Help with generating support material

I'm trying to understand how to use support material for overhangs. I created a simple hollow cube with a ledge in the center. I enabled creating support material and it generated some really weird material. I had hoped it would be easy to snap off the support material and have a well formed part.I was not so lucky. The material was hard to break off and left a very uneven underside on the inside of the cube.

If I don't enable support material, the center ledge sags a lot since it's spanning about 16 MM.

Can anyone provide some suggestions for settings for support material that may work better. I only enabled support material and left everything else at the defaults.

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3D Printer: Reprap Original Mendel with RAMPS 1.4 electronics, j-head MK V-BV 0.4MM extruder, Wade's geared extruder, setup for 1.75MM filament

Generating support is a science, an art and a... nightmare.
I was not able to generate reasonable support with Slic3r since 0.9.1b, so when I really need support, I'm using that version
Now, the truth is you can "support" your piece in different ways, this being much dependent on the piece configuration.
For example, particularly for your piece, I would "close" the hole with a tiny diaphragm, one layer height, and use bridging capability to cover the empty space below. Then, next layer will build on top of it. At the end, just cut or drill the diaphragm.
For 16 mm, it should not sag. Reduce bridging speed (e.g. 20 mm/s) and temperature (if needed) and you will have a pretty bottom.
Another way would be to build a hollow cylinder, one layer thick walls, that would support the... hole. When coming to the "ceiling", it will also use bridging, but the distance would be shorter. At the end, just remove the cylinder.

The part I'm really trying to print is the Wade's Geared extruder body. I measured the cavity on the bottom side for a bearing at 22 MM in diameter. The whole part is pretty large and I don't want to waste the time and material to print it many times until it works correctly. My first attempt without support material looked great for all the other surfaces except that one cavity on the bottom.

The part I want to print is available as an STL file, so I cannot modify it to add parts for support. That is why I'm hoping to get slic3r to add support correctly.

So for testing, I created a 25 MM cylinder with a 22 MM pocket on the top and bottom. Once I can support that correctly, then I'll try the part I really want.

I slowed down the bridging speed to 20 MM/s and lowered the temperature from 200 C to 190 C (I'm using 3 MM PLA that is recommended to use between 190 C and 210 C).

As you can see from the attached pictures, it didn't turn out very well.

Any other suggestions would really be appreciated.

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3D Printer: Reprap Original Mendel with RAMPS 1.4 electronics, j-head MK V-BV 0.4MM extruder, Wade's geared extruder, setup for 1.75MM filament

Try 0.9.1b with default settings for support.
However, it's something wrong with your bridging. I think you have some settings that do not work together well. I see concentric fill. I simulate with your model and with 0 top and bottom layers and the path was trying to lay circles in the air. Seems you have to have at least one bottom layer for bridging to work. And when you have, the first "disc" over the hole will have 100% linear fill at bridge speed, no matter which fill pattern you use for other purposes.
To modify an stl (just in case you need sometimes), you can import the stl in 123D Design (free from Autodesk) create the modifications with built-in primitives and then export as stl. Sometimes works

I backed up my settings for slic3r 1.1.7, removed it, and installed slic3r 0.9.10b and used the default settings (other than my filament specifics). It didn't bridge a gap that large either. Then I enabled support material and it actually worked. It supported the middle pretty well and I was able to break away the support material with a small flat blade screwdriver. For now I'll stick with the older version of slic3r.

Thanks for the help

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3D Printer: Reprap Original Mendel with RAMPS 1.4 electronics, j-head MK V-BV 0.4MM extruder, Wade's geared extruder, setup for 1.75MM filament

As for no-support:
Set the number of perimeters to 1 instead of 4. Your wall is less than 3 perimeters wide. Slic3r lays the fourth perimeter in the air. In order to get bridges, ends of bridging strands should be put onto something. Lateral adhesion is very unlikely to happen with nothing underneath.

I've basically given up on slic3r. I now use Cura and it works much better. With slic3r I had to use older versions to get support to work and newer version to get other parts to work correctly. Since the ini files are stored in a common path, I couldn't have different version setup at the same time.

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3D Printer: Reprap Original Mendel with RAMPS 1.4 electronics, j-head MK V-BV 0.4MM extruder, Wade's geared extruder, setup for 1.75MM filament