Thermal expansion on weld coated bar 2

[Sweguy]

Hello
I have a problem that I can`t find any information about in books or internet so I will try this forum.

Let`s say that you have a bar Ø100mm in 316 material.
This bar is coated with 2,5 mm of weld that has a lower thermal expansion coefficient. How can I calculate the total expansion?.

The weld will work as a bearing and the bar will be fitted into a hole that is the other bearing surface, this part is also made of 316 material and the inner Ø of the hole will also be coated with a weld material that has similar thermal expansion coeff. as weld No 1.

How can I calculate necessary gap between those two surfaces?

 

[Zapster]

Do you still have your Mechanics of Material textbook from college?

 

[desertfox]

Hello Sweguy

We might need more information like temperature range and overall dimensions of the outer bearing and length of bar and bearings and finally the different coefficients of expansion.
Why can you not use a conventional journal bearing in your application?
The expansion of both bar and bearing will depend on how each receives the heat and I am not sure I can give a complete answer because the heating of your components may be complex in terms of the heat transfer ie conduction,convection,radiation and on top of that the heating will probably be non-uniform which means that some parts will be hotter than others and differential thermal expansion will take place even if the materials have identical properties.
The calculation of the stresses is fairly easy if you have uniform heating of components, look in your books for compound bars subject to temperature stresses or shrink fits
that should give you the idea for the calculations.

regards

desertfox

 

[Sweguy]

Hi thanks for your answers.
I have checked all the books I have but i can`t find the answers there.

To calculate thermal expansion for each of the materials is no problem, the problem is I`m not sure how they behave together.

My idea how to solve this problem is as following:

Calculate how much bar material expands, calculate how much weld expands. Because weld has lower thermal coefficient it will create a pressure between those materials, calculate this pressure see how much those materials will expands/contracts due to that pressure.

Solution: the bar will expand due to the thermal coeff, will contract acc. to pressure, weld will expand because of thermal coeff, and because of pressure. When there is no gap between bar and bearing, I have the finished solution.

Is this correct thinking?

I can give the exact data.
Temp: 20-250 celsius degr.
Uniform heat the parts is completelely embedded in heat media.

Bar Ø165 thermal coeff 16,5 Mym/m*K material 316
Weld on bar therm. coeff 13,6 material stellite 6, outer Ø170.
Bearing Ø175 thermal coeff 16,5 Mym/m*K material 316.
Weld on bearing therm. coeff 12 material stellite 21, inner Ø170.

Bearing lenght 40mm.

 

[desertfox]

hi Sweguy

Well the modulus of elasticity of each material is also needed to do the calculation.
On the bar I have done a rough calculation and I get a change in diameter of about 0.2329mm when its at 250 deg C but I would like to double check my figures before I put a solution up on here.
Incidentally the coeff of expansion for steel you have quoted is only valid upto 100 deg C and it increases above that temp 19.9*10^-6.
I'll post my solution later on.
Your on the right lines with your last post though, the steel will want to expand more than the stellite and vice versa, so the stellite will end up in tension and the steel bar in compression.
You can approach this problem in this way, first calculate the free expansion of each material at whatever temperature and then subtract one from the other, this will give you the interference between the two materials at the required temperature. If you now treat that result as an interference fit between a solid steel shaft and stellite sleeve you can work out the interface stress and the resulting diameter change.

regards

desertfox

 

[eromlignod]

First of all, if you're concerned about the diameter, make sure you're using the VOLUMETRIC coefficient and formula, not the linear one.

Calculate the expansion of the inner cylinder first.

Then calculate what the thickness change would be for the outer "hoop" by calculating the change in the OD and the ID. Remember that the ID expands by the same amount that an imaginary cylinder of the same material inside would have. You'll probably find that the change in thickness is a very small amount, maybe even negligible.

Add twice this thickness to your inner cylinder diameter. If it expands less than the cylinder, there will be some compressive stress at the interface, but your cylinder is so large and strong in comparison to the thin ring that this compression shouldn't change the OD significantly. The hoop will also contract due to poisson's ratio, but again this would be by an insignificant amount.

Don
Kansas City

 

[desertfox]

Hi Sweguy

I checked my figures and attach a solution for the shaft with the stellite 6 welded onto it.
At 250 deg C your looking at an increase on diameter of 0.221mm according to my figures.
You can do a similiar exercise for the bearing housing so I'll leave that for you.

Hi eromlignod
I am not sure why your saying to use the volumetric coefficient of expansion as it looks like we are only concerned with the diameters in this problem.
All the texts I have seen on this type of problem use the linear coefficient of expansion unless of course I have missed something, in which case please shout up.

regards

desertfox

 

[eromlignod]

Yeah, I guess you're right, Fox. The diameter would undergo linear expansion in all directions just like the length. All these years I've been doing it the hard way!

Don

 

[desertfox]

Hi eromlignod

Thanks for the post just wanted to make sure i hadn't missed something

desertfox

 

[Sweguy]

Thanks for the good advices, one last question desertfox, the calculation you made, you calculated how much it will deform because of the difference in thermal coefficient.

Your answer 0,221mm, shall I add this number to the stellite expansion? so the total outer diameter change will be 0,221+0,53=0,751mm. Is this correct?

 

[desertfox]

Hi Sweguy

What I have calculated is the growth of the shaft at
250 deg C so the outer diameter of the shaft with stellite is 170dia + 0.221mm giving an overall of 170.221mm dia at that temperature.
Note though that I used a coeff of linear expansion for steel as 19.9 * 10^-6 which is only true above 100 deg C.

regards

desertfox

 

[Sweguy]

Now I`m really confused...

If a 165 mm bar of 316 material expands 0,7mm.
And if a Stellite ring with outer diameter 170mm and thickness of 2,5 mm, expands 0,5mm at the same temperature rise.

Then you put the stellite ring onto the 316 bar and they expands 0,2mm togetherwit hthe same temperature rise. How can that be? My common sence says that the total expansion shall be somewhere between 0,5 and 0,7 mm.
The stellite is forced to expand more then it wants, and the 316 bar is prevented to expand as much as it want.

 

[desertfox]

Hi Sweguy

Let me check my calc again.

Regards

desertfox

 

[desertfox]

hi Sweguy

Yes your right,you need to add the 0.221mm to the overall free expansion of the stellite ie:- 0.531+0.221+170 and that should give you a fairly good estimate of the expanded diameter based on some of the assumptions about material properties I have made.
Its worth pointing out that the stress at the interface of the stellite is in the order of 275N/mm^2 when the shaft and sleeve are at 250 deg C I don't know off the top of my head how strong the stellite is but I thought I would mention it anyway.
One small error in the calculations I made, is that when calculating the diametral interference I should have used 82.5mm radius for both materials and not 85mm however the error is very small, theres probably a larger error in the material assumptions mentioned earlier.

regards

desertfox

 

[Sweguy]

Thank you very much.

 

[desertfox]

Hi Sweguy

Your welcome.

desertfox

 

[zekeman]

I refuse to believe that with a coating of about 3% of the total diameter, the weld would have any significant effect on the overall expansion of the shaft. Its like expanding a rubber band around a steel shaft. I would let the main shaft grow according to the temperature and add the thickness of the weld, period.
I have no problem doing the analytic solution as an exercise for a 3rd year engineering student, but it is unnecessary here.
The main problem I see is that at high temperatures the mismatch in thermal expansion will cause significant interface stresses that might fracture the weld.