GTA
All Springer/NP/PCP Air Gun Discussion General => "Bob and Lloyds Workshop" => Topic started by: antithesis on March 06, 2020, 09:42:55 PM
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I'm not sure how to calculate stresses in a pressure vessel, but let's say I drilled a hole for a gauge block, like a disco or something... provided the orings do their job, is there any compromise of the strength in the surrounding metal?
And are there any links that may elucidate related principles, irregularities in pressure vessels and their effect on the structural integrity?
I know the metal between the seals should see no pressure, but the adjacent metel must pull or expand or be stressed, do the seals completely negate the effect?
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For the example you give, there is no pressure on the tube between the O-rings, so the parts of the tube that are under load are the section in front of the front O-ring and behind the rear one.... There is equal pressure both sides of the gauge block O-rings, because of the hole through it.... so there is no end force on the tube in between.... There is a compression load on the gauge block however, each end sees the same end force as the front fill plug or the valve....
Corrected below....
Bob
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When using a gauge block, there is no pressure between the o-rings, but there is tension in the tube at the hole. The resulting stress is much less than the combined stress in the pressurized portion of the tube. So even a large hole is ok.
If the hole were threaded directly into the air tube (no gauge block) then you might have a problem.
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its my understanding , that the hole compromises longitudinal strength before it compromises internal hoop strength.. So as the hole approaches half the tube diameter, a longitudinal failure is more likely.. so essentially , when dealing with proportionately small holes, the answer is no.. i may have that backwards, lol
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Scott, what causes a tension load between the O-rings?.... They are free to slide in the tube.... However, they are located in grooves in the gauge block, and apply a compression load to that block from both ends, equal and opposing....
I don't see it.... ???
If what you say is correct, then would not the total tension (axial stress in the tube wall) be twice that on an end plug?.... IIRC, that would mean that it would equal the hoop stress (which is twice the axial stress).... Again, I don't see it.... ???
On the other hand, it doesn't make sense that you could just cut through the tube between the O-rings and not have the front and back tubes depart from the gauge block.... hmmmmmmmmmmmmmmmmmm…. :o
Bob
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Now I know how you guys feel sometimes.... MY BRAIN HURTS !!!!
Bob
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.... Again, I don't see it.... ???
On the other hand, it doesn't make sense that you could just cut through the tube between the O-rings and not have the front and back tubes depart from the gauge block.... hmmmmmmmmmmmmmmmmmm…. :o
Bob
Your red response indicates that you do see it.
The tension force is:
area_ID x pressure
Tensile stress at hole (for small holes in thin tubes) is approximately:
tension/(((pi x tube_dia) - hole_dia) x wall_thickness)
The actual equation for thicker tubes with large holes becomes slightly more complex, but same result in that you are reducing the stress area.
The greater the hole diameter, the greater the stress in the remaining tube material.
If you drill several radial holes, eventually the tube will blow apart into two pieces, from the tension force.
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OK, I'm totally confusing myself, so I'm going to go back to square one....
Let's assume the gauge block is anchored into the front tube at the front O-ring, as if it was fixed solidly to it using threads or pins.... The end force on it from the HPA in the rear tube is the pressure times the area.... If it only had a very tiny hole (ie no hole) in it, the force pushing it forwards would be the same as on a valve or front plug.... That would be the ID x ID x PI/4 x Pressure.... There would be an equal force pulling forward on the wall of the tube, from the front O-ring all the way back to the valve.... This is the axial load, and causes a longitudinal stress in the tube wall equal to that force divided by the area of the tube wall....
Now let's use the same logic for the other end.... The block is located in the rear tube at the rear O-ring, and the tube wall is subject to the same stress, but in the opposite direction.... Logically, this would mean that the tube section between the O-rings would have twice the longitudinal stress of the rest of the tube, because the gauge block has equal and opposite load from both ends, and that is being countered by the tube....
Now let's drill a large hole through the gauge block.... Let's make it so large that we are only dealing with a thin-wall tube for the gauge block.... The area of the ends is reduced to the annular area remaining.... If the tube wall went to zero, there would be no compression force on the gauge block, and therefore the longitudinal stress in the tube must also drop back to what it was if there was no gauge block.....
Is it reasonable for the stress in the tube to be affected by the size of the hole in the gauge block?.... I would say no.... However, it is reasonable to assume that the stress would be the same throughout the tube, from end to end, regardless of whether there was a gauge block or not.... This assumes there is no hole in the tube between the gauge block O-rings....
Once we drill a hole in that area, we are reducing the cross-sectional area of the remaining tube wall.... If the hole equaled the ID of the tube, we would effectively have cut the area in half, which means we would be doubling the stress.... It therefore seems reasonable that the longitudinal stress in the tube between the O-rings of a gauge block is greater than what it is in the front and rear reservoir sections.... The increase in stress is inversely proportional to the decrease in the circumference of tube remaining.... If you drill away 1/4 of the circumference, the stress should increase by a factor of 4/3.... However, there may be a localized increase in the stress near the hole that increases the stress even more than that.... particularly with just a hole on one side....
Bottom line is, that I have convinced myself that yes, drilling a hole in the tube wall between two O-ring in a gauge block increases the longitudinal stress in the tube above what it is in the reservoir section of the tube.... That is not something to take lightly....
A similar thing occurs if you drill away too much of the tube to pin a valve.... If the total circumference of the tube removed by 4 valve screw holes is half the original circumference of the tube, you have doubled the longitudinal stress on the remaining tube wall.... For example, if you have a 1" tube, with a circumference of PI x 1 = 3.14", and you drill four 3/8 holes for valve screws, you have reduced the area between the holes to 3.14 - (4 x 0.375) = 1.64" times the tube wall.... about half the strength remaining....
I'm still not 100% sure I have this right.... maybe 99%.... ;)
Bob
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Thanks, Scott for giving me a cuff up the side of the head.... ::)
Bob
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Tie a rope to a 10lb weight. Lift it up with the rope. What is the tension in the rope?
Stress is the result of equal opposing forces. The forces are not additive. Two people pulling on opposite ends of a rope. What is the tension in the rope?
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I'm not sure of the exact hole configuration you are considering, but holes and other discontinuities usually have a stress concentration factor associated with them in the analysis.
https://www.fracturemechanics.org/hole.html (https://www.fracturemechanics.org/hole.html)
https://www.engineersedge.com/material_science/stress_concentration_fundamentals_9902.htm (https://www.engineersedge.com/material_science/stress_concentration_fundamentals_9902.htm)
Be safe
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I'm not sure of the exact hole configuration you are considering, but holes and other discontinuities usually have a stress concentration factor associated with them in the analysis.
https://www.fracturemechanics.org/hole.html (https://www.fracturemechanics.org/hole.html)
https://www.engineersedge.com/material_science/stress_concentration_fundamentals_9902.htm (https://www.engineersedge.com/material_science/stress_concentration_fundamentals_9902.htm)
Be safe
Thanks for the links...oh man what did I start? ( Bob, your antidepressant side effects includes headache)🤣
It's as simple as a typical crosman 7/8 gauge block, just not in a crosman tube.
Id is the same, and if the seals do their job I see no problem...but I knew there had to be stresses regardless of the proven arrangement. So if I needed reinforcement for peace of mind, I wanted to know where to do it....I suppose the best "play it safe" solution would be to add an external sleeve or block around the port in question, making it look good will be the tricky part
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The longitudinal stress in a tube is about half of the hoop stress.... Therefore, if you cut away half the circumference of the tube by drilling two opposing holes, the stress on the remaining web of tube wall between the holes (at the narrowest point) would still only equal the hoop stress.... We design PCP reservoirs so that the safety margin is at least 3:1, and in the case of a Disco tube, it exceeds 3:1 at 3000 psi.... With a 1/2" hole drilled in one side of the tube for a gauge port, there is still over 3/4 of the tube circumference remaining.... That means that the safety margin is still greater than for the rest of the tube.... It the seals fail, the HPA just vents out around the gauge, through the oversize hole.... exactly why it should not be a tight fit, or threaded into the tube wall....
Rest easy, Crosman aren't dummies....
Bob
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The longitudinal stress in a tube is about half of the hoop stress.... Therefore, if you cut away half the circumference of the tube by drilling two opposing holes, the stress on the remaining web of tube wall between the holes (at the narrowest point) would still only equal the hoop stress.... We design PCP reservoirs so that the safety margin is at least 3:1, and in the case of a Disco tube, it exceeds 3:1 at 3000 psi.... With a 1/2" hole drilled in one side of the tube for a gauge port, there is still over 3/4 of the tube circumference remaining.... That means that the safety margin is still greater than for the rest of the tube.... It the seals fail, the HPA just vents out around the gauge, through the oversize hole.... exactly why it should not be a tight fit, or threaded into the tube wall....
Rest easy, Crosman aren't dummies....
Bob
Al quoted me the same thing. And you are right, but it isn't a crosman tube in question....I was partly curious for future reference, and partly curious because I wanted to crunch some numbers and see if I could use a prod block and gauge to put a gauge on a hipacd gun...I just don't know with the wildly variable quality of the product itself, but having had this discussion I will take a spare extension piece, plug it, install the block, and pressure test it ...I wouldn't think the steel could be THAT crappy.
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I have no idea if a PRod gauge block will fit in a HiPac tube, nor what they used for material.... however, the same idea still applies.... If you are drilling a 1/2" hole in the side of a 3/4" ID tube, to install a gauge block, the longitudinal stress on the tube between the O-rings will be less than the hoop stress outside of that area.... In fact, you could drill a 1/2" hole on both sides and still have a higher safety margin, IMO....
Bob
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I have no idea if a PRod gauge block will fit in a HiPac tube, nor what they used for material.... however, the same idea still applies.... If you are drilling a 1/2" hole in the side of a 3/4" ID tube, to install a gauge block, the longitudinal stress on the tube between the O-rings will be less than the hoop stress outside of that area.... In fact, you could drill a 1/2" hole on both sides and still have a higher safety margin, IMO....
Bob
In this case it fits perfectly, but I'm going to smooth some of the sloppy circumferential drill marks so the orings stand a chance...once smooth they may actually help...plus lloyd got me wanting to mount a whole extra tube on it, and I'd still have room in the end plug for a gauge. ..and this particular gun I thought I was finally done with lol