# Linear Expansion



## Ray C (Mar 29, 2013)

All,

Here's a very nice table of linear expansion constants for a variety of materials. Just wanted to pass this reference along and include a practical example. FWIW: I keep a laser thermometer near the lathe and mill so I can accurately machine things for ambient conditions. This chart is printed and hanging on the wall.

http://www.engineeringtoolbox.com/linear-expansion-coefficients-d_95.html


For those who wish to know, the table tells you how much something expands based on temperature change. The chart shows ISO (mm/mm/K) and SAE (in/in/F) values. In SAE, this is interpreted as "Inches of change PER inch of material PER degree Fahrenheit". In ISO, it reads "millimeters PER millemeter of material PER Kelvin". (Kelvin = degrees (C) + 273.15).

Example: Let's say you have a 316 Stainless bar measuring 3.500" diameter and it's heated to 140(F) due to recent machining operations. What will the diameter be when it cools to 68(F)?

From the table, expansion coefficient for 316 Stainless is 8.9x10[SUP]-6[/SUP].
Temperature difference is 140-68 (= 72)
Amount of change: 8.9x10[SUP]-6[/SUP] X 3.500 X 72 = 0.0022.
Final diameter at 68F: 3.500 - 0.0022 = 3.4978"


Example: The same shaft from earlier is 36 inches long. How long will it be when it cools to 68(F)?
8.9x10[SUP]-6[/SUP] X 36 X 72 = 0.0231"
Final length at 68F: 36 - 0.0231= 35.9769"


Ray


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## Tony Wells (Mar 29, 2013)

Of course, this assumes a temperature constant through the cross section, which is rarely the case. Just a note.


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## n3480h (Mar 29, 2013)

I see the effects as a QC inspector at work.  Most days, it does not make a lot of difference, but if the parts just came off a hot or cold truck it certainly does make a difference.  We also track and record temperature with a data logger at the CMM and keep the area within a fairly close range so that our calibration checks remain reasonably accurate.  This is necessary because we are regulated by FDA and to maintain our ISO qualifications. It becomes more important when tolerances get very tight.  As a home machinist and aircraft engine builder, I witnessed the effects this week when I heated gears, slipped them onto a shaft, and let them cool.  They are not coming off the shaft anytime soon.


Tom


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