All:
Yesterday I had a discussion will my group about a suspected resonance. I'll skip the details of the specific matter to get to one of the questions that came up.

If you do a bump test on a system, and confirm its' natural frequency to be close to running speed, are there any means for determining how much of the recorded vibration signal would be there absent the resonance, vs with the resonance.

The point is that while you may have a peak in a bump test close to running speed, depending on the flexability/damping of the system, the peak could amplify the 1x severely or not at all.

I'd like to know if any of you have ever raised this question, and more specifically have you ever determined if a resonance was irrelevant by determining that most or all of the energy of the peak in question was from the system and not amplified by the natural frequency.

Also I'd like your opinions on using exciters for a natural frequency test. Attaching an exiter to a system changes the mass of a system, and thereby the natural frequency. But I suppose it depends on the ratio of mass between the exiter and the system being tested.

I know all this seems obscure, but in this case it is important to the analysis.

You may attach the exciter indirectly via a rod or??? Contact some OEM suppliers of exciters.

What's the shape of the resonant pattern or how does it broaden at its base? And again, how does the machine's component look in shape at its base and what is the source of the vibration - all considerations I think.

Maybe Bill F or Steven or someone will weight in with some really good experience. I'm sure Pete can do the math. But there are several things to consider.

I don't think I can provide an answer to satisfy even myself.

Natural frequencies can be excited or not excited. Resonance is the coexistence of a natural frequency with a force, more or less. Forces at the natural frequency do not have to excite the resonance; this is used in balancing generators all the time. Couple imbalance doesn’t excite the first mode for all practical purposes, and static imbalance doesn’t’ excite the second mode.

Resonant amplification depends upon the damping and how close to the natural frequency the force is. The greater the damping the force needs to be less close to the natural frequency, but the amplification will be lower because of the damping. Sharply tuned natural frequencies (low damping) may have the force closer without issues, but dare to get too close and this could result in very large amplitudes or damage.

The formulae are textbook and depend upon the forcing type (speed squared, constant, base excitation, etc. with or without damping even type of damping model). An Undamped model would look something like the following for amplification.

1/abs(1-f^2) where f is the ratio of the forcing frequency to the natural frequency.

Martin--

My understanding (and I've not done this yet) is that you can separate the amount of the effect of the forcing function from the amount that it is amplified through impacting testing w/a modal/force hammer using the right instrumentation and software.

In theory, you can both determine how related the input is to the output (coherence) as well as how much (amplitude) of the output is from the input (transfer function).

I'll let the "pros" handle this one on a more mathematical/scientific level--as well as confirm my understanding here!

Tony

The Exiter was attached at the lift point of the motor at the center, using the lift loop as the bolt.

Let me pose the question in a more practical way. Lets say you are testing an I-beam, you have your accelerometer and a deadblow hammer. You move along the structure, doing a series of bump tests.

At the end (node) you have to whack the structure really hard to get a reading of a particular amplitude. The next point (lets say an antinode)if you breath on it you get the same amplitude.

Now the basic rule is that if you add mass or stiffness the Natural will change. But an identical mass will have a smaller effect when placed on the node than at the antinode.. (Right?)

The reason I ask this is because we have a confirmed resonance on the inboard vertical point of a 40hp motor. But standing on the motor has no effect. The initial assumption was that there is no resonance because a mass change didn't effect the natural.

But now we think we have a rotor that is resonant; a bump test on the coupling confirmed this.

Tommorrow we will do a phase check between MIV and the coupling, to see if either is leading or lagging, or if they are acting as 1 system.

Using an instrumented hammer allows you to measure the transfer function, which is the relationship between the force of the impact and the response of the system to that impact at a given frequency. You could accomplish the same thing by measuring vibration on a rotor, then installing a balance weight and measuring the vibration again. This gives an influence vector which is essentially a transfer function as well.

So what that tells you is that for a given force applied to a system you will get a certain response at a given frequency. It does not tell you what the response would have been if the effect of the resonance was not there. The only way to figure that out is to change the resonance frequency and see what the new response is, but to do that you would have to change the mechanical system which negates the original question....

Now the common thing that is done is to look at the transfer function and evaluate how much higher the response is at resonance vs some other point for a given force input. So if for a point well away from resonance 2lbs of force yields 5 mils of response, and at running speed frequency 2 lbs of force yields 50 mils response and we determine that there is a natural frequency near running speed, then we can conlude the much higher amplification is due to the resonance, and if the natural frequncy was moved away from running speed the transfer function would be more like 2lbs force yields 5 mils response. If in our example the transfer function at running speed shows that 2 lbs force yields 6 mils response, we might conclude that the resonance is pretty well damped and not really much of a practical issue. I have evaluated equipment that ran for years in resonance, but the system was well damped, and as long as the unbalance forces were minimized, there was no problem. I love talking about this in classes, because vibration and machinery guys are absolutly paranoid about running a machine near a critical speed. But if the forces are low the damping is high, and there is little vibration response at resonance, is that critical speed really all that critical? I think not...

I don't really like the way your question is worded, since the system sets the natural frequency, there is no seperating them. We can only look at the amplification factor and decide if for a given force we can live with that amplification or not. If your machine is operating near a natural frequency, and the vibration level is too high, then you either need to reduce the forces in the system, or change the stiffness or mass to move the natural frequency, or increase the damping in the system. But the system response is what it is. If you don't like it you have to change the system.

As for the exciter, people use them all the time with good effect. Depends on what you are exciting versus the mass of the exciter as to what the effect will be. For a small turbine blade, the mass of an accelerometer may change the natural frequency. But the natural frequency of a 10000 lb structure will not be much changed by a 10 lb exciter. The natural frequency is the SQRT(K/M), so if you know the natural frequency,assume K is constant, and solve for M. Then solve for the natural frequency again with M + the mass of the exciter. If the natural frequency changes less than 2 or 3% you are in tall cotton.

As a purist though I like to use the machine as the exciter. Run up the machine, set up your vibration measurements, then shut down the machine while gathering data. This gives you a beautiful measurement of the response to the forces actually coming from the machine, without changing the system.

Oops, you posted more info while I was writing my last reply.

When we talk about adding mass, we're talking about modal mass, mass that contributes to the resonant vibration mode of interest. That is what Bill Foiles was getting at. If the bearing cap is resonant, standing on the motor is unlikely to add modal mass to the resonance and change it. If the rotor is resonant, standing on the motor is certainly not going to change it. If the stator assembly were resonant, standing on it might contribute to the modal mass and change the natural frequency.

Your basic rule is essientially right, but again it is a matter of adding mass that will participate in the mode in order to be effective.

You are also looking a bump testing backwards, what you want is to impart a constant force, and then measure the response at each point to get the mode shape. I suppose it works the other way as well, just more work doing it. Using a transfer function is the most effecient way however..

Oh, and if you really are interested in resonance on this machine, I recommend doing the rundown test. You might even take one set of data, measuring 1X amplitude and phase at various speeds, then add a known unbalance to the coupling and do it again. From that you can get the transfer function. Thats why we require unbalance response tests on 2000 HP and above API motors in our organization.

Steve's answer I'm sure is 100% right.

Another way to look at it

If you wanted to add mass to that motor to change the resonance, you would have to mounted rigidly to the motor to ensure the acceleraiton of the mass was the same as the acceleration fo the motor.

But the person standing on the motor is resiliently mounted. The shoes are like shock absorbers with a low-frequency pass-band perhaps below 2-3hz (think about how much softer is shoe material than steel). Hardly any of the higher frequency vibration gets through. The man standing on the motor hardly moves at all. So the force transmitted between man and machine is a static or very-low-frequency force and therefore not a sinusoidal force associated with mass acceleraion in your frequency range of interest. Therefore not equivalent to increasing motor mass.

I don't have one of those instrumented hammers and I don't expect I'll be getting one soon. So I'm am interested in this two tier test with adding an unbalanced weight.

Could you explain how we derive the influence of the resonance vs the influence of the added weight?

Here is some data. This is a skid with 3 parrallel pumps, about 40hp. At any given time 2 of them are running.
But the highest vibration is always on the center pump MIV, whether it is running or not.

Motor feet and base plate ar low amplitude

More data

2nd bump test at coupling

As I said before, MIV is obviously resonant at 3586, but standing on the motor has no effect.

Changing the balance of the coupling sounds interesting to me, but I need more info about how that works.

The coupling seemed hyper-sensitive to me because it took little energy to excite the resonance. It was more difficult to get the motor going... we had to strike it much harder.

You could gain some insight by testing the other motors. How does this differ from the other two, and how might you correct it?

As stated by Electricpete, standing on the motor is not a mass addition. With some folks I’ve known it would be an inert mass addition but not in terms of a structural mass addition. Bolt some mass on to an active direction or try a tuned absorber; either should move a resonance on a small motor.

quote:

Could you explain how we derive the influence of the resonance vs the influence of the added weight?

This question isn’t well posed. The added weight just supplies a force. Without resonances one would have a rigid (or free) system; as long as you have mass and stiffness, there will be resonances.

quote:

Using an instrumented hammer allows you to measure the transfer function, which is the relationship between the force of the impact and the response of the system to that impact at a given frequency. You could accomplish the same thing by measuring vibration on a rotor, then installing a balance weight and measuring the vibration again. This gives an influence vector which is essentially a transfer function as well.

This is the test to which I was referring. I need the formula for this transfer function and influence vector

I haven’t followed all the discussion to understand exactly what you’re asking or what you’re trying to do.

It seems like a reasonable conclusion that you have a resonance affecting your center pump, especially since the vib is there even without the center machine running. I think this is the same conclusion you already reached.

I would recommend the following options in order:

1 - Try adding some temporary braces or wedges different places around the support structure especially near motor to see if you can reduce the vibration. If it works, it helps prove you have a resonance (as if you needed more proof), and may give you a roadmap to what a permanent bracing solution will look like.

2 - Adding mass for troubleshooting or correction purposes is usually a little tougher to do. As you saw it needs to be rigidly attached, loosely attached does nothing. Therefore this more difficult approach is usually the 2nd option.

3 - A third (least preferred) option mentioned both for proving resonance and eliminating associated vibration is a dynamic vibration absorber.

This message has been edited. Last edited by: electricpete,

One more thing you might check is whether the resonance or excitation (coupled from other pumps) might be affected by the suction or discharge piping. Try measuring vib there and try temporary bracing there as well to see if it affects vibration.

If you could post a picture of your machine and support structure, I'm betting you would get a lot of good suggestions from the folks here on bracing possibilities and other things to check.

Ok, let me be clear:

We know we have a resonance.. obviously. It is at 1x turning speed.

Many things can cause high 1x turning speed. The thing I am getting to is this:

If there is a way we can determine the influence of the resonance there are some significant advantages:

1. If the influence is high, we can directly make recommendations to deal with the resonance.

2. If the influence is low, we can advance on some other known issues with this skid.

The alternative is to take action on one thing or the other without as much certainty about how beneficial the action will be.

If you have a natural frequency at running speed, I would say the influence is high. I'm not sure I've ever heard anyone suggest anything different.

My recommendation would be to not spend any more time on any other testing until you go out there and try some temporary bracing. Nothing more than a few pieces of 2x4 or 4x4 of various lengths to try to wedge in at convenient location or chain and turnbuckle to apply some tension. If you can reduce it through temp bradcing you know you can fix it through permanent bracing.

A 4th item to consider in the list of ways to address resonance would be fiddling with different types of washers at the motor feet as Arne has suggested in the past. We have never done that.

One more comment on the original question and I'll shut up.

As a rough approximation, IF you can successfully move the resonant frequency by approximately 15%, you should see approximately 10x reduction in vibration. That is based on your no-pumps-running bump test. The vibration at 3,000rpm (15% below resonant frequency) is about 0.0045 and the vibration at 3600 RPM (resonance) is 10x higher 0.045. Vibration 15% above resonant frequency drops down again by a factor of 10. (this assumes your bump test is not influenced by some other nearby machine running at 3600rpm... twf would help to confirm).

Whether or not you can be successful in changing that resonance is a tougher question. For vertical motor with resonance confirmed by bump test and typical pattern while runnign directional with highest vibration at the top of motor, I would have said 90% probability a brace will significantly reduce it. For your pattern, it's unknown to me and it's an open question how difficult it will be to change the resoancne.