An Improved Component-Mode Synthesis Method to Predict Vibration of Rotating Spindles and Its Application to Position Errors of Hard Disk Drives

[+] Author and Article Information
Takehiko Eguchi

 Hitachi, Ltd., Central Research Laboratory, 832-2, Horiguchi, Hitachinaka, Ibaraki, 312-0034 Japantakehiko.eguchi.wm@hitachi.com

Teruhiro Nakamiya

 Hitachi, Ltd., Central Research Laboratory, 1, Kirihara, Fujisawa, Kanagawa, 252-8588 Japanteruhiro.nakamiya.pk@hitachi.com

J. Vib. Acoust 128(5), 568-575 (Feb 25, 2005) (8 pages) doi:10.1115/1.2349539 History: Received November 01, 2004; Revised February 25, 2005

This paper describes an accurate mathematical model that can predict forced vibration of a rotating spindle system with a flexible stationary part. In particular, we demonstrate this new formulation on a hard disk drive (HDD) spindle to predict its position error signal (PES). This improved method is a nontrivial extension of the mathematical model by Shen and his fellow researchers, as the improved method allows the flexible stationary part to comprise multiple substructures. When applied to HDD vibration, the improved model consists not only a rotating hub, multiple rotating disks, a stationary base, and bearings (as in Shen’s model) but also an independent flexible carriage part. Moreover, the carriage part is connected to the stationary base with pivot bearings and to the disks with air bearings at the head sliders mounted on the far end of the carriage. To build the improved mathematical model, we use finite element analysis (FEA) to model the complicated geometry of the rotating hub, the stationary base and the flexible carriage. With the mode shapes, natural frequencies, and modal damping ratios obtained from FEA, we use the principle of virtual work and component-mode synthesis to derive an equation of motion. Naturally, the stiffness and damping matrices of the equation of motion depend on properties of the pivot and air bearings as well as the natural frequencies and mode shapes of the flexible base, the flexible carriage, the hub, and the disks. Under this formulation, we define PES resulting from spindle vibration as the product of the relative displacement between the head element and the disk surface and the error rejection transfer function. To verify the improved model, we measured the frequency response functions using impact hammer tests for a real HDD that had a fluid-dynamic bearing spindle, two disks, and three heads. The experimental results agreed very well with the simulation results not only in natural frequencies but also in gain and phase.

Copyright © 2006 by American Society of Mechanical Engineers
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Figure 1

Carriage coordinate system

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Figure 2

Locations of pivot bearings and heads

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Figure 3

Head element location on disk

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Figure 4

Experimental setup

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Figure 5

FE model of stationary base

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Figure 6

FE model of rotating part

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Figure 7

FE model of carriage part

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Figure 8

FRF of head 0, point A (horizontal)

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Figure 9

FRF of head 1, point A (horizontal)

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Figure 10

FRF of head #2, point A (horizontal)

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Figure 11

FRF of head 0, point B (vertical)

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Figure 12

FRF of head #1, point B (vertical)

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Figure 13

FRF of head 2, point B (vertical)



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