Forced Vibration System Response 1

[Gowrath]

I designed a spring and mass system (damping unknown) that is vibrated by applying a sinusoidal force to the mass using an electrodynamic shaker.

The mass is estimated to be 100 Kg.
The spring is actually 4 springs, each with a k value of 63.55 N/mm, supporting a platform (one spring at each corner) with the mass.

Attached is the system's frequency response curve.

If the shaker is set to vibrate at frequencies above the system's natural frequency, where the amplification ratio is very low, is it possible to control the acceleration that the mass is exposed to or will the inability of the system to respond fast enough, and thus have very small displacements, limit the acceleration?

Is it reasonable to expect the electrodynamic shaker system, provided the feedback correction is snappy enough, to increase the driving force and be able to execute the desired displacements (resulting in desired accelerations) or will the frequency response characteristics of the system prevent this?

Thanks.

 

[GregLocock]

Is this homework?

Which shaker and amp are you using?

Cheers

Greg Locock

I rarely exceed 1.79 x 10^12 furlongs per fortnight

 

[Gowrath]

This is not homework.
The shaker is an LDS V456.
The amplifier is an LDS P1000L.
The controller is an LDS VLL1.

 

[GregLocock]

OK, and what sort of acceleration level are you trying to achieve?

basically, if you are above about twice the resonant frequency then your mass is free free, so F=m.a

Cheers

Greg Locock

I rarely exceed 1.79 x 10^12 furlongs per fortnight

 

[Gowrath]

I've attached a list of desired accelerations.
Can you elaborate on the governing equation becoming F=ma at f>2fn?

Thanks.

 

[GregLocock]

Once you get above the resonant peak your response curve tends towards the mass line, ie w^2*m*x=F

I can't find the operating characteristics for a 456, can it deliver 2.2kN at 80 Hz? The manual should have some nomograms in it.

Cheers

Greg Locock

I rarely exceed 1.79 x 10^12 furlongs per fortnight

 

[GregLocock]

Sorry, in slightly more detail

for an sdof system

F=k*x+j*w*x*c-w^2*m*x

as w increases the w^2 term dominates, reducing the equation to F=m.a

Cheers

Greg Locock

I rarely exceed 1.79 x 10^12 furlongs per fortnight

 

[GregLocock]

I see from Ling's catalog that a 456 is good for 110 lbf peak, or about 500N, therefore it will not be able to shake that mass at 22 m/s/s at 80 hz.

In Layman's terms you are trying to shake a thing with the mass of an engine at the sort of acceleration you'd see an engine shake at, using a slightly overgrown speaker coil to shake it with. Not very likely.

Cheers

Greg Locock

I rarely exceed 1.79 x 10^12 furlongs per fortnight

 

[Gowrath]

I've attached the V456 Data sheet. It's the only one I have.
The shaker's max force is 489 N. Well below the force required to directly vibrate a 100 Kg load.
So I added springs with the intention of exchanging the springs every 10-15 Hz as I thought the shaker would attempt to accelerate the load at higher frequencies and exceed its max force (and trip).

I ended up vibrating the load throughout the 5-80 Hz range without replacing the springs.
I set the desired acceleration into the controller and let it run.

If force was not a limiting factor and I had a more powerful shaker, would it displace the load or would it too be limited by the system's frequency response?

Am I overlooking something fundamental here?
Is my mass experiencing the desired accelerations despite not being adequately displaced (if indeed it was not adequately displaced)?

I am interested in the accelerations that the load was exposed to.
My questions are:
1) Did the load experience lower accelerations than I designed (and dialed into the controller) due to the limiting factor of the system's frequency response?
2) If lower accelerations were experienced, would the shaker, receiving feedback from an accelerometer mounted on the load, try to increase the force (until it is exceeded) in order to produce the desired accelerations or would it not get a chance to increase the force as the direction of force keeps changing too quickly for the shaker to respond?

 

[Gowrath]

I've already run the vibration test and it worked. The problem is I cannot explain why.
The shaker vibrated the mass at frequencies where my (and your) calculations showed it could not.
This puzzles me.

 

[GregLocock]

You might well measure 22 m/s/s on some part of the structure at 80 Hz, but I doubt the whole thing is moving at that.

I would expect a shaker system to fail gracefully if you ask it to do the impossible, but I haven't used that particular combination so I don't know how it deals with out of spec requests.

How many accelerometers did you have on the test item?



Cheers

Greg Locock

I rarely exceed 1.79 x 10^12 furlongs per fortnight

 

[Gowrath]

I had one accelerometer, mounted on the platform, that was feeding the controller.
I was expecting the system to stutter and the shaker to trip the overload safety but it seemed to not even break a sweat.

The platform itself was not extremely rigid (it was made of wood) and the load was a human subject (this is part of orthopedic engineering research that I was doing) so anything could be going on.

Thanks for your help.

 

[GregLocock]

Oh, that explains it. Human beings are not rigid bodies at 80 Hz, so while the platform may have been moving at 22 m/s/s, very little of the subject would have been. One of the most important modes of the body is at 6 Hz, for example, which decouples the entire gut system from the skeleton.

If you need to investigate this further then there are various papers around that give spring/mass/damper models of humans, but I don't work in that field any more so have nothing to hand.

For what its worth here is the worksheet I made for the original problem.



Cheers

Greg Locock

I rarely exceed 1.79 x 10^12 furlongs per fortnight

 

[SomptingGuy]

When I worked in that field, we had a really good book: "Handbook of Human Vibration", M.J. Griffin. It's not too expensive, probably a lot less than you've already spent on your rig. Amazon stocks it.

- Steve

 

[SomptingGuy]

... I've just been skimming through the preview pages that Amazon provides. I'd forgotten just how good this book is. A must for anyone working in this field!

- Steve

 

[Gowrath]

Thanks GregLocock for your posts and calculations.
I think you are right. When I was building and testing the apparatus, I was able to affect the current consumption by changing my posture, especially by locking my knees at higher frequencies.
I skimmed through a couple of articles by Mansfield on the apparent mass of vibrating humans but I guess I should reread them carefully.

Thanks SomptingGuy, I'm familiar with the book. I've consulted it many times.