.
I will try that. I don’t know why I thought it would be easier to start with a plane. Haha
I’ve tried to work with them before, but personally not a big fan. Haha
