Dynamic Analysis of A Full Hard Disk Drive Model

Transcription

1 Page 1 of 23 Dynamic Analysis of A Full Hard Disk Drive Model Zhang Qide, Liu Ningyu, Ong Eng Hong and Kannan Sundaravadivelu Data Storage Institute, 5 Engineering Drive 1, Singapore Phone: , Fax: LIU_Ningyu@dsi.a-star.edu.sg ABSTRACT: In this numerical simulation, the characteristics of the turbulent flow-induced vibration of head unit in hard disk drives (HDD) have been investigated. The original geometry for both air flow simulation and head unit structure response analysis are three-dimensional full models including almost all important details in HDD. The problems are studied with wide disk speed of rotation ranging from 7200 rpm (desktop) to rpm (server). The results reveal the relationships between read/write head node displacements and the disk spinning speeds, as well as the differences of read/write head node displacements among four sliders, which provide a guideline to use the control technique to correct the errors. Index Terms Hard Disk Drive, Head unit, Turbulent flow, Vibration, Structure Response, Node displacement. 1. INTRODUCTION In current magnetic storage industry, the development of the underlying science and technology allow hard disk magnetic recording toward area density of 1 to 2 Terabits per square inch in the years. To meet this goal, the track density should increase to a remarkable value. The influence on the head positioning accuracy by aerodynamic excitation in the hard disk drives is growing by high-speed disk rotation and high-density recording. Therefore, designing the drive in

2 Page 2 of 23 consideration of the influence of aerodynamic excitation to the head gimbals assembly (HGA) becomes very important. For a modern HDD under extreme high speed rotation, the head unit included HGA, arm and E- Block, immerses in the HDD cavity turbulent flow. The turbulent force distributed on the surface of head unit causes a significant structure dynamic response to the head unit. The vibration and displacement of head unit influent the position of slider assembled on the far end of the head unit, causes a data track mis-registration. Several researchers have investigated the dynamic characteristics of head unit both numerically and experimentally. Armed on the dynamic behavior of sliders, Mizoshita et al. (1985), Jeong and Bogy (1992) investigated the dynamic characteristics of head slider both numerically and experimentally. Slavic et al (2007) studied the roughness-induced slider vibration numerically. Ono and Yamane (2007) numerically investigated slider dynamics in the near-contact region. As to the dynamic characteristics of the suspension or suspension assembly, many research work has been done numerically or experimentally, including Yoneoka et al. (1989), Jeans (1992), Zeng and Bogy (1998), Jeong et al. (1998), Weissner et al. (2003), Kilian et al. (2003), Kang and Raman (2006). The flow field around an E-block/arm assembly was studied numerically by Kubotera et al. (2002) and Tsuda et al. (2003), and the power spectrum of the arm torque was examined. The main objective of these investigations focuses on understanding how geometrical parameters influence various phenomena of interest in a suspension assembly, including natural frequencies and stiffness for different modes. These studies indicate that it is important to include more geometrical details in both the flow field and vibration analyses, and the simulation should be extended to a high disk speed of rotation. However, previous research work in both experiments and calculations used simple models of suspension assembly, which affected the results greatly. The every part inside the HDD enclosure has unique effects on the flow field, and therefore affects on the air force distribution on the head unit. In other word, the geometry of model has a dominated effect to the flow field and airflow force. In present work, we adopt a real hard disk drive with two disk and four sliders

3 Page 3 of 23 as the analysis model. By using LES (Large Eddy Simulation) technique, unsteady turbulent flow in this HDD is numerically simulated, and the aerodynamic force affecting on head unit is obtained from the simulation. Then calculated force is fed to a structure analysis to predict the airflow-induced vibration of head unit. Lastly, we calculate the read/write head node displacements for four sliders to reveal the dynamic behavior of sliders beyond the measurable region in HDD. 2. MODEL AND METHODOLOGY As shown in Figure 1, the three dimension fluid calculation model includes almost all details inside HDD cavity. The air flow field inside HDD is calculated by the finite volume based computational fluid dynamics (CFD) simulation code named FLUENT. The LES is used to model the turbulence in HDD with disk speed of rotation up to 15,000 rpm. A mixed mesh (Hex and Tetrahedral) that consists of about 3 million finite volumes is used for the air flow simulation. The air flow forces on head unit are collected as the transient excitation for structure vibration analysis. The structure analysis model is an isolated three dimensional head unit which does not included disks, top cover, and other parts that may connected with head unit. There are five arms and only the upper four arms assembled suspensions and sliders. Figure 2 presents a sketch of the dimensions and relative location between disk and head unit by side view and top view. The diameter of two co-rotation disks is 0.07 mm. Refer to the side view (x-z plane) of Figure 2, the distance between top cover and the bottom of HDD is mm. We named the upper disk as disk 1 and lower disk as disk 2. From the bottom of HDD (z=0), the two surfaces of disk 1 locate at z= mm and z= mm, respectively, and two surfaces of disk 2 locate at z= mm and z= mm, respectively. We assign the five arms from upper to lower as arm 1 to arm 5, and the four suspensions as suspension 1 to suspension 4, the corresponding sliders are

4 Page 4 of 23 slider 1 to slider 4. The sliders locate at middle position (MD) along disk radius, and its long axial has a 35 o slope to x-axial minus direction during current investigation. The finite element model of head unit is creates using Gambit, which consists 168,626 Tetrahedral elements defined by 45,316 nodes, with minimum face size of e-10 m 2, and minimum volume of e-15 m 3. The three dimensional vibration analysis of head unit is conducted using the finite-element based code of ANSYS. For finite-element analysis, the head unit is constrained by the two edges of the circle cylinder hole, which is assumed as the constraint of the spin axis on the arm. The time varying aerodynamic forces, obtained from the CFD calculations, were employed for a finite-element based vibration analysis. The material properties of the head unit are assumed as: Young s Modulus kg/m s 2, Poisson s ratio is 0.33, and Density: 2700 kg/m 3. The response of the head unit to the flow-induced excitations is obtained through a transient dynamic analysis. The basic equation of motion solved by a transient dynamic analysis is M U& + C U& + K u = F(t) where M is mass matrix, C is damping matrix, K is stiffness matrix. The four vectors, U &, U &, u and F(t) are nodal acceleration, nodal velocity and nodal displacement vectors, and load vector, respectively. At any moment t, this equation can be treated as a set of "static" equilibrium equations with an inertia force ( M U & ) and a damping force ( C U & ). 3. RESULTS AND DISCUSSION: (1) The mode shapes and natural frequencies The modal analysis is first performed to extract the first 40 natural frequencies of head unit and their corresponding mode shapes. Because the displacement of E-block has minor effect on the slider s location, therefore, the model analysis results listed in Table 1 do not include E-block s

5 Page 5 of 23 modal (such as set 5, set 7, set 12, set 13, etc.). For the same reason, the mode shapes of fifth arm are also excluded (such as set 6). In the last column of table 1, the numbers following the parts name are arranged by the order of displacement magnitude. The part number with maximum displacement is put in the first position after the parts name. For the situation that there are two parts move in oppositional direction, the op is used following the part numbers; and two parts move in the same direction, the co is used to indicate it. The modal analysis results indicate that one slider is affected by several modes. For example, if we concern about the slider 1, which is assembled on the arm in the middle location of the head unit. For the out-of-plane displacement of slider 1 (bending direction, z direction in coordinates shown in Figure 2), from Table 1, the bending modes influencing slider 1 are mainly the set 4 (2254), set 8 (4698) and set 29 (16527). Figure 3 shows the dominated mode shapes affected the location of slider 1. Certainly, the 2 nd bending modes have also contributions to displacement of slider 1. However, the 2 nd bending modes have higher frequencies and it is difficult to catch them accurately in current time increment. On the other hands, the 1 st torsion mode also has minor effects on slider 1. Thus during the dynamical characteristics investigation, we should trace the typical nodes on slider 1 (index as 9808 and 9809 for the two top corner nodes on slider 1 as shown in Figure 4), and analysis the frequencies of these nodes displacement. If the aerodynamic force could exite a frequency near the natural frequency of model, the significant big displacement will occur. (2) A comparison with measurement In this section, a structure forced vibration analysis is performed at disk speed of rotation rpm, with time step Δt= s. The turbulent flow forces on head unit and node displacements of several typical nodes is produced and analyzed. Because the measurement performed on the slider near the cover is much easy and accurate, we focus on the node displacement of slider 1 first.

6 Page 6 of 23 For structure vibration problem in hard disk drive, one of the most important issues we concern about is the positioning of sliders. The slider s node displacement is usually measured in the two directions, off-track direction and out-of-plane direction. The off-track direction is in the plane parallel to the disk wall (x-y plane in coordinates shown in Figure 2) and perpendicular to the long axial of head unit. The out-of-plane direction is perpendicular to the disk wall (z direction in coordinates shown in Figure 2). The aerodynamic forces in both off-track and out-of-plane directions are shown in Figure 5. It can be seen that the average force in out-of-plane direction is much smaller than that in off-track direction and the peak to peak value of the force perturbation in out-of-plane direction is also smaller than that in off-track direction. The force vibration appears turbulent properties of mixture of multi-frequencies and multi-amplitudes. The structure analysis produces the node displacement results for all nodes for head unit model. We focus on the displacements of several typical nodes firstly. In the four sliders shown in Figure 4, the two top corner nodes for each slider could be adopted as the indications of slider positioning. For the top corner nodes of all sliders (total eight nodes), the average value, peak-to-peak value and the root-mean-square (rms) value of node displacement are reported in Table 2. The results indicate: (i) for each slider, the node displacement value from two nodes on top corners have very small difference and we can adopt one of them to express the dynamic response of its slider. (ii) the results shown Figure 6 indicates that the off-track vibration is below 2.6 nm in average amplitude, and below 3.65 nm in peak-to-peak value, which are agreement with our inhouse measurements. (iii) the out-of-plane vibration has a much bigger value in amplitude as listed in Table 2, which is higher in amplitude compare to our measurement. The reason is that the current structure analysis model is sustained airflow force isolated. The real head unit model vibrates together with the disks through constraints of air bearings, and the vibration of head unit is

7 Page 7 of 23 constrained in disk normal (out-of-plane) direction. In the other hand, the input electrical control through coil to head unit may be another constrains we did not included in present simulation. In current investigation, by using this isolated head unit model, the out-of-plane vibration results is still valuable as a relative magnitude in comparison of the vibration patterns between different sliders, or between different disk spinning speeds. To analysis the node vibration spectral, a typical node, node 9808, the top corner node on slider 1 (as illustrated in Figure 4) is applied as an example. Slider 1 locates near the top wall and thus the measurement is easier to perform and reliable. The node 9808 has an average node displacement around 1.7 nm, and peak-to-peak node displacement near 3.2 nm in off-track direction as shown in Table 2 and Figures 6 and 7. A fast Fourier transformation (FFT) analysis is conducted on the perturbation components of node displacements for node In out-of-plane direction, as indicated by modal analysis, the dominated mode shapes affected out-of-plane node displacement for node 9808 is set 4, set 8 and set 29. Figure 8 reveals that at least two frequencies (2320Hz, 4800Hz) are among the modes excited by aerodynamic force in out-of-plane node displacement for node Here, the modes around set 4 and set 8 are quite obvious, and the frequency near set 29 can also be identified (16560Hz). In off-track direction, Figure 9 shows that the dominated frequencies of off-track vibration of node 9808 within are due to the torsion of arms and suspensions. The frequencies around 28480Hz are among the sway modes of suspensions. A comparison of modes between in-house measurement and present simulation gives a good agreement. (3) Differences between four sliders As mentioned in above section, the two top corner nodes have similar dynamic response and displacement magnitude, so one top corner node is used to present its slider in node displacement.

8 Page 8 of 23 Here, the nodes 9808, 9771, 4679 and 4644 are used to express the displacements of slider 1, 2, 3 and 4, respectively. As indicated in Figure 10, in off-track direction, the peak-to-peak displacement increases from slider 1 to slider 4. Slider 1 has the smallest average value and rms value of vibration (around 1.7 nm), and slider 2, 3 and 4 have higher value (around 2.5 nm). There is only small difference between the average values from slider 2 to slider 3. Refer to Figure 2, the location of slider 1 is next to the stationary top cover wall, where the displacement of flow field is weaker compared with that between two spinning disks in off-track direction. Although slider 4 locates between bottom stationary wall and spinning disk, due to arm 5 (without suspension 5 and slider 5) is below arm 4, the location of slider 4 is far from the bottom stationary wall compared to that of slider 1. Therefore, slider 2, 3, 4 have much higher vibration and the measurement on slider 1 could not provide a correct information about the dynamic behaviors of sliders in whole HDD. Because the average off-track displacements for all sliders are positive, so the rms results have small difference compared to the average results, so in below discussions, we will use the average results in off-track direction for the purpose of comparisons. In out-of-plane direction, as shown in Figure 11, the sliders near still walls have smaller peak to peak magnitudes of node displacement, such as slider 1 and slider 4. Slider 3 has the biggest peak-to-peak magnitude of out-of-plane node displacement. In out-of-plane direction, the sliders move toward the direction away from the disk. Slider 1 and 3 are above the disks and their average displacements are positive. Slider 2 and 4 locate below the disks and their average displacements are negative. Slider 1 has smallest rms vibration value (about 174 nm) among four sliders, and silder 4 has biggest rms vibration magnitude (about 324 nm) as shown in Figure 11. Because the average out-of-plane displacements for slider 1 and 3 are positive and for slider 2 and 4 are negative, so the rms results are suitable ones to express the displacement magnitude

9 Page 9 of 23 and the average value in out-of-plane direction will be used for the purpose of comparisons in below discussions. (4) Effects of Disk Spinning Speed Further study of flow induced vibration is performed by investigation of dynamic response of head unit with different disk spinning speeds. Three cases with disk rotation speeds ω=15000 rpm, rpm and rpm are studied in this section. The analysis of airflow induced vibration is performed with time step Δt= s for disk spinning speed of rpm, Δt= s for disk spinning speed of rpm and Δt= s for disk spinning speed of 7200 rpm. The every case used the same number of time step (1600) to finish one revolution disk spin. When disk spin velocity increases, the turbulent strength of air flow increase correspondingly, and the average aerodynamic force and force perturbation on head unit thus increase as shown in Figures 12 and 13. The severe track mis-registration problem may occur due to the vibration of head unit. The average values of vibration in off-track direction at three disk spinning speeds are shown in Figure 14. As expected, smaller disk spinning speed causes small slider dynamic response. A common phenomenon in three cases is that the slider 1 always has the smallest average off-track displacement, and the slider 4 has the biggest average off-track displacement among four sliders. The slider 2 and slider 3 appear almost the same average off-track displacement in each case. In the off-track direction and the out of plane direction shown in Figures 15 and 16 indicate that the disk spinning speed has a significant influence on the peak to peak node displacement value, especially on the out-of-plane direction. For all sliders, the higher the disk spinning speeds, the higher the peak-to-peak node displacement value in both off-track and out-of-plane directions. The sliders between two disks have a obvious increase in out-of-plane direction after disk spinning speed greater than rpm.

10 Page 10 of 23 In out-of-plane direction, as indicated by Figure 17, the rms value of displacement increases with the increase of disk spinning speed. The four sliders have the same change pattern for three cases: slider 1 shows a smallest rms value of displacement, slider 2 and slider 3 have similar rms value of displacement, which is higher than that of slider 1, and finally, the slider 4 has a highest rms value of displacement among all four sliders. These results indicate that in all three spinning speeds, the measurement on slider 1 would be not enough to gain the full information about the air induced vibration inside HDD. 4. CONCLUSION REMARKS In present work, a numerical investigation is performed to investigate the characteristics of the turbulent flow-induced vibration of head unit in a commercial available HDD. The threedimensional full models are adopted for both air flow simulation and head unit structure response analysis. The problems are studied with disk speed of rotation of 7200 rpm, rpm and rpm. The relation between node displacements and the disk spinning speed, as well as the differences of node displacements among four sliders are presented, which provide the basic data for control engineers. The present simulation indicates that the node displacement has a notable increase with the increase of disk spinning speed, thus in extreme high disk spinning speed, say rpm, the detail measurements and simulation for every single slider is necessary to analyze the possible track mis-registration due to slider displacement or even failure during the operation of HDD. It is also worth to emphasize that slider 1 has the smallest dynamic response among all sliders from the present numerical simulation. The information about positioning value provided by measurement of slider 1 might be underestimated. The numerical simulation is again verified necessary in the development of high performance HDD.

11 Page 11 of 23 The isolated solid model of head unit produced higher out-of-plane results in this investigation. Therefore, as further work, we are constructing a three dimensional solid model included head unit, disk and some side walls that may affect the dynamic response of head unit. It is expected that this full solid model will provide a better result in our further study. REFERENCES [1] Mizoshita, Y., Aruga, K. and Yamada, T. (1985) Dynamic Characteristics of a Magnetic Head Slider, IEEE Trans. Magn. 21(5), [2] Jeong, T. G. and Bogy, D. B. (1992) Unloaded Slider Vibrations Excited by Air Flow Between Slider and Rotating Disk, IEEE Trans. Magn. 28(5), [3] Slavic J. Bryant M. D. and Boltezar M. (2007) A new approach to roughness-induced vibrations on a slider. Journal of Sound and Vibration. 306, [4] Ono K. and Yamane M. (2007) Theoretical Study of Self-Excited and Forced Vibrations of Flying Head Slider in Near-Contact Region. IEEE Trans. Magn. 43(9), [5] Yoneoka, S., Owe, T., Aruga, K., Yamada, T. and Takahashi, M. (1989) Dynamics of Inline Flying-Head Assemblies. IEEE Trans. Magn. 25(5), [6] Jeans, A. H. (1992) Analysis of the Dynamics of a Type 4 Suspension. ASME J. of Vib. Acous. 114, [7] Zeng, Q. H. and Bogy, D. B. (1998) Dynamic Characteristics of a Suspension Assembly, Part 1: Modal Experiment. Adv. Info Stor. Syst. 8, [8] Zeng, Q. H. and Bogy, D. B. (1998) Dynamic Characteristics of a Suspension Assembly, Part 2: Numerical Analysis. Adv. Info Stor. Syst. 8, [9] Jeong, T. G., Chun, J. I., Cung, C. C., Byun, Y. K. and Ro, K. C. (1998) Measurements Technique for Dynamic Characteristics of HDD Head-suspension Assembly in Normal Operating Conditions. Adv. Info Stor. Syst. 9, [10] Weissner, S., Zander, U. and Talke, F. E. (2003) A New Finite-element Based Suspension Model Including Displacement Limiters for Load/Unload Simulations. J. Trib. 125, [11] Kilian, S., Zander, U. and Talke, F. E. (2003) Suspension Modeling and Optimization Using Finite Element Analysis. Trib. Intr. 36,

12 Page 12 of 23 [12] Kang N. and Raman A., (2006) Vibrations and stability of a flexible disk rotating in a gas-filled enclosure Part 1: Theoretical study. Journal of Sound and Vibration, 296, [13] Kang N. and Raman A., (2006) Vibrations and stability of a flexible disk rotating in a gas-filled enclosure Part 2: Experimental study. Journal of Sound and Vibration, 296, [14] Kubotera, H., Tsuda, N., Tatewaki, M. and Maruyama, T. (2002) Aerodynamic Vibration Mechanism of HDD Arms Predicted by Unsteady Numerical Simulations. IEEE Trans. Magn. 38(5), [15] Tsuda, N., Kubotera, H., Tatewaki, M., Noda, S., Hashiguchi, M. and Maruyama, T. (2003) Unsteady Analysis and Experimental Verification of the Aerodynamic Vibration Mechanism of HDD Arms. IEEE Trans. Magn. 39(2),

13 Page 13 of 23 Table 1 Modal analysis results summary Set Frequencies Mode shape Max (1 st, 2 nd, 3 rd ) st bending Arm Arm Arm Arm Suspension Suspension Suspension Suspension st Torsion Suspension 3, Suspension 4, Suspension 3, Suspension 2, Arm 3,4 op Arm 1,2 op Arm 1,3 co Arm 1,4 op Arm 2,4 co nd bending Arm 2,4 op Arm 4,2 co Arm Arm st sway Suspension 3,1,2, Suspension Suspension 1, Suspension 4,2, Suspension 2, nd bending Suspension 1,3 op Suspension 3,1 co

14 Page 14 of 23 Table 2. The node displacements (nm) for ω=15000 rpm, refer to Figure 4 for the nodes index. node Direction Average Peak-to-peak RMS 4644 Off-track Out-of-plane Off-track Out-of-plane Off-track Out-of-plane Off-track Out-of-plane Off-track Out-of-plane Off-track Out-of-plane Off-track Out-of-plane Off-track Out-of-plane

15 Page 15 of 23 Figure 1 Geometry of cheetah HDD and head unit Figure 2 Side view(x-z plane) and top view(x-y plane) of head unit.

16 Page 16 of 23 (a) Set 4, f=2254 (b) Set 8, f=4698 (c) Set 29, f=16527 Figure 3 Mode shaps for Set 4, Set 8 and Set 29. Here, f is natural frequency. Figure 4 The number coding of top corner nodes for four sliders.

17 Page 17 of 23 Airflow force on head unit (mn) ω=15000 rpm out-of-plane off-track Time (s) Figure 5 The aerodynamic force on head unit at 15,000 rpm Off-track node displacement (nm) 6 ω=15000rpm 5 Node 9808 on slider Time (s) Figure 6 The off-track node displacement for node 9808 on slider 1 at 15,000 rpm

18 Page 18 of 23 Out-of-plane node displacement (nm) ω=15000rpm Node 9808 on slider Time (s) Figure 7 The out-of-plane node displacement for node 9808 on slider 1 at 15,000 rpm Log (node_displacement) (nm) Out-of-plane displacement Node 9808 on slider Frequency (Hz) Figure 8 The out-of-plane node displacement spectral for node 9808 on slider 1 at 15,000 rpm

19 Page 19 of 23 Log (node_displacement) (nm) Off-track displacement Node 9808 on slider Frequency (Hz) Figure 9 The off-track node displacement spectral for node 9808 on slider 1 at 15,000 rpm Off-track displacement (nm) ω=15,000rpm average peak-to-peak root-mean-square Slider number Figure 10 Comparison of the off-track node displacement between 4 sliders at 15,000 rpm

20 Page 20 of 23 Out-of-plane displacement (nm) ω=15,000rpm average peak-to-peak root-mean-square Slider number Figure 11 Comparison of the out-of-plane node displacement between 4 sliders at 15,000 rpm Off-track airflow force on head unit (mn) ω= 7200 rpm ω=10000 rpm ω=15000 rpm Time (s) Figure 12 The off-track aerodynamic force on head unit at three disk spinning speeds.

21 Page 21 of 23 Out-of-plane airflow force on head unit (mn) ω= 7200 rpm ω=10000 rpm -2.0 ω=15000 rpm Time (s) Figure 13 The out-of-plane aerodynamic force on head unit at three disk spinning speeds. 3.0 Average off-track displacement (nm) SLIDER 4 SLIDER 3 SLIDER 2 SLIDER Disk speed (rpm) Figure 14 Average off-track node displacement for 4 sliders at three disk spinning speeds.

22 Page 22 of 23 Peak-to-peak off-track displacement (nm) SLIDER 4 SLIDER 3 SLIDER 2 SLIDER Disk speed (rpm) Figure 15 Peak to peak off-track node displacement for 4 sliders at three disk spinning speeds. Peak to peak out-of-plane displacement (nm) SLIDER 4 SLIDER 3 SLIDER 2 SLIDER Disk speed (rpm) Figure 16 Peak to peak out-of-plane node displacement for 4 sliders at three disk spinning speeds.

23 Page 23 of 23 RMS out-of-plane displacement (nm) SLIDER 4 SLIDER 3 SLIDER 2 SLIDER Disk speed (rpm) Figure 17 RMS out-of-plane node displacement for 4 sliders at three disk spinning speeds.