How to Calculate thermal expansion

# Thread: How to Calculate thermal expansion

1. Aluminum
Join Date
Jul 2006
Location
Cornwall UK
Posts
212
Post Thanks / Like
Likes (Given)
0
0

## How to Calculate thermal expansion

I have a shaft in that has a few dia's that are -.01/-.03mm tols on a short section thats 30mm OD, the 30mm section is in the middle of the shaft and is
17mm long. There is also a 12mm -0.01/-0.03mm section each end of the
shaft for about 15mm each end.

Materal is 316 stainless, and will be fully roughed out before letting to settle
before finish machining and "polishing" into tolerance.

How would I go about calculating the growth on diameter per degree C?

2. Everything expands at a linear rate with change in temperature. To compensate for different materials' rates of dimensional change, a correction factor called the "coefficient of thermal expansion" is used.

Keeping your units correct is important. I've added units for (mks | ips)

The equation is then:

δ = α * ΔT * x

Where:

δ = change in dimension (m | i)
α = coefficient of thermal expansion (1/ºC | 1/ºF)
ΔT = change in temperature (ºC | ºF)
x = dimension length (m | i)

The coefficient of thermal expansion can be looked up online or in a mechanics of materials text. Machinery's handbook will have the data too. For Stainless a rough number is on the order of:

17.3x10^-6 = 0.0000173 (1/ºC)

Good luck,
Henry Wettersten

3. Stainless
Join Date
Jul 2008
Location
Posts
1,860
Post Thanks / Like
Likes (Given)
487
409
This is by no means the total answere but I can tell you that the thermal expansion os s316 is 8.8 microinches per *F. You will have to do some conversions but this I hope may put on the right track.

4. Aluminum
Join Date
Jul 2006
Location
Cornwall UK
Posts
212
Post Thanks / Like
Likes (Given)
0
0
Thanks, just what I needed, so basicly its small enough of a change not to
stress too much over if I'm understanding correctly. Its all gunna be checked
and machined at 20c anyway so it shouldnt be an issue. Just wanted to be sure.

5. Hot Rolled
Join Date
Mar 2006
Location
Northern California
Posts
529
Post Thanks / Like
Likes (Given)
7
12
Great discussion guys. Sounded so useful I added a Thermal Expansion calculator to G-Wizard.

Thanks,

BW
CNC Cookbook: Blog

6. Diamond
Join Date
Dec 2008
Country
UNITED STATES
State/Province
New York
Posts
8,158
Post Thanks / Like
Likes (Given)
0
2168

## thermal expansion

thermal expansion can get difficult on bigger stuff. when doing coupling alignment on industrial motor to pump you have to measure temperature at each end of each item.
.....sometimes when the outboard end of a motor grows bigger the in board shaft end is actually going down lower.
......we would measure coupling alignment on machines hot from running and if measured every 5 minutes you can plot the changes as they go back to room temperature.
.....basically the coupling had to be out of alignment at room temperature so when it warmed up it was then in alignment.
.....sometimes simple math does not work as there may be more variable to the formula. better to measure item at hot temperature than guess what it is.
.....by the way measuring tools expand as the get warmer too. a tape measure at 100F is longer than one at 60F

7. Diamond
Join Date
Dec 2008
Country
UNITED STATES
State/Province
New York
Posts
8,158
Post Thanks / Like
Likes (Given)
0
2168

## Free Excel Thermal Expansion Calculator

i often use Excel or OpenOffice Calc to do math formulas.
.
attached Excel file for Steel and aluminum. it shows 12" aluminum 30 degrees F warmer growing 0.0047" bigger.
.
had to explain to my boss that part made on CNC measured exactly within 0.001" spec dimension but when it cooled off after machining was done it was under size 0.004"
.
he asks did you take fine cuts and measure twice? i did measure but he was a little slow in understanding metal can measure exactly spec to millionths of an inch and after cooling off be undersized.

8. Diamond
Join Date
Dec 2008
Country
UNITED STATES
State/Province
New York
Posts
8,158
Post Thanks / Like
Likes (Given)
0
2168

## thermal expansion calculator

updated free excel file with many machinist calculators and tap drill chart with a updated thermal expansion calculator and latest end mill speed and feed and horsepower calculator
.
was machining acetal / delrin and wrote dimension down hot off the machine and checked each after 15 minutes. As the dimension getting smaller seemed unusually large i looked up thermal coefficient of expansion and saw it was much higher than steel.
.
with calculator you can enter length and temp difference , say 6 inches and 30 degree F and the expansion amounts in many common materials are listed.
.
excel file is free and i am not selling anything. motivation is always learning and sharing with others and together we get better at our jobs.

9. Plastic
Join Date
Dec 2013
Country
UNITED STATES
State/Province
Michigan
Posts
2
Post Thanks / Like
Likes (Given)
0
0
Hi Henry,

Kevin, Here...New guy
I work with electric motors(making and replacing shafts for rotors,making new couplings,etc.). We use that formula especially to drop a new shaft into some iron(we'll put the iron in the oven for it's specified time) for a new rotor.My question is:why doesn't this formula always work out for couplings? Could it be the difference with flanges,keyways,shoulders for different fits? for the most part when it comes to couplings it's torches and inside Mics.what could I be missing? For a silly question....say a 12.000 O.D. hunk of stock,3.000 thick, with a .500 I.D.Kinda curious to see what you get to open the I.D. to .5005.

Thank You,
Here to learn.
Kevin McC.

10. SIM
Titanium
Join Date
Feb 2004
Location
Staten Island NewYork USA
Posts
3,462
Post Thanks / Like
Likes (Given)
932
1574
On a small shaft like that growth is almost negligible for your tolerance...My.02

However, I'd use the same method we use even on our larger shafts. That is...just let it cool to room temp before moving to your finishing cuts. One piece...walk away, grab a cup of coffee, do a quote, clean machine area. If you have several parts...rough the batch and run second op for finish.

I use my hand as a temperature probe.

No spreadsheets, formulas or calculators required. Measuring tool is same temp...

My KISS alternative...

...and why are you polishing? Should be able to hit those numbers on a CNC without a problem.

But if you do polish...watch your heat..that can really warm up a part.

Although hearing and learning the formulas for expansion are pretty cool.

11. Diamond
Join Date
Jun 2004
Location
Melbourne Australia
Posts
5,147
Post Thanks / Like
Warning, 4 year old thread thanks to out new mate Kev
Kevin, Here...New guy
And the irony. that friigin Excel spreadsheet & DMF. Prick cant even get a drill size correct, but as long is its on the spreadsheet..
There's a reason why he calls him self Dumb. Mo Fo

12. Titanium
Join Date
Nov 2011
Location
Missouri, USA
Posts
2,782
Post Thanks / Like
Likes (Given)
1354
2710
Originally Posted by kamikazekato
Hi Henry,

Kevin, Here...New guy
I work with electric motors(making and replacing shafts for rotors,making new couplings,etc.). We use that formula especially to drop a new shaft into some iron(we'll put the iron in the oven for it's specified time) for a new rotor.My question is:why doesn't this formula always work out for couplings? Could it be the difference with flanges,keyways,shoulders for different fits? for the most part when it comes to couplings it's torches and inside Mics.what could I be missing? For a silly question....say a 12.000 O.D. hunk of stock,3.000 thick, with a .500 I.D.Kinda curious to see what you get to open the I.D. to .5005.

Thank You,
Here to learn.
Kevin McC.
The formula for thermal expansion is a very, very, very simplified and generic calculation that doesn't account for many real-world variables. Geometry makes a huge difference in HOW it grows, what direction, etc.

(I've had more than one very experienced person tell me that stress relieved, cast, forged, cold rolled materials all react a little different to large temperature differences as well. I have no academic/scientific source for that, and only a couple times when something "weird" happened that I thought it may be an explanation; so nothing more than anecdotal guessing, I suppose)

I've used the formula very successfully for machining very precise hole locations in very large plates (very large, for us, is >60" and our max is typically ~100") and in aluminum, where the coefficient value is relatively large, growth can make a huge difference when your shop is 90F and you're still inspecting to proper conditions in a lab at 68/69F. However, in large assemblies where strange things can happen, sometimes it doesn't go so simply. Or if it's a shape with a lot of cutouts, changes in cross section, etc. Then it's anyone's best guess.

13. Hot Rolled
Join Date
Oct 2014
Country
UNITED STATES
State/Province
Maine
Posts
613
Post Thanks / Like
Likes (Given)
21
290
Originally Posted by JNieman
(I've had more than one very experienced person tell me that stress relieved, cast, forged, cold rolled materials all react a little different to large temperature differences as well. I have no academic/scientific source for that, and only a couple times when something "weird" happened that I thought it may be an explanation; so nothing more than anecdotal guessing, I suppose)
This wouldn't surprise me in the least, as the crystal/grain structure is different. I recall reading a NIST monograph on measuring gage blocks, and they discussed how the CTE of 52100 varied between the hardened and unhardened sections. This meant that a thin gage block, which is fully hard, had a slightly different overall CTE than a long gage block that was only hardened on the critical faces.

#### Posting Permissions

• You may not post new threads
• You may not post replies
• You may not post attachments
• You may not edit your posts
•