Do resonant frequencies produce harmonics 2

[GMarsh]

Hi,

I have a plate vibrating due to some forced excitation. When I take FFT of measured acceleration signal on the plate, I am getting a dominant mode and its harmonics. I see no link to this dominant frequency and exciting frequency (they are very wide and far). But the dominant frequency in FFT is very near to one of the resonant frequencies of the structure.

Before I conclude that the external excitation is exciting one of the resonant modes, I want to know if a resonant mode ever displays harmonics in FFT of acceleration signal.

Thank you.

Regards
Geoff

 

[GregLocock]

Yes, sort of. In a non linear system you often get 3rd, 5th etc multiples of a strong frequency, due to contact/clearance/rattles.

What you shouldn't get is much response at frequencies other than harmonics of the drive signal. It is possible, but you need a rather elaborate non linearity to get that.

Oh, and stick slip can cause some pretty odd responses.

If you do a sine sweep and plot a waterfall of the response then things may become clearer.

Cheers

Greg Locock


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[GMarsh]

Hi Greg,

Many thanks for such a prompt and useful response. Happy to see the answer! But as I said I am noticing dominant response and its harmonics which are no way connected to exciting frequency. In numbers, I am exciting at 26.6 Hz but I am finding dominant response around 4870Hz and then 9740Hz, etc.

There is a resonant frequency for the structure at 4874Hz. So I am wondering even if resonant mode gets excited, will it show harmonics like this ? What could be physical meaning of these harmonics ? Structure is vibrating at multiples of its mode shape ?? Not fully convinced.

Thank you.

Kind regards
Geoff

 

[GregLocock]

Weird.

Can you do a sweep?

Cheers

Greg Locock


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[GMarsh]

Greg, Thank you again.

Unfortunately I have only impact hammers and few accelerometers.

I have the above finding by doing FFT of acceleration signal with one of the accelerometers mounted on structure.

Any other ideas ?

Kind regards
Geoff

 

[izax1]

Geoff
Some questions for carification.

Is 4870 Hz the lowest mode of the plate (is it the 1st natural frequency) or are there lower modes that you have missed in the measurements?
Is the plate only a square flat plate?
What are the boundary conditions?

To me it seems like something is omitted in the test (input or output)I cannot see where you should get much non-linearity in the sytem you are describing.

 

[GMarsh]

Hi izax1,

Thank you.

I am sorry. I should have written shell in the first place. It is a 2mm thin shell of 100mm height, clamped at bottom. By mistake I mentioned as plate as on a theoretical perspective I am looking at it as a curved plate. This shell is being excited at the top. By mounting the accelerometers on shell I am acquiring the vibration signal and doing FFT of it.

4870 Hz is not the 1st mode. Fundamental frequency is around 1300 Hz. When I did modal testing on structure, I got all the modes till 8000 Hz. Compared with FE also.

In fact there is some non linearity in structure. I won't get identical drive point FRF even if I hit at same point.

Puzzled with this.

Kind regards
Geoff

 

[GregLocock]

Hang on are you hitting it or shaking it? If the former where is the 26.6 Hz coming from?


Cheers

Greg Locock


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[GMarsh]

Greg, Thank you.

A milling tool with 2 cutting edges is rotating at 800 rpm and is machining it at top of shell - so basically the cutting edges are impacting at 800 * 2 = 1600 rev/min which translates to 1600 / 60 = 26.6 Hz.

Being a circular shell the tool moves along the periphery of the shell at feed of 0.2mm / rev of tool while rotating at 800 rpm all the time.

When the acceleration signal acquired on the shell near to machining zone was converted through FFT, I get dominant response peak at 4870 Hz and its multiples.

Geoff

 

[hacksaw]

this only gets better...

have you given any thought to the frequency content of a sharp impact generally?

 

[GMarsh]

hacksaw, Thanks for your response.

In fact whatever frequencies I am saying as dominating are observed for one impact only. That is, I took FFT of time signal corresponding to one impact - start to end of impact.

Geoff

 

[hacksaw]

a sharp impact can excite more than one mode

 

[electricpete]

I think there are two possibilities:

1 (unlikely imo) - the system may have two resonant frequencies which happen to differ by a factor of 2 (would be quite a coincidence for anything but very simple system).

2 - the high vibration at 4870 is interacting with some non-linearity of the system to create non-sinusoidal motion with fundamental frequency of 4870 and (since non-sinusoidal), harmonics of that fundamental frequency so 2*4870 = 9740.

To tell the difference, try taking a time waveform sampled at much higher than twice the highest frequency of interest. Zoom in on the time waveform and see what you've got. The difference between 1 and 2 would be obvious in time waveform.

=====================================
(2B)+(2B)' ?

 

[GMarsh]

Thanks for all your replies.

electricpete - By 'fundamental frequency' do you mean this is first mode? It's not. As said earlier, the fundamental mode is around 1300Hz.

Reg non-linearity - the structure is held with bolts : 8 no.s M6 and 16 no.s M12

Do you mean we see harmonics whenever non-sinusoidal vibration exists ?

I am attaching the zoomed in time waveform and its FFT. I have marked the frequencies also. This is not constant always (i.e. depending on which cutting tooth impact I analyse for FFT). It moves anywhere from 4800Hz to 4880Hz. But mostly occurring around 4870Hz.

When I did experimental modal analysis in that same set up I found two similar mode shapes at 4790Hz and 4874Hz. In fact they are symmetric modes of same mode shape. I think due to nonlinearity these symmetric modes are spaced that apart. But I don't know out of all the modes available what makes this 4874 mode favourable.

Many thanks & kind regards
Geoff

 

[electricpete]

Your waveform shows an impact-like event at 17.0065 followed by another at 17.0457
Spacing is 0.0392 or roughly 25.51 hz which is roughly the 26hz frequency you mentioned.

I’d like to see zoom in much more so you can see a waveform oscillating at 4870 and see to what extent is is sinusoidal. For example, zoom in the high-amplitude time region from 17.0125 17.015 and you’d get about 10 cycles of 4870 so it’s spread out enough to judge it.

By "fundamental frequency", I meant not the first resonant frequency, but the frequency at which [assumed] periodic vibration repeats.

Do you mean we see harmonics whenever non-sinusoidal vibration exists ?

Yes (IF the vibration is periodic... a characteristic which is a traditional assumption of spectrum analysis...without the assumption everything is murkier).


=====================================
(2B)+(2B)' ?

 

[GMarsh]

Thanks a lot for your support electricpete.

Please find attached the two zoomed signals from 17.0125 to 17.015 and 17.0225 to 17.0250. First one is when the impacting tool is in touch with structure. Second one is when tool has left structure and workpiece is vibrating freely (of course due to previous forced vibration). They don't look purely sine.

Sampling rate: 1e6 points/sec

Also I took FFT of the acceleration in these bands. In the first band you can see the peak shows 4804Hz and its multiples. The next point on frequency spectrum is again 5204 only. In second band, 5196 is dominant, but 4796 and its harmonic 9592 are also clearly seen. As said earlier the two symmetric modes are at 4791 and 4874 Hz. So not quite sure if structure is vibrating at one of these.

Now if this peak varies like this from 4869Hz to 4804Hz to 4796Hz, etc. can I consider that it is a resonant vibration of structure - this is my main focus.

Kind regards
Geoff

 

[GregLocock]

I think you are overanalysing this situation. I think you can see where the 4800 +/-200 Hz is coming from the question is where is the 9600+/-200 Hz coming from.

Have you tried a modal with the cutter in contact with the workpiece?

If we ignore health and safety, can you try a modal on the running system?



Cheers

Greg Locock


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[hacksaw]

if you are dealing with a 100 mm dia s.s. cylinder having a 2 mm wall, the circumerential modes fall in a sequence like

i fo(Hz)
2 524.2
3 1482.4
4 2842.3
5 4596.5
6 6742.8
7 9280.6

what are the dimensions of your work piece

 

[electricpete]

How is your accelerometer mounted?


=====================================
(2B)+(2B)' ?

 

[GMarsh]

Greg, hacksaw, electricpete - I am thrilled and thankful to see your support.

Greg -

Are you saying a resonant mode can appear within +/-200Hz band during operational condition ?

By modal in running system, do you mean operational modal analysis ? I wanted to do this, but I have only two suitable accelerometers. So did modal by impact hammer. So at a given instance I may be able to acquire only a reference and one additional acceleration signal. So I think it is difficult to do operational modal.

hacksaw -

Dimensions of workpiece: 365mm OD, 2mm wall, 100mm wall height, material: nickel-based superalloy.
I did some analysis on circumferential modes of this casing, of course for FE modes. They fall in a pattern as shown in attached document. This is in-line with shell behaviour explained in textbooks.

electricpete -

What is your comment on sinusoidal behaviour of signal? I am inconclusive due to the nature of peaks. Do you think they are genuine harmonics?
Please see the actual structure and accel mounting in attached document. Please note that the accelerometers are in-fact mounted close to the top edge than shown in figure. Signal I have analysed is exactly behind that of accelerometer when tool is cutting at that point.

Many thanks to you all.

Kind regards
Geoff