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. Therefore, the height of the journal surface from the reference surface deformation can be determined by considering a material point Xr,j on the journal surface in the direction er,r(x1,Θ) from the center of the bearing in the corotating frame:

In general, XC is a function of the axial coordinate x1 and RJ can be a function of both Θ and x1. After deformation, the current position of this point in the corotating frame is

Note that the current position is no longer aligned with the radial direction er,r(x1,Θ). The position of the point on the journal surface that is aligned with the radial direction er,r(x1,Θ) can be approximated by

Similarly, the coordinates of the material point Xr,j without the deformation, in the spatial frame are:

Then, the height of the journal surface from the reference surface in the radial direction er(x1,Θ) in the spatial frame, corresponding to the radial direction er,r(x1,Θ) in a corotating frame, is

If the reference surface is a cylindrical surface, then Rj is independent of both Θ and x1, and er,r is only a function of Θ. Then

Now, to determine the height of the bearing surface from the reference surface, consider a radially aligned material point Xb on the bearing corresponding to the point Xj in the spatial frame. Then

C is the initial clearance between the journal and bearing. After the deformation, the current position of this point in the spatial frame is

Note that the current position is no longer aligned with the radial direction er. The position of the point on the bearing surface that is aligned with the radial direction er can be approximated as

Then, the height of the bearing surface from the reference surface in the radial direction er in the spatial frame is:

For a cylindrical reference surface, Rj is independent of both Θ and x1, and er is only a function of Θ. Then

If a point X on the reference surface corresponds to the point Xj on the journal surface and Xb on the bearing surface, then

The spatial component of the velocity of the journal at the point X on the reference surface 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 Solid Rotor interface, the variables ur,j and Ω are supplied to the Hydrodynamic Bearing interface to compute the film thickness and average velocity of the fluid, which is then used for determining the distribution of the fluid pressure in the bearing. Distributed forces 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 due to the pressure loads. The contribution to the virtual work on the journal due to the force applied by the fluid film is: