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Effects of Thermal Expansion on Preload of on Composite Cylinders

Effects of Thermal Expansion on Preload of on Composite Cylinders

Effects of Thermal Expansion on Preload of on Composite Cylinders

(OP)
I have graphite cylinder fitted into an aluminum cylinder. The aluminum cylinder is first placed over the graphite cylinder with a 0.05-0.1mm gap, heated uniformly to 400 degrees and stretched longitudinally . Upon cooling the Aluminum cylinder shrinks plastically resulting in a 10 MPA contact pressure at the contacting interface. The dimensions are listed below:

Aluminum Cylinder/Jacket

OD: 60mm
ID: 57mm
CTE: 24.5E-9
E:   71 MPA

Graphite Core

OD: 57mm
ID: 11mm
CTE: 8.9E-6
E    14.5 MPA

How do I determine the effects on the pre-load for a 166 deg uniform temperature change. I reasoned that only some preload will be lost given an initial 10 MPA pre-stress.Note that aluminum expands about 3 times faster than graphite.

RE: Effects of Thermal Expansion on Preload of on Composite Cylinders

(OP)
Thank you for your prompt reply GregLocock  

Yes, it experiences plastic deformation. There is actually a 0.05mm- 0.1mm gap between the aluminum and graphite before the Aluminum is heated to 400 degrees and stretched. Upon cooling, the aluminum cylinder`s inner diameter does regain it initial radius.

In shrink fits, the inner diameter of the outer shell is normally smaller than the outer diameter of the inner cylinder.

In the case above, the aluminum starts off with a larger diameter and is stretched longitudinal by applying heat such that it does not regain it original diameter upon cooling. Because of this, the hoop stress is basically equal to the yield strength of the material. The prestress/preload is found by the equation:

P = (t/Ri)*theta

P=preload/contact pressure/shrinkage pressure
t=wall thickness of aluminum
Ri= inner radius of aluminum
theta= yield strength

This information is taken straight from the original designers/manufacturers of the part under question.

I have checked Shigley, but still not sure how to determine the change in preload as the temperature rises.Also note that these are 2 thick walled cylinders.

RE: Effects of Thermal Expansion on Preload of on Composite Cylinders

Lame's equation admittedly only applies if the stresses are under the elastic limit.

Sorry, I don't off hand know how to handle plastic deformation in this case - often energy methods work well.

 

Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies  http://eng-tips.com/market.cfm?

RE: Effects of Thermal Expansion on Preload of on Composite Cylinders

That is an interesting method for creating a shrink fit.  Stretching the outer tube reduces the tube inside diameter, I assume until it just touches the core OD.  Then release the stretching force and allow the aluminum tube to cool and shrink.  I would expect applying the thermal expansion equations would lead to the solution for reduced shrink fit stress.  I would expect that heating the assembly to 400 degrees would return the aluminum to its diameter before cooling.  The graphite core will have increased in diameter at the same time so there will still be some interference.

The method allows for a free fit assembly at room temperature.  Interesting.

Ted

RE: Effects of Thermal Expansion on Preload of on Composite Cylinders

(OP)

Thank again for your replies,

Yes, it is very interesting indeed and was accomplished. This part came from overseas actually. This is how they created the shrink fit.

The basically stretched and heated the aluminum to a point where it would shrink back to a diameter smaller than that of the graphite if one could magically make the graphite disappear. So in essence, it actually would not go back to its initial diameter which exceeded that of the graphite by 0.1mm.

This is evidence that it experienced plastic deformation to the point where it wants to shrink back to a smaller diameter instead of its original larger diameter. It was important to ensure thermal contact between the two cylinder to reduce the thermal resistance.

The temperatures that it is expected to reach during operation is about half the 400 degrees it was heated to achieve the fit and hence contact pressure.

so in that instance, I do not think the two will lose contact even though the aluminum expands 3 time faster than the graphite, but there will be some lost of preload. That is what I want to determine.

Thank again

RE: Effects of Thermal Expansion on Preload of on Composite Cylinders

Brady, I think your second sentence is not really relevant.  Who cares what the processing path, poisson stretch etc. was?  You have this assembly in equilibrium, at room ambient, with a known interface pressure!  The nominal geometry, as well as CTE's and elastic mods are also known.  I would try -
a. Check published data for CTEs as a function of T. (Maybe you will luck out and it can be assumed constant over the temperature range.  Otherwise find some empirical eqn.)
b. From the known interface pressure, back calculate the diametral interference that would produce this.
c. Raise T by 166 degC for a new diametral interference.
d. Calc a new interface pressure.

(Hope that was good advice.  I haven't tried it, but I believe all the necessary material properties are known.)
 

RE: Effects of Thermal Expansion on Preload of on Composite Cylinders

(OP)
Thank you Bestwrench , I have actually calculated the diametrical interference. The CTE can be assumed constant. But I am still not sure how to accomplish C and d from your advice. How do i account for the interface pressure which is trying to avoid thermal expansion. Also, if i assume no preload and raise the temperture, there will be a gap between the two piece because the aluminum is on the outside.

Can you elaborate a little on c and d.

Thank you

RE: Effects of Thermal Expansion on Preload of on Composite Cylinders

if you've calculated the diametrical interference, then you know the ID of the sleeve, ie the real ID if it wasn't stretched over the tube.  wouldn't this be the starting poiint for heating the tube to 166deg ? you know C so you can calc the expansion of the sleeve.  and so get the new un-stretched ID; if less than the tube OD then there'll still be some strectch, some preload, in the sleeve.

no ?

RE: Effects of Thermal Expansion on Preload of on Composite Cylinders

Calculate the shrink of the aluminum as it cools from 400C of the contact diameter 57mm.  I calculate the reduction in diameter to be 0,5244mm.  That would be the approximate interference ignoring contraction of the graphite due to compression of its diameter and expansion of the aluminum due to the interference pressure.

Calculate the increase in diameter due to increasing temperature.  As long as the increase is less than 0,5244mm the parts will remain in contact.

Ted

RE: Effects of Thermal Expansion on Preload of on Composite Cylinders

(OP)
Thank you guys. I think I know the step to arrive at the new interface pressure.

Given that I can prove that they will stay in contact. This means that the change in their radius will be equal. I can find the diametrical interference for a 166C temperature rise. Using those new diameters,I can equate the formulas for deformation in the aluminum and the graphite to find the new interface pressure. Is that right? I am sure it is.

The last question is:

Do i also apply a temperature rise to the graphite as well and use its expanded diameter OD along with the expanded diameter for the aluminum? Or do I just apply the temperature rise to the aluminum ?

 

RE: Effects of Thermal Expansion on Preload of on Composite Cylinders

"This means that the change in their radius will be equal."  i don't think this is quite right ... the graphite tube is going to be extremely stable with temperature (as shown by it's C).  but you've calc'd the ID of the sleeve having been stretched and heated and thoroughly deformed, and this is smaller than the tube OD, hence the preload between the surfaces.

now if you heat the combined tube and sleeve, the sleeve ID will expand more than the graphite tube OD, but the sleeve expansion is based on it's unstretched ID; and so long as this is thermally expanded ID is less than the tube OD (expanded if you want, but there'll be Very little difference) then there'll be interference, and you'll be able to calculate the contact stress.

no ?

RE: Effects of Thermal Expansion on Preload of on Composite Cylinders

(OP)
I understand what you are saying rb1957. So given that I can find the total deformation. I am not sure what radii to use for the OD of the graphite and ID of the aluminum, i.e, the dimension after they have been assembled. do i used the 57mm as the common interface diameter.

How do i find the final contact radius after assembly ?
I know that the graphite OD will get smaller due to the contact pressure.

RE: Effects of Thermal Expansion on Preload of on Composite Cylinders

Knowing contact pressure you can calculate the final assembled interface diameter.

Then calculate the thermal change in diameter for the graphite and for the aluminum.  The hot outside diameter of the graphite will be larger than the hot inside diameter of the aluminum by the amount of remaining interference.

Ted

RE: Effects of Thermal Expansion on Preload of on Composite Cylinders

How could you possibly "know" the contact pressure? That in itself must be calculated number.

RE: Effects of Thermal Expansion on Preload of on Composite Cylinders

i guess i assumed (yeah, i know) that you had followed the ID of the sleeve through it's tortuous manufacturing process, in order to determine the diametrical interference.  Possibly you're inferring the ID based on the interference stress.  However you've done it, you know (as posted) the diametrical interfernce as manufactured, so you know the ID the sleeve wants to be at (post torture), and this is the diamter that now expanding when you heat the combination again, to 166deg.  The Al sleeve will expand much more than the graphite tube, but the Al ID may (or may not) be in contact with the tube OD.

it does seem to be a very complex manufacturing process, it must've been fun developing it !  many pieces for the "rogues galley" i suspect.

RE: Effects of Thermal Expansion on Preload of on Composite Cylinders

Hi brady1

Please check your data in your original post ie E = 70Gpa for aluminium and E=14.5Gpa for graphite, according to the sites I have looked at and also CTE expansion for aluminium is 23.6 * 10^-6.
I used this formula as you to obtain the interference fit between the two components  and using your interface pressure:-

        p*r^2/(E1*t)   +    p*r^2/(E2*t)  = interference
                                             radial

p= 10Mpa  r= common interface radius ie 57/2 (your case)
E1=elastic M of aluminium E2= elastic M graphite

This gives an intereference of 0.0658mm which isn't enough intereference for the two parts to stay together for the temperature rise you quoted unless my figures are incorrect hence the request to check your data.
Finally the formula is for thin cylinders and not thick cylinders although your aluminium cylinder is thin, the graphite one is classed as thick but I believe its good enough for an estimate.
My final comment is a question, after cooling of the aluminium are there any residual stressses in it because they need to be taken into account, if they are present or at least I believe so.

desertfox
 

RE: Effects of Thermal Expansion on Preload of on Composite Cylinders

(OP)
Compositepro the initial contact pressure is was found based on the fact that the aluminum experienced plastic deformation during processing.During processing, it is known that the relative lengthening is three times larger that the permanent deformation at the yield strength. Therefore, the final tensile strength in the aluminum is practically equal to the yield strength. The pressure applied to the graphite is found using a known equation where:

P = (a/R)* hoop stress

This pressure is due to the aluminum attempting to shrink during cool, but cant because of the presence of the graphite.

remember that the hoop/circumferential stress is equal to the yield strength

desertfox there are residual stresses after cooling the aluminum like i have stated in this posted and those above. The aluminum want to shrink by an amount equal to 400C*24.5*10^-6*(57)= 0.5586mm.

As long as the operation temperature stays below 400C, the part should remain in contact like hytools suggested. I believe they will.

I have the device and know its final parameters and can calculate the interference.

Thank you

RE: Effects of Thermal Expansion on Preload of on Composite Cylinders

brady1

If you heat up the aluminium it wants to expand not shrink as stated in your last post.
Also notice you gave GTE 24.5*10^-9 in your original post now in your last post its 24.5*10^-6 which I mentioned in my previous post.
Finally please upload your intereference calculation which you state is 10MPa, because my calulation shows the radial intereference to by only 0.0658mm radially based on your 10MPa.

desertfox

RE: Effects of Thermal Expansion on Preload of on Composite Cylinders

(OP)
The CTE is actually 24.5*10^-6 .My mistake. The yield strength for this aluminum is between 100-170Mpa.according to the manufacturer`s the aluminum underwent deformation such that its final stress is equal to its yield strength. I used 100Mpa to be conservative.

The manufacture went on to calculate the contact pressure using the formula:

theta(tangential)=(p*di)/2t

and p= (2t*theta(tangential))/di
    p= 2*(2mm/28.5mm)*100Mpa=7Mpa

so use 7Mpa instead of 10Mpa

where:

theta(tangential) is that tangential stress and equal to the yield stress. In that case i used 100Mpa.

P= contact of radial pressure

di= internal radius of sleeve

t= wall thickness

this formula is stated in shigley as the average tangential stress and is valid for thick and thin walled cylinders.

You can use this information and that provided above to find and analogous diametrical interference.

Also in the manufacturing process, it was heated and stretched over the graphite. Upon cooling, it shrunk imparting a pressure(p) that can be found using the formula that i stated earlier.  

RE: Effects of Thermal Expansion on Preload of on Composite Cylinders

I have a shrink fit program that uses as references to "Theory and Design of Pressure Vessels by John F. Harvey, Van Nostrand Reinhold Company, 1985.   Additional formula and examples based on Mechanical  Engineering Design by J.E. Shigley, second addition 1972. It appears to use use Harvey as the primary reference in respect to temperature effects.

It will calculate with an initial clearance and the loss interference pressure due to temperature or spin giving negative values. It uses a logarithmic temperature distribution in the cylinders.   

The sad part is that I don't have it running now.  It is a DOS program that runs on Symphony and the program is on 51/2" floppy and they want $75.00 to put it on a disk or 3 1/4" floppy.   

RE: Effects of Thermal Expansion on Preload of on Composite Cylinders

brady1

Okay the formula your using calculates the hoop stress in a cylinder for a given internal pressure, a thin walled cylinder is considered to have uniform hoop stress and so the formula you have used will give you the internal pressure to put the whole cylinder into its yield state

p= 2*(2/28.5)*100= 14Mpa using your figures not 7Mpa

further the wall thickness of the aluminium is 1.5mm not 2mm
60-57 =3.

Now forget the heating and shrinking bit and consider that you require to put the aluminium into it yield state by virtue of an interference fit so we need 14Mpa at the interface of aluminium and graphite, now to calculate the intereference using the formula I posted yesterday:-

 p*r^2/(E1*t)   +    p*r^2/(E2*t)  =  radial interference

you will find this formula on page 74

see page 72 and 73,74 of this reference:-

http://books.google.co.uk/books?id=x1EYegEAsCQC&pg=PR7&lpg=PR7&dq=schaums+strength+of+
materials+by+william+j+nash&source=bl&ots=qIPFARgcAu&si
g=qKrZARq3KtmrCfOeFk0LreW4Yh4&hl=en&ei=m3W_S8mbFZ260gS
03P2ZCQ&sa=X&oi=book_result&ct=result&resnum=10&ved=0C
DAQ6AEwCQ#v=onepage&q&f=false


According to me E for aluminium = 70Gpa not 70Mpa as stated in your original post and E for graphite 14.5Gpa not 14.5Mpa
now:-

 14*28.5^2/(70*10^3*2) + 14*28.5^2/(14.5*10^3*23)=0.115315mm

that figure is the radial interference between the graphite and aluminium components needed to put the aluminium into its yield stress, any increase on this interference will cause the aluminium to exceed its yield stress, go further and you will fracture the aluminium.
Now for the temperature rise, any stresses caused by the temperature rise can simply be added algerbraically to the mechanical stresses induced by the interference.
However aluminium will expand at a much greater rate than the graphite and therefore with the interference as calculated the composite will fall apart.
The residual stress you refer to is the yield stress in tension which in this case doesn't help you.
When I first mentioned residual stress, I had a compressive residual stress in mind but clearly from your posts you don't have that.

desertfox

 

RE: Effects of Thermal Expansion on Preload of on Composite Cylinders

What is the aluminum alloy?  Any concern that 400C is in the annealing range?

desertfox, you are correct that the aluminum sleeve will reach yield strength as it shrinks tending to go more than your calculated interference based on reaching yield.  It should not fail until the elongation reaches, what?, 10-30%, depending on alloy and condition.

Ted

RE: Effects of Thermal Expansion on Preload of on Composite Cylinders

(OP)
It is a Russian grade aluminum alloy AMg2M-AMg6M. The yield strength lies in the range 100-170MPa.

RE: Effects of Thermal Expansion on Preload of on Composite Cylinders

(OP)
Yes it is.

RE: Effects of Thermal Expansion on Preload of on Composite Cylinders

hi hydtools

That was very clever of you to find that link.

This is interesting problem and I take your point about it shrinking further than the intereference calculated by my formula.
However if we take poissons ratio to be 0.3, although I know it changes depending on temperature and consider the increasing length as being 0.006, as given in your link then the change in diameter is only 6.84*10^-4 which again wouldn't give enough interference.
Okay if it works I must be wrong so what am I missing (grin)

desertfox

RE: Effects of Thermal Expansion on Preload of on Composite Cylinders

(OP)
Hu hytools

I really do not think that the composites will fall apart like hytool said. It makes sense that to relax the shrinkage pressure, one would have to raise the temperature to at least 400 C as used in creating the fit.

In designing this composite, the importance of a very low contact resistance was taken into account. In operation the device sees a maximum temperature rise of only 160 C compared to its 380 C rise during manufacturing. Any ideas on this? Does this convince you that the two part will stay in contact.

I am not discounting the fact that they can come apart though.

RE: Effects of Thermal Expansion on Preload of on Composite Cylinders

Hi brady1

Well just looking at my figures particularly the last calculations, which if I doubled the radial interference to get the diameteral interference, which is 0.23mm and compare it with the expansion of the  aluminium cylinder for a 160 deg rise which is 0.223mm I would say its on the borderline of seperating, whilst I haven't taken into account the extra interference due to Poisson's ratio, which very small compared to the previously calculated figure I suppose it might help in keeping the composite together. I did think at first, which was my mistake that it was going upto 400 degrees in service.
If your asking why the aluminium was at 400 degrees for manufacturing then thats fairly easy to answer ie:-
hot working will prevent work harding, lowers forces required to stretch tube, refines grain structure to name but a few.

desertfox

RE: Effects of Thermal Expansion on Preload of on Composite Cylinders

(OP)
Is anyone of you familiar with zone-normalized deformation ?
 

RE: Effects of Thermal Expansion on Preload of on Composite Cylinders

Hi brady1

Do you mean strains beyond yield into the plastic zone?
If you do just looking at a text book, your aluminium cylinder won't have any residual stress because all the wall section as been put into yield.

desertfox

RE: Effects of Thermal Expansion on Preload of on Composite Cylinders

brady1,
I think you are pulling that phrase from the above linked Russian report.
I think the authors have incorrectly called the annealing of the aluminum as it is stretched 'normalizing'.  Normalizing is used only with ferrous metals.  The authors may have more properly coined the phrase as zone-annealing deformation.  They heated to an annealing temperture the aluminum tube in zones as the as it was stretched in order to soften the cold working due to stretching.

Ted

RE: Effects of Thermal Expansion on Preload of on Composite Cylinders

(OP)
Hi,

Thank you desert fox and hytools.

So when the author says that the aluminum shrink plastically. That does not mean that the aluminum was deformed, does it.

If the aluminum was annealed, does that means that its yield strength was decreased to the 100Mpa yield strength that they used to find the shrinkage pressure.

My material science knowledge is a little rusty.

brady

RE: Effects of Thermal Expansion on Preload of on Composite Cylinders

What is meant by shrinking plastically is that the aluminum reaches its yield strength as it shrinks around the graphite and continues to remain in the plastic region as it further cools and shrinks.  Once the aluminum enters its plastic region it shrinks without significant increase in stress.

The author initially deformed the aluminum tube by stretching it.

Yes, when the aluminum is annealed its strength is reduced.  Strength increased by cold working, the stretching, or aging is reduced by annealling.  We do not know what the original condition (strength) of the tube was before being stretched.

Ted

RE: Effects of Thermal Expansion on Preload of on Composite Cylinders

This is not a very good job but it's the best I can do with what I have.

The syntax shown is for Symphony or Lotus 123.  This is the Thermal Stress part of the program I mentioned in a previous.  I hope you can glean some information from it.
All units are US standard.  There maybe an error on page A-8 for the C2 value he uses the B value for the C cal lout and caries through with it.


http://my.engineering.com/pg/file/unclesyd/read/272637/thermal-1

http://my.engineering.com/pg/file/unclesyd/read/272639/thermal2

http://my.engineering.com/pg/file/unclesyd/read/272648/thermal3

http://my.engineering.com/pg/file/unclesyd/read/272649/thermal4

http://my.engineering.com/pg/file/unclesyd/read/272666/thermal5
 

RE: Effects of Thermal Expansion on Preload of on Composite Cylinders

Hi unclesyd

Only downloads thermal2 and thermal5 have anything to read all the rest are blank including shrink1 and shrink2.

desertfox

RE: Effects of Thermal Expansion on Preload of on Composite Cylinders

I think it's working now.  I click on the icon.

On page A-2 the last line on the shrink fit part is missing.

Axial = (F1)= 3082 psi

 

RE: Effects of Thermal Expansion on Preload of on Composite Cylinders

RE: Effects of Thermal Expansion on Preload of on Composite Cylinders

Hi unclesyd

I did get to see the other files you posted, however as far as I can see all these examples are interference fits within the elastic limits of the materials unless I am missing something, whereas the OP as completely yielded the outer cylinder in his case so what effect will that have on any future expansion due to temperature rise?

desertfox

RE: Effects of Thermal Expansion on Preload of on Composite Cylinders

Doesn't the thermal expansion stay the same regardless if the Aluminum has been yielded. The OP posted a stress imposed by his fit as it now stands stands. To get this pressure there has to be some interference at the interface.  Since he states that is temperature is the same for both the Carbon and Aluminum at some point he Aluminum will created a gap.  
My line of thought was one could get the interference from his stated pressure just for information.  By setting up and using the Thermal part he could tell when his interference is approaching 0 or loss of interference                                                           
  

RE: Effects of Thermal Expansion on Preload of on Composite Cylinders

Hi unclesyd

The thermal expansion will stay the same I agree, however when the aluminium is above its yield stress while hot and then cools, will the interference be any greater than my earlier calculations due strains without increase of stress as the material as yielded.
Put a better way during construction of the composite tube the aluminium cylinder is completely yielded before it cools and shrinks onto the solid core, ie it under goes plastic deformation, if you look at the link given by hydtools you will see that the aluminium tube bore is actually larger than the solid core before the composite tube is made.
So that being the case how much more interference is there due to that plastic deformation? I have had a couple of goes even trying to establish strains while the aluminium is hot but I am not 100% sure if I am right.

regards

desertfox

RE: Effects of Thermal Expansion on Preload of on Composite Cylinders

(OP)
From the process, it seems like the material was process annealed. This means that it was cold worked and heat treat to a temperature above it recrystallization temperature. The purpose of annealing the Aluminum while stretching negates strain hardening.

Also, if you read a little about hot working you will learn that hot working in that manner is plastic deformation without strain hardening. Also, notice that they said the hoop stress is equal to the yield strength. If the hoop stress is just equal to the yield, one can assume the new worked aluminum is not plastically deformed in the sense that it will not return to its original length.

 

RE: Effects of Thermal Expansion on Preload of on Composite Cylinders

Hi brady1

On the bottom of page 20 though of hydtools link, it says that "At the stage of cooling the aluminum pipe shrinks plastically" and goes on to say that the permanent elongation is about 3 times larger than it would be at the yield stress for the material.
Also when a material reaches yield it can under go permanent strain without increase in stress and this is prior to any increase in material strength due to work hardening.

desertfox

 

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