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.
I improved the component mode synthesis (CMS) model for free and forced-vibration analyses of hard disk drives using attachment modes. The convergence and the accuracy of the proposed CMS model was improved substantially by applying an attachment mode to a FDB shaft and a pivot shaft in the stationary part model. Different formulations were used for the FDBs and the pivot bearings because of their different damping properties. In the proposed formulation, additional general coordinates corresponding to the attachment modes of the FDB shaft are introduced into the system coordinates; on the other hand, the attachment modes of the pivot shaft moderate the stiffness and damping properties of the pivot bearings. To check the improvement of the convergence and the accuracy, I performed the free and forced-vibration analyses using the previous and proposed CMS models and a full finite element (FE) model. The convergence of the natural frequencies and the frequency response function (FRF) of the disk/spindle system were extremely improved. Moreover, the FRF of the head actuator better matched the full FE model than the previous CMS model when the same number of component modes are used.
In this paper, contributions of airborne and structure-borne vibrations to head positioning error of a HDD at high frequencies up to 10 kHz were investigated. The L8 array test was conducted with four two-level factors about vibration isolation between fans and HDDs: A) Removing bracket, B) Attaching foam on backplane, C) Filling foam in the next column, and D) Filling foam in the upper and lower slots. The test results showed there were less interaction between airborne and structure-borne vibration. Then, we set a model of fan vibration transmission and the model parameters were determined so that errors between the estimated and measured values were minimized. As the results, it was confirmed that about 80% of the power of PES was caused by the airborne vibration at the normal case.
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