Heat expansion of tubes/rings 1

[RUSO]

Can anyone tell what the equation/s would be to find out how much the outside and inside diameter of a tube or ring expands?? I just had a bearing fall out of my housing cause heat expanded the housing faster than the bearing.

Thanks...Ruso

 

[desertfox]

Hi RUSO

The formula for expansion is:-

x=dia * coeff of linear expansion * temperature change


coeff of linear expansion for the material of the bearing housing should be found in the relevant material spec.
Temp change is just the ambient taken off the temp the bearing housing reaches.

hope this helps

regards desertfox

 

[25362]

Yours is an example of linear thermal expansion.
The volumetric expansion coefficient [dV/V)/dT] is generally taken as 3 times the linear coefficient [(dL/L)/dT]. So, if a 75L steel tank full of gasoline at the same temperature, are both heated by 20 K (36[sup]o[/sup]F), gasoline would spill out.

The linear coefficient of thermal expansion for steel: 12x10[sup]-6[/sup]/K
The volumetric expansion for gasoline: 95x10[sup]-5[/sup]/K

Excess volume of gasoline after heating:

(75)(20)(95x10[sup]-5[/sup] - 3x12x10[sup]-6[/sup])= 1.37L = 0.36 gallons

Therefore, it is recommended never to fill a car gas tank to the very top.

 

[borjame]

"25362" is right but don't take volume into account here, your bearing's linear dimensions are what matters, so listen to desertfox. If this is a transient problem, meaning you are heating up the parts over time, make sure you note that a material's coefficent of expansion(alpha) is temperature dependent. Sounds like the ring's alpha is higher than the ball's.

 

[desertfox]

Hi borjame

Thanks for your comment, the question as written is purely
a linear dimension problem relating to the diameters of the
bearing and housing.



regards

desertfox

 

[chicopee]

What have you done to correct your overheated housing?

 

[andycapp]

Not necassarily a simple problem.
If the device involves a steel bearing in a steel housing, and the differential expansion is transient, i.e during warm up, then you will need to look at the source of heat and determine relative rate of heat transfer and consequent expansion rates.
Alternatively, if the two metals are dissimilar and the problem is constant, you can determine the relative expansion empirically by considering the housing hole area and the bearing overall area and multiplying each by twice the linear expnsion coeficient for the respective materials.