Problem with Lionel K-4 wheel flange

I have the Legacy version of the K4, never saw this happen.  Truthfully, I don't recall ever seeing this on any Lionel locomotive.

You can actually glue those back on with something like Loctite 380.  I've had that issue with 2-rail locomotives several times, that's how I fix them.

Had the same thing happen on my Century Club II Niagara. I judiciously used super glue in four evenly spaced spots around the rim and pressed it back in place. No issues since the re-installation.

There is actually some "special" stuff to do this exact job, though I don't have it in stock.  Loctite has a whole page of Retaining Compounds specifically for press fit parts.

Thanks for the advice. Will try the loctite. Crazy Glue can get sloppy and is not forgiving.

Yep, CA adhesive is touchy and frequently gets to places you don't want it getting to!   Many times I use a toothpick to apply the right quantity so it doesn't get away from me.  A little does go a long ways.

"Pressed on" is not an improper way to manufacture mechanical items; it's done commonly in all sorts of machinery, some costing many, many times that of a little locomotive. It must, of course, be done correctly with the correct methods, and there are inevitably bad parts. So, your loco isn't cheaply made, or the like.

Real steam locomotive "tires" (the proper term), which were both the flange and running surface, were applied to the wheels (driver centers - the "big" part)  in a heat-shrink manner: the tire/flange was heated on a fire (later a natural gas tool), placed on the wheel center (correctly) and allowed to cool. No other attachments were used. Sometimes - rarely - this tire would come off the wheel - so your problem is very prototypical. However, they couldn't use Loctite to fix it...

The CA or (probably better) Loctite should do the job just fine. Just be careful that you mount it square.