Pressure Loading 1

[SlipperyPete]

I'm doing some stress analysis for a filter system that is subjected to 1,500,000 pressure cycles from 0 to 260bar, with a pulse rise rate of 100,000 to 200,000psi/sec. Previous analyses have been carried out assuming a steadily applied load repeated for the required number of cycles. However, I'm sure that there should be a factor for a rapidly applied (or impulse) loading.
I previously asked this question of someone in the fuel injection industry and was advised that "if the pressure rise rate is slower than the structural frequency of the component then the stress will track the pressure. As structural frequencies of metal components are normally quite high it can be assumed that the stress will track the pressure. The pressure rise would need to be faster than the speed of sound in metal before you could get an “impact”."
Can anyone on the forum provide any corroborating opinion on this? Also, I'm not sure how you would equate a 'pressure rise rate' to a 'speed of sound'? Any advise gratefully received as the item in question seems to be failing at fewer cycles than predicted by the analysis.

 

[Denial]

Some RAG (rough as guts) thinking.

Your pressure is fluctuating through a range of ±130 bar = ±1800 psi
Its peak rate of change is 200,000 psi/sec.
Assuming it varies sinusoidally, these two values together suggest the fluctuation has a natural frequency of
200000/1800 = 110 radians/sec.
If it does not vary sinusoidally, break it down into its Fourier components, the lowest of which will be at this frequency. Some higher component might be significant (relative to the natural frequency of your item).

You don't give any info that might offer a handle on the likely natural frequency of your item, and I am not asking for it. It it were simply a long straight length of thin-walled pipe, radius R, wall thickness t, wall material Young's modulus E, some very hasty algebra I have just scribbled on the back of half an envelope suggests the natural frequency for axisymmetric radial expansion/contraction oscillations would be
sqrt(2*pi*E*t/(m*R))
(radians/sec again)
but I will not be held to this result.

If this calculated result was well in excess of the 110 rad/sec of the applied pressure loading, then one could safely ignore the dynamic effects.

Note that the speed of sound in the pipe material does not come into this.

 

[Denial]

Forgot to say that in the above formula m is the pipe's (empty) mass per unit length.

 

[SlipperyPete]

Many thanks for your response Denial, which goes a long way to explaining the issue. I've made some rough (pessimistic) assumptions to some of the variables and the response is an order of magnitude above the pressure loading natural frequency. It therefore seems that the advice I received from my fuel injection contact was correct and the stress will track the pressure

 

[btrueblood]

Are failures occurring near an elbow, valve or other "end" of piping? I'd look at the longitudinal structural modes also, likely to be orders of magnitude lower than the radial modes. Also, fluid mass can add to the structural mass when considering dynamic response, result may be lower frequencies than predicted for empty tube.

 

[SlipperyPete]

The failures are occurring within a thread root. This is the predicted high stress region but the analysis also indicates that the stress levels are well below the fatigue limit.

 

[btrueblood]

"the stress levels are well below the fatigue limit. "

Stress based on quasi-static analysis? If the stress doubled, as it easily could if the loading rate was close to the response of the tube, would the stress still be below the fatigue limit?

"The failures are occurring within a thread root."

So, maybe a tensile failure is occurring, thus my comment about longitudinal modes (add bending modes to the list...)

It might be simpler (than doing a full modal analysis of the piping via FEA) to instrument the installed device using strain gages and/or accelerometers, and see if you can capture the dynamic response of the device?