Cancel
Showing results for
Did you mean:
Highlighted

# Modal Projection Tool Vs. FFT

Genius

Hello,

I am testing a pilot operated relief valve.

while testing it, I noticed that the pilot valve oscillates very heavily.

A FFT from the mass displacement indicates me 2 frequencies (130 Hz and 260Hz)

I remembered there is a projection tool for getting more information on oscillations.

So I analyzed the modes, and I can't get the 2 frequencies shown with FFT.

Am I doing something wrong with this tool?

Maxime

7 REPLIES 7

# Re: Modal Projection Tool Vs. FFT

Siemens Phenom

Hi,

the oscillations appears after 2.5 seconds so you should have a look at the linearization results at 5 seconds.

# Re: Modal Projection Tool Vs. FFT

Genius

Hello @Emmanuel_D

My Fault

Here the results at 5s:

I understand I have 3 modes: 220 / 1812 / 12070 Hz

But FFT indicates 2 modes: 130 / 260 Hz

# Re: Modal Projection Tool Vs. FFT

Siemens Phenom

Try doing the FFT aroud 5 seconds instead of using the whole time trace. You should get a cleaner FFT.

FFT results are a combination of frequencies which are "forced" on your system and natural frequencies. For example; if you were to apply a pulsating flow rate you will observe a combination of the excitation frequency of that pulstating flowrate (input) and the natural frequencies of the system (this is what linearization and modal projection gives you).

Finally, the results of the linearization can be very dependent on the instant they are performed (especially for non linear system). From the plot, it looks like you have something going to an end stop. Zoom in around 5 seconds and try doing the linearization in contact and out of contact. You may end up with linearization time at 5, 5.01, 5.02 seconds for example.

# Re: Modal Projection Tool Vs. FFT

Genius

So I generated a FFT using interval 4.9-5.2 s
It returns the same frequencies (130 / 260 Hz)

I am not familiar with FFT but I understand : if I generates a FFT of the displacement of the pilot-operated spool, the FFT "interpolates" the signal in a Fourier Serie, with which it is easier to see the dominant frequencies of the original signal.
Correct me if I am wrong

So if the FFT shows 130 & 260 Hz frequencies, it means the spool oscillates with 130 Hz (I checked by measuring the period between 2 oscillations, and I have 7.65ms period)

I understand the eigenvalue (at t=0s) as the natural frequency of the system. For a spring.mass it corresponds to [sqrt(k/m)]/(2pi)

The eigenvalues at t >0s are no more the natural frequencies of the system, but the combination of the natural frequencies of "forced" and natural frequencies as you notd

If am I right untill here, I would have made a huge step in this field

So if I have an FFT around 5s, I should retrieve the dominant frequencies in the eigenvalues at linearization time 5s or in the modal projection tool also at t=5s, or am I wrong?

For instance I zoomed on to the plot of the spool around 5s, and you see the oscillation modes at t=5s and also the modal projection results at t=5s
Both eigenvalues & modal projections give me 3 modes: 220 / 1812 / 12069 Hz
FFT still returns me 130 & 260 Hz.

You are also right the pilot-operated-spool opens & closes very quickly (max stroke 0.6mm).
But in the modal projection, the component which contributes to those oscillations are not this pilot-operated spool which opens and closes quickly, but another spool which also oscillates because of the pilot-operated one

# Re: Modal Projection Tool Vs. FFT

Siemens Phenom

@mAx wrote:
...

I understand the eigenvalue (at t=0s) as the natural frequency of the system. For a spring.mass it corresponds to [sqrt(k/m)]/(2pi)

The eigenvalues at t >0s are no more the natural frequencies of the system, but the combination of the natural frequencies of "forced" and natural frequencies as you notd

...

Eigenvalues always give natural frequencies of the system, whatever the time they are performed.

For a mass spring, with a linear spring and no contact; the results of the linearozation will always be the same. If the spring was non linear; the frequency would change depending on when you perform the linearization. If you had endstops, doing the linearization in or out of the contact will give very different results.

On the other end, the FFT is performed on the actual response of the system. This is where you get the combination of natural frequencies and excitation frequencies. See below, I excite the system with 1 Hz force, the natural freq of the system is 5 Hz, with the FFT you get both contributions.

Going back to your example, it looks like at 5.0 s you are in the upper endstop. But this would more points around that time to be sure.

I would add a few linearization times around 5 so that:

- you have a couple of points in the upper endstop,

- you have a couple points in between the 2 endstops,

- you have a couple of points in the lower endstop.

# Re: Modal Projection Tool Vs. FFT

Genius

Thank you very much for your explanations, it very helps

Back to your example: in the fft of your mass you get both contributions: I guess 1Hz & 5Hz

If you would have non-linearities, does it mean that the response may have other contributions than the natural frequency and the excitation?

This is exactly what I am not understanding: I have a peak at 130 & 260 Hz, but I can't get those frequencies in the eigenvalues. (I entered linear-times from 5.001 till 5.01, but still can't see 130 & 260 Hz)

At t=5s the spool isn't at its upper end-stop.

The spool only opens a little bit and close (periodically)

The spool only enters in contact with lower end-stop

So at t=5s there is no contact

My system isn't excited directly: I raise the flow rate at the inlet of my valve, with a restrictor in parallel for raising the load pressure.

As the load pressure reaches the pressure-set, the pilot-operated spool opens and starts vibrating

# Re: Modal Projection Tool Vs. FFT

Siemens Phenom

Back to your example: in the fft of your mass you get both contributions: I guess 1Hz & 5Hz

If you would have non-linearities, does it mean that the response may have other contributions than the natural frequency and the excitation?

This is exactly what I am not understanding: I have a peak at 130 & 260 Hz, but I can't get those frequencies in the eigenvalues. (I entered linear-times from 5.001 till 5.01, but still can't see 130 & 260 Hz)

Practically, the linearization which is computed at given instants, can give very different results depending on exactly when it is performed. So, in a way, yes, non-linearities introduce new eigenvalues. But a linearization performed at the right moment should allow you to identify those frequencies.

As a general method: plot the time evolution of the state variables of your model (pressure/displacements for an hydraulic circuit). From those plots, identify moments of interest: max/min/in-between and define those moments as linearization times. Also, I think that: ideally, linearization should always be performed in an equilibrium condition but this is difficult to achieve...