Balance criteria based on design vibration limits 1

[geesamand]

I have a machine with a 400rpm overhung rotor that must be balanced to limit overall vibration. The bearing-side of the machine must be limited to .003" pk-pk displacement vibration and 0.3 in/s peak velocity vibration. The whole rotor assembly can be considered "rigid".

ISO 1940-1 does not advise how to estimate the required balance quality for a rotating assembly based on vibration limits.

I'm conceiving that since imbalance produces forces on the rotating shaft, and forces produce deflection in the machine, and the stiffness of the machine can be estimated, then we can calculate unbalance that will keep the deflection of the machine to .003" pk-pk where it counts.

Does this calculation approach generate reasonable estimates for balance quality?

I've tried the google but I have been unable to tease out this particular subject from everything else vibration related.

David

 

[Tmoose]

In addition to support stiffness (in dimensions, all the way to ground, often thru several layers of indeterminate and indeterminable stuff beyond your control) the "sYstEm" mass must be considered to understand where resonant frequencies might lie, and how they will affect the system response.
If I manage to accidentally park my operating speed right on a resonant frequency the vibration amplitude can easily be 10X higher than my balance tolerance "deserves."

Be sure not to pick "transmissibility" curves, as they show the force transmitted thru a supercritical or isolating support will be small.
I believe you are interested in the motion of the bearings (vibration) which will be large (full rigid rotor CG offset) when operating supercritical.

http://upload.wikimedia.org/wikiped...vg/524px-Resonant_frequency_amplitude.svg.png

As a very rough first cut I would assume the entire rotor mass (grams) is it's eccentricity (CG offset) is the 3 MILS pk-to-pk/2. As if the support stiffness + zero, and I was 20% away from resonance. A small bunch of testing done in the previous millenium made when field balancing commercial machines like HVAC equipment and fairly rugged looking process fans makes me think that //might// be pretty close to what you will find.

The spec is not helpful. If the vibration is mainly at 1X rotating speed (as expected for an unbalance spec trying to limit vibration) :
- 0.3 ips (peak) at 400 rpm ~ 14 mils pk-pk.
- Conversely 3 mils pk-pk at 400 rpm ~ .065 ips pk

http://www.mobiusinstitute.com/Calculator.aspx?id=2509

Will the "rotor" be balanced while mounted on it's own shaft, supported at the actual bearing locations. Or, on an arbor?
If on an arbor, shaft runout, and arbor-to-rotor, bearing-to-shaft and shaft-to-rotor fit can have a proFOUND negative effect on the assembled balance.

Finally, significantly overhung rotors can behave in interesting and unexpected ways.

http://www.update-intl.com/VibrationBook5h.htm

 

[geesamand]

Tmoose, thanks for some very thoughtful questions and suggestions.

- I provided overall machine vibration limits. The imbalance will contribute vibration at 1x 400rpm, which is within the range where displacement offers the best response. As you noted, the velocity limit is only relevant for higher frequencies (e.g. 1800cpm motor shaft or gear meshes).

- We are well away from resonances (1st critical ~= 1000cpm), and we have stiffness criteria for the mounting base.

- The rotating assembly is a solid horizontal shaft, about 50" long total. As it's fully machined and has straightness criteria, we do not perform balancing on this part. The bearings are 20" apart and on one end, with an impeller (20" dia / 15" long) on the opposite end. So the impeller behaves as an outboard rotor. The impeller is two-plane balanced with an extra-tight static unbalance limit to help account for the eccentric rotation due to shaft straightness. The impeller and shaft are not balanced as an assembly in order to promote parts replacement/interchange.

My first inclination was to simply apply balancing criteria to keep the deflection of the shaft under 3 mils as you suggested, but that seemed very conservative given that the rotor is overhung and the vibration limits are based on experience measuring near the bearings. So I then considered modeling the deflection of the machine near the bearings and applying the 3 mil limit there.

Thanks,

David