The flex of any metal under a load depends only on a property called Young's Modulus which is given the symbol E in equations. This is for elastic deformation which returns completely to the original state when the load is removed.
It does not matter how the metal was made or what condition the metal is in; cast, extruded, rolled, hardened, annealed, normalized, the
ELASTIC DEFORMATION remains the same. What does change for different conditions of the metal is how much load can be applied and how much deformation can be caused before entering the realm of Plastic Deformation; hardened steel can carry a significant load and be considerably deformed and it will spring back. The same steel in an annealed condition under the same load will simply bend permanently,
but the first little bit of deformation on the annealed steel
before the
elastic limit is reached will be the same for the same loads.
Young's Modulus is a measure of stiffness; it is not relevant to strength. Stiffness is how much force is needed to deflect something elastically; strength is how much force is needed to deform something permanently, or break it.
In the case of machine tools stiffness is the important property and if something is stiff enough to perform adequately it is almost certain to be strong enough.
Now to get to your question; which is stiffest cast tooling plate, extruded bar or rolled plate? They are the same. Although I will mention just in case a nitpicker intervenes, there may be a minuscule difference because they are different alloys. But differences between alloys of the same base metal are so small you can ignore them.
The hardness or temper of the three forms will be different and if each was loaded to failure the cast tooling plate would probably take the greatest load and would probably break with a bang without much plastic deformation. The other two would start deforming plastically at a much lower load and would bend significantly and then sort of tear rather than break sharply. This is why cast tooling plate has gained a reputation for being brittle, it is brittle but it is strong, in your application you don't need to worry about it breaking unless you stand on the roof and throw your machined down onto a concrete druveway
.
So which should you use?
I think cast tooling plate is the best by far and that is not because of strength or stiffness issues it is because this material has hardly any residual stresses. You can machine it, take cuts off the surface, cut tee slots, etc and it stays very close to being as flat and accurate as it ever was.
Extruded and tempered bar stock and rolled plate is a very different thing. These forms of aluminum alloy have high stresses in the material as a result of the way they are made with rolled plate maybe being the worst.
The stresses vary across the thicness and if you machine one side off a piece of bar or plate they become unbalanced causing the metal to deform until they are balanced once more. The amount of deformation is not predictable but some deformation will happen. Also with aluminum alloys it will continue to happen slowly over a long time.
It is possible to machine rolled plate and get an acceptable level of distortion but this requires experience, planning your procedures and a lot of luck. You try to take equal amounts of each side and you approach your final dimensions slowly by rough machining everything, pre-finishing everything and then finishing everything with your fingers crossed all the time.
I will leave it to someone else to post deflection formulae.
06-28-2007, 10:02 AM
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