# Novel Numerical Analysis of a Self-Circulating Bearing
## 1 Introduction  
With the development of technology in hard-to-access locations such as wind turbines, the development of a self-sufficient lubrication system is more relevant than ever. The bearing discussed here is a self-circulating bearing that would allow the initial charge of fluid to the system to lubricate the bearing throughout its life without the need for an external pumping system. The technology for this self-contained, independent fluid system comprises a fluid journal bearing with a porous bushing surrounded by a fluid reservoir, where the pressure differences in the passive reservoir circulate fluid into and out of the bearing clearance [1]. As in typical fluid journal bearings, there is a shaft surrounded by a fluid film. The fluid film has a convergent section, where the fluid pressure increases until the position of minimum clearance (section 1 in Figure 1). Continuing counterclockwise around the bearing, the divergent portion of the bearing continues until the position of maximum clearance in the bearing with decreasing fluid film pressure (section 2 of Figure 1). The fluid film is surrounded by a porous bushing, as opposed to a solid bushing in a standard fluid journal bearing. Surrounding the porous bushing is a passive reservoir of fluid that is initially charged to a specified pressure. The passive reservoir is bounded by a solid casing to keep the fluid contained. The numerical model presented here is the first step towards having a custom numerical model of a self-circulating bearing that will allow for the study of the bearing's characteristics and limitations. Numerical modeling would enable designers to design the bearing more efficiently and to understand the factors that affect the bearing's performance. Porous journal bearing modeling is a mature field, with the current investigations focused on improving numerical models alongside explorations into enhancing bearing performance. As detailed below, researchers have relied upon simplifications to solve the complexities of porous journal bearing modeling. The numerical approach presented herein is a novel closed-form solution that improves computational speed and effort, offering the opportunity to predict three-dimensional behaviors within the porous bushing. This information will improve the predictions on the bearing stability during operation. While the technology discussed here differs from a porous journal bearing, there are shared characteristics; therefore, a brief overview of the current porous bearing technology is warranted. The initial porous journal bearing numerical models started with limitations for either short or long journal bearings [2; 3; 4; 5; 6]. Once finite bearings became standard, the boundary condition between the fluid film and porous bushing became a point of interest [6; 7; 8; 9; 10]. The three-dimensional representation of the porous bushing was the next phase of improvement in the late 1990s, which utilized various boundary conditions at the external ends of the bushing to simplify the problem for a numerical solution [3; 11; 12]. More recently, investigators have focused on incorporating nanoparticles within lubricants to increase viscosity and thus bearing load capacity [13; 14]. Textured porous bearings have also been an area of focus for reducing friction and enhancing performance [15; 16; 17]. [PERSON] et al. were the first to attempt to model the fluid reservoir surrounding a porous slider bearing [18]. [PERSON] et al. continued modeling the bearing, expanding it to a 3D cylindrical geometry in commercial software, which focused on reservoir depths and their effect on the self-circulating system [19]. The different physics between a slider and journal bearing prohibited this work from being built upon in the current paper, as was warned by the authors [18]. Another adjacent technology that should be discussed is that of porous air bearings.