How to measure/calculate eigenfrequency

[es335]

Hi.

I want to make an analysis of a device to find its eigenfrequency. But I am not sure how to do it.
I seem to remember something about an FFT analysis of the frequency recorded, but that’s it. If anyone could help me with direct informations, I would be most grateful. Links are also welcome.

A discussion on what equipment I need is also welcome. I guess that an accelerometer and frequency filter is necessary, but is that it? Don’t I need to excite the device with e.g. a hammer and don’t I need to know the force this hammer is putting on the device?

Oh, btw. The device is a complex metal geometry, but if it is easier to explain a simple metal rod can be used as example. This would also give me a chance to actually build a test rig and compare it with calculations.


Cheers.

 

[MikeyP]

With a complicated structure, you will almost certainly have to resort to a full-blown modal analysis (see the book Modal Testing: Theory and practice by DJ Ewins for example).

There are simpler approaches which would yield less satisfactory results but which may be adequate for your situation (although I think it unlikely)

The simplest of all is to hit the structure with a hammer, measure the acceleration at some point on the structure. Fourier transform that data and look for the peaks. The peaks will occur close to the natural frequencies in most cases.

The problem with this is that:

1) There will be a lot of noise which will generate spurious peaks in the spectrum.

2) Your excitation location and/or accelerometer location may be at an anti-node.

3) There may be peaks close to each other which are indistiguishable

4) There may be some modes excited much more than others. The larger response may obscure the smaller one.

5) The force generated by the hammer blow is a poor approximation of a Dirac delta function and may lead to spurious peaks in the spectrum.

A more sophisticated solution is to measure the force applied by the hammer and do a little post processing to yield the transfer function between the exciter and response. This solves problems 1 and 5. Problems 2, 3, and 4 can only be addressed by using many accelerometer locations (in all 3 directions) and at least 2 exciter positions. The signal processing then becomes more complex and decent modal analysis software is required.

I suggest you do some reading.

M

--
Dr Michael F Platten

 

[electricpete]

I think it's a great response by Mike.

The only comments I can add:
When working with rotating equipment we often simply use something similar to uninstrumented hammer. (for typical industrial motors we would use a 2x4).

Related to item 5, I picture that the spectrum we read is the product of the actual desired impulse response and the fourier transform of the non-ideal impact force. The non-ideal impact force shape is kind of like a low pass filter. Will do well for low frequency and limit at high frequencies. I have seen various published curves for various types of impacting tools. Find one above the frequency of your interest. Also remembering that we are only looking for the frequency of a peak and not the magnitude, I am not terribly concerned about high frequency attenuation for our purpose. 2x4 seems to work good for industrial motors where we are normally most interested in resonant frequencies 120 hz and below.

Some tips on #1: separating the noise from the impact response (assuming you don't have an instrumented hammer to do some fancy correlation).
- Look at a time waveform. If you can recognize an impact and a ring-down, then the time frequency of oscillation of the ringdown is pretty good number for the single most dominant resonant frequency at that point (although there may be others only detectable through FFT).
- Experiment with different frequency resolutions:
I like frequency resolution whenever possible. In our environment the background noise is all discrete / narrow frequency peaks from operating rotating equipment nearby. The impact test peak will be a lot broader. The difference in shapes becomes more noticeable at high resolutions... unless your have a signal to noise problem.... higher frequency resolution means the sample duration increases magnitude of your single-impact peak will decrease relative to background peaks. If you increase resolution too far you may lose your impact peaks in the noise floor.
- Record two FFT's: one while impacting and one while not impacting. Do a mental subtraction of the not-impacting spectrum to get a better feel for what is really coming from the impact.

 

[vanstoja]

For your "complex metal geometry" device (possibly rod-like), you would do well to describe it's overall geometry, methods and locations of constraints, number of subcomponents (if more than one) and function. You will not be getting eigenvalues of a "device" unless it is a relatively simple beam, plate, shell structure with easily definable boundary constraint conditions. What you may be able to get by vibration or impact testing are structural response frequencies or (if energizable) operating deflection shape (ODS) frequencies. Depending on physical size, shape changes and number of subcomponents you may need multi-axis accelerometer mountings for bending, extensional and torsional mode response frequencies. If you don't care about what modes are responding to produce the vibration spectral output, then a simple "bump" test may suffice if the device is large enough and robust enough to whack it with a hand hammer, a sledgehammer, a rubber or metal mallet or a wooden 2x4, 4x8 or whatever. If you want to find out the cause of the dominant peaks in the vibration spectrum are in order to control levels or shift frequencies away from possible excitation frequencies, the you will need to pursue some degree of structural modal analysis which may involve impact hammers, shakers and more complicated excitation methods which are are all described and ranked in the open literature or on the internet.