Thermal Effects on a Preloaded Bolt 2

[GarrettCasey]

I've done a search to no avail. What I have is a bolt that is a stainless steel M4x0.7, 15mm long bolt that is inserted through an aluminum housing and bolted to a brass resonator. The portion of the bolt that is threaded into the resonator is 8.5mm long, the rest is the part going through a clearance hole in the aluminum housing. It is preloaded with 24 in-lbs of torque. I can calculate/simulate the effects of the preloaded bolt with no change in temperature. However, I am interested in seeing the effects that temperature has on the system. I have done multiple searches with no luck... maybe someone can point me in the right direction?

 

[rb1957]

the different materials have different coefficients of thremal expansion ... the thermal strains/deflections will change the load in the bolt.

a google for "thermal loading on bolts" gave a hit to roymech.co.uk which'll explain this in detail ... sort of wonder what searching you did ??

 

[MintJulep]

Calculate the elongation of the bolt and compression of the joint members associated with preload.

Calculate the thermal expansion of each item separately, making some necessary assumptions about the uniformity of temperature throughout the assembly.

Add the thermal expansion results back into the preload only numbers.

Back-calculate the remaining preload on the bolt.

 

[TVP]

Here is an example of some multi-material joint studies with temperature variation, etc.:

http://www.kamax.com/fileadmin/user_upload/dokumente/veroeffentlichungen/joining_of_mg.pdf

 

[zekeman]

Compression strain in the aluminum is

eal

Tension strain in the steel is

est

Let the length of engagement be unity, then the relaxed state for the aluminum and steel bolt would be

steel 1-estl
aluminum 1+eal
est= strain of preload in steel bolt
eal strain of preload in aluminum

But the force of preload is
(1) F=est*Est*Ab=eal*Eal*Aal
Were
Ab= crossectional area bolt
Aal aluminum bolt contact area

from this equation
(2) eal/est=K=Ab*Est/(Aal*Aal)
Est, Eal moduli of elasticity for steel, aluminum


Now heat up both lengths dT then the new relaxed lengths are

steel 1- est+ast*dT
Aluminum 1+eal +aal*dT

where
ast,aal = coefficiemnts of thermal expansion

Now the new difference in strains is

eal+est+(aal-ast)*dT

so the new preload will be in the ratio of the two strain differences

F*[eal+est+(aal-ast)*dt]/(eal+est)=F*(1+(aal-ast)*dt]/(eal+est)

where the eal and est are obtained from eq (2)


=\

 

[zekeman]

correction

F*[eal+est+(aal-ast)*dt]/(eal+est)=F*(1+(aal-ast)*dt]/(eal+est)

should be

F*[eal+est+(aal-ast)*dT]/(eal+est)=F*[1+(aal-ast)*dT/(eal+est)]

 

[flash3780]

zekeman's got it right above. I think that this is covered in Bickford's book, the Design and Behavior of Bolted Joints.

Also, Unbreako has a good reference in their engineering guide. The section discussing high temperature joints is a great reference for this type of problem. It's available for free on the web:

http://unbrako.com/docs/engguide.pdf

 

[Cockroach]

This is a classical statics problem studied in first year engineering. There is a solution posted in Beer & Johnston. Basically a statically indeterminate problem, so you solve for the last unknown variable using deformation. In this case, deformation is thermally induced.

I'll work it out in the general case since you've stated no temperature change.

Kenneth J Hueston, PEng
Principal
Sturni-Hueston Engineering Inc
Edmonton, Alberta Canada

 

[desertfox]

Hi GarrettCasey

have a look at this site and scroll down till you come to the heading thermal loading:-

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

basically you need to get the overall joint and bolt stiffness for your configuration, this site will show you how.

desertfox

 

[GarrettCasey]

I ended up using that roymech.co.uk website. I don't know how I missed that on my search, but it ended up being very useful in solving the problem. Thanks!