Springs in Series 1

[ldeem]

I am dealing with a problem where I have a aggregate processing steel structure and the vibrating screen has been switched out for a unit with much higher dynamic loads. This has resulted in excessively high vibrations in the structure which is affecting the screen.

The screen sits on its own spring isolation base. One idea I had was adding additional isolation under the screen base. So there would basically be two sets of springs in series.

I understand spring constants in series are 1/k=1/k+1/k

My questions is
1, Does this idea make any sense? I am thinking more isolation would decrease the dynamic loads the structure sees. I don't think the screen vendor will be agreeable to modifying their design so I am stuck with trying to add additional isolation.

2, I spoke with an application engineer at an elastomeric isolator company who thought the idea could work. He suggested I calculate the Transmissibility just considering the elastomeric system (which I understand how to do). But then a another vendor of spring base systems didn't even want to look at application.

The screen runs around 14.6 Hz and weights 25,000 lbs. I don't know exactly the spring base fn but similar systems are around 1 to 2 Hz.

 

[GregLocock]

Yes, softer springs, or springs in series will work. In cars we often use subframes to get better attenuation, so the system becomes screen-k1-subframe-k2-structure. This decreases the transmissibility of the vibration to 12 dB/octave instead of 6 for a simple spring on mass system, when done properly. if you know the problematic frequencies then this sort of calculation is helpful.


Cheers

Greg Locock


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[drawoh]

deem,

What is the difference between springs in series, and softer springs?

Perhaps you are thinking of the case where you have a spring, a mass, another spring, and another mass, all in series, creating a multiple degree of freedom system.

--
JHG

 

[Strong]

Springs in series behave like resistors in parallel. The spring with the lowest stiffness becomes dominant. This would be the case if the springs were actually mounted on top of each other. Otherwise if springs are separated by a mass element, then as mentioned there would be multiple Fn degrees of freedom.

Walt

 

[ldeem]

The springs are separated by a beam that is quite light compared to the overall mass of the system.

This is an aggregate processing screen application.

The current system is like this (one on each long side of the screen)

SS - spring that supports the vibrating mass
B -W12 support beam
G -W21 support girder (part of the structure where high velocities are measured)

SS SS
BBBBBBBBBBBBBBBBBBBB
GGGGGGGGGGGGGGGGGGGGGGGGGGG

my idea is
NS- New spring or rubber isolator

SS SS
BBBBBBBBBBBBBBBBBBBB
NS NS NS NS NS
GGGGGGGGGGGGGGGGGGGGGGGGGGG

I have operating dynamic loads after the equipment spring (at location B). I also have analysis of the structure that tells me if I can reduce operating dynamic loads by 75% the velocities will come to an acceptable level. My biggest question is can I just treat NS as a separate isolating system using simple method of calculating ratio of excitation frequency to natural frequency of NS and then using transmissibility chart to determine if the operating dynamic loads meet the target?

 

[drawoh]

Strong,

I hate analogies.

If you stack springs and apply a force to them, each spring will deflect according to its spring rate. There is no such thing as a dominant spring. There will be an equivalent spring rate for the stack, which will be lower than each of the individual spring rates.

--
JHG

 

[GregLocock]

Given he'd already got the spring in series equation I think the OP is safe enough there. The more elegant form to my mind is k_both=k1*k2/(k1+k2)

OP I can't understand either of your typographical drawings, perhaps it is time to indulge in some Paint-CAD?


Cheers

Greg Locock


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[ldeem]

The attached drawing shows what I am working with.

The typographical representation didn't work out.

 

[GregLocock]

A subframe that only weighs 12% of the main vibrating mass is not going to have a very big effect, from memory, but 12% is at least in the bounds of reasonableness. So your system is m2=20100, m1=2500, k1= ? k2=? and you are trying to minimise the excitation of the base in this system when m2 is driven at 14.6 hz

Time to do some maths

Cheers

Greg Locock


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[ldeem]

Greg, thank you this is very helpful.

 

[Mohanlal0488]

Hi Ideem

I currently work for a company that does the design of screens, I work as a structural engineer designing solutions based on the products the company develops.

In general our rule of thumb is using 60% of the mass of the screen when designing a subframe. You can easily assess the loads at the base of your subframe by simplifying the screen into a 2DOF freedom problem (as shown by Greglocock). The solution to such a problem can be easily developed using the ODE45 function on Matlab, if you don't have a copy you can use GNU Octave.

Let me know you need any help, I'd be happy to post some of my past code using ODE45 functions.

 

[Mohanlal0488]

Sorry just to add one extra comment on reviewing the attached drawing.

I am not sure of the size of the main support beam, but it does look relatively deep.
I would model the beam using plate elements so that localized frequencies can be assessed based on lateral restraints which you may have. The interface between plate and beam elements can be easily provided by means of rigid link clusters.

I have seen it far to many times where the support beam has been modelled as a beam element and localized effects cannot be assessed. After a while fatigue becomes a huge issue, as deep beams may have a slight lateral vibration, causing failure at points of lateral restraint.

 

[ldeem]

Mohanlal0488 thank you very much for your input. At this time the decision has been made to go with reinforcing the structure in place of adding a secondary isolation system.

I appreciate your comment on the lateral vibration. In field measurements I found a lateral vibration which I attributed to some misalignment of the screen.