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AD_1078019710-Marble
10-Marble
March 25, 2024
Solved

Planetary gear forces

  • March 25, 2024
  • 2 replies
  • 4197 views

Hello everyone,

 
I hope somebody can assist me with this. I am working on a calculation for a planet gear with 4 sun wheels and 1 planet wheel. The aim is to determine the forces on the sun wheel. Initially, I have 3 equations and 4 unknowns. By making an assumption based on symmetry, I now have 4 equations. Unfortunately, I am not getting the correct results. Does anyone know where I can find more information on this or perhaps have a tip? Is my assumption correct regarding the average forces over the teeth? Thank you in advance.
Best answer by ChrisKaswer

I am attaching a PDF of the program I resurrected. I am not sure it will answer your specific question as it was originally created to calculate planet pin forces for any type of planetary arrangement with links to other planetary systems. This tool is not calculating forces on the sun gear, but I am sure it can be edited to do so. Please take a look at the inputs and outputs it is working with and let me know if this will help with your goal.

2 replies

W
Werner_E25-Diamond I
25-Diamond I
March 25, 2024

I can't comment on the correctness of your calculations and assumptions but all I can say is that the first and second row of your matrix A are clearly linear dependent (on is all 1, the second is all 1/4). The rank of the 4x4 matrix is 3 and so, as you also show in your sheet, the determinant is zero and therefore you can't calculate the inverse of that matrix. The corresponding system of equations would not have a single solution but probably an infinite number of solutions, depending an a parameter. Its also possible that there exists no solution at all.
I understand that you are looking for a unique solutions, so you will have to look for an additional. independent equation.

 

BTW, in your vector b the first entry should be exactyl 4 times the value of the second entry. Maybe due to some round off errors it isn't

Werner_E_0-1711366184187.png

 

    A
    AD_1078019710-MarbleAuthor
    10-Marble
    March 25, 2024

    Dear Werner

     

    Thank you for your assistance an tips again!

     

    I'm thinking that based on the assumption of symmetry, where the arms are equal in length and the forces are equal on these arms, this could potentially be the solution. Indeed, the determinant of the first partial sheet doesn't give

    a solution. Based on the four-moment equations per gear arm, this could provide a solution. ( Assuming that the arms, tolerances, and geometric dimensions of the wheels are equal. There are likely other methods; I'd appreciate hearing about them, any points of improvement, or if I'm completely off track.

    W
    Werner_E25-Diamond I
    25-Diamond I
    March 25, 2024

    We sure need someone with expertise in Mechanical Engineering to join this thread. I can help with the Math  and the usage of Mathcad/Prime but nothing more..

    V
    vnamboodheriCommunity Manager
    Community Manager
    April 1, 2024

    Hello @AD_10780197, 

     

    It looks like you have some responses from some community members. If any of these replies helped you solve your question please mark the appropriate reply as the Accepted Solution. 

    Of course, if you have more to share on your issue, please let the Community know so other community members can continue to help you.

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