Gas-bearing support stiffness evolution and nonlinear coupling effect on vibration characteristics of gear-rotor systems

Gas-bearing-supported gear–rotor systems are widely used in precision measurement equipment, where vibration performance is critically influenced by the bearing support characteristics. In this study, a nonlinear dynamic model of a gear–rotor system supported by gas bearings is established, in which the bending–torsional coupling effect and the bearing support stiffness are explicitly taken into account. Based on isothermal compressible gas lubrication theory, the Reynolds equation is solved using a finite difference scheme to obtain the gas film pressure distribution of the gas bearing. The influences of rotational speed from 500 to 1500 r·min⁻¹ and gas film clearance from 7 to 11 μm on the gas film pressure characteristics and the equivalent support stiffness are investigated. The equivalent stiffness is subsequently incorporated into the dynamic equations of the gear–rotor system to analyze its vibration responses. The results show that increasing rotational speed significantly enhances the gas film pressure and enlarges the high-pressure region along the circumferential direction due to strengthened hydrodynamic effects. In contrast, an increase in gas film clearance leads to a pronounced reduction in pressure magnitude and load-carrying capacity, resulting in a nonlinear decrease in the equivalent support stiffness. Dynamic analysis indicates that rotational speed plays a dominant role in the vibration behavior of the gas-bearing-supported gear–rotor system, while variations in gas bearing stiffness substantially affect the vibration response characteristics.