Multi-Objective Optimization of Grooved Gas Journal Bearings for Robustness in Manufacturing Tolerances

A tolerancing method highlighting trade-offs against key design variables of mechanical systems is proposed and applied to herringbone-grooved gas journal bearings. Gas bearings typically suffer from a subsynchronous instability, demanding a very tight tolerance on the bearing clearance and groove depth. Classical optimization techniques look for the most stable design, which does not necessarily lead to most robust design against manufacturing deviations. The proposed method uses a normalized multidimensional lookup table of stability score (critical mass), covering a large design space of gas bearings. It then dimensionalizes the table for a specific rotor–bearing system, highlighting regions of the hyperspace where the system is stable. The hyperspace is sliced into 2D maps and a Monte Carlo method creates windows within the stable domain along the two most critical design variables regarding manufacturing: the bearing clearance and the groove depth. Width and length of the windows represent the manufacturing tolerance allowed for the two parameters to remain stable. A Pareto front of optimum windows in the entire hyperspace is then compiled. It displays the trade-off between the tolerance against deviation in clearance and groove depth, allowing the designer to select a nominal geometry tailored to the available manufacturing methods. A test rotor is analyzed with this method and the effects of pressure, speed, viscosity, radius, mass, and centrifugal growth on manufacturing tolerances are investigated, highlighting that the radius and viscosity have the greatest impact on the robustness.