In the working process of the gas bearings, the unbalanced force of the rotor will increase nonlinearly with the increase in the rotating speed, resulting in an increase in the rotor’s vibration amplitude. On the other hand, with the increase in the rotating speed, the hydrodynamic effect will increase, and the nonlinear increase in the gas film force and stiffness will inhibit the increase in the vibration amplitude. In order to deeply study the influence of the unbalanced force and nonlinear gas film force on the vibration amplitude of the ultra-precision aerostatic motorized spindle, taking the double slit throttling gas bearing as an example, according to the equilibrium equation of the rotor under the combined action of gravity, the gas film force, and the unbalanced force, a calculation program based on the finite difference method for solving the rotor’s equilibrium position is completed. The calculation results show that: the hydrodynamic effect can significantly increase the bearing capacity and cause the change of the static equilibrium position of the rotor, but the offset amplitude of the static equilibrium position of the rotor gradually slows down with the increase in the rotating speed. The hydrodynamic effect improves the stiffness near the static equilibrium position of the rotor, making the rotor vibration track tend to be more “round”. Although the unbalanced force of the rotor increases nonlinearly as the rotating speed increases, the maximum offset between the dynamic equilibrium position and the static equilibrium position of the rotor under the action of the rotating unbalanced force is approximately linear with the rotating speed. Compared with the air supply pressure, the rotor unbalance and rotating speed are the main factors affecting the rotor dynamic equilibrium position offset. This study has a reference role in the in-depth study of the influence of rotating speed and rotor unbalance on the rotor static equilibrium position and dynamic equilibrium position offset, as well as in the design of gas bearings and the prediction of rotor vibration amplitude.

In the working process of ultra-precision aerostatic motorized spindles, the journal and the rotor must have a certain eccentricity to have a certain bearing capacity and stiffness, which will induce the unbalanced magnetic pull (UMP). The intercoupling of the UMP and the gas film force will affect the motion state of the rotor and the accuracy of spindles. In order to deeply study the influence of the UMP caused by the rotor eccentricity on the equilibrium position of aerostatic spindles, a physical model of an aerostatic spindle based on slit throttling gas bearing is established and the coupling effect between the rotor and the motor rotor is studied and analyzed as a whole. The equilibrium position of the rotor under the combined action of gravity, the gas film force and the UMP is deduced, and a gas–magnetic field coupling calculation program based on the finite difference method is proposed. The calculation results show that with the increase in rotational speed, the equilibrium position of the rotor will move to the center of the journal in the micron scale, and the moving amplitude will gradually slow down. The UMP caused by rotor eccentricity can offset the rotor equilibrium position in nanometer scale, and the influence degree decreases sharply as the rotor moves to the journal center. With the increase in rotational speed, the direct stiffness and the cross stiffness will increase, and the amplitude of the cross stiffness is greater than the direct stiffness. This study is of great significance for further studying the influence of the rotor eccentricity on the equilibrium position and the accuracy of the rotor.

With the purpose of studying performance of the vortex pump for transporting solid-liquid two-phase with light particles whose relative density smaller than 1, the numerical simulation of solid-liquid two phase flowing in the whole channel of a vortex pump with the particle diameter being 0.5 mm, 1 mm, 2 mm, 3 mm and the initial solid phase volume concentrations being 10%, 20% and 30% are respectively carried out by using the commercial software ANSYS Fluent by adopting RNG κ-ɛ turbulent flow model, Eulerian-Eulerian multi-phase flow model and SIMPLEC algorithm. The simulation results show that in the impeller region, the particles concentrate on the non-working surface of the blades, and the particles are rare on the working surface of the blades. As the initial solid phase volume concentration and particle diameter increase, the pump delivery head of vortex pump decrease. The pump delivery head of vortex pump with different initial solid phase concentrations and different particle diameters are predicted and compared with those obtained by an empirical formula, and they shows good agreement.

To accurately grasp the vibration stability of spiral groove dry gas seals (S-DGSs), the angular vibration stability thresholds of S-DGSs, which vary with the operating and structural parameters, were investigated by using carbon dioxide and hydrogen real gases as lubricants. The numerical results show that the vibration stability of the S-DGS in angular direction is independent of spring stiffness. Under the same conditions, the real gas effect enhances critical transverse moment of inertia and frequency ratio in carbon dioxide case, whereas it reduces both stability thresholds in hydrogen case. A spiral groove number N_g, land-to-groove ratio κ, and spiral angle δ that are too large or too small all contribute to an increased risk of S-DGS angular instability. By considering critical frequency ratio as the target, the optimal range of spiral groove structure parameters have been obtained by using a single factor analysis method.