Focusing on the nonlinearly changed dynamic stiffness of bearings with working speed

a numerical approach is presented to calculate the dynamic stiffness of a single bearing and a bearing group based on the ball bearing quasi-static model

the dynamic equation is established according to the finite element model of the rotor-ball bearing system

the eigenvalues then are obtained by numerical iteration and the critical speed is sought out. Due to the influence of speed on dynamic stiffness of bearings

the finite element model ought to be updated according to the calculated dynamic stiffness by last iteration. Combining the optimization toolbox of Matlab

the inner diameter of rotor and the bearing span are optimized by simplex method. The analysis results show that the stiffness of spindle bearings is obviously influenced by the working speed and inner ring centrifugation

which should be taken into consideration during the dynamic analysis of a high-speed rotor-ball bearing system

and the first critical speed of the rotor-ball bearing system increases by 7.65% after optimization.