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Gears: when Base circle less than the root circle/dedendum

  1. Nov 12, 2016 #1
    Hey guys,

    Trying to design a spur gear but I am very confused as the root circle/dedendum ends up being greater than the base circle. What do I do in this case? The gear I'm trying to design has a 68.33mm pitch diameter, 60 teeth, the pressure angle a standard 20 degrees. What am I doing wrong here? Any help is appreciated!

    -Bob Khan
  2. jcsd
  3. Nov 12, 2016 #2


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    Show us your workings please .

    Is this a homework problem ?
  4. Nov 12, 2016 #3
    Thanks for the reply. Not a homework problem though.

    Desired pitch diameter: 68.330mm
    desired teeth #: 60
    pressure angle: 20deg
    Base circle diameter = cos(phi)*pitchdiameter =64.209mm
    diameteral pitch = t/pitchdiameter= 0.878mm
    addendum = module = 1/diametral pitch = 1.139mm
    dedendum = addendum*1.25 = 1.424mm
    Addendum circle diameter = pitch diameter + 2*addendum = 70.610mm
    dedendum circle diameter = pitch diameter - 2*dedendum = 65.480mm

    If the calculations are correct, (which I think they are as they been done few times) these are the pertinent values. So clearly the base circle is less than the dedendum circle diameter. I noticed that reducing pressure angle does fix this, but is that the only solution? Should I consider something else? Appreciate anybody who can help!
  5. Nov 12, 2016 #4


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    That is exactly what you should expect. Moving out along a radius ...

    Base circle diameter = cos(phi)*pitchdiameter = 64.209mm
    Dedendum circle diameter = pitch diameter - 2*dedendum = 65.480mm = Root circle
    Desired pitch diameter: = 68.330mm
    Addendum circle diameter = pitch diameter + 2*addendum = 70.610mm

    They are in the correct order,
    Last edited: Nov 12, 2016
  6. Nov 13, 2016 #5
    Well in most cases, the base circle is larger than the dedendum circle in diagrams I have seen:


    Either way, what I am understanding is that it doesn't matter? Like the involute line starts from the base circle but it doesn't matter that the bottom of the gear tooth still starts at the dedendum circle?
  7. Nov 13, 2016 #6


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    How is the involute curve defined inside the base circle ?
    Involute teeth have a 0° contact face at the base circle. Undercut teeth are weaker than stub teeth.
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