I posted a few days ago about cylinder break in. The issue was that I was feeling vibration from the engine (O-360). No power loss and nothing unusual in the mag run up. The vibration is not severe and really only detectable under takeoff and cruise. The mechanic claimed #1 cylinder was not holding compression and pulled the cylinder. He said an exhaust valve was burnt. Seemed like a reasonable diagnoses and we replaced the cylinder with new. Flew the plane yesterday and no change, vibration still there. The mechanic says compression is good in all other cylinders.

Any ideas what could be causing this vibration? Right exhaust pipe past the muffler was detected to be a little loose. No prop issues (fixed pitch). The vibration appeared suddenly, put the plane away and no issues, next flight the vibration was there on takeoff.

From your Avatar you appear to have a 180A, ie fixed pitch.
The spinner bulkheads have a habit of cracking at the bolt holes.
The tail pipes are meant to be loose ish at the muffler U clamp, if not then that can cause vibration.
Are the #10 lower cowling screws in place?
Are the elevator hinge pins and bushings snug and the pins locked from turning?
Is it a fuselage or an engine vibration.
Has the prop been inadvertently bumped. Track the two blades.

After the vibration was first noticed, when we went to remove the lower cowl bowl, I noticed that one of the bolts (lower left side) had broken loose. The metal that projects off fuselage broke at that screw location and the screw was no longer doing anything. Do think that could be the issue?

Yes. The two lower cowl #10 screws are critical fasteners.
I have experienced this vibration cause more than once.
Make sure also the cowl is not hanging downward because of wallowed out holes from poor refitting.
Double check the front cylinder baffle rubber is upward halfway up the cylinders at least. Is top cowl contacting front plug wires or rocker covers.

I have a fixed prop as well, and due to the same vibration I had the prop balanced for $150.00.

It was like night and day.

Completely smooth through all RPM ranges and certainly less fatigue on engine components.

I can say that it is not the prop itself. I put it away myself in its own hanger. Nothing hit the prop and the aircraft only has 1000 TT.

When the O360 is shut down, it always produces a shake.
That last shutdown's shake could easily have caused a small crack to tear.
Repair boot cowl so the cowl screw has something to attach to.
Take the time to remove spinner and search for bolthole cracks.
Inspections are often done with the "hope" of finding nothing.
Inspections should be done "knowing" you can find something.

Something else to take into consideration is rotating parts installed with new cylinder? Lycoming's pistons weight can vary something like 20 Grams, that is a considerable variation? If prop has never been dynamically balanced, I'd suggest that would be worthwhile investment. Furthermore, it will tell you how much it is shaking after completion, and if you have it balanced by someone familiar with his equipment, he can even tell where vib is coming from to some extent?

Of course I'd check all the items as Jeremy pointed out at beginning of post and address those issues as well? I'd still balance prop if it's never been done, as balancing to engine can really make a difference... Good luck!

We are going to repair the lower cowl screw. I will be not only amazed but slap happy if that fixes the problem. It does appear to be a fatigue issue so it just might be the problem. We are almost sure that the vibration is not the engine itself. The vibration literally started overnight.

I will keep everyone informed and thanks for the help.

The following issues have caused vibration for me over the years. Mags due for overhaul, burned plug wire ends, bad plug, fouled plug, cracked spinner, cracked spinner bulkhead ( I replaced my spinner and bulkhead with the carbon fiber ones, they are pricey and the distributor is a big PIA to deal with and once installed the prop/spinner assembly needed to be dynamically balanced), worn Lord mounts and leaking intake tube gasket.

Cowl screw repaired, flew the tonight and no vibration. Jeremy was right. Just amazing. We are going to replace the engine mounts anyway. They are 20 years old.

Thanks everyone for this great web page!

Amazing that I might be right, or amazing that I was right.?
One screw story;
Your illustrious forum operator, manager, inventor, administrator, was picking up an M7 IO540 from Moultrie many years ago.
She set off west but experiencing an engine vibration, returned to the factory where the nose of plane was rolled inside the door.
Cowl removed and a piece of debris discovered in an injector.
Off she went again into the sky only to discover a different vibration.
The factory were now skeptical, she's 'just' a girl, she's a 'blonde' but she was adamant and got David Maule the president to go up in the plane with her.
David agreed about the vibration so nose of plane went back inside the door at the same place. In discussion with the mechanics, someone looked down and there on the floor beneath the cowl, was the "forgotten to be tightened" missing screw.

There is a much more expensive story of two missing screw attachments at this same place on cowling perhaps for campsite flyin discussion some day.

One of the things I had done on my recent purchase was to have all the cowl fasteners upgraded to camlocks,I too have seen vibrations from loose cowlings