Frequency analysis of disturbance torque exerted on a carriage arm in hard disk drives using Hilbert-Huang Transform

Currently, hard disk drives (HDDs) are widely used as external storage devices. In HDDs, flow induced vibrations (FIVs), i.e., the vibrations of carriage arms and disks due to the internal flow of HDDs, are serious contributors to head positioning errors. To develop higher capacity HDDs, reducing head positioning errors is inevitable. Many experimental and analytical studies have been conducted thus far to reveal the internal flow in HDDs and to understand the mechanisms of the disturbance torque exerted on head-stack assemblies for mitigating FIVs. Most studies have exclusively used Fourier spectral analysis for frequency domain analysis (e.g., [1]–[3]). The Fourier spectral analysis, however, must be used for signals under restricted conditions: the system must be linear, and the signal must be stationary and periodic. The internal flow of an HDD is an extremely complex phenomenon, and it is governed by non-linear Navier- Stokes equations. Therefore, the results of the Fourier spectral analysis are not always adequate. Further, if both fine frequency-resolution and high frequency spectra are required for Fourier spectral analysis, the time series data must have a long time-span and a fine time-step. Because it takes a significant amount of time to conduct a computational fluid analysis with such requirements, the results of the Fourier spectrum analysis tend to have a coarse frequency-resolution. The Hilbert-Huang transform (HHT) proposed by Huang et al. is a useful method for analyzing a nonlinear and non-stationary signal, and it has been applied to seismic signal analysis [4]. HHT consists of two parts: ensemble empirical mode decomposition (EEMD) and Hilbert transform (HT). EEMD is a way to decompose time series data into intrinsic mode functions (IMF) considering the envelope of the waveform. After EEMD is conducted, HT is executed, and the analytic signal is generated afterward. Then, the instantaneous frequency and amplitude are calculated from the analytic signal as time series data; therefore, it is possible to analyze the nonlinear and non-stationary signal. In this study, we applied the HHT to the time series of the torque exerted on the carriage arm, which is calculated using finite element analysis. Then, a frequency analysis using FFT and HHT was conducted, and their results were compared. 2. Computational fluid dynamics analysis of HDD A finite element (FE) model for fluid dynamics analysis was produced by referring to a 3.5-in HDD. The computational region for air flow was the inner space of the HDD, which was cut out between two disks. The FE model had a voice-coil-motor (VCM) carriage and a flexible printed circuit. The head suspensions were excluded from the FE model. The disk diameter was 95 mm, and the rotational speed of the disks was 7,200 rpm. The VCM surface was divided into five areas, and the disturbance torque exerted on each area was calculated. ANSYS CFX, a code for fluid analysis, was used for air-flow simulation. Large eddy simulation (LES) was employed as the turbulence model. The time step was $2.0 \times 10 ^{-5}\mathrm {s}$, and the number of time steps was 15,000. Thus, the time span of the simulation was 0.3 ms, and the last 5,000 time-series data were used for frequency analysis. At first, contour-plot animations of the flow velocity and vorticity were made and visually observed. When the carriage arm is at the position where the head is tracking the outermost track, several periodic flow patterns are observed: vortex shedding at the arm-tip at approximately 500 Hz, fluctuation of strong vorticities inside the arm hole at approximately 1000 Hz, and vorticities between the disk and arm and the outside of the disk at 700 to 1000 Hz. Next, a Fourier analysis was conducted using the same simulation results. Although the time series of the torque exerted on the carriage arm seems to have a regularity or periodicity involving such specific frequencies as seen in the animations, there was no specific peak in the Fourier spectra, as shown in figure 1. At low frequencies less than 1000 Hz, the magnitudes of the Fourier spectra are almost constant, and with increase in frequency, the magnitude of the Fourier spectra decrease. Then, the frequency analysis using HHT was performed. The disturbance-torque time series, which is identical to the data used for FFT analysis, were divided into 11 IMFs by the EEMD process. Each IMF was analyzed using HT. Figure 2 shows the HHT results. Fluctuations in frequency were observed at approximately 500 Hz and 800 Hz. The spectra at these frequencies are caused by flow-fluctuations such as vortices, as observed in the flow-animations. Comparing the HHT with FT spectra, the results confirmed that, in the Fourier spectra, the energy of the non-stationary phenomenon, whose frequency and amplitude are fluctuating at a specific frequency, diffuses over a wide frequency-band, and that forms the broadly expanded spectra, especially at low frequencies. Therefore, it is necessary for more precise head positioning to decrease torque-fluctuations due to non-stationary phenomena, such as a vortex shedding around an arm, which are not always observed in the power spectrum obtained by the FFT analysis.