Tube Vibration and Forcing Frequencies 1

[thexder00]

I'm relatively inept at vibration analysis and frequency response, but I'm trying to predict vibration problems with tube and shell heat exchanger designs. I've followed J.M Chenoweth's guidelines in the Heat Exchanger Design Handbook and have come up with all the forcing frequencies (turbulent buffeting, vortex shedding, acoustic vibration, etc...) and the natural frequency of the tubes based on heater geometry and baffle spacing.

I found a natural frequency of ~104 Hz but forcing frequencies of 1523 Hz and 2469 Hz based on some rough, but relatively accurate cross flow velocity profiles. This is based on an old design and design values. The heater itself has not had any severe vibration issues that I'm aware of during its service. My question is how could these extremely high forcing frequencies affect the vibration of the tubes. Will they excite the higher harmonics and could these higher harmonics cause higher tube deflection and stresses than the fundamental resonance?

Also, for future evaluations, how could higher forcing frequencies (say 1.5 times higher than fundamental frequency) affect tube vibrations from a prediction point of view? I'm ultimately trying to correlate tube vibration with fatigue to predict tube failures.

I know I'm asking about a lot of stuff, but any input would be greatly appreciated.

Thanks in advance.

 

[Twoballcane]

Well first the first Fn is most of the time the worst case for deflections and stress. Any harmonics will be the lesser case. Your forcing frequencies are so high that the tubes will move with the vib, but no mode shapes will take place.

You can use Miner's comulative fatigue damage theory to "predict" when the tube may fail. However, since Fn is not excited, there will be no mode shapes to create stress on the tubes.

Tobalcane
"If you avoid failure, you also avoid success."

 

[Rob45]

Higher frequencies equate to lesser displacements, so the stresses would likely be very small indeed with the forcing frequencies you've noted.

 

[thexder00]

Thanks for the input. Is there a cutoff for which modes (i.e. 1st, 2nd, 3rd mode/harmonic) will produce noticeable stresses within the tubes, or is it simply a function of the geometry? For future evaluations, I would like to be able to safely judge whether a forcing frequency will cause stresses in the tubes or won't. Do I need to know the mode shapes in order to determine whether the induced vibrational stresses will be detrimental or not?

Thanks in advance

 

[Twoballcane]

>>Is there a cutoff for which modes (i.e. 1st, 2nd, 3rd mode/harmonic) will produce noticeable stresses within the tubes, or is it simply a function of the geometry?<<

No not that I know of, but the 1st is the worst and in MHO should be the only one you should be looking at. The harmanics just scares managment.

>>Do I need to know the mode shapes in order to determine whether the induced vibrational stresses will be detrimental or not?<<

Yes you will need to find out what the mode shapes are so you can determin where in the structure will see the most displacment thus have the most stress at it's pivot point. If it is a simple pipe fixed at both ends, you can say the first mode would be the middle of the pipe will go up and down so the high sress would be at the fixed ends. But, that's if the forcing frequencies are very close to the Fn. If you have piping going all over the palce and straped in different palces, well you may have to isolate and calculated from there.




Tobalcane
"If you avoid failure, you also avoid success."

 

[thexder00]

The tubes will be fixed at each end to the tubesheets, however, the tubes are simply supported by baffles in between the tubesheets. The baffle spacing and number varies from design to design, so it looks like I need to do a little more in depth research into mode shapes for various arrangements. I appreciate the input, it's been a huge help.

 

[WCL]

Good discussion on frequency effects. I agree that the first mode is probably the only one you'll need to worry about. The displacements at the higher mode frequencies become significantly less. You have to have displacement to get fatigue.

How about his primary goal, predicting the vibration frequencies leading to fatigue predictions? Anyone have thoughts here? In my experience this is difficult:
1. Use some analytical technique to estimate the natural frequencies; FEA, handbook, etc. Lots error potential based on simplifying boundary conditions. Also, what are the real dimensions of the parts involved?
2. What's the forcing function?
If analytically determined:
This may be dependent on the "system" the part is used in. If I know the frequency of the forcing functions, what's the time dependent signal (essentially the transfer function)look like at the critical location? If there is no excitation at the resonant frequency there probably is not a problem.
Go measure the response:
Use the analysis to locate strain gages. That eliminates the concern for #3.
3. At resonance, damping controls displacement. What value should be used?

Bottom line is NEVER try to get something to live at resonance!

 

[thexder00]

WCL,

Thanks for the insight. I have a means of estimating the natural frequency and the forcing frequencies within the exchangers (Chenowyth's work in the Heat Exchanger Design Handbook). The transfer function is not something that I know at the moment, and is something I should look into. The value for damping is also unkown. I'm using a general number that was estimated for most heat exchangers.

As far as fatigue is concerned, right now I'm assuming that the greatest induced moment will be at resonant displacement. So I've estimated the reaction moments based on this and found the stress induced in the tube (assuming 2-D movement). Then I've assumed zero mean stress so that the stress amplitude is just twice the maximum stress. I have not taken into account any axial forces or shear forces caused by the vibration.

If anyone has any better suggestions for doing this, I'm always open to improvement.

Thanks again to all who've responded.

 

[WCL]

"right now I'm assuming that the greatest induced moment will be at resonant displacement. So I've estimated the reaction moments based on this and found the stress induced in the tube (assuming 2-D movement)."

How did you estimate this induced moment (which leads directly to the stress)? To me that's the problem I've always had. I can calculate the resonant frequencies but what's the amplitude?? Is there something in Chenoweth's guidelines that gives forces or pressures?

 

[thexder00]

I estimated it using beam stresses under displacment and just used the tube's moment of inertia in the equations. The formulas I used I found in "Mechanics of Materials, 2nd Edition" by Roy R. Craig, Jr. Now, this may not be a correct way of doing this, but this is the only way I could correlate the resonant displacement to an applied stress. Chenoweth has an equation for tube amplitude at resonance, which I assumed in the first mode would be in the center of the tube span. These are all assumptions, so I can't guarantee the accuracy of the equations.