Materials used in CNC build projects

[routercnc]

Sorry Ross, I'm going to disagree with your disagreement :exclaim:

I think that a stiffer machine will vibrate less than a weaker machine. Why? Well the first explanation is Hooke's law:
force = stiffness x displacement
or
displacement = force / stiffness

For a given force (from the cutter), a higher stiffness gives a lower displacement.

But we are also talking about dynamic stiffness and need to consider resonances. Undamped natural frequency = SQRT (stiffness / mass). A stiffer system will have a higher natural frequency, and in turn these have lower amplitudes. I believe this is to do with higher frequencies having more energy in the wave. Since you are putting the same energy into the system (from the cutter), the higher frequencies must vibrate at a lower amplitude to keep the 'area under the graph' the same in both cases.

Higher frequencies can be confused with 'more vibration' because to the touch they will tend to give more of a tingle as the frequency increases, but if you were to measure the displacement it would be lower. Run a sine sweep through a loudspeaker and watch the cone. Low frequencies you will see it move - at high frequencies it will virtually be stationary. I know there are problems with this analogy but I couldn't think of a better one!

In addition, a stiffer system, with a higher natural frequency, would be more unlikely to be driven at that natural frequency by a cyclic input (e.g ballscrew rotation), and less likely to go into resonance. Again the displacement is less.

When you talk about damping, this comes from 2 sources:
Inherent damping in the material (e.g wood is well damped, aluminium has some, and steel has less)
Mechanical damping at the interfaces (e.g. microscopic bolted joint movement)

You can apply external damping to panels (e.g. damping sheet) which this turns the vibration energy into heat, but this isn't really applicable for structures.

Damping only has an effect on the amplitude of the resonances. It has absolutely no effect elsewhere i.e. away from resonances. So a less sturdy machine has no way of 'damping' the vibration soley from being 'less sturdy'.

Another way to reduce vibration is to add mass. Although this lowers the natural frequency, because of Newton's Law:
force = mass x acceleration
or
acceleration = force / mass

Addition of mass, reduces acceleration during vibration.

How do I know all this stuff? Well, my day job is a Noise and Vibration Engineer and we have to measure this sort of thing, and solve problems relating to it.