# Mechanical vibrations - waterfall plots

1. Dec 20, 2013

### jason.bourne

hi!

i'm beginner in the subject of vibrations.
i'm trying to understand the waterfall plots.

i have attached a waterfall plot.

waterfall plots are used when the operating speeds are varying (run up or coast down).

in this plot, as the speed varies with increase in time, does the amplitude of the machine changes at a particular natural frequency?

from elementary vibrations all i know is at a given natural frequency, a machine/component will start vibrating at natural frequency with large amplitude of a fixed value.

for a case of a multi-cylinder IC engine, as the speed of the crankshaft is varied how is the rainflow plot going to look like when the speed of the engine crosses critical speed of shaft?

2. Dec 20, 2013

### xxChrisxx

There isn't anything attached.

Before looking at colourmaps, it's best to understand what a noise spectrum shows. This will be a level vs frequency. A waterfall/colourmap is a stack of these that occur at time intervals. This makes a level vs frequency vs time.

You see three main things.

1. Orders
Frequencies that track with a change in speed. They are referred by how many times it occurs per revolution

1st order = once per revolution (fundamental order)
2nd order = twice per revolution (1st harmonic)
4th order = four times per rev (2nd harmonic)
etc

Using an I4 as an example:
1st order 600rpm 600/60 = 10Hz
1st order 1200rpm 1200/60 = 20Hz
1st order 1800rpm 1800/60 = 30Hz

http://www.vibratesoftware.com/html_help/2011/Diagnosis/Engine_Speed_Related.htm [Broken]
These show up a diagonal lines on a colourmap.

2. Resonances
Are where the frequency is independent of speed.
These will be vertical lines on the colourmap.

3. Impacts
Single events that excite a broad range of frequencies.
These show up as horizontal lines.

Where orders cross resonances, you typically see a peak in the amplitude.

Last edited by a moderator: May 6, 2017
3. Dec 21, 2013

### jason.bourne

thanks Chris.
i got it what you said.

check out this waterfall plot in the attachment.

from what you explained, i think the set of vertical lines are resonance as they are parallel to frequency axis.
in this plot, with increase in time, does the amplitude of the machine changes at a particular natural frequency?

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4. Dec 21, 2013

### xxChrisxx

Well they aren't resonances, as they don't appear to be a response. A resonance will be a high period of response to a broadband excitation.

They just look like constant tones.

5. Dec 21, 2013

### jason.bourne

Chris are you having a sample waterfall plot through which you can explain me these concepts of orders/resonance/impact on it?

its pretty confusing.

6. Dec 21, 2013

### AlephZero

In your OP you mentioned IC engines, run-up and run-down, etc, but the image you attached looks like the response of something vibrating after an impact, like a bell being struck.

The plot shows the mode frequencies (corresponding to the table below it) and the rate of decay of each. The first mode decays slowly (i.e. the sound rings on for a long time), the others much faster. The heights show the different amplitudes of the response in each mode, for example the third mode started at a high amplitude but died away very quickly, compared with the first that started lower but died away much slower.

The plot you would get from a machine that was accelerating or decelerating through a range of speeds, would look completely different to the plot you attached.

7. Dec 21, 2013

### jason.bourne

okay. how about these following plots?

plot A: can i say that there is a order at 23 Hz with almost constant amplitude?
an order of 7.5 Hz is being excited at resonance so we see peak amplitudes over the speed
range.

am i correct?

plot B: how do we interpret the decaying vertical lines at approximate frequency of 1500 rad/sec?

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8. Dec 21, 2013

### AlephZero

Plot A is a a bit confusing. I think the "Hz" scale should be raised verticaly up the paper to the bottom edge of the plot (i.e. at displacement 0).

The constant amplitude line is then at 25 Hz and my guess it is some sort of electrical noise being pictked up by the measuring system (e.g it could be half the freqquency of the 50 z mains in Europe), or else it is an intentional frequency calibration signal added to the measured data.

There are 3 "diagonal" traces that presumably are related to engine speed. The two with the highest frequencies look like they might be first and second harmonic of something like the engine RPM. The lowest one doesn't seem to match up with the other two. Ignoring the possibility that this is a multi-rotor jet engine or something similar (with rotors running at independent speeds) the bottom line could be a something non-synchronous, like oil whip in the bearings. Whatever it is, it gave the structure a good shaking when it hit the mode at about 11.5 Hz (see next paragraph).

Then, you have a vibration mode of the structure at about 11.5 Hz which is excited 3 times as the three "engine order" lines cross that frequency. When the vibration level is high, I guess something nonlinear is happening which either excites some higher modes at around 21 and 32 Hz, or else those biips are harmonics at 2x and 3x the 11.5 Hz frequency.

It is MUCH easier to read numbers from these charts if you can plot them viewed directly from above (so the axes are not skeved), and showing the amplitudes (vertical on your plots) by different colors. You can also superimpose a grid on the plot, so it's easier to identify harmonics of the engine speed, responses that are at the same frequency, etc.

In plot B, the diagomal line presumably corresponds to the engine RPM. The big spike is presumably a mode at about 1800 rad/sec that got excited at top speed. The whole plot looks suspiciously clean and tidy. Maybe it came from a simulation? it so, and the simulation started at max RPM and decreased, that big spike might just be an artefact from the response when the model was started.

These plots aren't magic bullets - you need to know something about what was being measured or calculated to interpret them.

9. Dec 21, 2013

### xxChrisxx

Colourmaps are massively easier to interpret. Without a context its very difficult to say whats going on.

10. Dec 24, 2013

### jason.bourne

understood to a greater extent. very helpful. thank you guys !!!