I will tailor my discourse to the opposite party, Simon. In your case, with your engineering precision I might say "the finned exhaust clamps incorporate a recess to accommodate the flanged side of the collets, which in turn mate against the downpipe flange and thence the fibrous gasket"
But you really can't quibble with "frilly thing" as a concise and succinct expression of the same thing. Mars and Venus I suppose...
