## 5 Calculations in a Universal CFD Program
### Optimization of the Maximum Load Capacity of the Bearing  
In the first step of the conducted CFD analysis, the pressure distribution and reaction forces of the lubrication film in the X and Y directions were determined for the selected initial journal position. The relative eccentricity (\(\epsilon\)) and the angular position of the journal center (Angle) were used as input parameters when creating the response surfaces. A range of variation of \(0.0\leq\epsilon\leq 0.6\) was specified for the relative eccentricity, and \(268\leq\text{Angle}\leq 365\) for the angular position of the journal center. Two response surfaces were created: the reaction force of the lubrication film in the vertical Y direction, and the reaction force in the horizontal X direction. The expected values of the objective function were taken as follows: the reaction force in the vertical direction Y was 18 N, and the reaction force in the horizontal direction X was 0 N. The points from which the response surfaces were created were selected using the optimal space filling (OSF) algorithm. Optimal space filling is a method used in ANSYS that is part of project optimization techniques (design of experiments, DoE) and is used to generate plans for numerical experiments. Its main objective is to efficiently sample the design space while minimizing the number of simulations required, thus optimizing the design process. The OSF method is particularly useful when the problem under investigation involves numerous input variables and requires a substantial amount of time  
Figure 5: Discretized lubrication space domain of a gas bearing. Figure 6: Boundary conditions of the flow model for the dynamic bearing with a marked local coordinate system. to analyze. At selected points, pressure values and the reaction forces of the lubricating film in the X and Y directions were calculated using CFD. The nonparametric regression method was used to create the response surfaces. Optimization, i.e., the selection of the point where the reaction forces most accurately matched the requirements, was carried out using the multiobjective genetic algorithm (MOGA) method. This method is used as a multicriteria optimization technique in the Ansys DesignXplorer module. Genetic algorithms are metaheuristic optimization methods inspired by biological evolutionary processes such as natural selection, crossover, and mutation. In multicriteria optimization, the aim is to find a solution that simultaneously satisfies multiple criteria, often in conflict with each other. In Ansys, the MOGA method is used for project space exploration, sensitivity analysis, parametric optimization, and evaluation of different project scenarios. In multicriteria optimization, instead of a single objective function, there are several objective functions that reflect different aspects of the design problem. Numerical algorithms implemented in the ANSYS Workbench environment were used to generate reaction force maps for the gaseous lubricating film shown in Figure 7. The maps created allowed the static equilibrium point of the journal (C) to be determined, where the reaction force in the Y direction was 18.269 N and the force in the X direction was 0.129 N. The position of point C is defined by the following coordinates: eccentricity (\(\epsilon\) = 0.166) and angle (Angle = 339.18\({}^{\circ}\)). On the load capacity maps, point C is marked in black. For selected values of relative eccentricity (0.05, 0.10, 0.15,..., 0.60) and selected angles (270\({}^{\circ}\), 280\({}^{\circ}\), 290\({}^{\circ}\),..., 360\({}^{\circ}\)), the following conclusions can be drawn when analyzing the changes in the reaction forces of the lubricating film depending on the position of the journal center in the lubrication gap:  
* The reaction force in the Y direction (Figure 8a,b) increased with increasing eccentricity. The highest value of the reaction force in the Y direction was approximately 95 N and occurred at a relative eccentricity of 0.6 and an angle of 310\({}^{\circ}\).