Multi-Objective Optimisation of Herringbone Grooved Gas Bearing Supporting a High Speed Rotor, Taking into account Rarefied Gas and Real Gas Effects

Currently the herringbone grooved journal bearing (HGJB) has applications in the domain of small, low power energy related applications, where high rotational speeds are required for reaching reasonable efficiency and where standard oil lubricated bearings are limited or even unable to operate over the life time required. Furthermore the presence of oil requires auxiliary control systems reducing the overall system efficiency and reliability. High-speed rotors running in hermetic units processing refrigerant vapor require the bearings to operate with this same gas at thermodynamic conditions that are potentially very close to the saturation curve. In this region the usually applied perfect gas theory does not yield valid results when applied to the Reynolds-lubrication equation. Furthermore, depending on the processed gas and its thermodynamic condition, the Knudsen number may reach values where it is advisable to take gas rarefaction effects into account. In applications where the rotor is heavily loaded in terms of mass and inertia, the bearing design highly affects the dynamic stability of the rotor. In order to reach good stability margins, the bearing geometry tends towards low clearances leading to higher power losses. It has to be noted that bearing losses not only deteriorate the overall efficiency, but also as the unit size are getting smaller and smaller, cooling becomes an issue. The narrow groove theory (NGT) is modified in order to take into account the rarefied gas as well as the real gas effects depending on the thermodynamic and physical properties of the processed gas and on its thermodynamic state. The bearing module implementing the modified narrow groove theory allows calculating the stiffness and the damping matrices for a given bearing geometry. It is then linked to a rotor dynamic model that enables to calculate the critical speeds and the corresponding dynamic stability for a given rotor supported on herringbone grooved dynamic gas bearings. The latter module is linked to a multi-objective optimizer based on evolutionary algorithms. In this paper the evolutionary optimizer is used for two objectives: maximizing the stability margin and minimizing the bearing power loss. The optimizer yields in a Pareto curve representing a family of optimum solutions. One has the choice between a solution with a high stability margin but with high bearing losses to get dissipated or vice versa. A low power rotor for a refrigerant gas process illustrates the optimizing procedure discussed in this paper.