Iron tsuba up through the late Muromachi and Momoyama tend to show obvious characteristics that we associate with hand forging and inhomogeneous iron. There are surface textures, visible laminations, iron bones, etc. The iron tends to be quite dense and shows a great deal of richness, not just to the surface, but "into" the plate. [Note that some, like Kyo sukashi are very well-mixed and tightly forged. This is probably to allow cutting their very fine sukashi designs w/o hitting openings, hard or soft spots. The iron quality of pre-Edo Kyo sukashi tsuba is still very different from those that come later.]
As we move into the early Edo period some of this continues, but tsuba in general start to move to a more restrained surface texture. Often the iron is still very good quality, but rather plain. Decoration of the surface with inlays and overlays becomes more widespread and prominent. Some groups started to move to iron that was almost completely without character, the so-called factory plate. After about 1700, most (not all) iron tsuba used these bland plates and relied on decoration by inlay, carving and openwork to carry off the piece. This iron is not very dense and shows no signs of working or inhomogeneity.
There are certainly groups that continued to use forged plates during this time, but even those usually don't have the same character as the earlier work. In late Edo, as with swords, there was something of an attempt at the revival of the old ways in iron tsuba. You see copies of Nobuie and other Owari area groups, Katchushi style work, Myochin pieces with elaborate mokume patterns, etc. Most of these fall well short of the older pieces,but some are quite good. They're at least more interesting than "factory iron." Some, like the Norisuke's copies of Yamakichi tsuba, go completely over the top with iron bones that are bigger and more numerous than the original pieces.
Exactly what these factory iron plates are is a little less clear to me. You hear a lot about sand iron vs. factory iron. The raw material for iron smelting is no doubt a big factor, but even the "factory" iron was probably sand iron. As we know from swords, the production of iron during the Edo period became centralized near the major population centers and the regional characteristics were lost. Most would say that the quality suffered as well.
Certainly this "factory" iron could still be forged and folded, although some of the effects that were achieved with the older iron sources and processing was probably no longer possible (also probably true with swords). I imagine that the introduction of borax flux probably had effect on tsuba making similar to what it had on sword making. Between a more homogeneous starting iron and a move toward emphasis on decoration of the plate, there probably was not a lot of incentive for tsuba makers to spend a lot of time forging and folding their iron plates. It wasn't really getting them anywhere.
I don't know of any evidence for rolling mills and the like being used in Edo period iron manufacture. So, I assume that someone had to do some hammering to produce iron sheet. I imagine that this could be done more cost effectively at the iron works or by some middle man than by the tsuba maker or someone in his shop. The tsubako probably initially got rough sheet that he would cut to shape and forge (but not fold) as needed to the desired thickness and/or surface texture. Eventually, as with today, they could probably get whatever thickness plate desired and could simply cut,polish and decorate the plate as is, or give whatever superficial surface texture was desired. My guess is that this is the process behind we refer to as a factory iron tsuba today.
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