Experimental dynamic characterizations and modelling of disk vibrations for HDDs

Transcription

1 ISA Transactions 47 (2008) Experimental dynamic characterizations and modelling of disk vibrations for HDDs Chee Khiang Pang a,b,, Eng Hong Ong a, Guoxiao Guo a, Hua Qian a a A*STAR Data Storage Institute, Singapore , Republic of Singapore b Department of Electrical and Computer Engineering, National University of Singapore, Singapore , Republic of Singapore Received 11 November 2006; accepted 29 May 2007 Available online 11 September 2007 Abstract Currently, the rotational speed of spindle motors in HDDs (Hard-Disk Drives) are increasing to improve high data throughput and decrease rotational latency for ultra-high data transfer rates. However, the disk platters are excited to vibrate at their natural frequencies due to higher air-flow excitation as well as eccentricities and imbalances in the disk-spindle assembly. These factors contribute directly to TMR (Track Mis- Registration) which limits achievable high recording density essential for future mobile HDDs. In this paper, the natural mode shapes of an annular disk mounted on a spindle motor used in current HDDs are characterized using FEM (Finite Element Methods) analysis and verified with SLDV (Scanning Laser Doppler Vibrometer) measurements. The identified vibration frequencies and amplitudes of the disk ODS (Operating Deflection Shapes) at corresponding disk mode shapes are modelled as repeatable disturbance components for servo compensation in HDDs. Our experimental results show that the SLDV measurements are accurate in capturing static disk mode shapes without the need for intricate air-flow aero-elastic models, and the proposed disk ODS vibration model correlates well with experimental measurements from a LDV. c 2007 Published by Elsevier Ltd on behalf of ISA. Keywords: Hard-disk drives; Disk mode shapes; SLDV 1. Introduction With the introduction of perpendicular recording technologies, magnetic data storage capacities in HDDs are growing at an amazing rate of more than 100% every year. As such, a high disk-spindle spin speed is essential to facilitate ultra-high data transfer rate for faster user data access in magnetic recordingbased mobile storage devices. However as the rotational speed of spindle motor increases, air-flow induced mechanical vibrations and air turbulence worsen, degrading R/W (Read/Write) head positioning accuracy which limits the achievable projected data storage density. The disk fluttering phenomenon becomes more serious and dominates the contribution to TMR. Corresponding address: A*STAR Data Storage Institute, No. 5, Engineering Drive 1, Singapore , Republic of Singapore. Tel.: ; fax: addresses: Pang Chee Khiang@dsi.a-star.edu.sg, ckpang@nus.edu.sg (C.K. Pang), Ong Eng Hong@dsi.a-star.edu.sg (E.H. Ong), Guo Guoxiao@dsi.a-star.edu.sg (G. Guo), Qian Hua@dsi.a-star.edu.sg (H. Qian). Disturbances into the HDD servo system arising from disk platter resonances are not new to the HDD research community. In previous works, their effects are usually neglected due to either lower spindle rotational speeds or perceived nonrepeatable nature of disk axial vibration, hence rendering them as NRRO (Non-Repeatable Run-Out) which includes broad band white noise and some narrow band coloured noise with random phase. Little is hence known about the frequency spectra of the dynamic mode shapes of the disk under static and operating conditions, or the disk platter resonances impact on the sliders (carrying the R/W heads) off-track in the in-plane direction. In recent years, the effect of disk fluttering on TMR and the effect of different substrates on disk vibrations are studied. McAllister proposed to approximate the PES (Position Error Signal) contributed by disk vibration via bandpassing overall PES in a frequency range where large disk flutter modes appear in the PES frequency spectra, thereby reducing disk platter resonances as a repeatable component in [1,2]. Imai et al. proposed a method to reduce disk vibration by altering the /$ - see front matter c 2007 Published by Elsevier Ltd on behalf of ISA. doi: /j.isatra

2 86 C.K. Pang et al. / ISA Transactions 47 (2008) air-flow path inside an enclosed HDD in [3]. More recently, Guo et al. conducted experiments to characterize disk platter resonances and their impact on head/slider off-track, and investigated disk flutter magnitude with respect to the radius of the disk and modelled the disk flutter vibration amplitude as a linear function of disk radius in [4]. On theoretical developments, Shen et al. proposed mathematical models to explain and predict natural frequencies of the disk-spindle system in HDDs with Rayleigh dissipation function and Lagrange s equations in [5,6]. Experimental mode shape measurements using a SLDV for flexible structures were also carried out by Stanbridge et al. in [7,8]. The problems and guidelines for using the SLDV for modal analysis are also documented by Martarelli et al. in [9]. In this paper, the first four dominant natural mode shapes of a static annular disk used in current HDDs are first obtained using FEM analysis and verified with SLDV measurements. After decoupling the repeatable and non-repeatable axial vibrations for a disk under nominal operating conditions, a RLS (Recursive Least Squares) algorithm is implemented to identify natural frequencies and vibration amplitudes of forward and backward travelling waves of a rotating disk-spindle system regressed on spindle rotational speed in rpm (revolutions per minute). Using the experimentally identified RRO (Repeatable Run-Out) and disk ODS vibration model, the actual head offtrack displacement is projected in rpm at different locations to create a disturbance simulation model for track-following servo controller design in future HDDs. The rest of the paper is organized as follows. Section 2 introduces the nomenclature of disk mode shapes with FEM analysis for the first four dominant disk mode shapes. Section 3 verifies the simulated disk platter resonances with SLDV measurements. Section 4 analyzes the time domain disk fluttering signal at the OD (Outer Diameter) of a disk in time and frequency domain to reduce the disk ODS vibration to a repeatable component with the regression of disk natural frequencies and vibration amplitudes on spindle rotation speed in rpm for higher disk-spindle system rotational speeds for future HDDs. Section 5 proposes the disk ODS vibration model for HDD track-following servo controller design evaluation. Our conclusion and future works are detailed in Section Mode shape analysis For an general single input LTI (Linear Time-Invariant) flexible mechanical system, the mathematical model with N th DOF (Degree Of Freedom) can be expressed as M z + Cż + Kz = Fu (1) where M, C, and K are the mass, damping, and stiffness matrices of order N N, respectively. z and F are the N 1 displacement state and excitation vectors, respectively, and u is the excitation function to the mechanical system. As such, the mode shapes of the system are given by the orthogonal eigenvectors of the homogeneous solution (i.e. when u = 0) and the corresponding natural frequencies are computed by their eigenvalues. Fig. 1. Nodal circles and diameters (m, n) of a typical annular disk with a central hole. Fig. 2. Simulated (0, 1) mode of constrained 0.8 mm thick 3.5 Al disk with natural frequency at 594 Hz. In a 3.5 HDD employing 0.8 mm thick Aluminium disks in today s lower end desktop HDDs, the disk can be considered as a circular lamina with a central hole categorized into m nodal circles and n nodal diameters designated by the couple (m, n). The relationship between the modal indices m and n of the annular plate is shown in Fig. 1. It should be noted that this nomenclature and the results proposed in the rest of the paper can be applied to higher end desktop or mobile HDDs employing glass disks. This nomenclature will be used to characterize and model the disk vibration phenomena in the rest of the paper. The 3D mode shape in the z-axis can be expressed by the polynomial series V z as V z (x, y) = V mn x m y n m n = V mn sin m ω x t sin n ω y t (2) m n where V mn is the set of polynomial coefficients with ω x and ω y as the vibrational frequencies in rad/s about x- and y-axes, respectively. V z is the z-axial displacement at each (x, y) coordinate (expressed in terms of modulated harmonics of the vibrational frequencies) and forms a mode shape surface when intrapolated (or weaved ) together. For simplicity but without loss of generality, the simulated first four dominant disk mode shapes for a 0.8 mm thick 3.5 Aluminium disk constrained at its ID (Inner Diameter) by the spindle motor in the x y plane namely (0, 1), (0, 2), (0, 3) and (0, 4) modes and their corresponding natural frequencies are shown in Figs. 2 5, respectively. It is worth noting that the simulations are done with the disk in static conditions i.e. when the disk-spindle system is nonrotating.

3 C.K. Pang et al. / ISA Transactions 47 (2008) Fig. 3. Simulated (0, 2) mode of constrained 0.8 mm thick 3.5 Al disk with natural frequency at 719 Hz. Fig. 4. Simulated (0, 3) mode of constrained 0.8 mm thick 3.5 Al disk with natural frequency at 1151 Hz. Fig. 5. Simulated (0, 4) mode of constrained 0.8 mm thick 3.5 Al disk with natural frequency at 1877 Hz. 3. Experimental disk mode shape measurement using SLDV Experimental mode shape characterization allows modal testing and identification of the vibrational properties and behavior of the disk without rigorous theoretical analysis. In this section, the simulated disk mode shapes obtained in the previous section via FEM analysis are compared with experimental results captured from SLDV measurements. In previous experimental works ([1,2,5,6,10] etc.) done on the disks used in HDDs, a point-by-point measurement of the disk at the OD with a LDV or capacitance probe was usually employed and the collected data was then transferred to a modal analysis software package for reconstruction of mode shapes and calculation of the corresponding natural frequencies. For the experiments reported here, the PSV-200 SLDV by Polytec GmbH is used. The SLDV compact vibrometer scanning head is centered over the spindle motor with mounted disks as shown in Fig. 6. The SLDV data management system, software for x y control of the in-built scanners, data processing, and various spectra display are shown in Fig. 7. The schematic diagram of the experimental setup used for measuring natural frequencies and mode shapes of the disk is shown in Fig. 8. With the SLDV, the advantages of non-contact laser vibrometry together with modal reconstruction are incorporated into a single automated turnkey package. The SLDV can capture the mode shapes and natural frequencies of a stationary or spinning disk, scanning the entire disk and non-obtrusively measuring the out-of-plane velocity and displacement of vibrations of the disk in both static and rotating conditions [11]. Also, the system allows quick data logging and gathers complete calibrated data from an entire disk surface using realtime data validation algorithms to ensure that the frequency measurements acquired at every scanned point are with high resolution and SNR (Signal-to-Noise Ratio). The modal Fig. 6. SLDV setup for measuring dynamic mode shapes. The SLDV is centered over the spindle motor with constrained 0.8 mm thick 3.5 Al disk pack. Fig. 7. SLDV data management system. Left: Display of mode shapes and scanning results. Top right: displacement measurements. Middle right: velocity measurements. Bottom right: data management system with in-built modal analysis and reconstruction software package. analysis software package in-built in the SLDV allows a fast and accurate visualization of mechanical vibrational characteristics [7,8]. Using the SLDV, the ODS of the spinning disk under operating conditions without any external excitation can also be captured Natural frequency measurement Before measuring the disk mode shapes using the SLDV described in the previous section, the natural frequencies of the constrained annular disk is obtained via an experimental approach. In this section, a single point measurement using the LDV at the OD is used to capture the natural frequencies of the disk. It is worth noting that the SLDV can also be used for this part of the experiment.

4 88 C.K. Pang et al. / ISA Transactions 47 (2008) Fig. 9. Experimental (0, 1) mode of constrained 0.8 mm thick 3.5 Al disk at natural frequency of 603 Hz captured with SLDV. Fig. 8. Schematic diagram of experimental setup for measuring natural frequencies and disk mode shapes using the SLDV, LDV, impact hammer, and DSA. Table 1 Simulation and experimental natural frequencies (Hz) Modes (0, 1) (0, 2) (0, 3) (0, 4) Simulation Experiment Percentage variation (uncertainty) (%) Fig. 10. Experimental (0, 2) mode of constrained 0.8 mm thick 3.5 Al disk at natural frequency of 701 Hz captured with SLDV. For the experiments reported here, an impact hammer excitation is chosen for its speed and accuracy in exciting small homogeneous structures such as the disk platter over the traditional shaker setup, which is commonly employed for larger mechanical structures with lower natural frequencies. The impact hammer is connected to a current amplifier to trigger the LDV and DSA (Dynamic Signal Analyzer) for synchronizing scanning and data logging when the stationary disk is excited at its OD. The natural frequencies of the first four dominant (m, n) mode shapes can then be observed from the FRF (Frequency Response Function) displayed on the DSA. The comparison between the natural frequencies derived from FEM analysis and LDV experimental measurements are shown in Table 1. The simulated natural frequencies of the first four dominant (0, n) mode shapes of the 0.8 mm 3.5 Al disk from FEM analysis tally closely with the measured natural frequencies using the setup shown in Fig. 8 with little uncertainty from the simulation results. The simulated first four dominant (0, n) mode shapes at the corresponding natural frequencies will be verified with SLDV measurements in the next subsection Mode shape measurement In this part of the experiment, the disk modes are excited using an impact hammer when the disk is non-rotating. The mode shapes can then be reconstructed with the modal analysis software package in-built in the SLDV. For mode shape measurement using an SLDV via area scanning, the center frequency of the bandwidth of the area Fig. 11. Experimental (0, 3) mode constrained 0.8 mm thick 3.5 Al disk at natural frequency of 1191 Hz captured with SLDV. scan in the SLDV is set to the experimental natural frequency of the (0, n) mode shape to be measured. Similarly, the impact hammer is connected to a current amplifier to trigger the SLDV for synchronizing scanning and measurement when used to excite the natural frequencies of the stationary disk at its OD as can be seen from Fig. 8. Interested readers are kindly referred to [7] and [8] for more details on calibration and guidelines when using the SLDV for modal analysis of mechanical structures. The mode shapes measured using the SLDV for the first four dominant (0, 1), (0, 2), (0, 3) and (0, 4) modes of the stationary 0.8 mm thick 3.5 Al disk are shown in Figs. 9 12, respectively. The experimental first four dominant (0, n) mode shapes of the 0.8 mm 3.5 disk measured using the SLDV tally well with the simulated modes shapes obtained via FEM analysis.

5 C.K. Pang et al. / ISA Transactions 47 (2008) Fig. 12. Experimental (0, 4) mode constrained 0.8 mm thick 3.5 Al disk at natural frequency of 1887 Hz captured with SLDV. 4. Modelling of disk mode shape as repeatable component With the experimental natural frequencies of the first four dominant (0, n) modes of the disk and their corresponding mode shapes known, the disk ODS will be modelled as a repeatable component regressed on different spindle rotational speeds in rpm in this section. It should be noted that no external excitation was introduced into the disk-spindle system in this part of the experiment. Fig. 13. Campbell diagram of z-axis vibration of 0.8 mm thick 3.5 Al disk platter at OD RRO estimation Similar to obtaining the experimental verification of the natural frequencies of the disk, the LDV is used to measure the out-of-plane displacement of the disk in the z-axis as shown in Fig. 8. By focusing the laser beam onto the OD of the disk, the time domain signals and linear amplitude spectra of the vibrations can be obtained with the oscilloscope and DSA, respectively, at different spindle rotational speeds. The z-axis amplitude-modulated displacements of the disk vibrations at the OD are measured from 3000 rpm (50 Hz) to rpm ( Hz) in incremental steps of 1000 rpm (16.67 Hz). Converting the time domain data into linear amplitude spectra via a FFT (Fast Fourier Transform), the frequency spectra is plotted along different rotational speeds in a Campbell diagram (or so-called spin-up waterfall plot) and is shown in Fig. 13. It can be seen clearly from Fig. 13 that the RRO components locked to the harmonics of spindle rotational speed (due to the usage of earlier generations of ball bearing spindle motors instead of current higher end air or fluid bearing spindle motors) dominate the z-axis disk vibration spectra, appearing as line spectra in frequency spectra on the Campbell diagram. As such, the information and contribution by the disk ODS and other NRRO components are hindered. In this subsection, the z-axis RRO components will be estimated and removed. For illustration purposes but without loss of generality, a typical time domain disk fluttering vibration of a 0.8 mm thick 3.5 Al disk rotating at rpm is shown in Fig. 14. With the collected time domain data of the rotating disk at different rpms, the disk axial z-axis vibration signal is Fig. 14. Time domain OD disk axial vibration in the z-axis of a 0.8 mm thick 3.5 Al disk spinning at rpm. detrended (i.e. removal of DC component) and the RRO components arising from the spindle motor are identified with the following identity using the known spindle rotational speed R ω sin(ωt + λ ω ) = a ω sin ωt + b ω cos ωt (3) where w is the corresponding spindle rotational speed with a ω and b ω being the coefficients of the sinusoidal vibration signal to be identified. As such, R ω = aω 2 + b2 ω and λ ω = tan 1 b ω aω which can be obtained from the known a ω and b ω. Using the following standard RLS algorithm commonly used in signal processing and control engineering applications ψ R,λ (l) = ψ R,λ (l 1) + K R,λ (l)ε R,λ (l) K R,λ (l) = P R,λ (l 1)ϕ R,λ (l)[i + ϕ T R,λ (l)p R,λ(l 1)ϕ R,λ (l)] 1 P R,λ (l) = [I K R,λ (l)ϕ T R,λ (l)]p R,λ(l 1) (4) by replacing ψ R,λ with the magnitude R ω and phase λ ω estimation at each desired rotational frequency (or its harmonics), the magnitude R ω and phase contribution λ ω due

6 90 C.K. Pang et al. / ISA Transactions 47 (2008) Fig. 15. Decoupled time domain OD disk axial vibration in the z-axis of a 0.8 mm thick 3.5 Al disk spinning at rpm. Solid: Locked to spindle speed. Dashed-dot: Mode shapes and other NRRO components. Fig. 17. Campbell diagram of disk mode shapes and other NRRO components after removal of DC and first three dominant spindle rotation RRO harmonics. From Figs , it can be seen that the proposed usage of the RLS algorithm in (4) is effective in decoupling the DC and RRO components from the disk fluttering vibration, revealing the contributions by disk mode ODS and other NRRO components. It should be noted that by extrapolating the natural frequencies of the forward and backward travelling disk ODS mode shapes wave backward to zero rpm using the Campbell diagram in Fig. 17, the natural frequencies of the first four dominant (0, n) modes of the stationary disk obtained from SLDV measurements in the previous section can also be verified Natural frequencies and vibration amplitudes of ODS Fig. 16. Campbell diagram of DC and first three dominant spindle rotation RRO harmonics. to the RRO components arising from the rotating disk-spindle assembly at the corresponding spindle rotation speed ω can now be identified. ε R,λ and I are the error at each each estimation update instant and the identity matrix, respectively. As such, the effect of z-axis RRO on disk vibration at its OD can be decoupled from the collected time domain data at different rpm to obtain the contributions from disk ODS and other NRRO components. The main advantage of using the RLS algorithm is its fast computation, ease of implementation, as well as parametric updates when new data are available online. The time domain signal of the disk axial vibration recorded at rpm (200 Hz) after removal of the z-axis spindle RRO components is shown in Fig. 15. The linear amplitude spectra of the estimated DC and RRO components are shown in Fig. 16 and the remaining decoupled information (consisting mainly of disk ODS at their corresponding first disk mode shapes, rotating natural frequencies, and NRRO components) are shown in Fig. 17. With the natural frequencies of the first four dominant (0, n) modes of the stationary 0.8 mm thick 3.5 Al disk and their contributions to disk axial vibration in the z-axis at different spindle rotation speeds in rpm at OD, the natural frequencies and vibration amplitudes of the disk ODS mode shapes can now be identified in this subsection. It is assumed that the NRRO is a zero mean white noise of appropriate variance (power) for simplicity but without loss of generality Natural frequencies and spindle rotational speed From a ground-fixed observer, the natural frequencies of ODS of a spinning disk can be described by a linear relationship governed by the mode of vibration (0, n). ω ODS n = ω n + α n ω (5) where n is the number of nodal diameters and ω is the rotational speed of the disk-spindle system in rpm. As the (0, 0) mode has no branches, identification is carried out for n = 1, 2, 3 and 4 which are the four main disk mode shapes measured in the previous section. Similarly, the constant α n will be determined for different ODS (0, n) for the first four dominant disk platter resonance mode shape using the RLS algorithm in (4). The identified values of α n results are summarized in Table 2. An experimental approach of determining α n is more attractive than a theoretical solution due to its simplicity and

7 C.K. Pang et al. / ISA Transactions 47 (2008) Fig. 18. Proposed HDD servo simulation toolkit with repeatable (RRO and disk ODS) and non-repeatable components (NRRO). Table 2 α n for (0, n) Mode Shapes of a rotating disk regressed on rpm n α n ± ± ± ± reliability on extrapolation at higher rpm in future HDDs. More importantly, the unbiased estimates of the parameters α n can be updated when new data are available using the RLS algorithm in (4). The regressed values of α n will be used for construction of a disk ODS vibration simulation model to be described in Section Vibration amplitudes and spindle rotational speed In this subsection, the mean amplitude of disk fluttering vibrations at the OD of the 0.8 mm thick 3.5 Al disk are projected and regressed on rotational speed ω in rpm. In [12], a linear relationship of disk ODS vibrations against disk-spindle system rotational speeds in rpm was used by Pang et al. For a higher rotation speed such as rpm (250 Hz) and above to be employed in future HDDs, a quadratic relationship for vibration amplitude zn ODS against disk-spindle assembly rotational speed ω in rpm is required z ODS n = β 2 n ω2 + β 1 n ω + β0 n (6) and the RLS equation in (4) is employed for parametric estimates of βn 2, β1 n, and β0 n. With the identified disk ODS resonance frequency ωn ODS and amplitudes zn ODS, the magnitude and phase of the disk ODS can then be identified, reducing the ODS of the first four dominant (0, n) modes to repeatable components which can be compensated by the servo control when scaled to in-plane R/W head off-track from simple geometry. It is worth noting that the proposed methodology for reduction of disk ODS into repeatable components can be applied to a general (m, n) mode shape as well. 5. Disk ODS vibration simulation model In this section, the disk fluttering vibrations in the z-axis is converted into x y plane R/W head off-track effects with the decoupled frequencies and amplitudes of the z-axis RRO and identified repeatable disk ODS vibrations regressed on disk-spindle pack rotational speed in rpm to create a disk ODS vibration simulation model, useful for servo controller designs in future HDDs with higher TPI (Tracks-Per-Inch) and rotational speeds. To convert the disk axial displacement at its OD to R/W head off-track, the following geometric model derived experimentally in [4] is used Ot = 0.032h. (7) This geometric model in (7) averages the first four dominant modes of the disk resonances namely (0, n) modes for n = 1, 2, 3 and 4, which is congruent with the scope of interests in this paper and approximates a direct relationship between head off-track Ot to disk fluttering magnitude h. The effects on different locations on the disk can then be further scaled down with simple trigonometry with prior knowledge of the identified z-axis disk ODS vibration displacement and arm location with respect to center of the disk-spindle system. With a pre-specified disk-spindle rotational speed ω in rpm, the contribution of the in-plane R/W head off-track from the disk ODS can now be known from (7) and trigonometry for possible servo compensation. The functional block diagram used to simulate the effects of axial disk fluttering on slider off-track is shown in Fig. 18. The effects of NRRO can be approximated by a zero mean white noise source with variance of 0.01 (µm) 2. The simulated time domain disk ODS axial vibration at rpm (200 Hz) with the corresponding NRRO components are shown in Fig. 19. To illustrate the effectiveness of the proposed disk ODS vibration model at different disk locations, the experimental results of a disk rotating at rpm is compared with the simulated results after modelling at MD (Middle Diameter) for brevity but without loss of generality. The experimental disk axial vibration and that simulated using the proposed HDD servo simulation toolkit with disk ODS disturbance model for a 0.8 mm thick 3.5 Al disk spinning at rpm in frequency domain is shown below in Figs. 20 and 21, respectively.

8 92 C.K. Pang et al. / ISA Transactions 47 (2008) It can be seen from Figs. 20 and 21 that the proposed HDD servo simulation toolkit is effective in predicting the experimental spectra of in-plane RRO as well as disk ODS frequencies and amplitudes, as can be seen from the match in amplitude in terms of the dominant line spectra and baseline spectrum in frequency domain. With the proposed methodology, the linear amplitude spectra of the repeatable components consisting of RRO from disk-spindle rotation at frequency ω and the first four dominant (0, n) disk ODS can be reconstructed and compensated. An example of an application of such compensation methodologies via active control is presented in [13]. 6. Conclusion Fig. 19. Modelled disk axial vibration of disk spinning at rpm in time domain. Solid: simulation model. Dashed-dot: NRRO components. In this paper, the first four dominant (0, n) static mode shapes of a 0.8 mm thick 3.5 Al disk are simulated with FEM and compared with measurements using a SLDV. Using the z- axis disk ODS displacement at the OD of the disk, the natural frequencies, vibration amplitudes, and phases are regressed on disk-spindle rotational speed in rpm using an experimental approach. With the conversion of the disk OD information to in-plane R/W head off-track at different locations on a disk, a time domain HDD servo simulation toolkit with disk ODS disturbance model is constructed based on the identification results for projection on higher rotational speeds. Future works include scanning the disk for modes involving generic (m, n) modes as well as Vold-Kalman filtering of disk and suspension/slider vibration signals for order analysis. References Fig. 20. Experimental linear amplitude spectra of disk axial vibration at rpm at MD. Fig. 21. Linear amplitude spectra of disk axial vibration at rpm using proposed simulation model at MD. [1] McAllister JS. Characterization of disk vibrations on aluminium and alternate substrates. IEEE Transactions on Magnetics 1997;33(1): [2] McAllister JS. The effect of disk platter resonances on track misregistration in 3.5 disk drives. IEEE Transactions on Magnetics 1996; 32(3): [3] Imai S, Mori K, Okazaki T. Flutter reduction by centrifugal air-flow for high rotation-speed disks. In: Proceedings of the international conference on MIPE p [4] Guo L, Chen Y-JD. Disk flutter and its impact on HDD servo performance. IEEE Transactions on Magnetics 2001;37(2): [5] Shen IY. Closed-form forced response of a damped, rotating, multiple disks/spindle system. Journal of Applied Mechanics: Transactions of the ASME 1997;64: [6] Shen IY, Ku C-PR. Nonclassical vibration analysis of a multiple rotating disk and spindle assembly. Journal of Applied Mechanics: Transactions of the ASME 1997;64: [7] Stanbridge AB, Martarelli M, Ewins DJ. Measuring area vibration mode shapes with a continuous-scan LDV. Measurement 2004;35: [8] Stanbridge AB, Ewins DJ. Modal testing using a scanning laser doppler vibrometer. Mechanical Systems and Signal Processing 1999;13(2): [9] Martarelli M, Revel GM, Santolinli C. Automated model analysis by scanning laser vibrometry: problems and uncertainties associated with the scanning system calibration. Mechanical Systems and Signal Processing 2001;15(3): [10] Zhang QD, Winoto SH, Guo GX, Yang JP. An experimental study on vibration of disks mounted on hard disk drive spindles. Tribology Transactions 2003;46(3):465 8.

9 C.K. Pang et al. / ISA Transactions 47 (2008) [11] Polytec Website [Online]. [12] Pang CK, Ong EH, Guo G. Experimental dynamic modeling and characterizations of disk platter resonances. Digest of technical papers IEEE international INTERMAG. Amsterdam, The Netherlands BS-12. [13] Guo G, Zhang J. Feedforward control for reducing disk-flutter-induced track misregistration. IEEE Transactions on Magnetics 2003;39(6):