Cheshirechappie":tfh84krf said:
It may be worth a quick note to the effect that the stiffness of a plane iron, using classical beam theory, is proportional to the cube of the thickness. Thus, an iron 2.4mm thick is almost twice as stiff as a 2mm thick one. (A 3mm thick iron is more than three times stiffer than a 2mm one.)
Whilst true in principle, when you get a plane iron in actual use, it's a bit more complicated than that approximation. In a Baily style plane, the cap iron is normally clamped to the plane iron with uneven pressure distribution (i.e. the line just behind the edge is the bit you want to clamp hard). Whilst I baulk at trying to calculate the second moment of area of such a system, provided that the cap iron doesn't move in use, then even without factoring a preload force, surely it's the cap iron + iron system that should be considered, not the iron on it's own?
The primary effect of the preload would be to increase the net force before the tip of the iron separates from the cap iron - so provided that there's not a gap in use (i.e. no shavings manage to worm their way under the cap), then surely it's reasonable to consider the thickness to be cap iron + iron; as a closer approximation?
The net consequence of that suggests that the effects given above, as relative measures, will overstate the effect of considering a thicker iron. in isolation. Thicker is, of course, stiffer; but if we're taking even a 1.2mm cap iron into account, then to end up twice as stiff, you have to go from a 2mm iron to a 2.8 mm iron. (Obvious problem here is if the two materials are significantly different materials … that's going to complicate any analysis).
I'm sure that this model disagrees with reality in a number of aspects, of course - but I _do_ think that it gets closer than considering the plane iron in isolation (as that's not how they are actually deployed, in use).