APVC20 0 9 13 th Asia Pacific Vibration Conference 22-25 November 2009 University of Canterbury , New Zealand 1 Forced Vibration Analysis of the Flexible Spinning Disk-spindle System Represented by Asymmetric Finite Element Equations Kiyong Park, Gunhee Jang* and Chanhee Seo Department of Mechanical Engineering, Hanyang University Seoul, 133-791, Korea *Corresponding Author, Email: ghjang@hanyang.ac.kr Abstract This paper proposes an effective numerical method to determine the forced response of the disk-spindle system represented by asymmetric finite element equations. The asymmetric global finite element matrices are transformed to the modal domain by using the mode vectors from the standard eigenvalue problem. Even though the asymmetric equations of motion in modal domain are coupled, the degrees of freedom in modal domain are much reduced so that they are numerically integrated. Then the results are transformed to determine the forced response of the system. The proposed method is verified by comparing with the response from the other methods. It shows that the proposed method is accurate and computationally effective to determine the forced vibration of a spinning flexible disk-spindle system supported by bearings. Key words: eigen value problem, adjoint eigen value problem, biorthogonality 1. Introduction Rotating machines have been applied to many industries such as turbomachines in large machines and computer hard disk drives (HDD) in small machines. In most cases, their dynamics determine the performance of the whole system. One of the examples is the dynamics of flexible spinning disk-spindle system in a HDD supported by complicated base structure and fluid dynamic bearings (FDBs), because it plays the major role in determining the shock characteristics and the disk memory capacity of a HDD. Fig.1 shows the photograph of the motion between spinning disk and a head due to external shock. The flying height of a head is around 10 nm so that it is very difficult not only to measure the motion of a head with respect to spinning disk by using a high-speed camera but also to predict the motion between spinning disk and a head due to various shocks. Many researchers have developed the simulation model to investigate the free and forced vibration of a HDD. Tseng et al. proposed the analytical model of the HDD spindle system with FDBs by including the flexibility of housing (1) . They extracted several lower natural frequencies and mode shapes of the supporting structure of the HDD spindle system by using the finite element method (FEM). The extracted mode shapes were applied to the HDD spindle system with rotating flexible disks to determine a set of equations of motion by using the Lagrange equation. Recently, Jang et al. proposed a consistent method to predict the natural frequencies and mode shape of a rotating disk-spindle system in a HDD with FDBs considering the flexibility of a complicated supporting structure by using the FEM and substructure synthesis (2), (3), (4) . They derived the finite element equations of each