Stability analysis of a whirling disk-spindle system supported by FDBs with rotating grooves

This paper investigates the stability of a whirling disk-spindle system, supported by coupled journal and thrust bearings with rotating grooves. The stiffness and damping coefficients of the FDBs change periodically with the whirling motion of the disk-spindle system, which makes it difficult to define the stability problem in the inertia coordinate. However, with the introduction of the coordinate system which rotates with the disk-spindle system, the stiffness and damping coefficients are constant, which makes it possible to define the stability problem in the rotating coordinate system. The Reynolds equations and the perturbed equations of the coupled bearings were derived with respect to the rotating coordinate and were solved using FEM to calculate the stiffness and damping coefficients. The critical mass of the rotor-bearing system was determined by solving the linear equations of motion. As a result, the stability increases with an increase in the whirl radius and with a decrease in the rotating speed. It also decreases with an increase in the tilting angle under a small whirl radius while it increases with an increase in the tilting angle under a large whirl radius.