In our rolling mill we did not have an anvil on which the "bloom" was beaten by a trip-hammer as is done in the Old Country.

The "squeezer" which combines the functions of hammer and anvil did the work instead.
When I became my father's helper he began teaching me to handle the machinery of the trade.

The puddling furnace has a working door on a level with a man's stomach.

Working door is a trade name.

Out in the world all doors are working; if they don't work they aren't doors (except cellar doors, which are nailed down under the Volstead Act).
But the working door of a puddling furnace is the door through which the puddler does his work.