The fluid pressure in the bearing depends on the thickness of the lubricant, which strongly depends on the motion of the journal in the bearing. The thickness of the fluid film can be obtained by calculating the gap between the journal and bearing surfaces. In the Hydrodynamic Bearing interface, the initial journal surface is considered as the reference surface for the analysis. In the Beam Rotor interface, all the degrees of freedom are defined to have components in the spatial frame. Therefore, the current position of the point on the journal surface corresponding to a point X on the reference surface is given as:

where Xbm, ubm, and θbm are the position, displacement, and rotation of a point on the beam rotor nearest to the point X on the reference surface. The height of the journal surface from the reference surface is the normal component of the relative position of the point on the journal surface relative to the point X on the reference surface, and is given by

Similarly, the current position on a point on the bearing surface corresponding to a point X on the reference surface is

Here, hb1 is the initial height of the bearing with respect to the reference surface and is called initial clearance. However, this point on the bearing surface is not aligned with the original reference normal nref. The position of the point that is aligned with the original reference normal can be obtained approximately by the following:

Then the height of the bearing surface with respect to reference surface along the reference normal nref is given by

Here, the fact that the tangential gradients of X and nref are in the plane of the reference surface and hence are perpendicular to nref has been used.

The spatial component of the velocity of the journal at the point X on the reference surface has a component due to journal rotation and is given by

Similarly, the spatial component of the velocity of the bearing at the point X on the reference surface is given by

Therefore, from the Beam Rotor interface, the variables uj and Ω are supplied to the Hydrodynamic Bearing interface to compute the film thickness and average velocity of the fluid, which are then used for determining the distribution of the fluid pressure in the bearing. The distributed force per unit area fjA on the journal and fbA on the bearing as a function of the point X on the reference surface can be calculated using the pressure distribution in the bearing. This is implemented in the weak form by writing the contribution to the virtual work from these loads. The contribution to the virtual work on the journal due to the force applied by the fluid film is