Dynamic Coefficients
The linearized stiffness coefficients k and damping coefficients c can be obtained in the global coordinate system as:
and
where fj, uj and vj are the distributed fluid force on the journal, the journal displacements, and the journal velocity, respectively. The fluid force is a function of film height h, the journal velocity, the fluid pressure p and the pressure gradients. Hence, the two integrands can be expressed as:
and
where the displacement and velocity perturbation pressure, pu and pv, are the derivatives of the pressure with respect to the journal displacement and velocity respectively.
The above stiffness and damping coefficients are determined with respect to displacement and velocity perturbations in the global directions. These are then transformed to the local directions using the following transformation matrix:
Here ei, i ∈ {1,2,3} define the basis for the local coordinate system. The stiffness and damping coefficients defined the local coordinate system are given by:
The physics interface defines built-in variables for the stiffness and damping coefficient in the local coordinate system. As an example, the built-in variable <phys>.<feat>.k11 is the local stiffness coefficient kl,11 and <phys>.<feat>.c23 is the local damping coefficient cl,23. Note that variables are also available for the dynamic coefficients in the global coordinate system. For example, the variables <phys>.<feat>.kgxy and <phys>.<feat>.cgxy are the stiffness and damping coefficients kg,xy and cg,xy, respectively.