Assignment 1. Computation of journal bearing#

It is possible to use the Reynolds equation to compute de eccentricity and the angle of a journal bearing with fluid film lubrication, given the load $W$

Consider that the journal is displaced in the $x$ negative direction, so that $h(\theta )=h_0(1+\epsilon \cos (\theta ))$ where $\epsilon =\frac{e}{h_0}$ is the relative eccentricity and $h_0=\frac{1}{2}(D_b-D_a)$ is the average gap thickness. The journal is rotating in the positive direction of $\theta$ (polar coordinates)

1. Calculate the pressure distribution $p(\theta )$ and the value and direction of $\mathbf{W}$, in the approximation $\epsilon \ll 1$.

2. What happens to the journal if $\mathbf{W}$ increase a little bit?

3. Apply the results to this real example, and discuss the value of the maximum load given by the manufactures at this rotational velocity.