spherical container dimensioning under external pressure

[matri]

Hello everyone,

In recent times I am dealing with the sizing of a spherical container made of polypropylene under external pressure. the container in its final version will have to provide a system for its opening, so that it has access to its content.
being just an electronic ing and not knowing where to start I did some research on the net, at the following link:
http://books.google.it/books?id=f3fgh8yiet8c&dq=calcolo+e+disegno+meccanico+per+disegnatori+operai+e+tracciatori%e2%80%9d&printsec=frontcover&source=bl&ots=zmgtd1u&sig=im0niwdpie1vivuhsda3bp48rlk&hl=it&ei=l87esui_kqyba73iyayc&sa=x&oi=book_result&ct=result&resnum=1&ved=0caqon page 173 I found the formulas that should have helped me, in fact I can not find reconversions, or rather, the formula used for this sizing in the other documents that I found preview the replacement of the diameter with the radius of the container.
I certainly know that after the size of the thickness I will have to do the verification to the buckling.

I hope someone has already dealt with such a case and is able to give me tips, thank you in advance.

 

[Fulvio Romano]

if the container is spherical can resist even infinite pressure!
this naturally in the diaphragm theory and what would tell you a mathematician. . .

in reality, buckling is a bad beast, especially on spherical containers, in which to calculate the first way of deformation is not trivial.
perhaps it is the case of relying on the norms, as this thread recommends:
http://www.cad3d.it/forum1/showthread.php?t=5339Otherwise, I would help from a good fem... but also from someone who knows how to use it, because even in that case it is not trivial.

 

[matri]

Hi.

Thanks for the answer! I had already examined the post you recommended to me, I am "procuring" the recommended norm, although that should be a reference, from what I understood it refers to metal containers under pressure, mine is polypropylene.

regarding the fems, it could be the solution to verify the goodness of the calculations, perhaps requiring this verification to the manufacturer before making the sample of the container. Maybe something I could do with matlab, but I think it's not exactly what........ .

Thank you.

seas

 

[Fulvio Romano]

with matlab you may, but you should know how well the theory of instability. Anyway, if you place size and pressure at stake, maybe you're wrapping your head before you break it. . .

 

[AlbertoC]

with matlab you may, but you should know how well the theory of instability. Anyway, if you place size and pressure at stake, maybe you're wrapping your head before you break it. . .

with matlab you could implement the equation system (if you knew it) :smile:.
unless you are a researcher :biggrin: you cannot calculate the distribution of tension on a spherical region with pressure from the outside.
then arises the difficulty of expressing the resistance of a real component with imperfections and perhaps openings or joints (the voltage as a minimum triple in the around of a hole). You can't do without a finite element solutor.
Hi.
tree

 

[AlbertoC]

with matlab you could implement the equation system (if you knew it) :smile:.
unless you are a researcher :biggrin: you cannot calculate the distribution of tension on a spherical region with pressure from the outside.
then arises the difficulty of expressing the resistance of a real component with imperfections and perhaps openings or joints (the voltage as a minimum triple in the around of a hole). You can't do without a finite element solutor.
Hi.
tree

:redface: ..tensione...

 

[boscar]

Hi, I'm a mechanical ing student. I saw your problem and went to browse my sizing skript that I had at home.

In the annex you can find the pages to which I am referring, the text is in German, but from the formulas you should have no problem understanding.

in the first pages are illustrated the various eqations of tension, deformations, etc....poi is shown how to get to the differential eqs and finally there are the analytical solutions plus some examples.

I didn't find the ball.

but I have reasoned in the following way:

- if you take a section of a ball-shaped container on which you want to calculate the voltage, you get a geometric figure that corresponds to a ring.
-the ball is simply a solid rotation created by this ring
-The skript is illustrated how to calculate the tensions of a container (with thin walls) with a cylindrical shape subject to external pressures, which section corresponds precisely to a ring!

now you can calculate radial and angular voltage according to formulas 10.26, 10.52 and 10.53 where:
- pi = internal pressure is equal to zero (I don't know if this assumption can go well in your case)
- pa = external pressure
- re = internal radius
- external radius
- r is the variable

If the data is entered, the data can be found on the basis of the radius r.

Note:
- sigma r = radial voltage
- tile sigma = angular tension (v drawing on page 204 to better understand)

finally thanks to formula 10.53 you can find sigma v.
It is precisely this last value that you have to compare with the value of the material you use. ( sigma v < safety factor)

Now I can only say that I have no practical experience and so I can't tell you whether or not this procedure is correct. (function with cylinders, but not with balls).
I also searched for documentation on your problem and found practically nothing.
Maybe with these calculations you can have an idea which way to start.
it would not be bad to hear the opinion of other people of the forum!

 

[matri]

Good morning to all,

Many thanks for all the answers you gave me, the last one I have to study. . .
What seems obvious to me is to let go of the idea of using matlab, I do not see it in my reach, both for the technical base that I miss both for the time that I do not have available.

to give you a little clearer idea of the problem I have to deal with, I add that this container will be part of a network of wireless sensors for monitoring some environmental parameters (temperature and humidity) within the silos for storage of cereals. This means that we will have to make an opening to be able to insert the electronic part and a hole, to allow the air to come into contact with the sensor.
Moreover, the surface we think will certainly not be smooth and perfect, but rather wrinkled, in order to allow a uniform spatial distribution of the sensors within the silo.
as a starting idea, you want to realize a ball with an external diameter of 15cm, you think to use the pp, because suitable for contact with food material, its compression load (at least the only one I found) is 510mn/m2, young module of 1.14gpa and module of poisson equal to 0.3.
to calculate the pressure to which the container will be subjected, I put myself in the worst case, that is to be on the bottom of the most capacious silo on the market, and I calculated that the pressure exerted by the grain cylinder that would oversteel the container is 62475 n/m2, for my scruple I also made the calculation considering the pressure exerted by a grain cylinder with diameter of 20cm (111066 n/m2).
using the formulas indicated in the link found in the first message I made a first calculation of the thickness, it comes out a value less than the mm.......that to the eye seems absurd!

I thank you again for all the info and I continue to study.... .

 

[boscar]

Hi.
I found a sheet on the net with formulas related to your problem.
Maybe they can help you! !

 

[Fulvio Romano]

Hi.
I found a sheet on the net with formulas related to your problem.
Maybe they can help you! !

Well, "empirical form" is an expression that usually puts tranquility. the analysis is of elastic buckling (there are no plastic hinges), so the formula should also apply to non-metallic materials.

verify that the polka dot module in steel and in your material has the same sign, if so not, the formula could be inflated.

use high safety factors (I believe at least 5), or choose such a thickness that the critical sigma is higher than the compression transfer sigma, so you have a "tough surface", who knows if you can say.

 

[boscar]

Hi.
I just wanted to add that I think it is risky to use formulas that you do not know.
I also believe that my last post is the solution to your problem, but I have never analyzed such a case. So I suggest you be careful.
using high safety factors you can save in many situations however there is always the exception that confirms the rule.

Have you already thought about building the ball and doing evidence? Maybe you can solve the problem like this! !

 

[matri]

Hi.
thanks to the report, it was one of the first documents I looked at when I realized that buckling analysis in my case is very important.

the polypropylene that we intend to use has a coefficient of poisson between 0.3 and 0.4, the precise value me should supply the company that will handle the molding of the container, this means that those formulas I can consider. the cisure factor I took into consideration in calculations is 10, just to get away from the compression breakage load.
x to respond to boscar, we will realize prototypes, but of a different material than the definitive one, we can also do partial tests, in the sense that in the company we bought a silo from 5t, while the one on which I made the accounts is from more than 5000t and not at our disposal shortly, therefore, the analysis to buckling with a serious cad I think it can be the most logical solution.

the aspect of the matter that does not convince me is that the formula I used for the calculation of the thickness of the container, found on a manual (the one connected in the first message) is: s=(d*p)/(4*sigma_compressione), where d is the diameter of the container and p the external pressure and s the thickness of the container.
I also considered the en13445- part3- that deals with defining the requirements for the design of pressure vessels not exposed to flame built in steel, but that I have nevertheless taken into consideration given the messages of another discussion that had occurred on this forum. to make it short, the formula that reports the norm is like the previous except to the denominator factor 4 is replaced by 2.
the third "version" of the formula is similar to the first except that to the numberer the diameter is replaced by the radius and to the denominator I find 2 instead of 4. the latter comes out by setting the static balance, at this link they explain it better than me http://www.efunda.com/formulae/solid_mechanics/mat_mechanics/pressure_vessel.cfmMy problem is to understand which of the three bells to listen to, my colleague advised me to try them all and take the result that tests the buckling, it is the quickest solution but not the one that helps me to understand the motivations at the base....you want what do you suggest?

Marriage

 

[AlbertoC]

Hi.
thanks to the report, it was one of the first documents I looked at when I realized that buckling analysis in my case is very important.

the polypropylene that we intend to use has a coefficient of poisson between 0.3 and 0.4, the precise value me should supply the company that will handle the molding of the container, this means that those formulas I can consider. the cisure factor I took into consideration in calculations is 10, just to get away from the compression breakage load.
x to respond to boscar, we will realize prototypes, but of a different material than the definitive one, we can also do partial tests, in the sense that in the company we bought a silo from 5t, while the one on which I made the accounts is from more than 5000t and not at our disposal shortly, therefore, the analysis to buckling with a serious cad I think it can be the most logical solution.

the aspect of the matter that does not convince me is that the formula I used for the calculation of the thickness of the container, found on a manual (the one connected in the first message) is: s=(d*p)/(4*sigma_compressione), where d is the diameter of the container and p the external pressure and s the thickness of the container.This is axial stress.I also considered the en13445- part3- that deals with defining the requirements for the design of pressure vessels not exposed to flame built in steel, but that I have nevertheless taken into consideration given the messages of another discussion that had occurred on this forum. to make it short, the formula that reports the norm is like the previous except to the denominator factor 4 is replaced by 2.This is the circumferential stress.the third "version" of the formula is similar to the first except that to the numberer the diameter is replaced by the radius and to the denominator I find 2 instead of 4.In fact this is still the axial stress.the latter comes out by setting the static balance, at this link they explain it better than me http://www.efunda.com/formulae/solid_mechanics/mat_mechanics/pressure_vessel.cfmthen there is also radial stress.My problem is to understand which of the three bells to listen to, my colleague advised me to try them all and take the result that tests the buckling, it is the quickest solution but not the one that helps me to understand the motivations at the base....you want what do you suggest?

Marriage

are valid expressions for cylinder internal or external pressure but without buckling analysis.
if the walls have not negligible thickness you use the simple and effective relationships of lamè:http://img35.imageshack.us/img35/9462/lamkj.jpg
ciao

 

[haga78]

......
x to respond to boscar, we will realize prototypes, but of a different material than the definitive one, we can also do partial tests, in the sense that in the company we bought a silo from 5t, while the one on which I made the accounts is from more than 5000t and not at our disposal shortly, therefore, the analysis to buckling with a serious cad I think it can be the most logical solution.
...... .

the test problem on prototype solve it by placing your ball in a container (resisting of internal pressure) in which you put compressed air at 1.2 bar, value that from what you have written should correspond to the max pressure on the sphere:finger:
the air can also enter with a simple hobbista compressor (which arrives quietly at 8 bar), but you have to get a container that resists 1,2 bar, on which you must first install a pressure gauge to reach, a valve for input (also with a rilsan tube) and the subsequent discharge of the air and a safety valve calibrated to the max project pressure of the container: be careful, the pressure devices are dangerous beasts, so be sure of the resistance of the container and do not perform :mixed maneuvers:!!!

 

[Fulvio Romano]

to reduce the risk of testing, instead of air uses water.
the effect is the same (at least for small dimensions of the container to be tested), and if something does not go in the right direction nothing explodes.
Moreover with water, to put pressure on the system you can use a column instead of the compressor.

 

[haga78]

to reduce the risk of testing, instead of air uses water.
the effect is the same (at least for small dimensions of the container to be tested), and if something does not go in the right direction nothing explodes.
Moreover with water, to put pressure on the system you can use a column instead of the compressor.

mmmmh...:finger: from good biker I like to choose the road all curved instead of straight