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Thread: Gears: when base circle diameter less than the root circle/dedendum

  1. #1
    Associate Engineer
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    Gears: when base circle diameter less than the root circle/dedendum

    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!


    -Sarah Anderson

  2. #2
    Administrator Kelly Bramble's Avatar
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    You need to show your calculations... Unsure what the challenge is..
    Tell me and I forget. Teach me and I remember. Involve me and I learn.

  3. #3
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    Quote Originally Posted by Kelly Bramble View Post
    You need to show your calculations... Unsure what the challenge is..
    Thanks for the reply!


    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

    The problem is that the base circle must be greater than the dedendum circle, but with the given gear parameters, this is not the case (unless an assumption of mine has gone awry). I also dont really want to compromise the desired pitch diameter and number of teeth, unless that is the only solution.

    If the calculations are correct, (which I think they are as they have 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!
    Last edited by sarahanderson8591; 11-12-2016 at 10:18 AM.

  4. #4
    Administrator Kelly Bramble's Avatar
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    Interesting question..

    Definition: "Base Diameter (Db) – is the diameter of the circle from which the involute form is generated."

    So, this is a reference for calculations.. Not sure the "base circle diameter" has a requirement to be of less diameter..
    Tell me and I forget. Teach me and I remember. Involve me and I learn.

  5. #5
    Principle Engineer
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    Sarah,

    The base circle is not larger than the root diameter. You have a sufficient number of teeth so that you do not need to undercut the flank at the bottom of the tooth.

    Take the time to learn to how to construct the involute curve.

    Also know that standard metric gear cutters are usually made in increments of 0.05 module. Expect the shop to use a 0.90. The mating gear must be cut with the same module although the exact cutter shape will vary with the number of teeth.

  6. #6
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    So basically what is being said is that it does not matter if the base circle is smaller than the dedendum circle diameter? I understand the involute curve, but now what I'm understanding from this post is that, in my case it starts below the root, which is still okay? ( meaning at the bottom of the tooth the involute curve has already been started?)

  7. #7
    Principle Engineer
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    You are correct - with a 60 tooth gear the involute portion runs to the bottom where you add a small radius to blend into the dedendum circle. You can generate the involute curve section above and below the tooth on your drawing, it just doesn't happen in metal.

    With about 14 or 15 teeth, depending upon the pressure angle, you get into a condition where the flank gets undercut and the tooth form is weakened at the root but, this will not happen with 60 teeth.

  8. #8
    Administrator Kelly Bramble's Avatar
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    FYI - engineersedge.com gear design equations and calculators..

    Spur Gear Design Tool

    Gear Design Known Center Distance and Ratio
    Tell me and I forget. Teach me and I remember. Involve me and I learn.

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