Full disclosure: I have never used square ground chain: curious about it; read a lot of the posts here, and other forums; have a Silvey RSII as a 'project grinder' that I have not gotten around to yet; asking a lot of questions to understand it better. Don't have a square ground cut log to compare!
So I am going to throw one more idea out here, which is consistent with what you are saying. Maybe the resultant angle on the side plate of square ground chain is more acute (i.e. narrower angle) so that it cuts more cleanly? You can control this side plate angle more
independently with a square chain file, and with the position of the tooth of a square grinder.
With a round file, or a conventional round grinder, the side plate cutting angle is dependent on the top plate angle of the file or the grinder head angle (and grinding wheel diameter).
But I am thinking that with a round grinder that has a sliding vise (Oregon 511AX, STIHL?), you could adjust that side plate angle slightly by controlling the part of the wheel that touches the cutter?
Could I get a 'boxed corner' on conventional chain by using a very small, square edged, round stone (i.e. a thick disc), held in something like a Dremel tool? Might need to be CBN or carbide to hold up. Mount it on a small mill or drill press? Note that the side plate would be slightly dished, versus 'square', but that is also true with the larger diameter Silvey wheels.
Philbert
I think is you use that grinding wheel your vertical side plate will end up angled wrong (aka outside side plate). None of the "square files" are actually square, they are all hexagons (6 sided). According to Madsen's, both the side and top plate cutting angles are about 45 degrees, resulting in "outside top plate" angle of 15 degrees. See their "Sharpening Angles of Square Ground Saw Chain" page, very informative.
Poor Man's Silvey?
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