Finite element modal analysis of a spinning flexible disk-spindle system in a HDD considering the flexibility of complicated supporting structure

The free vibration of a spinning flexible disk-spindle system in a HDD considering the flexibility of complicated supporting structure is analyzed by FEM and substructure synthesis. The spinning flexible disk is described using Kirchhoff plate theory and von Karman non-linear strain, and its rigid body motion is also considered. It is discretized by annular sector element. The rotating spindle which includes the clamp, hub, permanent magnet and yoke, is modeled by Timoshenko beam including the gyroscopic effect. The stationary shaft is also modeled by Timoshenko beam. The flexible supporting structure with a complex shape which includes the stator core, housing and base plate is modeled by using a four-node tetrahedron element with rotational degrees of freedom to satisfy the geometric compatibility at the interface node between the one-dimensional (1-D) beam element and the 3-D solid element. Rigid link constraint is imposed at the interface area between shaft and housing to describe the physical motion at this interface. The global matrix equation obtained by assembling the finite element equations of each substructure is transformed to the state-space matrix-vector equation, and the associated eigenvalue problem is solved by using the restarted Arnoldi iteration method. The validity of this research is verified by comparing the numerical results of the natural frequencies and mode shapes with the experimental ones. This research shows that the flexible supporting structure as well as the rigid link constraint between shaft and housing play an important role in accurately predicting the natural frequencies.