Hat problem: embroidery looks fuzzy, fine on flat though

Good cap backing is a must...the images provided don't seem to show any stability of it being present.

When doing the H test, be sure your show on the back of the design is 1/3 top thread, 1/3 bobbin thread, 1/3 top thread. If the bobbin thread is showing off center, it's not correct.

From the images, I would guess your top tension is too loose and your bobbin may be too tight....just an assumption on that one. Any way of getting a view of the back side of the design? When adjusting the bobbin, remember the slightest turn makes quite a bit of a change in tension. Tighten your top tensions a couple turns and test after each adjustment until you get the show on the back needed. When I pull my thread through the tensions, it's similar to that "feel" of reeling in a fishing line while trolling. Some tension, but no resistance.

Also, to finish off any embroidery, use a heat gun to tighten any minor imperfections. This will melt back the bobbin thread on the back side of the designs and also tighten any loose stitching on the front side.

Give a shout if you have any questions. I may be new here, but I'm not new to digitizing and embroidery.

I would agree with the above ... Especially on the stabilizer, also, the bottom picture of the black hat doesn't look like its hooped very well. The metal top band is not sitting on the seam of the cap, its pulled back onto the brow material.

You said you use SWF. Are you using the cap needle plate? SWF makes a needle plate that has a "collar" around the needle hole to tighten up the presser foot depth of the needle bars. Are you using that? That I have found to be a HUGE issue with SWF's

Also in agreement with streetlight, it does very much look like a tension issue. Thicker materials have a tendency to behave better with loose tensions. I have found that SWF's seem to run better when the tensions are on the tighter side when compared to other machine brands. However, as long are you are geting the 1/3, 1/3, 1/3 on the H tests you should be in the ballpark.

Try drastically changing the tension on the one needle. and see if it makes your problem better or worse, that will give you something to go by.

Hope that helps.

Try a new needle, and maybe check your bobbin thread. I ran into this problem once before by just changing hat types. The different material made all the difference. I switched to a sharper needle and re-adjusted the degree a bit on the needle. That helped. Also, you may need more backing.