Vibration Problem 1

[jheidt2543]

I am looking at an existing three story, steel frame building in which a vibratory machine has been installed on the second floor. The machine is transmitting vibrations through the steel structure. The Owner has installed the manufacturer's recommended vibration dampers on the machine, but there is still enough vibration to be uncomfortable to the workers.

The steel frame is concrete encased for fire protection. My gut feeling is that this should help dampen the vibrations, but I don't know how to model this. The beam cross-section is a standard wide flanged steel beam, within a rectangular concrete fireproofing coating.

Do I model the steel frame and just add the concrete as a uniform dead load? I could then run the model with and without the concrete dead load and see the effect of the concrete. Is there another, more realistic way?

At this point, there have not been any field measurements taken of the vibration. That will be one of my first recommendations.

 

[pjhype]

I am not sure that an analytical approach will get you meaningful answers. What would be the purpose of seeing the effects of the concrete on the steel structure? Would you recommend removing the concrete? Is there any way that you could verify the behavior of the structure without the concrete? Is there any way that you could add more damping to the steel structure through the concrete? Probably not. Because of this, I would think that you need to perform some tests.

I think that the first step would be to perform a floor vibration survey and determine whether the vibrations are primarily in the lateral direction or in the vertical direction. Get yourself some low frequency accelerometers and measure the floor vibration on different floors at different locations to determine this. If the vibrations are in the vertical direction, then the machine is probably causing bending vibrations of the floor, and you could probably fix this problem by locating the machine on top of a vertical pillar.

If the vibrations are in the horizontal direction (which is probably the case), you will need to isolate the vibrations with the mounts. You should measure the transmissibility (in three axes) between the machine and the floor. Correlate the peaks in the transmissibility with the peaks you found in the operational floor vibration survey. The high vibration levels can be caused by one (or a combination) of the following: poor vibration isolation, resonance of the machine on its mounts, or excitation of building structural modes. You can get a feel for the building structural modes by either measuring the vibration levels with the machine on and off, or you could get yourself a modal sledge hammer and excite the modes.

Once all of this is determined, you can start designing a better vibration isolation system. You should first develop a simplified model of a rigid machine on its elastomeric mounts and tune the model to match the transmissibility that you measured above. Note that if you cannot match the transmissibility with reasonable values for stiffness, you are probably missing something important. Once you have a good model, you can start evaluating the effects of stiffness and damping on mount transmissibility and/or tune the mounts so as not to excite building structural modes.

pj

 

[jheidt2543]

pjhype,

Thanks for your helpful suggestions. My original thought was to model the building structure to find out its modes, then see how close any of them were to the machine frequency. I am assuming that the concrete cover ADDS to the dampening of the building and so I wanted to include that in the model.

Your suggestion of field measuring the actual vibrations was a good one and was in the back of my mind. Perhaps that should be the first thing to do, then go through the building structure. I guess I was thinking that I should have some idea of what to expect before hand.

The machine vibrates at about 650 rpm with a product weight of 1,600 lbs. and a machine weight of 7,500 lbs., for a total moving weight of 9,100 lbs. The machine is supported on four legs bolted to a 6" thick concrete floor slab over steel beams on a bay spacing of 20' x 30'.

 

[pjhype]

jheidt,

I've measured vibration levels on several floors and found that typically (depending on construction), they will have vibration modes in the vertical direction in the neighborhood of 12-18 Hz, and in the horizontal direction in the 8-14 Hz range. A machine operating at 650 RPM will give you an excitation frequency that is definitely within the frequency range of interest (10.8 Hz).

You could try to develop a model of the floor/structure, but I've always found this to be difficult and in the end, not worth the effort. You will end up not matching the floor frequency, and tuning your model to get the right frequency. In the end, all you have is a model of a machine installed on a flexible foundation, which you could have modeled right from the start. If, on the other hand, you are allowed to modify the building structure, there will be some value to modeling the structure, however, this is usually not the case.

Getting back to your problem, if the owner of the building installed rubber isolators, I would guess that they are probably too stiff to provide isolation down to 10 Hz. If you look at a transmissibility curve for a single degree-of-freedom system, you will see that for reasonable damping ratios for elastomeric mounts, you will need to tune the mounts to less than 7 Hz to get isolation above 10 Hz.

I would highly recommend that you perform the vibration tests as outlined in my previous post. You should be able to collect all of the test data in one day and analyze the data in one or two days. This data will give you valuable insight into the building structural dynamics as well as the required mount design.

pj

 

[jheidt2543]

pjhype,

Thanks again for some very helpful suggestions. I will look into the field testing and let you know how it goes. The work may not be performed for a month or so, but in the mean time I will do some more research on the mounts installed etc.

Thanks!

 

[jheidt2543]

pjhype,

Well, we finally had a firm run the vibration tests with a nifty looking, hand-held accelerometer. We took about 15 readings on the floor slab at various locations around the machine and the plant. The information was downloaded to a PC and the data printed out in a chart for each reading location.

Here is one set of readings. I estimated the major peak values from the graph I was given, frequency on the x-axis and acceleration on the y-axis:

FREQUENCY (Hz) ACCELERATION (g's)

7.5 1.30E-04
11 1.30E-02
19 1.85E-04
38 1.75E-04
42 1.35E-03
49 1.60E-03
67.5 1.00E-03
77 1.85E-04
83 1.20E-03
94 1.00E-03
97 1.10E-03

There are locations with higher acceleration values than I've shown above. All of the references I have, graph amplitude rather than acceleration against frequency, where do I go from here? I will be getting recommendations from the damper manufacturer, I would just like to learn a little something in the process.

 

[pjhype]

jheidt,

Are these accelerations in the vertical or horizontal direction, or both? If they are in the vertical direction, you might consider moving the machine to a column location which would be stiffer than in the middle of the floor. If the accelerations are in the hozizontal direction, you will need to either move the machine to a different floor, develop a better vibration isolator, or use a tuned mass damper.

Assuming that you want to develop a better vibration isolator, your next step is to determine the transmissibility of your mounts. The vibration peak at 11 Hz is likely due to the 650 rpm excitation. If the mounts are too stiff, they will have a natural frequency higher than 11 Hz and will not provide attenuation at 11 Hz. If the mounts are tuned to 11 Hz, they will amplify the 11 Hz vibration. The transmissibility is determined by taking the (output) vibration levels on the floor and dividing them by the (input) vibration levels on the machine above the mounts. Alternately, you could obtain the transmissibility by performing an impulse test with a modal hammer and accelerometer.

If your machine behaves like a single degree-of-freedom oscillator, the transmissibilty function indicates that you will need to tune your mounts to less than 7 Hz in order to get attenuation at 11 Hz. The typical problem with trying to isolate low frequency vibrations is that the resulting mounts would need to be very compliant. If your machine does not have a moving stage or if it does not need to transfer a lot of mass, this should not be a problem. Otherwise, you may need to deal with unacceptably large static displacements. If you can get away with a low frequency isolator, I would recommend that you look into using a pneumatic mount, as these will provide a natural frequency lower than a typical rubber mount and can also provide more damping.

pj

 

[sismico]

jheidt2543,

I have been involved in such a similar problem. It seems that many steel buildings with steel deck floors are very suceptible to vibrations most of them in vertical direction. According with some measures using accelerometers and sismometers in different part of the building we found that vertical vibrations are in 10.5, 14, 16, 17.5 & 19.4 Hz. These frequencies appear with/out machinary function.
I am with the deal to reduce the vibration amplitud under acceptable values and verify the structure for any fatigue damage.
Any advice will be sincere apreciate.