Analytical Evaluation of the Static and Dynamic Characteristics of Three-Lobe Journal Bearings With Finite Length

The three-lobe bearings widely used in rotating machinery follow the design data evaluated using numerical methods for the solution of the Reynolds equation. This paper defines exact and approximate analytical solutions of the Reynolds equation for the case of three-lobe bearings with finite length. Dynamic characteristics are provided analytically with closed-form expressions for laminar regimes of operation, using an approximate analytical solution that proves to be reliable and of low cost of evaluation time. The results for eccentricity ratio, equilibrium locus, stiffness and damping coefficients are presented for a range of Sommerfeld number and different cases of load orientation and compared with theoretical and experimental data from the literature.

Analysis of ideal MHD equilibrium and axisymmetric stability for finite aspect ratio tokamaks with elliptic cross-section and flat current profile

To calculate the equilibrium and stability of finite aspect ratio tokamaks, even for circular and elliptical plasma cross-sections, intricate numerical methods must usually be employed, which require a fast and large computer. So far, these calculations have been carried out analytically only for infinite aspect ratio. In fact certain analytical equilibrium solutions at finite aspect ratio are known, but these do not include such important cases as elliptical cross-sections. In this paper, finite aspect ratio equilibrium solutions are derived for circular, prolate and oblate elliptical cross-sections and for a flat current profile. In addition, the problem of axisymmetric stability is studied for prolate elliptical cross-sections, the approach being almost entirely analytical.