Planetary gear forces

[AD_10780197]

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.

[Werner_E]

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

[AD_10780197]

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.

[Werner_E]

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..

[ChrisKaswer]

I can chime-in in the next few days/week when I have time to resurrect my old files - I created a transmission analysis tool that uses the "matrix approach" to solve various arrangements of planetary gear sets connected together. This was way back in the day when we had "MathConnex" - that tool was a fantastic way to visually link different Mathcad files together along with other I/O files like Excel (just like LabView or MATLAB Simulink). I can suggest an approach that should directly address your need, but please sit tight until I can dig it up and make sure it still works in Prime!

Cheers,

Chris

[ChrisKaswer · Accepted solution]

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.

[AD_10780197]

Dear ChrisKaswer,

Thank you for your information. I will study en look at your pdf over in the weekend. Once I have it modified it, I will share it with you. For now, thank you and have a great day.

Best regards, 

[vnamboodheri]

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