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RE: DYNAMICS: Machine Run-Up

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Bill-
As a force input to the structure from the machine, the vendor is correct. If you look at an eccentric mass, m rotating about a center as creating the force (a reasonable and simple model of the machines dynamic behavior), the momentum, p(t) = mv where m is the eccentric mass and ve is the velocity.

The instantaneous velocity, v=2*pi*f*R where f = frequency, in hz and R = eccentricity in consistent units. The horizontal and vertical velocities can be expressed as:
vh= v* cos(theta) where theta is measured from the vertical axis
vv= v* sin(theta)


Tthe force at any instant is F = m*dv/dt or expressing in horizontal and vertical components:
Fh=  -m*v*cos(theta) = -m*dv/dt
Fv=   m*v*sin(theta) = m*dv/dt
Both the horizontal and vertical components vary as the frequency but are out of phase with each other by 90 degrees, thus at half the frequency either instantaneous component will be half what it would be at the maximum frequency.

What you will find out as you run up the machine is that you will get resonances at each structure frequency.  How bad the resonance depends on how fast you pass the frequency and whether there is any damping. Thus your response will not be linear between 0 and f max but your input to the structure will be.

The most similar practical analogy I can give you is the problem encountered with driving sheet piles with a vibratory hammer. If you hit resonance with the soil, very damaging vibrations can occur.
Hope this helps.

Regards,
Bill Cain, S.E.
Berkeley, CA

> From: bill(--nospam--at)polhemus.cc
> To: seaint(--nospam--at)seaint.org
> Subject: DYNAMICS: Machine Run-Up
> Date: Wed, 10 Dec 2008 12:55:49 -0600
>
> Any one ever done a time-history dynamic analysis involving rotating
> equipment "running up" from a standing start?
>
> What did you consider?
>
> I've got a machine skid with excitation loads from the vendor running
> full-out at 30,000 RPM, and he recommends a linear relationship for
> speeds less than that (I.e. Half the load amplitude at 15,000 RPM).
> Oh, and the skid's sitting on a steel platform, which is why this is
> critical.
>
> I'm using STAAD.PRO and I guess I could code it for discrete time-
> stops along the way but I'm not sure how accurate it'd be.
>
> Any other suggestions?
>
> William L. Polhemus, Jr. P.E.
> Via iPhone 3G
>
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