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

Abstract

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.

Experimental and parametric studies of 0.85-in. hard disk drives spindle motor vibration

“…Such method can also be generalpurpose for arbitrary rotor geometry (Tseng et al 2005) or special-purpose for disk drive applications (Tseng et al 2003;Hasegawa et al 2003;Eguchi and Nakamiya 2006;Eguchi 2007). For example, an in-house spindle model developed at the University of Washington (Tseng et al 2003) is a special-purpose model focusing on disk drive applications.…”

Prediction of position error signal of a hard disk drive undergoing a long seek

“…These available models all assume a stationary housing, a rotating spindle motor carrying multiple disks mounted on the housing, and a stationary head stack assembly (HSA) attached to the housing via pivot bearings (Eguchi and Nakamiya 2006). Since HSA is assumed stationary, Eguchi et al's model can successfully predict PES of HDD during track following.…”

Effects of stray magnetic forces on position error signals during a long seeking-and-settling process

“…The basic configuration is similar to that of Eguchi and Nakamiya (2006) except that the HSA is subjected to an arbitrary seek profile that is assumed known a priori (e.g., specified by users). With this powerful tool, we can systematically analyze how various sources (e.g., voice coil motors) affect PES after a seeking-and-settling process, which remains open thus far in the literature.…”

“…For example (Eguchi and Nakamiya (2006), predict PES using a component-mode synthesis approach. Their model assumes a stationary housing, a rotating spindle motor carrying multiple disks mounted on the housing, and a stationary head-stack assembly (HSA) attached to the housing via pivot bearings.…”