Aluminium Expansion 1

[tomcannon]

Hi, can someone please help me with how to calculate the expansion of aluminium with heat? I know the alloy will probably affect the result, but I'm just after a guide amount at this stage. For reference the piece in question is 65mm deep, and temperature change will be between circa 10degrees C and 100degrees C.

Thanks.

 

[kingnero]

2D (area) or 3D (volumetric) expansion?
I'd say a quick google will solve your question, as these thermal expansion coefficients (and formulae) are widely available on the web.

 

[ione]

Have a look at the link below

http://www.engineeringtoolbox.com/thermal-expansion-metals-d_859.html

 

[tomcannon]

Thanks, that link says it is approx 13 micro inches per farenheit, as in 13 thou? Seems too much as I probably have the wrong end of the stick!

Basically it is a big block of ally, with several holes going through one plane, which is 65mm thick, I just want to find out how much it will stretch a steel stud that passes through the hole when heated up, so I can look into whether the stud is operating in its elastic range.

Sorry if this all sounds so amateur, I haven't really done much of this since 2 years of it at college several years ago so I'm very rusty and really appreciate the help!

 

[desertfox]

Hi tomcannon

Extension = original length * coeff lin exp * temp change

= 65mm * 23*10^-6* (100-10)= 0.13455mm or
about 0.005"

However if your bolt is subject to the same temperature change then the problems a little more complicated, because the aluminium won't expand by the amount above, what will actually happen is that the bolt will see some more tensile stress ie expand more than it wants to and the aluminium will be held in slight compression by the bolt preload, what you should check for is that the aluminium doesn't get over stressed during the expansion.
see this link:-

http://www.roymech.co.uk/Useful_Tables/Screws/Preloading.html#Thermal Loading

desertfox

 

[tomcannon]

Thanks very much. The application is actually a cylinder head, and what I am doing is making some studs of my own, so I'm trying to get a good mix of the right stud shaft diameter so that it can elongate with the aluminium, so that when it cools down it still has clamping force. The problem is the ones I can buy are so fat that I doubt they stretch at all, so it is possible for them to lose clamping force one everything has cooled down again.

 

[rb1957]

"... how much it will stretch a steel stud"

then how much the Al expands is less than 1/2 the problem; the steel stud will affect the result.

As others have said, google "thermal expansion coefficients" and you should be able to help yourself.

 

[tomcannon]

The other part is how much force the expanding aluminium is capable of producing, is there a relatively easy way of working this out? In addition to the strength of the stud this should enable a stretch calculation?

I always try google before posting on here but the problem is getting few appropriate results and even then you often get different information and you dont know who has written it, hence why I trust the views of knowledgeable individuals on here more.

Thanks

 

[desertfox]

Hi tomcannon

I'll try and pst an example of what your up against in the next few days.

desertfox

 

[tomcannon]

That doesn't make it sound simple! Thanks for your help in advance though.

 

[zekeman]

If it is a very thick block, you can assume worst case that the aluminum will expand .000013 inches for each inch per deg F and the steel will expand only .0000065.The difference is .0000065 in/in deg F

for 100 C the diff temp is 212 F and the strain on the bolt is .0000065*212= .00137. The stress on the bolt would be this * the modulus of elasticity or
E*.00137=30,000,000*.00137=41000 psi.
due to thermal expansion. You have to add the preload stress in the bolt to this to get the final value. Careful torqueing of the the bolt is necessary to get a handle on this value.

 

[ione]

Zekeman,

deltaT = 100 °C = 180 °F

 

[tomcannon]

Thanks guys this is excellent help for me, the studs I will be making from EN24, heat treated to V grade- the properties are shown on this page

http://www.westyorkssteel.com/EN24.html

 

[zekeman]

"deltaT = 100 °C = 180 °F

Yes

 

[rb1957]

i think ione's point was the "212" zeke used in the calc ... deltaT = 100C, "212" should be "180" ... no?

 

[tomcannon]

100C = 212F?

 

[dinjin]

I think you would also have to look at the washer diameters to make certain they do not imbed in the aluminum and loose preload. As long as you do not have an opening of the joint creating alternating stresses, you should be ok.

 

[ione]

rb1957,
that was exactly my point

and Tomcannon
yes because you are taking account a temperature variation (deltaT)

A numerical example:
-) convert 100 °C to °F and you get 212 °F
-) convert 0 °C to °F and you get 32 °F
-)deltaT = 100°C - 0°C = 100 °C = 212 °F -32 °F =180 °F

 

[tomcannon]

Ah of course, thanks. The washers will be hardened approx 3/4" diameter and will not embed, they are standard items for other studs which do not have a reduced shaft so do not stretch much if at all.

 

[desertfox]

Hi tomcannon

I have uploaded a file which shows how to calculate the stresses purely due to the expansion of the bolt and aluminium, I assumed a bolt size of M10 based on your washer size of 0.75" OD and I used the washer area for the area of the aluminium subjected to the increased force.
Now to detemine whether your bolt or aluminium yields under the expansion we need to add the mechanical stresses of tightening the joint to those generated by the temperature rise.
So if you tighten your bolt to say 70% of yield and yield is 800N/mm^2 then bolt stress from tightening will be 0.7*800= 560 N/mm^2 and equal a bolt preload of about 63kN, now the stress under the washer in the aluminium will be 244N/mm^2 which in my opinion is high and you need to add another 38N/mm^2 to this figure giving a total stress 282N/mm^2 post expansion, your bolt meanwhile has an increased stress of 125N/mm^2 giving a total of 685N/mm^2 post expansion.
I would worry more about the aluminium embedding as opposed to the bolts stretching elastically.