Transactions of the Korean Society for Noise and Vibration Engineering (한국소음진동공학회논문집)

The Korean Society for Noise and Vibration Engineering (한국소음진동공학회)
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Finite Element Modal Analysis of a Spinning Flexible Disk-spindle System Supported by Hydro Dynamic Bearings and Flexible Supporting Structures in a HDD

유연한 지지 구조와 유체 동압 베어링으로 지지되는 HDD의 회전 유연 디스크-스핀들 시스템에 대한 유한 요소 고유 진동 해석

  • Published : 2005.03.01
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Abstract

The free vibration of a spinning flexible disk-spindle system supported by hydro dynamic bearings (HDB) in an HDD is analyzed by FEM. 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 flexible supporting structure with a complex shape which includes stator core, housing, base plate, sleeve and thrust pad is modeled by using a 4-node tetrahedron element with rotational degrees of freedom to satisfy the geometric compatibility. The dynamic coefficients of HDB are calculated from the HDB analysis program, which solves the perturbed Reynolds equation using FEM. Introducing the virtual nodes and the rigid link constraints defined in the center of HDB, beam elements of the shaft are connected to the solid elements of the sleeve and thrust pad through the spring and damper element. 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 eigen value 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 with the experimental ones. Also the effect of supporting structures to the natural modes of the total HDD system is rigorously analyzed.

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References

  1. Zang, Y. and Hatch, M. R., 1996, 'On the Whirl Dynamics of Hydrodynamic Bearing Spindle in Information Storage systems', International Symposium on Information Storage and Processing Systems, Vol. 2, pp. 73-84
  2. Tseng C. W., Shen J. Y. and Shen I.Y., 2003 'Vibration of Rotating-shaft HDD Spindle Motors with Flexible Stationary Parts', IEEE Trans Magn, Vol. 39, pp. 794-799 https://doi.org/10.1109/TMAG.2003.808926
  3. Reddy J. N., 1993, An Introduction to the Finite Element Method, 2nd edn. McGraw-Hill
  4. Jang, G. H. and Kim, Y. J., 1999, 'Calculation of Dynamic Coefficients in a Hydrodynamic Bearing Considering Five Degrees of Freedom for a General Rotor-bearing System', Journal of Tribology, ASME, Vol. 121, pp. 499-505 https://doi.org/10.1115/1.2834095
  5. Pawlak, T. P., Yunus, S. M., and Cook, R. D., 1991, 'Solid Elements with Rotational Degrees of Freedom: Part II-Tetrahedron Elements', International Journal for Numerical Methods in Engineering, Vol. 31, pp. 593-610 https://doi.org/10.1002/nme.1620310311
  6. Cook, R. D., Malkus, D. S., and Plesha, M. E., 1989, Concepts and Applications of Finite Element Analysis, 3rd edn. John Wiley & Sons
  7. Lehoucq, R. B. and Sorensen, D. C., 1996, 'Deflation Techniques for an Implicitly Restarted Arnoldi Iteration', J. Matrix anal. Appl. SIAM, pp. 789-821
  8. Saad, Y., 1995, Iterative Methods for Sparse Linear Systems, PWS Publishing Company, Boston
  9. Hinton, E. and Owen, D. R. J., 1977, Finite Element Programming, Academic Press, London