If you knurl deep enough to more than bottom out the tips of the knurl in the valleys of a forming type knurling wheel thin, very sharp, slivers of metal will be produced as the knurling wheels cut (scrape?) excess metal from the sides of the formed knurls to make room for the wheel.
Presumably if you do your calculations correctly and start with exactly the right size of material a knurl with full depth valleys and full height peaks is produced immediately before this cutting / scraping process starts.
If you are a production line manufacturer wishing to reliably produce knurling of a specified shape and depth, whether full or partial, its clearly essential to do the maths and not only start with the correct size material but also finish with the correct depth feed on the knurls. Hence the reference given earlier by Graham Meek with its details of 5 type off knurl.
In our case where we just want a nice looking knurl or three any deviation of the starting stock from the nominally correct diameter will merely offset the centre line of the knurl slightly with no obviously visible effect. Unless the knurl is driven deep enough to reach its full depth there will be sufficient space inside the knurling wheel to accommodate the slightly higher peaks needed to accommodate deviations from the theoretically correct starting diameter. In general for any practicable combination of knurl pitch and workpiece size the difference in diameter between dead right and half way to needing either one more or one less “knurl tooth” to cover the diameter is very small. Which is why the “drive it in hard and it will sort it out school” approach is valid. There just isn’t much physical variation to cope with.
My observations suggest that double knurling is more an operator technique thing than a size thing. Folk getting double knurls still tend to suffer even when starting from dead nuts size because they don’t manage to get enough force on one of the knurls for both to start cleanly.
These days I mostly use a Marlco scissor style tool. An industrial piece of kit that is beyond reproach.
I found the once common, inexpensive, rotating head style with three knurls a total pain to use with successful results a matter of pure luck. Presumably then knurls need to be presented to the work with almost exactly equal force if good results are to be produced. Logically setting the thing dead on centre would meet this criteria but I never found it reliable.
Interestingly I have Pratt & Whitney branded single size knurling tool with a similar style of pivot but offset so one knurling wheel is lower than the other. In case the upper knurl is presented to the work at centre height. The pressure exerted as knurling begins bringing the other knurl into contact a tiny bit later. This tool is absolutely reliable. I imagine the lower knurl pretty much always works on material partially formed into a knurl by the upper one giving it a easier time of things so slip is quickly eliminated.
I also have a hand held “nut-cracker” style tool which works well. That has three knurling wheels arrange in a triangular pattern. I imagine these generate a similar operating on a partial knurl effect significantly reducing the squeeze needed to form a good pattern. Too gentle a squeeze produces the familiar misalignment but the hand generated forces needed for decent results are clearly considerably less than those produced by a machine.
Clive