Oil film stiffness and damping coefficients

[mcatltu]

Hello,

I have a question about calculating oil film stiffness and damping coefficients. From literature, it says that

Kxx = dFx/dx
Kxy = dFx/dy
Kyx = dFy/dx
Kyy = dFy/dy
Cxx = dFx/dxdot
Cxy = dFx/dydot
Cyx = dFy/dxdot
Cyy = dFy/dydot

My question is that if you have a limit cycle (journal closed orbit), how can you find bearing coefficients from the orbit?

My external load applied on journal is the unbalance (omega is equal to the rotational speed of journal)

m*xdotdot + Fx = m*a*omega^2*cos(omega*t)
m*ydotdot + Fy = m*a*omega^2*sin(omega*t)+W

Where "Fx,Fy" are nonlinear forces, "W" is the gravity load, "t" is time, "m" is rotor mass, "a" is the distance from centre of rotor gravity to the centre of rotor geometry.

Thank you for your help.

 

[electricpete]

Great question.

As you know there are a lot of specialized programs that develop those coefficients based on study of the geometry, loading etc.

I can't recall ever hearing anyone mention estimating them from the filtered orbit, but it seems like a worthy goal.

As a starting point it seems logical to try to work with a matrix model.
M*q'' + C*q' + K*q = Q
where q are generalized coordinates and Q are generlized forces. There is a lot of literature about modeling a machine in this form.

For a forced response, we don't need full modal analysis, just assume Q= Q0*exp(i*w*t) and the equation becomes
q*(-M*w^2 + i*C*w + K) = Q0

You know some or all of q depending on your model. You know Q0 from your assumption of known unbalance force and weights acting on the system. You know M. You may know parts of K such as those associated with shaft. There are unknown parts of C and K that you want to solve. Hopefully there will be enough equations to solve the unknowns if things were set up well.

That is just some rambling thoughts fwiw. A long way from solving anything.

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[unclesyd]

Here is a Master's Thesis by Thomas Wising that maybe of assistance in your quest.
This is quite a long document.

http://etd.ohiolink.edu/send-pdf.cgi/Wirsing Thomas.pdf?acc_num=csu1210683430

 

[mcatltu]

Thank you all for your reply.

electricpete, I am still not sure what you mean but thanks again.

unclesyd, I'll look into the thesis. Thank you very much.