# Modal Testing and Frequency Response Interpretation

I'm studying vibrations in a gearhead, for which I have a general dynamic model of 12 degrees of freedom (only translational coordinates) and I have calculated its natural frequencies.

Now I want to try and correlate my model with a physical system. I did some impact testing with a hammer and measured the response with one accelerometer placed on the horizontal direction of the gearheads case.

My theory on mechanical vibrations and modal testing is quite basic and I don't know how to proceed and interpret the results of the readings.

I tried simulating the forced response in order to correlate the model I'm using to the measurements. For example, in one of the experiments, I hit the gearhead horizontally and measured the response on the opposite side of the gearhead with the accelerometer, in the same axis. In the forced response simulation, I applied a unit force on what would be that equivalent degree of freedom.

In the magnitude response of the test, I have a few peaks ranging from　2khz to 24khz (its also the width of my window res). But in my force response simulation I get resonance peaks much higher, from　9khz up to 80khz. The natural frequencies range from 1khz to 16khz. I have a few questions regarding what I'm trying to do:

1. Should the natural frequencies I calculated all show in the forced response simulation within a frequency range of up to 20khz, or only those close to the degree of freedom of the applied force in the force vector? In my results so far, none of the peaks in the forced response are close to one of the natural frequencies.

2. How can I correlate the test measurements with the forced response simulation? none of the peaks in the magnitude response of the tests seem to be close to the simulation.

3. From the modal test results, I measured some of the peaks and about 3 of them are very close to some of the natural frequencies, does this mean that this frequency were excited in this specific test? or can it be just coincidence? as I explained before, in the forced response simulation I couldn't find any relation.

I should also note that my model is undamped, and my equipment was quite limited (only one sensor and small hammer(22khz)).

I read some theory on varius text books on vibrations and modal testing, they all show how to interpret a general FRF of course, but I can't find practical examples relating a theoretical model and modal testing like I'm doing, not explained in detail at least, most just skip to results, so the general methodology is what I'm lacking.

Thanks.

You can't make much use of just one FRF, especially if none of the peak responses line up between the model and the test.

Fix the accelerometer at the position of one of your model DOFs and then impact the model at all 12 DOF positions (in the correct directions, of course). Move the accelerometer to the other DOF positions in turn, and repeat.

You should be measuring the hammer force as well as the accelerometer response, so you can make the FRFs constisent with each other.

You also need to do some analog filtering of the measured signals before you digitize them, otherwise the results will be a mess to interpret because of artefacts caused by aliasing. For example if you digitize at 22k samples/sec but don't do any filtering, you can't tell the difference between resonances at 11+1 = 12kHz and 11-1 = 10kHz in the digitized data and the FRFs - or even worse, there is no difference between resonances at 21kHz and 1kHz!

You will then have 144 FRFs in total. You can cross-correlate them to see which peaks are "real" and which are just random artefacts. More important, you can also find the mode shape corresponding to each peak, and try to identify that in the modes from your model.

You need some software to do this, of course. Commercial modal analysis software isn't cheap, but there are some free packages - for example http://hosting.umons.ac.be/html/mecara/EasyMod/index.html (which also needs Matlab). That is not a personal recommendation for EasyMod - I've never used it - but modal analysis and testing seems to be a speciality in Belgian universities so it "comes from a good home" IMO.

A good book to read is Ewins, D.J. “Modal Testing; theory, practice and application”. You can probably find the first edition free on the internet - that will tell you more than you ever wanted to know about the subject. Note the words theory, practice and application in the title. It's a good book because it describes all three aspects. Just having a mathematical understanding of FRFs (which is about as much as you will learn in a typical B-Eng degree) is only a part of the total picture!

Note, it is not at all unusual for a first attempt at modelling to give modes that are all "way off" from anything you measured - but unless you can identify some corresponding pairs of modes in the test and model data, you won't get very far trying to improve the situation except by pure good luck.

• thank you @alephzero! this is all great info, your last comment gave me some motivation about this being quite normal. How can I determine the mode shape based on the peaks? I categorized the type of mode shapes based on the results from my model, the eigenvectors signs and values, but I don't understand how to identify them from a peak. Sep 16, 2017 at 16:58
• Get the software and/or read the book. There's nothing incredibly difficult about it, but you don't want to try re-inventing all the details for yourself. Basically you find the modes that are the best fit to the measured FRFs, in terms of frequency, damping, and mode shape for each mode. Just using the peaks of the FRF as modal frequencies is often a fairly crude estimate, and the amplitude of the response at any frequency on the FRF is depends on all the modes you excited, not just the one "nearest to the peak". Sep 16, 2017 at 19:34
• Note it's quite common for the mode fitting to reveal a few "mistakes" in the measurements like inverting the polarity of a signal, or getting in a muddle over naming all 144 FRFs consistently. You can usually sort such things out by noticing that a mode is "obviously the same as something in the model" except that one or two measured points are moving the opposite way, etc. But simple wire frame animations are much easier to understand than "tables of signs and values" and any half-decent modal analysis software should be able to display those on screen. Sep 16, 2017 at 19:38
• thanks again @alephzero, I got the book you recommended, I can find most answers there but I also need to revise a lot of theory, I found out how to calculate the mode shapes with easymod too! I'm still not getting correlation between my model and experiments though. Would increasing the DOFs of the model by adding the rotational coordinates yield more accurate results (of the natural frequencies) even if for the first tests I'm not applying rotation to the gearhead? Sep 17, 2017 at 23:32