Request for Help on Modal Interactions and Frequency 1

[Bewler]

I'm working on multiple projects and it seems many mechanical engineers in my group understand frequencies and modal analysis. I have a bachelors degree in mechanical engineering but didn't have any courses in vibrations and response and I feel under taught in this part of mechanical engineering. Are there any good references or lectures to help me acquire a better understanding in this part of mechanical engineering? I'm not sure where to begin. The only items I've been taught are the natural frequency and to use FEA to quickly estimate the natural frequencies in Solidworks. Any help is Appreciated

 

[phamENG]

Bewler, I can't help you much with the mechanical engineering portion, but as you posted this in the Structural Engineering forum I'll take a stab at it as somebody who usually pretends his designs are not moving.

I have recently taken an interest in structural dynamics, and the determination of structural frequencies and mode shapes. By recently I mean in the last few weeks, so I'm not very far into it. I can tell you that Dr. John Biggs from MIT has a book Introduction to Structural Dynamics that is helpful. I don't believe it's in print any more (Dr. Biggs passed away 10 or 20 years ago), but most libraries can do an interlibrary loan, you can buy a used copy online, or if you're crafty enough there are scanned PDFs floating around out there.

Good luck.

 

[WARose]

I've always thought that 'Structural Dynamics, Theory & Computation', by Mario Paz is one of the best texts I have on vibration.

 

[dold]

Ditto of what phamENG said. I've also recently become interested in this topic. Mainly because I've only ever needed/been instructed to use simplified analysis methods and I feel like it's time to bone up on more advanced principles, not out of necessity but curiosity. And I've been dabbling in some analysis software and I feel like I've only utilized 1/4 of the functionality of the program. I.e., I don't even really know how to get started with dynamic analyses. If anyone else has any suggestions I'd think a lot of users here would be interested. Or at least three of them...

 

[RPMG]

The natural frequency is the sqrt( stiffness / mass ). In solidworks, this is an eigenvalue problem with stiffness and mass matrices. High stiffness = high frequency. High mass = low frequency. If the spinning mechanical unit and supporting structure frequencies are close, it could resonate, and that's bad.

I am of the opinion that text books will lead you down the rabbit hole. Most of the book will be about numerical techniques and ramp vs. impact loading, and very little will address supporting mechanical units. I recommend working with your colleagues.

I've attached a stiffness chart from "Seismic Principles" by Paul W. Richards.

 

[WARose]

Agree with RPMG.....it takes time, experience, and coaching to get proficient with this stuff.

 

[ldeem]

I do a couple of projects a year with vibrating equipment. Sometimes original design and sometimes fixing existing problems. From my perspective as the person designing the support structures the main issues are:

1. Accurate information about excitation frequency, amplitude and load.

2. Accurate modeling of real world structures. For example a we assume double clip angles are pinned but in reality there is some small moment transfer.

3. The biggest issue is interpreting results. I use STAAD modal analysis methods so I get a series of response frequencies and contributions. Comparing the excitation frequency to responses and determining what is acceptable is difficult. I am not aware of many good design guides that cover this but in my experience staying 20 to 25% away from the excitation frequency works.

4. I also look at both local support conditions and global structure. For example I will use SDOF method on an equipment support beam and then do a STAAD analysis on the whole structure. I also use static load factors which are sometimes provided by equipment manufacturers.

My area is heavy industrial and mines so I design for things like vibrating screen, crushers, etc.

 

[XR250]

If you are doing ME projects, you should get a book on Vibration Analysis that is not rooted in numerical methods.

I'm an ME and that is what we used in undergrad.

 

[canwesteng]

There's a terrific set of notes from Brown university I found online that are my go to

 

[ThomasH]

Hello,

I have worked with dynamic problems for several years by now. It has been a wide range of things, like vibrating machinery, comfort due to people walking on a floor or comfort due to wind dynamics. I could give more examples but what I can't give is a single textbook that covers it all. Somebody mentioned Mario Paz, another is "Dynamics of Structures" by Clough and Pinzien, there are other books that I think are good as well but I believe that an understanding of the basic theory is important.

I may step on a few toes her but in my experience many structural engineers calculate a natural frequency and consider that a "dynamic analysis". Is 6 Hz a good comfort criteria for a floor?
I would say "No", it is not a comfort critera at all, without context. The frequency tells you when it vibrates, not how much, and how much is usually the comfort criteria. If we only focus on the frequency we can simply increase the frequency by decreasing the mass and at the same time we may increase the vibrations. End of rant .

I think that one good source of information is also different articles and thesis work (often PhD). I have several of those that are useful. Another source is different manuals but the quality can differ at lot. Building a reference library is the same as building experience, it takes some time. Google is good, but not enough .

What I would not recommend is using software, any software, without having a reasonable understanding about what happens inside the "black box". I have a colleague who says, "if you can't do it by hand, don't use a computer". I won't go that far but do a simple (understandable) analysis by hand before using the computer, that I think is reasonable. But "playing" with parameters on the computer, that can be good for the understanding. One thing that can be done in a computer that usually can't be done in reality is to change only one parameter with total control.

Good Luck

Thomas

 

[ldeem]

ThomasH - I am curious about your approach. I have been of the opinion that the best approach is to push the modal frequency (I can't stand the term natural frequency because it implies only one critical frequency) away from the excitation. I believe this simplifies the problem and removes the excitation frequency as a variable.

I try to have dominate modal frequencies 20 to 25% away from the excitation frequency.

In my area I am typically working with structures and vibrating equipment. In a few cases I have added forcing functions to my model to be sure it doesn't create a controlling load case or excessive deflections. I usually only do this in situations where the load is usually large.

In your practice have you found cases where excitation frequencies 20% or more off the dominate modes still control the design? I don't deal with wind or human comfort in my work.

 

[ThomasH]

Ideem,
I usually prefer the term eigenfrequency or natural frequency and mode shape. And of course it is plural, but often only the lowest is of interest. Modal for me typically concerns the analysis type .

Concerning vibration machines, my experience is that often the manufacturer requires a foundation to designed with eigen frequencies 20 to 25% away from the engine speeds. Often multiples of the engine speed is included. We often also add a requirement that the foundations mass shall be a factor like five times the engines mass. The used factor depends on the how the engine works, rotation, translation etc.

I have been in situations where we met the mentioned "rules of thumb" but could not meet the requirements for max vibration velocities based on a given force. The reasons can be a high load or a very stringent requirement. In the particular situation it was a high load causing problems, significant problems. And I have also seen designs where the engine's speed was close to the eigenfrequency and still, no excessive vibrations. It depends on several other factors as well and some of those factors are difficult to know at the design stage. Assuming/"guessing" damping can be interesting .

For engine foundations, avoiding resonance is usually a good start. But if you design a high-rise building avoiding resonance is often not an option, you have to deal with it. And for some types of dynamic loads, resonance in not an issue at all.

Thomas

 

[WARose]

I try to have dominate modal frequencies 20 to 25% away from the excitation frequency.

That's a good rule to have......but in some cases that can really be cutting it fine. The X-Factor in a lot of this type of analysis is the (dynamic) spring constant for the foundations. If it's obtained without really good testing (cross hole shooting, etc).....the guess at the actual value may be way off.....and putting you where you don't want to be.

Assuming/"guessing" damping can be interesting.

And dangerous too. Another reason to have some really good safety factors in this (without good testing). Damping can be especially unpredictable because it varies by frequency, material type, and so on.

 

[ldeem]

Thank you ThomasH and WARose for your input. It is very valuable to hear other opinions especially on a topic like this where few hard and fast design rules.

I recently had a project for a dual pump platform I designed. The platform was light but seemed to have reasonable dynamic properties in design. In the real world it had excessive vibration when both pumps were running and resulted in shortened bearing life. I had them add concrete blocks to increase the mass and that fixed the problem. Fortunately there was plenty of strength in the platform and room to set the blocks.

 

[human909]

I agree with most of the above. I've normally found it easier and just as effective (so far) to focus on the lowest modal frequency of the structure. Though I normally try for 50%-100% difference for frequency. 25% is too slim for me, varying dead loads or vibrations, or connection stiffness can readily eat into this.

I've dealt with vibratory sifters of various kinds. Often their frequency lines up approximately with the typical frequency response of steel flooring. The solution that generally works is to use oversized beams about twice as stiff as you would otherwise use. It has been effective so far. For the cost of a few beams it is worth the potential headaches. One plant I know has heavy vibration for 3 floors because they got this wrong. One wonders whether there are fatigue concerns with several steel floor vibrating heavily 24/7.....

EG one piece of machinery has this comment:
The machine must be mounted on a solid floor that does not have a natural frequency between 10 and 22 Hz or that bends no more than 0.3 mm under a static load.

We are in the process of building another plant. The steel design is mostly out of our hands. The members underneath the same units have a frequency very close to the machinery. So we'll see what happens. I raised the issue but their engineers think it is fine. (They apparently did a dynamic analysis so in theory it should be more comprehensive than simply looking at the first modal frequency of the support beams.)

Anyway that is my 2cents. I'm no expert but I try not to be ignorant either...

 

[ThomasH]

And dangerous too

I agree, hence the smiley.

But estimating the damping is often something that must be done in order to perform the design.

Thomas