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Algebra was far too long ago

  1. Oct 27, 2003 #1
    OK.
    Here's the situation:

    I am trying to build a spreadsheet to solve for planetary gear configurations.

    I have done most of the work already, but I am getting stuck when solving for planetary differentials.

    If you don't know, a planetary gear differential is basically a gear set-up that has three shafts that can be used as inputs or outputs.

    Let:
    S = Speed (in RPM)
    N = Number of teeth on the gear
    r = ring gear
    c = planet carrier
    s = sun gear

    The relationship can be described by the following equation:

    (Sr-Sc)/(Ss-Sc)=Ns/Nr

    There are six different configurations I am trying to solve for.

    Unfortunately, Algebra and I have been apart for far too long.
    Think maybe you can help?

    Configuration 1
    Ns: known
    Nr: known
    Sr: known
    Sc: known
    Ss: not known

    Configuration 2
    Ns: known
    Nr: known
    Sr: known
    Sc: not known
    Ss: not known

    Configuration 3
    Ns: known
    Nr: known
    Sr: known
    Sc: not known
    Ss: known

    Configuration 4
    Ns: known
    Nr: known
    Sr: not known
    Sc: known
    Ss: not known

    Configuration 5
    Ns: known
    Nr: known
    Sr: not known
    Sc: known
    Ss: known

    Configuration 6
    Ns: known
    Nr: known
    Sr: not known
    Sc: not known
    Ss: known

    Any help would be greatly appreciated.
    Especially if you show me how you did it.
     
  2. jcsd
  3. Oct 30, 2003 #2

    NateTG

    User Avatar
    Science Advisor
    Homework Helper

    Usually, you can only solve for as many unknown quantities as you have equations. Since all you've got is
    (Sr-Sc)/(Ss-Sc)=Ns/Nr

    That means that you'll need to bring in some additional information for the examples that you give where there are multiple unknowns (2,4, and 6). Perhaps there is some additional relationship that you missed?

    In general, you'll probably want to assume that (Ss-Sc) and Nr are both not zero.

    Then you can easily convert the equation above into:

    Ns=Nr(Sr-Sc)/(Ss-Sc) (Multiply both sides by Nr)
    Nr=Ns(Ss-Sc)/(Sr-Sc) (Take reciprocal of both sides, and multiply by Ns)

    And these are fairily straightforward after taking a cross product:

    (Sr-Sc)/(Ss-Sc)=Ns/Nr
    =>
    Ns(Ss-Sc)=Nr(Sr-Sc)

    Sr=Ns(Ss-Sc)/Nr +Sc
    Ss=Nr(Sr-Sc)/Nr +Sc
    Sc=(SrNr-SsNs)/(Nr-Ns)

    Hope this helps
     
  4. May 20, 2004 #3
    Equation check (Sorry, should have attached to this one)

    I compared your equation to a generic equation for planetaries, which is:

    (P-1)(Sr/Ss) = P(Sc/Ss) - 1

    and which, for a ring-gear planetary:

    P = (Nr = Ns)/Ns

    If the author of these equations was correct, then the following was derived:

    (Sr - Sc)/(Sc - Ss) = Ns/Nr

    If so, then your directions will be reversed. I'd like to know which is correct.
    Kenneth Mann is online now Reply With Quote
     
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