equipment vibration

huangyhg

equipment vibration
i am designing a 20' tall elevated concrete platform that supports two centrifuges designed to extract sludge from treated wastewater. the equipment operates at a speed of 2500-4200 rpm. the equipment criteria states "the stiffness of the supporting structure should be adjusted so that the natural frequency of the structure with machine is 30% above the frequency at operating speed".
i have calculated the frequency of a relatively stout concrete structure to be less than 2 hz. for purposes of wind design, asce 7-98 defines a rigid structure as one with a natural frequency greater than or equal to 1 hz. there is no way i can achieve a frequency 30% above 4200 rpm (70 hz)!
what's the deal? anybody out there ever run into this? i've tried looking it up on the internet without much success, except to be able to purchase expensive books on the subject.
spats - give the internet one more try, go to my web page (link below) and download the following three documents from the home page:
"basic vibration & vibration isolation theory"
"principles of foundation design for engines & compressors"
"don't gamble on machinery foundations"
then go to my portland cement association page; this document may be of interest:
"fastening & bedding columns & machine bases"
may not be exactly what you need, but it is a start.
i would expect that they are recommending you to be above the operating range so that as the machine starts and stops you will not pass through the natural frequency of the structure.  sometimes this is really not possible.  we design many supports for vibrating equipment operating in the 800 rpm range.  what happens is that we make sure that the critical modes are more than 50% out of the operating range.  when the machine starts you will have a very short period (1 second or so) noticeable movement in the structure.  depending on the speed-up is how long the structure will noticeably vibrate.  under operation the structure performs satisfactory.  during shut down you will generally have a longer period of vibration as the structure approaches natural frequency, reaches it, and then ramps down.  this can be detrimental to the structure if you have not considered the excessive stresses you will get from the displacements.  basically this is standard vibration analysis which you can determine displacements given in any vibration textbook.  the question will be as follows.  i would assume that the only way you could make a structure that stiff would be to use shear walls.  i would ask the customer what they would like.  explain to them that you can design the structure to meet the frequency expectations but it will cost $xxx.  then explain that you can design the structure also for $xxx but you will experience some vibration during shut-down and start-up.  generally they have an idea of what to expect from their structure so they may be fine with it.  also note that i am assuming that the problem is lateral frequencies and not vertical.  generally if it’s vertical you can easily place a column or a stiff support under the machine to control the vertical vibration.
in response to aggman:
the vertical frequency of the stucture is only about twice the lateral frequencies, so even it is not close. i can't add columns directly under the equipment anyway.
shear walls are also out of the question.
my platform is 18'x25' in plan, has four 18" square concrete columns with 18"x32" deep perimeter beams, and an 8" one-way slab. no reasonable amount of beefing up is going to work. there is no "$xxx" that would satify the criteria because there is virually no possible solution.
could you explain the 50% rule in more detail?
spats, you're an engineer, not a magician.  if you need a 12" slab under the machine to satisfy stiffness requirements, do it.  if you have to run a 24"w x 40"d beam under the machine, do it.  if these aren't feasible, tell the owner that he has three options.
1) change the required frequency of the supporting structure.
2) realise he needs a beefier structure, and he won't be able to have a 12' cieling under the support structure.
3) explain to him what aggman mentioned.  during operation, the structure will be sufficient for the stiffness requirements.  during power-up and shutdown, there will be frequency problems.  if he's ok with it, then you're ok with it.  if not, see options 1 and 2.
the 50% rule is a guideline that we have often used.  basically if we can mathmatically prove that the natural frequency of the structure has a phase shift of 50% or more than we have always felt confortable with the performance of the structure.  if you study dynamics you will see that as the forcing frequency and the natural frequency approach each other the amplified displacements will magnify following a curve much like a bell curve.  if you are more than 50% beyond or below the peak than generally the amplified displacements are minimal.  also the odds of your model actually representing the actual field measurments is relatively small so this gives you some margin of error.
i've designed several of these and i've never seen a manufacturer too interested in the structure frequency.  usually, i have to search out the information and we just try to provide a relatively stiff support system.  the reason the supplier isn't that interested is that their equipment has vibration isolation and should only transmit a small vibratory force.
if you have to provide a natural frequency of 30% over 4200 rpm you're going to have a real problem.  when i get into the office after the weekend i'll take a look at my designs and see what the i ended up with.
it might be worthwhile contacting the equipment manufacturer and getting their input on the issue.  assuming your intallation is how this is typically done, they should have some idea of how to approach it.  it may be that the equipment needs to be at ground level, for example.
spats,
the operating speed of your equipment is 42 hz to 70 hz which much higher i think than you can get as a fundamental mode of a normal structure.  the objective when designing a support for equipment is to keep the natural frequencies of the support/foundation system out of the operating range of the machinery or you will end up with resonance problems.  the technical reasons for this are as described by aggman and the 50% rule sounds about right to me.  
one consequence of having a natural mode lower that the operating speed is that you pass through it on startup and shutdown.  the owner needs to understand this.  if ok make sure the structure is strong enough for a short duration period of heavy vibration, otherwise at operating speeds it should be ok.  vibration could be a problem however if the centrifuges are near office areas or other sensitive equipment.
be careful with vibration isolators.  these are basically springs, and when put on top of structural supports (which are springs) you can get undesired results.  i think you should start with a rudimentary dynamic analysis to predict the first few natural frequencies (3 to 5) to assess roughly where you are.  re  
just to add an observation from a vibration point of view.
i think you and the spec writer need to have a short discussion. i suspect he meant the frequency of the floor and so on, not the whole building.
you and he might decide that a better approach is to define an allowable vibration limit in the rest of the building, then you can do the job properly with an isolating floor.
cheers
greg locock
it seems as though your client's specification may be forgetting the other scenario.  the natural frequency of machine foundations is ordinarily designed to be either less than 0.5 or greater than 1.5 times the operating frequency of the machine (or thereabouts).  it may be that your client has eliminated the lower bound to avoid the possibility of resonance during start-up and shut-down.  however the machines, as you've described them, should be reasonably robust.
the natural frequency increases as the foundation weight decreases and as the soil bearing contact area increases.  so you could try minimising the foundation mass and maximising the plan area -- a long, broad, thin slab (which may not actually be that desirable).  as a rule of thumb for preliminary sizing, footings for reciprocating machinery should weigh approximately five times as much as the machine.
the british code of practice cp2012 code of practice for foundations for machinery: part 1. foundations for reciprocating machines is a good guideline.