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Is a tuned damper effective in forced vibration?
5

Is a tuned damper effective in forced vibration?

Is a tuned damper effective in forced vibration?

(OP)
Hi,

I have a structure on which a tuned damper is mounted, tuned for one of the resonant modes of structure. Now this structure is also being subjected to a forced vibration.

Now I am interested to know if the tuned damper will have effect on minimising forced vibration (because of added mass or some other effect)? If yes, how does the effect vary with amplitude of forced vibration?

I am also interested in simulating this through FE ? Any idea how to apply forced vibration with known frequency and amplitude in FE?

Thank you

Regards
Geoff

RE: Is a tuned damper effective in forced vibration?

How close is the forced vibration frequency to the resonant frequency?

Is this structure you "have" actually built and in service?

RE: Is a tuned damper effective in forced vibration?

(OP)
Thanks for your reply.

They are few kHz apart.

I have not built this structure. A model similar to this is in service. My interest is to find out the effect of tuned damper in presence of forced vibration and if possible simulate it.

RE: Is a tuned damper effective in forced vibration?

You don't say what type of structure you are dealing with, so I'll stick to generalities.

(1) Tuned mass dampers are effective under a lot of circumstances, but not under all circumstances. If your structure has a single (potentially) troublesome frequency, its response-versus-frequency curve will have a single peak that is sharp and high. Add a correctly tuned TMD to the structure and that single high peak turns into two lower peaks that are close to each other and are less sharp.

(2) Regarding modelling this with FE, it can certainly be done. You are looking for what is usually called "harmonic analysis".

RE: Is a tuned damper effective in forced vibration?

Quote:

Is a tuned damper effective in forced vibration?
That is the typical application. There is nothing about "forced vibration" that suggests tuned damper will not work.

As others mentioned, the effectiveness of your particular installation depends in part on tuning (how close is absorber tuned to forcing frequency). And how closely it needs to be tuned depends on things like mass ratio.

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(2B)+(2B)' ?

RE: Is a tuned damper effective in forced vibration?

Might be worth reading wiki on the suject. i wrote the non buidling bits. A typical use for a TMD on a car is on the driveline, to suppress the bending mode of the engine and gearbox, which is excited b combustion forces, or the crankshaft harmonic damper, which works torsionally.

The trick with TMDs is to mount them where the mode in question is very active, and to ensure you have enough mass, and, often, not too much damping. The maths is easy.

Cheers

Greg Locock


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RE: Is a tuned damper effective in forced vibration?

An excellent, brief, practical, clear description of TMDs, how they work, when they work, how to optimise their performance, etc is given in Appendix D of the book "Vibration Problems in Structures", by Hugo Bachmann, Walter Ammann and others. Published by Birkhäuser-Verlag in 1994, second edition 1996.

The four pages of that Appendix are pretty much all you need (providing you know a fair bit about dynamics to begin with).

RE: Is a tuned damper effective in forced vibration?

(OP)
Thanks to all of you...

Now I will explain what I meant by forced vibration. Greg gave a very good example of forced vibration (combustion forces) exciting a 'resonant' mode (bending in the said example).

Now my problem is I am not targeting any resonant mode that is excited due to forced vibration. My interest is that forcing frequency itself ! Now this may sound stupid as I studied in some book that the very concept of 'damping' applies only to resonant modes (whether they are free or forced), but not for non-resonant modes.

Here in my case I am asking exactly same thing - damping a non-resonant frequency. One which is being externally applied.

Imagine a plate or drum being beaten by a rod at certain frequency AND amplitude. Now I am interested in knowing the effect of tuned damper (designed & mounted already for one of the resonant modes of plate or drum) on the vibration minimisation due to external frequency of beating rod. Also, if there is an effect, how does it vary with the amplitude of that external force?

My first guess is that the tuned damper would act only like an added mass (as far as external frequency is concerned) - no more effect. But I am not fully sure.

I am sorry if I am not clear still. I am willing to explain further.

I read most of tuned masses literature and designed one damper also. But this is off-shoot topic on which I am working.

Denial - Are you sure we can simulate forced vibration (the type which I mentioned above) using harmonic analysis ? I think it is used only for finding natural response of structure.

Many thanks.

RE: Is a tuned damper effective in forced vibration?

A tuned damper by its nature will respond to any base excitation at its tuned frequency. So for example if you had a motor running at 50 Hz, with no modes below 90 hz, you might still have a 50 Hz problem, and you could try to improve it with a 50 Hz TMD.

It is not likely to be a convenient solution, and I can't think of an automotive example that is very clear.

Cheers

Greg Locock


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RE: Is a tuned damper effective in forced vibration?

Geoff,

Harmonic analysis, certainly when the term is used in structural engineering dynamics, calculates the sinusoidal response of a structure to a set of sinusoidal exciting actions. The exciting actions must all be acting at the same frequency. This frequency does NOT have to correspond with any of the structure's natural frequencies. When the structure has these exciting actions applied to it, it will respond sinusoidally at the same frequency as the exciting actions (once any transients have died out). Harmonic analysis directly calculates this sinusoidal response.

RE: Is a tuned damper effective in forced vibration?

If vibrations due to the acting forces are too high, the construction is to compliant (you call it too weak if you want)

RE: Is a tuned damper effective in forced vibration?

(OP)
Thank you once again to all the comments.

Now I think the comments are answering my question - though we can design a damper for a forced (non-resonant) frequency such as the 50Hz example given by Greg, the performance may be not great if the structure is flimsy with heavy forced vibration.

Anyway, I will do a quick simulation in FE - as Denial suggested Harmonic should work and see what can be performance improvement in minimising the forced vibration.

Thank you.

RE: Is a tuned damper effective in forced vibration?

Sorry if I'm repeating stuff but I'm left wondering what it is you came away with.

Quote:

Now this may sound stupid as I studied in some book that the very concept of 'damping' applies only to resonant modes (whether they are free or forced), but not for non-resonant modes.

Here in my case I am asking exactly same thing - damping a non-resonant frequency. One which is being externally applied.

Tuned mass damper does not necessarily rely on damping. It can reduce vibration at a certain location using mass and springiness with no damping at all.

Tuned mass damper is not limited to a resonant system (as stated by Greg), the damper is tuned to the forcing frequency of interest.

Quote:

My first guess is that the tuned damper would act only like an added mass (as far as external frequency is concerned) - no more effect. But I am not fully sure.
That would be incorrect. In theory, the vibration is forced to zero at location of attachment of the tuned mass damper. That assumes the damper is tuned to the forcing frequency. The larger the effective mass (*) of the damper compared to the effective mass of the system, the less critical is exact tuning (wider frequency band for reduction).

* Sorry to use the term "effective" mass. It is based on analysis of SDOF system corrected by SDOF TMD... then the mass is clear. For more complicated systems, if we have the system and absorber individually modeled, then we can replace each of them with SDOF system that gives similar frequency response in the frequency band of interest for purposes of determining the mass ratio. Modeling absorber should be easy as we have conceptualized it as sdof during the design.

Once again, sorry if I'm repeating what you already know.



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(2B)+(2B)' ?

RE: Is a tuned damper effective in forced vibration?

(OP)
electricpete - You need not say sorry. I should say thanks instead. You corrected my statements.

Though I know the concept and saw few tuned dampers with only mass and spring, I made a wrong statement to the effect that tuned mass damper relies on damping. I am sorry. It is just a slip. Yes the effect of adding damping in a tuned mass damper is only to minimise or level out those split modes formed on either side of the targeted frequency.

Now regarding the other concept only I posted this question - that is whether a tuned damper can be used to damp a 'non-resonant' mode? My understanding after above comments is: yes it can be done. But it may not be effective significantly if the structure is weak and vibration is very strong (which is what rob768 stated).

I am now posting another question - while designing a tuned damper for forced frequency (let us take Greg's example of 50Hz on a system which has no resonant modes nearby), can we say that increasing the mass ratio will help in minimising the forced vibration amplitude on the structure? I know you already stated that increasing mass ratio will make it less effective on tuned frequency. But just looking at compromise solution to improve the situation.

Many thanks.

RE: Is a tuned damper effective in forced vibration?

Based on analysis of undamped SDOF system corrected by undamped SDOF damper (which ends up being a 2DOF composite system):

The frequency response H(w) = X(w)/F(w) has a zero at the tuned damper frequency and a pole on each side. Obviously you want to get near the zero and far from the pole. If the TMD mass is small compared to the main mass, then the two poles on each side are very close to the zero... tuning is critical and sometimes practically impossible when the TMD mass is too small. If you have a larger TMD mass, you have a better chance of reaching a given target of vibration reduction with a given tuning error.

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(2B)+(2B)' ?

RE: Is a tuned damper effective in forced vibration?

Added clarification in bold below (no edit feature... kicks my butt every time)

Quote (electricpete clarified)


Based on analysis of undamped SDOF system corrected by undamped SDOF damper (which ends up being a 2DOF composite system):

The frequency response H(w) = X(w)/F(w) has a zero at the tuned damper frequency and a pole on each side. Obviously you want to get near the zero and far from the pole. If the TMD mass is small compared to the main mass, then the two poles on each side are very close to the zero... tuning is critical and sometimes practically impossible when the TMD mass is too small. If you have a larger TMD mass, then the poles move farther away from the zero, and therefore you have a better chance of reaching a given target of vibration reduction with a given tuning error.

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(2B)+(2B)' ?

RE: Is a tuned damper effective in forced vibration?

Coping with tuning error is not the only advantage of larger tuning mass....also helps better cope with small changes in forcing frequency. (if the forcing frequency moves to close to your pole, you're in trouble... larger TMD gives more frequency separation between the poles and the zero).

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(2B)+(2B)' ?

RE: Is a tuned damper effective in forced vibration?

(OP)
electricpete, thanks for the info again.

I am writing a small code for studying response of 3-DOF system with tuned damper. I hope to study the effect of mass ratio, etc. I will get back to here if I have some doubts. Many thanks.

RE: Is a tuned damper effective in forced vibration?

Handwavy sort of explanation - imagine a large strucure vibrating at 50 hz, with no nearby modes. Now add a small spring mass damper system tuned to the exact frequency. It will of course go off like billy-oh, and so the damping will start to extract energy from the total system. But if you add too much damping then the little mass won't shake much and so less energy is extracted. So there is an optimum 'ratio' of damping to TMD mass. Obviously if the TMD is too small it will have no noticeable effect. They can still be useful -it is not uncommon to mount TMDs near mounting points for the system in an attempt to minimise vibration transfereed through the mount. Theoretically this shouldn't help.

Cheers

Greg Locock


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RE: Is a tuned damper effective in forced vibration?

Following on from Greg's most recent post.

The reference I gave above gives a formula for the optimum amount of damping, based on a 2-dof representation of the system. This is
Sqrt[3(mt/ms)/8/(1+(mt/ms))^3]
where mt is the mass of the TMD and ms is the mass of the structure being damped.
The text then says "This formula is, strictly speaking, only valid for an undamped primary system, but it can also be used for a damped system with good approximation".

When I was designing a damping system as part of the design for a very flexible pedestrian bridge I used this formula. As a check, I developed a spreadsheet that rigorously solved the dynamics of a 2-dof system. I used that spreadsheet to confirm (for my particular set of problem parameters) that this formula did in fact give the optimum damping. The formula passed the test.

RE: Is a tuned damper effective in forced vibration?

(OP)
Hi all, it's a quite a good learning here.

Greg, thanks for your simple and short explanation.

Denial - Thanks for referring me to the formula and sharing your experience. I could see the 3 pages (169, 170 and 172) of the book in Google books. So I saw the formula you wrote. Having known the ms, do we iterate on mt till we approach desired damping factor ? And then the damping factor so reached is called 'optimum'. That means below that corresponding mt, mass of tuned damper would be insufficient and above that the excessive inertia force the mt causes is of no use. That is incremental benefit is less. Am I right in my understanding?

And this mass based damping will be over and above the loss factor of the damping material we use, such as viscoelastic tape. Right?

While verifying the formula with your spreadsheet calculation, what output did you consider for comparing? Is it frequency response amplitude (receptance) ?

I have few more doubts on what you said regarding pedestrian bridge, but I reserve them considering the length of this post.

Many thanks for all your support.

Kind regards






RE: Is a tuned damper effective in forced vibration?

You're beginning to ask me to ask too much of my memory, since I no longer have access to any of the work I did on that pedestrian bridge. And as your questions get more specific we begin to hit up against differing terminologies between structural and mechanical engineers. (Like, for example, "mass based damping".)

The model from which the formula comes is a relatively simple 2-dof model, a diagram of which is in the reference. The "primary structure" will not be a simple lumped mass sitting on a spring and a dashpot, that has to be capable of being reduced to the simpler form. If you have several different forms of damping in your actual structure (general structural damping plus "viscoelastic tape"), then maybe your structure cannot easily be reduced to the required simple form.

My "verification" of the formula consisted of applying a unit harmonic force to the spreadsheet 2-dof model, for a range of frequencies for the force (the range well covering the resonance values). That gave me the classic two-peaked response-versus-frequency plot. I repeated this exercise for several values of the assumed TMD damping. The damping value that gave me the lowest upper-peak-height corresponded with what the formula predicted. QED.

RE: Is a tuned damper effective in forced vibration?

Den Hartog's Mechanical Vibrations 4th ed also has a derivation of the same "optimum" damping (equation 3.36)

His "optimal" approach resulting in his equation 3.36 is a two step process:
step 1 - select an optimum frequency ratio based on the mass ratio: Fabsorber/Fsystem = 1/[1+(Mabs/Msystem)]
step 2 - select an optimum damping as given by Denial

Note that part 2 is predictated on part 1. i.e. it is not optimal damping for any absorber you throw in there, it is only optimal for the particular absorber that is tuned per step 1.

The sense in which the damping is optimum is that it minimizes the highest peak for any frequency of the damped 2DOF composite system. It may not be necessary to worry about any frequency if you know where your frequency of excitation will be and can tune accurately and use large enough absorber to provide sufficient excitation.

When compared with the undamped model, the damped absorber is much better at the frequencies of the undamped system poles (of course) and worse at the frequencies of the undamped system zero (of course). Whether that is the desired target I guess depends in part on your situation. For fixed speed machinery I think it may not be. The undamped absorber will do the best possible job of any absorber at the tuned frequency. It just does really bad at those adjacent frequencies of the poles. The undamped is the only kind I have ever installed (I work on fixed speed machines). Damped might possibly be better for some purposes, but it's a little foreign to me.

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(2B)+(2B)' ?

RE: Is a tuned damper effective in forced vibration?

Correction:

Quote (electricpete, corrected)

and use large enough absorber to provide sufficient excitationfrequency separation

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

RE: Is a tuned damper effective in forced vibration?

2
Some more thoughts. It’s not soley for your benefit....it’s helpful for me to summarize/repeat as I read through the information.

Attached is an Excerpt from Den Hartog’s Mechanical Vibrations 3rd Ed.
It is the same as the 4th ed discussed above except the equation numbers changed.
Equation 63 is the step 1 equation for “optimum” frequency of the absorber.
Equation 69 is the step 2 equation for “optimum” damping of the absorber.

By the way, I downloaded the entire Den Hartog’s 3rd Ed at one time from the Open Library Archive. It’s no longer available there for some reason, but Timoshenko vibration book is still there available for free download
http://archive.org/details/vibrationproblem031611m...
Timoshenko section 41 is dynamic absorber. He uses different symbols. He uses a lot of the same analysis as Den Hartog. I saw he came up with the step 1 equation in his equation 81. I didn’t see where he got to the step 2 equation (I got a little lost along the way).

The big picture contrast between undamped and damped dynamic absorber I mentioned above:
* undamped absorber has ideally zero response at the tuned frequency and infinite at the nearby poles. It is good if we have fixed exciting frequency and are confident through design of our absorber that frequencies of excitation and poles won’t drift too close together.

*damped absorber would make more sense for broadband or variable frequency excitation.

Some new ideas:
* The optimum design of the damped absorber relies on assumptions about the system you attach it to. How will it change if attached to system other than SDOF is a little unknown to me.

* In contrast, it is easy to predict ideal performance of undamped absorber regardless of the system you attach it to, in the following sense: The undamped dynamic absorber ideally puts the vibration at point of attachment to zero regardless of the system you attach it to. That’s a pretty simple result, made more valuable imo by the fact that the proof is pretty simple:
1 – you can prove it using electrical analogy to vibration of the flavor described in the quote at end of this post. In that case, the absorber is a resonant series L/C circuit connected to ground... which represents a short circuit to ground (zero electrical impedance [infinite mechanical impedance]. It will drag the voltage [velocity] to ground at that point, but possible at the expense of very high current [forces]. We also know true short circuit rarely exists, but still a useful tool for understanding the ideal limiting behavior.
or
2 – Look at transfer function Dm(w) / Db(w) for undamped SDOF system where Dm is mass position and Db is base position (input). It becomes infinite at w=wn. ASSUME (proof by contradiction) that we have motion at the base. That means we need infinite motion at the mass. We know we cannot have infinite motion at the mass, so our assumption of motion of the base must have been wrong. For any finite motion of the mass, the motion of the base must be zero. This is an ideal case but again still a useful tool for understanding the ideal limiting behavior and the ideal behavior is not affected by the system to which the absorber is attached.

One final thought to add – tuning of the undamped absorber for fixed frequency excitation can be fairly critical and faces some unknowns, but it doesn’t need be finalized on paper. The absorber should have tuning adjustment (move the mass in and out on the bar). Then we can install it and do a bump test near its point of attachment (looking for minimum of response at proper frequency). We may also be able to tune it to minimum response after the machine is started, although movement of absorber makes that difficult.

Quote (Electrical Analogy for Vibration)


1 - mechanical force f plays the role of electrical current I

2 - mechanical velocity difference v plays the role of electr voltage difference V

3 - mechanical mobility v/f plays the role of electrical impedance Z = V/I
(use the symbol Z throughout. We use the term impedance to represent either electrical impedance or mechanical mobility .. avoid the term mechanical impedance which is the reciprocal of mobility).

4 - A spring (k) acts like an electrical inductor of inductance L=1/k
The impedance is Zk = j*w/*k

5 - A damper (c) acts like an electrical resistor of resistance R = 1/c
The impedance is Zc = 1/c

6 - A mass (m) acts like an electrical capacitor of capacitance C =m **
The impedance is Zm = 1/(j*w*m)
** one terminal of this mass/capacitance is connected to ground.

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(2B)+(2B)' ?

RE: Is a tuned damper effective in forced vibration?

(OP)
Hi electricpete, Denial,

Many thanks for your time and detailed response. I am really inspired and motivated by your interest in explaining the things.

Actually I got hold of Den Hartog book 4th Ed. and reading it today whole day. I thought it is necessary before commenting anything here. But I see you also attached digital version of that part of text here. Good for my future reference. A treasure !

Denial - Now I understood what is 'mass based damping' :) Earlier my concept was wrong. I was thinking that the optimum damping equation which you wrote refers to the structural damping of the added masses in tuned vibration absorber. So I was creating such phrases! In fact Den Hartog explains so nicely about 'Optimum tuning' and 'Optimum damping'. What electricpete wrote simply in two steps is summary of that. First we do optimum tuning and then optimum damping. And the formula was actually derived to be a non-dimensional. So it looks like that.

My understanding of damping in that optimum damping equation is: It is for tuned vibration damper only. Also called as damped vibration absorber. It is not for tuned vibration absorber i.e. the one without damper. The equation is to choose optimum 'c/cc' for added viscous dashpot. I believe if we keep any other damping material also, such as viscoelastic tape, etc. we can use that equation by calculating its equivalent viscous damping from their structural damping factor.

The question which I wanted to ask about your pedestrian bridge is: can we design a tuned vibration absorber or a tuned vibration damper for a big experimental structure using analytical models of 2-DOF? In such case are we assuming it as lumped mass ? OR utilising experimental drive point FRFs? I want to use this analytical simulation for my structure also. No problem about incorporating damping. I can incorporate it as a complex stiffness = k(1+ i*eta). Sorry if this is testing your memory. You can then leave this. I just asked out of curiosity.

electricpete - While reading the Den Hartog book I was again puzzled by the question with which this thread started. In 4th ed, page 88, last line, he says "It was seen however that addition of an absorber has not much reason unless the original system is in resonance or at least near it." Again on page 92 he gives example of electric hair clipper where he is trying to design a tuned vibration absorber for 120Hz forced frequency of electromagnet. That is : he is targeting forced vibration which has nothing to do with resonance of hair clipper body on which he mounted the absorber.

I think I need few more reads before firmly understanding the concept.

Many thanks.


RE: Is a tuned damper effective in forced vibration?

Quote:

electricpete - While reading the Den Hartog book I was again puzzled by the question with which this thread started. In 4th ed, page 88, last line, he says "It was seen however that addition of an absorber has not much reason unless the original system is in resonance or at least near it." Again on page 92 he gives example of electric hair clipper where he is trying to design a tuned vibration absorber for 120Hz forced frequency of electromagnet. That is : he is targeting forced vibration which has nothing to do with resonance of hair clipper body on which he mounted the absorber
That's a $64,000 question.

A few thoughts to consider:

Based on the proofs above, the undamped dynamic absorber ideally works to remove vibration at the absorber-tuned frequency, regardless of the attached system (so it is not limited to a system where the forcing frequency that we are tuning for corresponds to resonance of the original system). So it's not so much a question of whether we can be successful at reducing vibration (as long as we're using big enough absorber), as it is a question of whether application of absorber to reduce vibration will accomplish anything useful.

Does it make sense to add an absorber to reduce forced single-frequency vibration in a non-resonant system?
I'd say it depends.

Let’s say I have a 1200rpm 50hp horizontal rolling bearing motor with 1.0 ips horizontal, 0.5ips vertical running speed vibration measured on the bearing housings. Let’s also say the machine is operating far below resonance both directions, although a little further below in vertical direction than horizontal direction since stiffer vertical direction has higher resonance (all of that seems typical for this description machine to me). Let’s say I know or suspect that the cause is unbalance of the rotor. Obviously the ideal solution is to balance it but that maybe the machine needs to continue running and that’s not practical. For this scneario: Should I use absorber to reduce the vibration at the bearing housing?

The system resembles single degree of freedom system far below resonance. The SDOF mass is roughly the rotor mass. The bearing and frame transmit the force to the base. Since far below resonance, the system is spring dominated, the amount of unbalance force that goes into mass acceleration is small, almost the entire unbalance foce is trnasmitted through the bearing and frame to the foundation.

I could could attach a dynamic absorber to the frame near the bearing in such a manner to drive the horizontal vibration towards zero.
If my concern is the force transmitted through bearing, I have done nothing to address it because the force transmitted through bearing is the same (the unbalance force). Adding the ideal dynamic absorber in this case is equivalent to adding an ideally infinitely-stiff brace to the frame near the bearing to drive vibration at that location to zero. We can easily see in the case of the brace that we have only further increased the resonant frequency of the system, it remains very far below resonance (Even moreso than before), so the force transmitted through the bearing is still the unbalance force in this far-below-resonance (spring controlled) system. The result for the dynamic absorber is the same as for the infiitely-stiff brace... I just thought it was a little easier to explain using the infinitely-stiff brace. I hope in this situation it is clear the dynamic absorber does nothing if my goal is to reduce load on the bearing.. . On the other hand if machine were operating near resonance, then the resonance could magnify the unbalance force such that the force seen at the bearing could be many times higher than the unbalance force. In this case, it is helpful (reduce bearing load) to add a brace or to add a dynamic absorber.

Consideration of the above scenarios may be part of the basic thought process by which Den Hartog implies dynamic absorber is generally not real helpful unless used near resonance.

So can we come up to an exception to the "rule" that absorber is only useful in resonant system?
Sure. Den Hartog gave one that you mentioned (hair clipper).

I’ll give another one: let’s go back to the machine above and put it back far below resonance. But let’s say there are cracks on the foundation below the machine running perpendicular to the shaft under the coupling. We suspect the vibration is aiding the crack growth. We also suspect the vibration crack is causing misalignment between motor and load which is causing our 1x vibration (new scenario... not unbalance anymore). Now should I add an absorber to the machine frame? Yes, it would reduce the force transmitted from frame to vibration and reduce the crack growth and help break the cycle. Maybe not a permanent solution but dynamic absorber should help. And it will help even if you are not near resonance.

I had to stretch to come up with scenarios that were simple enough to yield an obvious yes/no answer to the question: should we add a dynamic absorber” (although the cracked foundation is pretty close to a scenario at our plant where we have installed an absorber). In most cases I suspect the answer is not that clear.

Certainly the insight from people like Den Hartog and our own Greg Locock will be valuable as a starting point.

By the way, the particular sentence you quoted at bottom of page 88 occurs in the context of a seguee into a discussion of the particular behavior of dynamic absorber applied to a resonant system. It is Den Hartog’s way to start general and wander to many particular special cases. Maybe he is just justifying to small extent why it is worth to examine that special case (resonant) more closely than the others.

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(2B)+(2B)' ?

RE: Is a tuned damper effective in forced vibration?

My pedestrian bridge work was different from what I understand you are trying to do. I had a significant vibration mode whose frequency corresponded horribly closely with the footfall frequency of pedestrians, so I was specifically worried about resonance effects. Bear that in mind as I attempt to answer your question.

I set up a detailed FE model of the bridge, and subjected that to a modal analysis. This showed (as I had expected) the potential resonance problem I mentioned in the preceding paragraph. If a structure has one predominant vibration mode of interest it is possible to produce an approximate 1-dof model, with an effective mass value, an effective stiffness value, and an effective damping value. This I did. I then converted this 1-dof model into a 2-dof model by adding a TMD. Using Bachmann's formulae and my spreadsheet-based 2-dof model, I configured my TMD. I then added the resulting TMD into the original detailed FE model to obtain final confirmation of the TMD's efficacy. (Actually, this wasn't the final confirmation at all. The final confirmation came once the bridge was constructed. The dynamics was tested with the TMD deactivated. Based on the results of this test the TMD was given a final tuning, and was then activated. The dynamics was then re-tested. The results were pretty much as predicted.)

I gave a talk on the dynamics of pedestrian bridges a couple of years ago, and this included some discussion of TMDs. The text of the talk is available on my web site (http://rmniall.com).

RE: Is a tuned damper effective in forced vibration?

I think the Den Hartog problem is slightly different to why I'd use a TMD on a non resonant forced vibration issue. A typical steel structure has a q of the order of 1e2-1e3, and it is often impractical to add damping generally to the structure to get the forced response down. However, a small amount of damping can be exercised very effectively by a TMD, and without adding any damping in important load paths. This will help suppress the peak and hopefully lose it in the floor of all the other noise. Of course with pure tones you often need to pull 6-10 dB out of them to really kill them, and that is difficult.

Cheers

Greg Locock


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RE: Is a tuned damper effective in forced vibration?

(OP)

Quote:


On the other hand if machine were operating near resonance, then the resonance could magnify the unbalance force such that the force seen at the bearing could be many times higher than the unbalance force. In this case, it is helpful (reduce bearing load) to add a brace or to add a dynamic absorber.

electricpete - I am sorry. I didn't understand why you said in a spring controlled system unbalance force gets transmitted to bearing, but not at resonance. When you mount dynamic absorber on frame, the load gets transmitted through bearing whether it is at resonance or not. Of course at resonance it gets amplified - so more force. It will get minimised only at the frame after passing through the bearing. I agree with your second example of crack growth. There mounting a dynamic absorber helps is minimising vibration transmitted from frame to foundation. But in 1st case (assuming you mounted it on frame), in any way the bearing sees the load - less or more.

Greg - your statement makes meaning for my application, of course in reverse. In fact as a conclusion to all this discussion I will post my problem where I seek all of your valuable opinions. I didn't post it in the beginning as the whole discussion goes biased and we would miss this wonderful discussion.

Denial - Though you targeted damping of resonant situation, I learned one very useful point from what you wrote - we can model a big system or structure with 1-DOF with its dominant mode of interest, of course with its effective mass, stiffness and damping. This will be useful in simulating analytically designing damper in resonant situations. Your website is useful for the downloads!

Many thanks to you all.

RE: Is a tuned damper effective in forced vibration?

Quote (Greg M)



Quote (electricpete)

On the other hand if machine were operating near resonance, then the resonance could magnify the unbalance force such that the force seen at the bearing could be many times higher than the unbalance force. In this case, it is helpful (reduce bearing load) to add a brace or to add a dynamic absorber.

electricpete - I am sorry. I didn't understand why you said in a spring controlled system unbalance force gets transmitted to bearing, but not at resonance. When you mount dynamic absorber on frame, the load gets transmitted through bearing whether it is at resonance or not. Of course at resonance it gets amplified - so more force. It will get minimised only at the frame after passing through the bearing. I agree with your second example of crack growth. There mounting a dynamic absorber helps is minimising vibration transmitted from frame to foundation. But in 1st case (assuming you mounted it on frame), in any way the bearing sees the load - less or more.
It sounds to me like you said roughly the same thing I said.
I'm not sure what the question or conflict is.
Sorry if I’m being verbose, but I’ll try to say it again in a (hopefully) more organized manner:

My assumed system:
Fubalance == Mrotor == Kbearing === Kframe===Ground

Far below resonance, the load on the bearing is approx Fub (because mass acceleration forces are negligible far below resonance).
At resonance, the load on the bearing is many times higher than Fub (resonant amplification)

Now what happens when we add a dynamic absorber or an infinitely stiff brace (both have same effect, which is to effectively stiffen the frame)
Far below resonance, the load on the bearing is still approx Fub. The absorber accomplished nothing.
At resonance (initially), the load on the bearing will decrease below what it was at resonance. The absorber helped.
This example illustrated a possible reason that Den Hartog suggests absorber is only useful at resonance.

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

RE: Is a tuned damper effective in forced vibration?

Clarication

Quote (electricpete, clarified)

Now what happens when we add a undamped dynamic absorber or an infinitely stiff brace (both have same effect, which is to effectively stiffen the frameat the tuned frequency)

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(2B)+(2B)' ?

RE: Is a tuned damper effective in forced vibration?

(OP)
Ah, I got it. Bearing is connected to frame and absorber is mounted on frame, near to the bearing. So both the absorber and rotor will vibrate at same frequency. Net result is reduction of loading on bearing! Thank you, electricpete.

Now finally I am posting here my actual problem and the tuning dilemma!

I have a thin walled casing - 2.5mm wall thickness and ~100mm height and ~400mm diameter. I mill this casing with a tool rotating around the periphery (schematic attached here). I observe tool's natural frequency strongly imposed in the FFT of the acquired acceleration signal. For lower depths of cut, I also see workpiece's first mode dominating along with the tool's frequency.

Now before this discussion I was of the view that a tuned damper is meant only for resonant vibrations and hence designed one for workpiece first mode. I used six of them as that first mode has 6 petals (circumferential waves) or antinodes. Now having damped the workpiece modes over wide range (with more tuned dampers and hence higher mass ratio), I am left with tool mode again. Of course the amplitude of vibration reduced significantly, nearly 3 times. But frequency spectrum of machining vibration signal still shows distinctly tool mode. I am not sure if I have to live with it or any further gains can be achieved by targeting the tool mode. As you can see this is forced vibration with forced natural frequency, and the source of vibration is moving around the casing.

Also considering the casing has wide range of frequencies 1K to 16K (that's my measuring range), I am not sure if I have to stick with traditional 5% mass ratio or go to some 20-25% to damp entire range. What do you say?

I see someone else recently asked question of tool mode appearance in milling in another post in this forum. Will be good if he can have a look at this.

Thanks to you all and look forward to your opinions.

RE: Is a tuned damper effective in forced vibration?

ok, now you’re way out of my area of knowledge so I have nothing useful to contribute.

fwiw, I had been thinking you had single frequency driving force which is why I talked about undamped absorber. Now it's sounds to me like you have a resonance of the tool maybe excited by broadband excitation from the cutting process. In that case, the undamped absorber would just give you two new resonances at slightly different frequencies which will also be excited by the same broadband excitation... doesn’t accomplish anything. Damped absorber attached to the tool now makes more sense to me. You're probably way ahead of me on that.

I’m sure you’ll get more useful advice from the others.

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

RE: Is a tuned damper effective in forced vibration?

(OP)
Thank you electricpete. Yes tool is excited by broadband excitation.

I wish to hear any other views from others as well - Greg, Denial, etc. In fact both Greg and electricpete had a look at this structure (photo) earlier as part of our discussion on FFT of signal acquired, modal testing, etc. where some of your views greatly helped me.

Many thanks.

RE: Is a tuned damper effective in forced vibration?

(OP)
It is resonant mode of tool.

RE: Is a tuned damper effective in forced vibration?

With a right handed cutter, you are 'climb-milling' (chip starts thick), which is known to excite pretty much every available vibratory response.

Reverse something, e.g. the orbit direction, so you are 'up-milling' (chip starts thin), and you should see a bit less response.

Mike Halloran
Pembroke Pines, FL, USA

RE: Is a tuned damper effective in forced vibration?

(OP)
Mike, Thank you. What you said correlates with my observation. I use down milling. So that's why tool mode is very strong in FFT.

I still have doubt if it is worth tuning a damper for this tool's frequency and mount the damper on workpiece? As tool is rotating, we cannot obviously put a damper on that.

electricpete - From this configuration - i.e. a thin walled ring - for a forced vibration situation, do you see this as stiffness (spring) controlled system or mass controlled system ? We can consider it as stiffness controlled as mass is very less. But the applied forced vibration amplitude is very high. So this leads me to doubt whether it can be called as stiffness or mass controlled? If it mass controlled, I would try to design a tuned damper with a high mass ratio. Do you think it is ok?

Many thanks.

RE: Is a tuned damper effective in forced vibration?

Are you working near the cutter's optima?

By which I mean, maybe you can get away from the resonance by doubling the spindle speed, and maybe dropping the feed rate a little if that burns edges. Your cutting tool salesman should be working with you to find the sweet spots here. Trust him; it's in his interest to make you delighted with his brands of consumables.

If it's not possible to effect improvements with feed/speed adjustments, the next thing I'd try is building a dam around the worktable and doing the milling with the piece submerged in coolant. ... not for the cooling, but for the damping.

Mike Halloran
Pembroke Pines, FL, USA

RE: Is a tuned damper effective in forced vibration?

(OP)
Hi Mike, firstly there is no regenerative chatter. So now sweet spot requirement. I made sure that spindle speed also doesn't cause any chatter. If it is needed I have Metalmax kit with me.

Immersing the whole cylinder in coolant is good but not feasible as I have some instrumentation there to measure cutting force, etc.

RE: Is a tuned damper effective in forced vibration?

Harris" Shock and Vibration Handbook has a whole section on machine tool vibration. My copy is in a box someplace, but I think it had some Discussion of "impact dampers" and other curiosities that could be applied to tooling, although maybe not easily to rotating tools.

First tact often was to evaluate stiffness of the tooling, spindle, spindle mounting, workpiece holding with the intent of correcting weak spots, of which there often were many

There was a lot of work going on in the 90s and early 2000s by GM and Ford and FAG bearing.(Probably still is) Some of the info was available then. There were lots of theories, some confusing to me and over my head. Using vibration feedback to trigger speed changes was catching on.
Here is an article on instability with some machine tool content from Sound and Vibration in 1997. Those years are not available on the S&V website.
http://www.xcitesystems.com/pdf/UnderstandingSolvi...

RE: Is a tuned damper effective in forced vibration?

(OP)
Hi Tmoose, thank you for providing me with the article.

As I said earlier there is no instability in the process. Only strong forced vibration.

I checked the book which you said. It has short discussion on minimising impulsive forces on machine tool structure for which they suggested improvement in stiffness. And in the place where they discussed about dampers there is no discussion about forced vibration. For tool they suggested variable pitch cutting teeth. No more inputs.

As discussed earlier, I wish to design a tuned damper. But not really sure about its efficacy. But will give it a try. But I am just looking to understand the dynamic characteristics of a thin wall casing - is it a stiffness controlled system or mass controlled system in the presence of a forced vibration.

Thank you.

RE: Is a tuned damper effective in forced vibration?

Quote:

But I am just looking to understand the dynamic characteristics of a thin wall casing - is it a stiffness controlled system or mass controlled system in the presence of a forced vibration.
I'm not sure about where you are headed with that question. I'd like to clarify the terminology. The way I've heard those terms mass-controlled and spring-controlled is for a system that can be represented as a SDOF system. If the exciting frequency is far below the SDOF system resonance, it is spring controlled. If exciting frequency is far above resonance, it is mass controlled. I guess the extension of that concept to a continuous or multi-degree of system would look at the closest resonance to the exciting frequency (which generally has the most effect of the vibration of the forced system *). If the exciting frequency is far below the closest resonance, it is spring controlled....If far above the closest resonance it is mass controlled. If excitation is between resonances (and it is not clear that one of them has much more effect on the response than the other), then the term might not be applicable. So, I guess if you wanted to answer the question you'd have to try to identify the workpiece modes that are or can be excited by the tool vibration and compare their frequencies to your exciting frequency (which we assume is a tool resonant frequency). Sounds like a challenging task. And I'm probably missing the point because I never understood the purpose of your question.

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

RE: Is a tuned damper effective in forced vibration?

(OP)
electricpete - many thanks for clarifying to my confusing question. You guessed right. My forced vibration frequency is between two resonant frequencies. So I don't know how to define this - stiffness or mass based because it changes with respect to the frequency I consider. Hence that question. But now I understood that the definition indeed varies w.r.t. the frequency we look at this forced vibration.

In any case it looks imperative to improve upon stiffness and mass if the forced vibration frequency is not lying close to one of the resonances. Now can I use this as argument to design a tuned damper with higher mass ratio - higher than the traditional 5% (as recommended in some books).

Thank you.

RE: Is a tuned damper effective in forced vibration?

Hi Geoff,

Dec 15 - "I have not built this structure. A model similar to this is in service. My interest is to find out the effect of tuned damper in presence of forced vibration and if possible simulate it."

Dec 20 - "As I said earlier there is no instability in the process. Only strong forced vibration."

Dec 20 - "there is no regenerative chatter."

What issues does the in-service unit have?
Are the "force" measurements from strain gage?
Do you process the signal and "see" vibration at tooth pass frequency?

regards,

Dan T

RE: Is a tuned damper effective in forced vibration?

(OP)
Hi Dan,

I work on a research project on damping machining vibrations. Presently the component which the industry gave is being machined at reduced parameters due to forced vibrations and hence consequent problems such as heavy vibrations, noise, etc. My task is to design some damping solution. Now had there been any regenerative chatter I would have used my Metalmax kit and solved it straight away.

As part of my project I use Kistler dynamometer (piezoelectric) to measure cutting forces. Tooth passing frequency and its harmonics we see of course. But it is significantly modulated at tool's resonant frequency. So for all practical purposes it can be taken as tool resonant mode only.

I usually prefer to post the problem in its scientific relevance rather than as solving an industrial problem. Hence I didn't give this background at the start.

But I learnt some good things about tuned damper design through this discussion. Thanks mainly to electricpete, Denial, and Greg.

Thank you.

RE: Is a tuned damper effective in forced vibration?

This is not relevant to GMarsh's problem, but might be of interest to some other people following this thread.

I mentioned above a spreadsheet I developed some years ago to analyse two-degree-of-freedom problems. Inspired by this discussion I have dug up that spreadsheet, and put some time into improving its clarity and making it a bit more robust. It is now available for download from my web site (whose URL I have already given above in a post on 19Dec12@05:33).

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