## Two machines on same structure - combined vibration question

## Two machines on same structure - combined vibration question

(OP)

I have a structure with two vibrating screens (14.4 Hz and 16.6 Hz) they are on separate levels but share columns. We are having a lot of trouble with one screen but no one has been able to find vibration reading that show a problem. My question is how do the vibration forces combine from two different pieces of vibrating equipment? I have read about beat frequencies but that seemed very specific to audio frequencies. Plus (as I understand beat frequencies) it would be 16.6-14.4=2.2 Hz. When I do FFT from my field reading I don't see anything in this area. I am recording 59 seconds of data so it seems like I should collect several instances of a 2.2 Hz signal.

Is it possible the two signals could peak at the same time but infrequently? I am wondering if that is happening and sending a shock wave through the structure but it just hasn't been captured in recording data yet.

FFT's shows strongest reading at the machine vibrating frequency. So that gives me confidence my data collection and analysis is ok.

The machine supplier has said the structure is at fault but they haven't shared their data or said that some parameter is out of spec.

Is it possible the two signals could peak at the same time but infrequently? I am wondering if that is happening and sending a shock wave through the structure but it just hasn't been captured in recording data yet.

FFT's shows strongest reading at the machine vibrating frequency. So that gives me confidence my data collection and analysis is ok.

The machine supplier has said the structure is at fault but they haven't shared their data or said that some parameter is out of spec.

## RE: Two machines on same structure - combined vibration question

## RE: Two machines on same structure - combined vibration question

It reflects simple trig identities, like

[cos(A-B) + cos(A+B)] = 2*[Cos(A)*cos(B)]

A beat is not necessarily a problem. It is often just more noticeable with our senses. I agree with previous poster, we don't really know what the problem statement is.

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(2B)+(2B)' ?

## RE: Two machines on same structure - combined vibration question

If you have two vibration sources, the amplitudes add together, giving you maximum displacement, velocity and acceleration. Your structure needs to cope with this. Your structure must not resonate at either frequency.

Let's be practical. Is there any need for your structure to be light weight? Can you reinforce it and make it stiffer?

--

JHG

## RE: Two machines on same structure - combined vibration question

A sketch of the layout would be handy.

The solution is the same as any other cyclic vibration problem, reduce excitation, isolate, or change the structure.

Cheers

Greg Locock

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## RE: Two machines on same structure - combined vibration question

Like what happens on my old Volvo around 60 mph when the steering wheel vibration increases and then fades to nearly zero every 10-20 seconds. I imagine the tires are rotating at slightly different RPM, and the wheel/tire unbalances add for a little while, and then cancel out, taking advantage of some small looseness in the steering or Macpherson strut suspension.

## RE: Two machines on same structure - combined vibration question

Cheers

Greg Locock

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## RE: Two machines on same structure - combined vibration question

image seems to have stopped working

https://res.cloudinary.com/engineering-com/image/u...

Cheers

Greg Locock

New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?

## RE: Two machines on same structure - combined vibration question

The structure is existing and is basically a two level braced steel frame with a vibrating screen (spring isolated machine) on each level. The original design worked well and ran for several years. The top level screen was changed out for one that runs at the same frequency but has a much greater dynamic load. This resulted in high measured velocities which were fixed by adding additional supports.

The top level screen continues to experience frequent spring isolator breakage. The equipment supplier has stated the structure is the problem but they do not provide any data to support their claim.

Another engineer recently focused on the two screen somehow affecting each other in a negative way. This got me to thinking about how the two screens may vibrate in sync at some frequency that is near a natural frequency of the structure. I can understand how the amplitude of the two sources of vibration would combine by principals of superposition but I couldn't figure out what the resulting frequency would be since the two sources can start at different times. That is when I read about beat frequencies but all the literature I found was related to audio signals.

I think my question has been answered (thank you to everyone); that is yeas the two sources of vibration will combine and it will be the difference in frequencies. Now I need to go back and look at my strural anays to see if I have any modes near this frequency.

Does anyone have a good reference book suggestion for this type of problem?

## RE: Two machines on same structure - combined vibration question

It sounds more like the isolators are not suited for the new, larger loads. You could test this by running just the lower machine and see if any vibration is moving the mounts for the upper screen by more than a few percent of the travel when the upper machine is running. I suppose it's possible the upper isolaor springs have a natural frequency matched to the primary mode of the lower machine, but you will see that running the lower one alone as well.

## RE: Two machines on same structure - combined vibration question

TTFN (ta ta for now)

I can do absolutely anything. I'm an expert! https://www.youtube.com/watch?v=BKorP55Aqvg

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## RE: Two machines on same structure - combined vibration question

Just to circle back, if you have machines at 16.6 and a sinusoid at 14.4, that will indeed cause a beat that sounds like 2.2hz. But

it should not excite any resonance at 2.2hz. In amplitude modulation terminology, the 2.2hz (or actually half of it... 1.1hz) plays the role of an “envelope” frequency and (14.4+16.6)/2 = 15.5hz plays the role of the “carrier frequency.More specifically, let’s look again at that simple trig identity I mentioned: [cos(A-B) + cos(A+B)] = 2*[Cos(A)*cos(B)]

Let A = 2*pi*15.5*t; and B = 2*PI*1.1*t

Then the left side of the identity is cos(2pi*15.5*t -2pi*1.1*t) + cos(2pi*15.5*t +2pi*1.1*t) = cos(2pi*16.6*t) + cos(2pi*14.4*t)

And the right side is 2*[ cos(2pi*15.5*t)*cos(2pi*1.1*t)

LHS = RHS...

cos(2pi*16.6*t)

+cos(2pi*14.4*t) = 2*[ cos(2pi*15.5*t)*cos(2pi*1.1*t)These are just different ways to express the same thing. The left side is a sum of sinusoids, the right side is a product of sinusoids.

The right side is what you’d recognize easily in the time waveform.

The left hand side is what you’d see in the spectrum. 2.2hz does not appear in the spectrum and will not excite any resonance. Adding excitations at different frequencies does not create any new frequencies in a linear system.

Sorry if I misunderstood your comment.

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(2B)+(2B)' ?

## RE: Two machines on same structure - combined vibration question

Consider I have two pieces of equipment on spring isolation bases. They both move in oval pattern but for the sake of this discussion consider just the forward and back motion. They both operate a different speeds but occasionally both will be at the far forward position at the same time. So at that time both are creating a force through their isolation systems in the same direction at the same time. The frequency of this occurrence (I think) is then the 2.2 Hz and the amplitude the sum of the two forces. Is this not the right way to think about it?

On to a second question, I looked at some similar screens and isolation spring resonance is commonly around 2.2 Hz. If what I wrote in the above paragraph is happening would it make sense that the spring is being excited near its resonance frequency and so seeing very large forces in the spring?

## RE: Two machines on same structure - combined vibration question

Perhaps my idea to mention amplitude modulation made things way more complicated than they need to be. A signal with modulation index <1 will have carrier frequency present but a signal with modulation index 1 will not.

Forget amplitude modulation and look at the trig identity. It is an equality. Only one side of the equality represents the spectrum (the side that is the sum of sinusoids). That side of the equation has only the machine frequencies, not the difference frequencies. The other side is the side where half the difference frequency shows up as an multiplier (envelope).

You mentioned superposition. Superposition relies on having a system that is linear time invariant. In a steady state LTI system, the only frequencies that are present are the frequencies of the excitation (input). That's because the only operations done within such system are addition, multiplication by a scalar, differentiation, integration, delay...none of which can transform a sinusoid to a sinusoid of a different frequency. It's an important concept imo.

> Consider I have two pieces of equipment on spring isolation bases. They both move in oval pattern but for the sake of this discussion consider just the forward and back motion. They both operate a different speeds but occasionally both will be at the far forward position at the same time. So at that time both are creating a force through their isolation systems in the same direction at the same time. The frequency of this occurrence (I think) is then the 2.2 Hz and the amplitude the sum of the two forces. Is this not the right way to think about it?

I'd say it's correct that you have a peak of the envelope occurring at a repetition rate of 2.2hz, but you don't have a signal that is exactly periodic at 2.2hz (or 1.1hz) if you look closely at what the signal is doing within that envelope. If you created such system and looked at it on a spectrum analyser (frequency domain) you should see only 16.6hz and 14.4hz. If you looked at it on an oscilloscope display (time domain) you could make out features related to 2.2hz/2 and 15.5hz, both those frequencies are not present in the spectrum and will not excite a resonance.

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(2B)+(2B)' ?

## RE: Two machines on same structure - combined vibration question

consider a single degree of freedom spring/mass/damper system

Tune it to 2.2 Hz

Apply the 14.4 and 16.6 Hz, forces, simultaneously.

What frequency(s) will it vibrate at?

Now run it at 14.4 and 15.5, or 14.4 and 17.7

Is the amplitude greater or smaller?

My guess is that the 15.5 case will give the biggest maximum displacement, simply because we have a lower frequency input into a low pass filter. The 2.2 is not a real physical excitation in some fundamental fashion.

Cheers

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Greg Locock

## RE: Two machines on same structure - combined vibration question

## RE: Two machines on same structure - combined vibration question

Greg Locock

## RE: Two machines on same structure - combined vibration question

Greg Locock

## RE: Two machines on same structure - combined vibration question

Greg Locock

## RE: Two machines on same structure - combined vibration question

This is the force into the ground

here's the model

So the 2.2 hz exists, it is excited by the chirp, but makes no odds to the response to the excitation at 14.4 + 15.5,16.6 and 17.7 Hz.

Note that this model assumes that the subframe is very heavy compared with the vibrating tables, which may or may not be true. I'll come up with a better model later.

Cheers

Greg Locock

## RE: Two machines on same structure - combined vibration question

## RE: Two machines on same structure - combined vibration question

Greg Locock

## RE: Two machines on same structure - combined vibration question

I could guess some interesting relative model values and I'll bet Greg could guess even better. I wonder if op can share with us more details of what he has measured in terms of spectra or TWF on the machines (and maybe the structure? and maybe bump tests?). ok, maybe that's too much to ask for... the first question just to double check:

were both frequencies 14.4 Hz and 16.6 Hz evident on the spectrum of the troublesome machine?(and what were their relative magnitudes, and was directionality apparent in one or both frequencies)=====================================

(2B)+(2B)' ?

## RE: Two machines on same structure - combined vibration question

Ahhh... the heck with it!

I'd like to revisit that question and try to understand your results.

My logic agrees with what you said in that post above. We have a linear system model. We can predict the responses to each of the sinusoidal inputs. The total response waveform is the sum of the individual response waveforms.

Now one question is how do we characterize that sum waveform in terms of a magnitude. There are two common options:

- 1 - RMS. The RMS of the total response should be the sqrt of the sum of the squares of the RMS of the individual responses. But we can't judge that from the waveform, so it's not worth further discussion.
- 2 - True peak.

That's how I think it should work. SoASSUMING(assumption 1) that the frequencies are not related by a ratio of integers, then we know that the "phase" relationship between the two peaks (maybe strictly speaking I can't call it phase, we can also call it the time between the positive peak of the two sinusoids) will drift somewhat randomly between 0 and half the period of the higher frequency sinusoid. ThereforeASSUMING(assumption 2) we examine the waveform over a sufficiently long period of time, then they will eventually line up so that their peaks are at/near the worst case combination (which gives the peak of the sum as the sum of the peaks) at some point during that long simulation.ASSUMING(assumption 3) that indeed the 15.5 has a lower individual response than the 16.6 and 17.7, then I'd expect the peak of the combined waveform would be highest when we combine 14.4 with 15.5 (rather than combining it with 16.6 or 17.7)But that is not what we see on your graphs. The system including 16.6 input gives the highest combined peak. So in my mind, among the three assumptions identified / bolded above, one of them

mustbe wrong:- Assumption 1? Sure we violated the "ratio of integers" assumption (since our frequencies are not irrational numbers), but those integer ratios are high enough that
- Assumption 2? The simulation looks like it has run long enough so that the peaks have stabilized and we are close to the true peak so
- Assumption 3? This has my vote for the assumption that was violated. Mabye the individual response of 15.5 is not lower than the individual response to 16.6 and 17.7 for the particular system and output that your are plotting. I have to immediately followup by admitting that I don't understand exactly what your system looks like and what is the output that you are plotting.

That's the way I see it, maybe I'm completely missing something somewhere.I doubt that is the problemI doubt that is the problem.Another unmistakeable feature of the graphs as mentioned before is the envelope of the input shows up in the response much better in the combination with 16.6 (where the envelope frequency matches a resonant frequency). I have no idea why that would be.

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(2B)+(2B)' ?

## RE: Two machines on same structure - combined vibration question

(b) I've decided I don't really like that model

(c) it is two mass/spring SDOF blocks in parallel, sitting on top of a grounded sdof block. So it is the same architecture as Ideem drew. Due to a modelling assumption that is incorrect the results can only be correct if the mass of the thrid sdof block >> mass of the other two.

Greg Locock

## RE: Two machines on same structure - combined vibration question

GregLocock, can you tell me what k,m c are? I can guess k is spring constant and m is mass but not sure what c is.

I have recorded acceleration data after machine 1 (where machine 1 attaches to the main structure), I would be happy to share the raw data if it is of use. I have used it to calculate velocities using Vibration Data Toolbox.

Prior to modifications I did a startup and shutdown to verify my model frequencies. They were in the ball park. The structure has since been modified and I haven't done any new shutdown tests.

Main issue is machine 1 springs keep failing. The equipment supplier doesn't provide any guidance on maximum support structure velocities (or any other dynamic acceptance criteria).

## RE: Two machines on same structure - combined vibration question

Yes raw data is always fun.

Greg Locock

## RE: Two machines on same structure - combined vibration question

Here are the weights and some of the dynamic information added to the schematic.

A printout of all the structural frequencies is in the attached excel file.

Either this post or the next (if the file doesn't attach) are the velocities I measured on the machine 1 base at three different dates. The 10/20/2020 is before structural modifications.

## RE: Two machines on same structure - combined vibration question

## RE: Two machines on same structure - combined vibration question

Greg Locock

## RE: Two machines on same structure - combined vibration question

The vibrating screens are for aggregate processing.

It looks a lot like the link below except there is another screen below the top screen.

The screen/machine is for sorting rocks into different sizes. It's basically multiple levels of big mesh screens that sit inside a frame that is supported on springs. A motor with eccentric weights spins around and causes the frame to vibrate at the frequencies in the diagram. The problem is springs on machine 1 keep breaking. I thought maybe the two machines running at the same time were creating a "new" vibration in the structure by superposition and that was close to a resonance in the structure which in turn was causing the springs to break.

Based on what I read in the thread superposition is not the right way to think about the problem.

Link

## RE: Two machines on same structure - combined vibration question

Given that the only coupling between the two lightweight screens is a five ton frame, conceptually it seems unlikely that screen1 is going to have much effect on screen2.

I'll have to rejig my model a bit, then I'll pull out the spring forces.

Greg Locock

## RE: Two machines on same structure - combined vibration question

## RE: Two machines on same structure - combined vibration question

I don't think anyone objected to superposition (the response at any location is likely the sum of the individual responses you'd get from each machine running). It's just the idea that superposition creates a new frequency that was objected to.

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(2B)+(2B)' ?