The centrifuge rotor system filled with partial liquid has an unstable region caused by fluid-solid coupling excitation above the critical speed, which directly threatens the safe and stable operation of the liquid-filled super gravity centrifuge rotor and severely limits the development of the centrifuge rotor to high-speed and large-scale. This research attempts to understand the mechanics of fluid-solid interaction and vibration reduction measures in the rotor of a liquid-filled centrifuge. The dynamic stability of the liquid-filled centrifuge rotor is calculated using a method that takes into account the dynamic equation of the rotor, as well as the hydrodynamic equation, continuity equations and viscous liquid boundary conditions. First, based on the perturbation form of the Navier-Stokes equation, the above unsteady hydrodynamic equation is solved by the finite difference numerical method, and the fluid pressure and fluid shear force at the wall surface are obtained and numerically integrated. Then, the fluid equivalent principal stiffness coefficient and cross stiffness coefficient are coupled with the rotor dynamic equation, and the damping exponents and whirl frequency of the dynamic equation are solved by the state space method. By comparing the waterfall plots of the changes in damping exponents and cross stiffness in the variable speed range of a liquid-filled rotor system, the calculation results show that the stability of the liquid-filled rotor is the result of the damping, stiffness, liquid filling ratio and fluid viscosity of the rotor system. Increasing the external damping of the rotor system and reducing the cross stiffness of the system has obvious effects on suppressing the instability of the rotor. This study avoids the phenomenon of extreme gradients caused by analytical solutions by solving the Navier-Stokes equations numerically rather than analytically. Additionally, state-space downscaling is used to solve the eigenvalues, greatly increasing computational efficiency and saving time a crucial factor when performing multi-operating condition calculations.