Quote:
Originally Posted by kalee20
Quote:
Originally Posted by Craig Sawyers
For what it is worth, the resonant frequency of a spring/mass (which is what an isolation mount for a valve is) is given by (1/2.pi).root(g/B)
Where g is acceleration due to gravity (9.81m/s^2) and B is how much stretch there is in the isolation springs. Therefore the resonant frequency depends only on the stretch of the suspension springs.
So if the springs stretch by 1 cm (10^-2 m), the resonant frequency is 5Hz, which looks fine. If they stretch by 1mm the resonant frequency is 16Hz, which is probably still OK.
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It's a bit of a misleading formula, this - the resonant frequency depends on the spring constant and the mass. Nothing to do with gravity, the resonant frequency will still be the same on the moon. But! The Spring constant is also the extension divided by the force to produce said extension, hence the g/B calculation also works. |
Not at all misleading. Sure the regular formula is given by the spring constant and the mass. But the extension of the spring is dependent on gravity, the mass and spring constant, which leaves the equation I quoted.
The only reason to look at it this way, is when vibration isolating something, you only need to look at how much the spring is stretched and that is enough to give you the resonant frequency without knowing anything at all about the mass and the spring.
Just as another for instance, the bed plate of an old SME arm used to have grommets, so the arm was isolated in some way from the plinth or arm board. The mounting screw is required not to compresses the grommet, so the grommet compression is only by the arm mass itself. Suppose that is by 0.1mm (which seems plausible). That means that the vibration isolation cuts in at 50Hz. Of course there are more complex rocking modes too, and for that reason the grommets were often removed and the bedplate screwed hard to the plinth. Current SME arms are bolted hard down by design.
The only (classical) way of working out the local gravity, for example on the moon, is to use a pendulum.
Craig