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# Random Vibration - Designing an Electrodynamic Shaker

10/06/2009 6:35 PM

Hello friends, I'm designing an electrodynamic shaker to perform a random vibration test and I want an idea about how much energy I need.

I have the PSD curve for the test as shown below:

With this curve I have calculated the rms values of acelerations, velocity and displacement with some formulas that I found in the book of Thorby:

The results obtained with a Matlab routine were:

a rms 9.4026*g

displacement rms (mm) 0.0020

velocity rms (m/s) 0.0357

la aceleracion rms en (m/s2) 92.2397

Power rms=arms * vrms * mass (W) 6.5950 mass=4 kg

??????????????

The value of the power seems to be wrong, because it's too low. On the other hand I have calculated only rms values and during the random vibration there will be peak values that will consume more energy, but I can't calculate them.

What's wrong oin my calculations?

or

is there any way to calculate the maximum power of the random vibration test with the psd Curve?

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#1

### Re: Random Vibration - Designing an electrodynamic shaker

10/06/2009 9:52 PM

Power rms=arms * vrms * mass (W) 6.5950 mass=4 kg

Which I take to mean PRMS = V * IRMS * M, doesn't look right at all. Where did this come from as you cannot convert to 'power (in Watts) required for vibration of mass 'x'' this way.

Are you planning on building your own electrodynamic shaker or are you trying to size your application and purchase one?

I have never used electrodynamic shakers (only impact hammer and offset cam motor shakers) but if you are just trying to estimate how much electrical power you need how about checking out companies that manufacture these for a 'ball park' estimate.

http://www.saraswatidynamics.com/Electrodynamic_vibration_shakers.aspx

etc.

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#5

### Re: Random Vibration - Designing an electrodynamic shaker

10/07/2009 1:36 PM

Prms= Frms*Vrms=m*arms*Vrms

that was my reason, but I gues it is wrong because I can't use this formula because the force changes in the random process.

I have to test a cube (m=1 kg) 10cmx10cmx10cm random vibration in only one axis.

I was considering only 1 kg of the mass and up to 3 kg of the table and fixtures.

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#2

### Re: Random Vibration - Designing an electrodynamic shaker

10/07/2009 6:50 AM

If you assume a sinus function for the amplitude then you obtain following equations:

- displacement z= a* sin(ω*t)

- speed z'= a*ω*cos(ω*t)

- acceleration z"=-a*ω^2*sin(ω*t) where

a= amplitude ω= 2*pi*f [1/s] f= frequency [Hz]

The force to bring the acceleration is F= M*z"; the power is given by product F*z'

P= M*a^2*ω^3*sin(2*ω*t)/2

P is maximal when its time derivative is zero this happens at 2*ω*t=pi/2 but at this angle sin(2*ω*t)=1 follows that the maximal net power is Pmax^[W]=M[kg]*a[m]^2*ω[1/s]^3/2

You have from your data determine the frequency where this value is maximal taking into consideration the WHOLE moving mass not only the one of your tested device.

In many cases the "dead mass" is several times bigger than the tested device.

Do not forget in your computing the weight which has also to be moved if your test is on the vertical.

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#6

### Re: Random Vibration - Designing an electrodynamic shaker

10/07/2009 1:45 PM

What I did was Power(rms)=mass*aceleration(rms)*velocity(rms)

the same that you say (P=F*v) but with rms values.

My problem is that my function is not a sinus but it's random. The test specification gives me the PSD curve as shown above. With that curve I can calculate rms values but not the maximum values (or maybe it's possible and I do not know how). Talking about mass, I was considering only my testet mass,the table and fixtures, I'm going to review that, thanks.

My move is horizontal in one axis. In a reply above I'm detailing the test.

Many thank nickname .

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#7

### Re: Random Vibration - Designing an electrodynamic shaker

10/07/2009 2:33 PM

According to a theory emitted by a Mr. Fourier every function can be replaced by the sum of sinus functions of different frequencies and amplitudes. His theory is the base on which the Fourier analysis has been build.

Your power and your force should allow the highest need. This need can be determined by considering your curve as above as a sum of sinuses.

So that even if you deal with random oscillations you come at the end back to the single function in the detailed analysis.

The RMS values are MEAN values and what you need is the PEAK value to allow you the function you aim at.

What kind of linear motor have you thought off? In fact before you make the choice it would be better to determine your requirements as force and power. If you know those I could give you hints for the motor and for the design, I build shakers but I do not build them any more so that...

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#13

### Re: Random Vibration - Designing an electrodynamic shaker

02/04/2010 4:53 PM

Hi nickname,

The needed force is 90 kgf rms i a range of 20-2000 Hz. The peak value of the random time history

is 3 times the RMS value. I would appreciate it if you would help me with the linear motor.

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#14

### Re: Random Vibration - Designing an electrodynamic shaker

02/04/2010 5:14 PM
Anonymous Poster
#3

### Re: Random Vibration - Designing an electrodynamic shaker

10/07/2009 8:36 AM

Interesting to note that you have been directed to some shaker manufacturer's. Since we are a shaker manufacturer, we might be able to shed some light on your questions, but I'm not too sure we are ready to do so if we are going to be helping you design shakers.

A couple of simple concepts to capture, however - the last person posting reminded you that you must calculate all of the moving masses in your power calculations - actually it is more basic than that, you have to include all of your moving masses in your force calculations.

F=(m1 + m2 + m3...)a for all equations of force. In an electrodynamic shaker, since the initial mass you are moving is the armature, you must add its mass to the masses of your fixtures and products. Always, no exceptions.

Secondly, you are talking about broadband energy here, not single frequency energy. That means that dynamic considerations such as response must enter into your considerations. If your test frequency bandwidth contains the resonance frequencies of the shaker's moving mass and/or your products moving mass, you will gain energy from the response. Unfortunately, for every gain there is a loss, so you will also lose energy at the "anti-resonances".

Electrodynamic shakers are usually rated in random taking into account a specific load, in fact, the ISO5344 specification requires the manufacturer to state the load used, because the load affects the rating.

Thermotron Industries, located in Holland Michigan USA, has been manufacturing electrodynamic shakers since 1978. Our shakers are installed at world-class manufacturing facilities throughout the world, and most of our original shakers built thirty years ago are still operational. Search for us on the web - we build robust, world-class equipment.

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#4

### Re: Random Vibration - Designing an electrodynamic shaker

10/07/2009 9:19 AM

Dear Guest,

May I take your attention on the fact that in the power computation the force is one of the factors via which the TOTAL mass comes to play. So that what you suggest is ALREADY contained in the equation.

The request was only for power and I answered the question. But in my answer is also the force mentioned and the equation for it contains the mass which is later indicated as to be TOTAL.

The maximal requested power depends on the amplitude and the frequency. From the accelerations curve (part of the spec) the designer can determine for each frequency the amplitude which will give the wished acceleration and use it in the further computing.

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#8

### Re: Random Vibration - Designing an Electrodynamic Shaker

10/07/2009 11:53 PM

You have not stated why you wish to build your own shaker, but unless this is being done as a university project or something like that, I would strongly suggest you reconsider that plan of action. You will most likely NOT be able to build such a shaker for the cost of a purchased one. The hydrostatic table bearing and the magnesium table surface will be expensive (and dangerous) to manufacture, and the table driving yoke, which will need to undergo quite a bit of engineering to ensure it does not have any resonant frequencies or harmonics within the test range of the unit. manufacturing it from magnesium will also be a non-trivial pursuit. Just remember that magnesium is quite flammable and you need to have a class D fire extinguishing system designed for magnesium at hand at all times during assembly, maintenence, and operation as well. Magnesium is generally used throughout the construction of such tables to minimize the moving mass of the system.

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#9

### Re: Random Vibration - Designing an Electrodynamic Shaker

10/08/2009 3:04 AM

Why magnesium, why hydrostatic bearings? Although magnesium is generally used it is not compulsory to use it.Hydrostatic bearings are used, if ever, only for very big loads and it is not the case.

Please do not forget that a solution is always related to order of magnitude.

You are right with respect to the resonances which could appear but it depends in which domain the test is done and if it is possible to do it in the overcritical range with respect to the own frequency.

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#11

### Re: Random Vibration - Designing an Electrodynamic Shaker

10/08/2009 2:16 PM

hydrostatic bearings to eliminate friction in the support table, remember powdered magnesium (from friction wear) and heat (from friction) is a BAD combination. the bed is floating virtually frictionlessly on a film of oil, so it completely eliminates any issues with wear or resonances in the bearing structure. this was how our Ling shaker table was designed. it also eliminates any vertical off-axis loads that the armature support must withstand. it also equaly supports the bed so that you don't get distortion of the test table due to where you mounted the test clamps.

Magnesium again to reduce the moving mass of the test table as low as possible. I suppose Aluminum-Lithium alloys might suffice as well. They were not available when our Ling was designed. I've found that even using magnesium bits for the test table and yoke, the moving mass of the table, yoke and test clamp came pretty close to equalling the weight of the downhole tools we were shaking. Several times we found we were banging (literally!) on the maximum armature mass limits and we had to go back and revise our test clamps or procedure to keep the mass below the max.

I would add that Vibe tables are widely available on the used market.

http://www.xytek-equip.com/vibrate.html

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#10

### Re: Random Vibration - Designing an Electrodynamic Shaker

10/08/2009 11:46 AM

Since our dear friend "nick name" appears to be extremely sensitive to statements added to his comments, I'll try to restate some of my earlier comments.

Shaker manufacturers do not rate their shakers in terms of power, they rate them in terms of force. That is why you need to be a bit more basic by looking at the force required, not power. That was the intent of my statement, not to pick a fight with the esteemed guru, "nick name." There is absolutely nothing incorrect in his statements, but they are not made from the point of view of a manufacturer or supplier of shakers.

Now, as to how to determine power, if you do a dimensional analysis of the random profile, and look at the units of g^2/Hz it may become evident that the graph you have there is actually power spread over the spectrum, so power is the area under the curve in any random profile. Of course, since it is a random profile, there are statistical issues involved here, but that doesn't matter for power, because power assumes rms values. Force, however, focuses on peak requirements, which is what the shaker must actually deliver at any instant in time.

Unfortunately, as a manufacturer, I must design the shaker to deliver force for many different applications, not power for one particular random profile. Were I to develop my product to take care of one random profile, I could optimize resonances and the like to deliver the test, but would benefit one customer with an extremely overpriced product.

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#12

### Re: Random Vibration - Designing an Electrodynamic Shaker

10/09/2009 6:01 AM

Thank you, Guest,for the nice comment on comment!

There are two aspects to be considered the one is the dynamics of the shaker itself which of course has to be guided by the force generation under worse conditions and I totally support this aspect. By the way for the interested person there are voice coil generators from an American company BEI which could, may be, offer a solution for the motor. There are advantage in an over-critical support.

From the other point of view it is a need to know how much power has to be delivered to the system from the electronic pilot. The request was for power indications so that I mentioned power in my answer assuming that this was the reason for the request.

For small masses, and the several generators I had to design were for small masses, it is possible if the axis is horizontal to avoid the bearing using an elastic bending support of the table with a high compliance in movement direction in order to have a very low own frequency and a defined zero position. The forces as weight are supported by compression/tension of this "elastic hinge". The only "friction" is due to the metal hysteresis and some alloys have such a low hysteresis that it can be totally neglected. The problem is only that the control loop has to be more complex.

The dead mass is important and in small shakers even bigger than the mass to be tested so that its value has to be as small as possible. But all depends also of the motor size and maximal forces involved. It is not always needed to make use of complex and expensive technologies if the requirement does not ask for.

This was my reaction to the recommended use of magnesium and hydrostatic bearings which, I am sure, were THE SOLUTION for the case Rorschach worked on but not appear to be adaptable for the case we discuss now.

I repeat there is not one only solution: the solution is not universal, the solution is the best for the context and has to be the most economical in order to obtain the requested result. There is a field unfortunately not always considered as it should be: Value Analysis.Its basics are: "Never do more than needed, it does not pay more!"