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  1. #1
    sconisbee is offline Aluminum
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    Default 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. #2
    register's Avatar
    register is offline Cast Iron
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    Default

    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/C | 1/F)
    ΔT = change in temperature (C | F)
    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/C)

    Good luck,
    Henry Wettersten

  3. #3
    doug8cat is offline Stainless
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    Default

    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. #4
    sconisbee is offline Aluminum
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    Default

    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. #5
    BobWarfield is offline Hot Rolled
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    Default

    Great discussion guys. Sounded so useful I added a Thermal Expansion calculator to G-Wizard.

    Thanks,

    BW
    CNC Cookbook: Blog

  6. #6
    DMF_TomB is offline Titanium
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    Default 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. #7
    DMF_TomB is offline Titanium
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    Default 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.
    Attached Files Attached Files

  8. #8
    DMF_TomB is offline Titanium
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    Default 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.
    Attached Thumbnails Attached Thumbnails calculatorapr22.jpg  
    Attached Files Attached Files

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