Vibration Calculation

[pgp001]

I have designed a turbine shot blast machine which has an air motor type vibrator attached to some dust extraction pipework, the purpose of this is to shake any residual harmful dust from inside the pipe prior to it being disconnected for maintenance.
My customer has asked me to produce a set of calculations which will give the life expectancy of all the associated pipework, welds, rotary valves etc within the vicinity of this vibrator.
I havn't a clue where to start, or even if what he is asking for is possible to calculate, any suggestion please.
Thanks
Phil

 

[electricpete]

I am far from knowledgeable in this type of thing.

The only failure mode I know of which lends itself to life expectancy calculation is fatigue failure.

The challenge will be to find a component whose stresses are below the endurance limit. If you find it you can calculate a life. Otherwise you are stuck with inifinite which obviously is not a good answer.

Once again this is far out of my area so here's hoping someone else chimes in.

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[electricpete]

One way to estimate stresses may be with vibration measurements. It is a complex subject once again far out of my area. One interesting result I have seen derived is that beams vibrating AT RESONANCE have a fixed relationship between maximum vibration velocity and maximum bending stresses regardless of beam size or mode. That simplistic conversion between inches per second (vibration velocity) and max bending stress is sqrt(3*E*rho). (I can provide derivation if anyone is interested). For typical steel 1 ips leads to max stress of around 250 psi (again under assumptions of beam geometry at resonance). You would have to have awfully high vibration velocity to approach fatigue under this calculation method. I suspect in the real world there are stress concentrators that make a huge difference.

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[GregLocock]

"I suspect in the real world there are stress concentrators that make a huge difference. "

Absolutely. Typically in welds or bolts we see stresses that are 10x-100x greater than the stresses in the main structure.

The way we approach this is to build an accurate finite element model (hah), measure the loads going into the structure over the duty cycle (hah) and then run a fatigue analyss (hah). Each (hah) represents up to a years work, and up to a million dollars.

/If/ you can measure the vibration then that can be used to drive the fatigue model, but it is not as accurate as measuring the loads.





Cheers

Greg Locock

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[DaveSco]

If you can collect vibration measurements up to 1000Hz (Velocity), these readings can be compared against MTD guidelines for pipework. If these spectra do not exceed these guidelines it can be said that the measured point is good for up to e.g. 1x10^6 cycles. Should they exceed these guidelines then stress analysis should be carried out on the pipework.

This is simplified, but if you identify points of risk, i.e. small bore connection to a heavy unsupported valve for example..then these are generally the areas you should look.

If this is helpful, I may be able to dig out some more indepth information on it for you.