Effect of an hourglass shaped sleeve on the performance of the fluid dynamic bearings of a HDD spindle motor

Transcription

1 DOI /s Technical Paper Effect of an hourglass shaped sleeve on the performance of the fluid dynamic bearings of a HDD spindle motor Jihoon Lee Minho Lee Gunhee Jang Received: 14 October 2013 / Accepted: 8 March 2014 / Published online: 1 April 2014 Springer-Verlag Berlin Heidelberg 2014 Abstract This research investigated the characteristics of fluid dynamic bearings (FDBs) in a HDD spindle motor with an hourglass-shaped sleeve. We demonstrated experimentally that the hourglass-shaped sleeve generated through the ball-sizing process is a major source of large repeatable runout and non-repeatable runout in a HDD spindle system. We also numerically proved the effect of hourglass-shaped sleeves on pressure, friction torque, stiffness and damping coefficients, critical mass, and shock response. Finally, we proposed a robust design for FDBs with hourglass-shaped groove depths to compensate for the decrease in the static and dynamic performance of FDBs with hourglass-shaped sleeves. The proposed hourglassshaped groove depth improves the performance of FDBs with both straight and hourglass-shaped sleeves. 1 Introduction The fluid dynamic bearings (FDBs) of a HDD spindle motor, shown in Fig. 1, support the rotating disk-spindle system using the pressure generated in the fluid lubricant. The radial and axial clearances of a 2.5 HDD spindle motor are approximately 2 and 30 μm, respectively, and herringbone or spiral grooves are inscribed in the sleeve of journal or thrust bearings to provide pumping pressure. One of the more difficult manufacturing processes is the inscribing uniform grooves, especially in terms of maintaining uniform groove depth in the range of several J. Lee M. Lee G. Jang (*) PREM, Department of Mechanical Engineering, Hanyang University, 17 Haengdang dong, Seongdong gu, Seoul , Republic of Korea ghjang@hanyang.ac.kr micrometers. Grooves are inscribed on the surface of the stainless steel sleeve by electrochemical machining, which generally roughens the surface of the grooved bearing sleeve. The ball-sizing process is used to scrape down these rough surfaces. When a ball passes through the sleeve of an FDB to smooth out the rough surface, compressive pressure is generated between the ball and both the sleeve inlet and outlet, forming an hourglass-shaped sleeve as shown in Fig. 1, and generally decreases the static and dynamic performance of the FDBs and the HDD spindle system. Many researchers have investigated methods to analyze FDBs to support a HDD disk-spindle system. Jang et al. (2006) and Jang and Lee (2006) proposed a numerical method to determine the pressure, friction torque, and stiffness and damping coefficients of the coupled journal and thrust bearings using a finite element method and the perturbation method. Several other researchers have also investigated methods to improve the dynamic performance of the HDD spindle system using FDBs. Jang and Yoon (2003) studied the stability of a rotor with stiffness and damping coefficients generated by a journal bearing with rotating grooves, which vary with time. Yoon and Shen (2005) presented a numerical model to predict the shock response of a rotating-shaft spindle system considering the effect of nonlinear FDBs. Kim et al. (2010) suggested a method to determine the stability of a general rotor-bearing system with five degrees of freedom. Also, Lee et al. (2013b) presented a robust design method for FDBs in a HDD disk-spindle system by modal analysis. However, all of the above research was restricted to the analysis of ideal FDBs without manufacturing imperfections. Major design variables of FDBs such as clearance and groove depth

2 1436 Fig. 1 Mechanical structure of the HDD disk-spindle system and the FDBs with, a straight and, b hourglass-shape tapered sleeves are within the micro-meter range, and there are many sources of manufacturing error of the FDBs in a HDD spindle motor, such as imperfect shaft roundness, nonuniform clearance due to sleeve or shaft tapering, and non-uniform groove depth. Even minor manufacturing errors of FDBs in a HDD spindle motor may affect the dynamic performance of a HDD spindle system. Some researchers have investigated the dynamic performance of tapered bearings with micrometer-scale clearance. Zhang et al. (2012) investigated the steady-state performance and the stability charts of tapered micro gas bearings. Koak et al. (2009a) proposed a model for the motion of a HDD spindle system perturbed by manufacturing errors in FDBs. Also, Koak et al. (2009b) investigated dynamic characteristics of a HDD spindle system with an imperfectly round shaft. However, the effect on the performance of FDBs of hourglass-shaped sleeves as generated in real manufacturing processes has not been investigated previously. This research investigates the characteristics of the FDBs of a HDD spindle motor with an hourglass-shaped sleeve. We measured the power consumption, repeatable runout (RRO), and non-repeatable runout (NRRO) of the HDD spindle system with straight and hourglass-shaped sleeves. We investigated numerically the effect of hourglass-shaped sleeves on pressure, friction torque, stiffness and damping coefficients, critical mass, and shock response. Finally, we proposed a robust FDB design to compensate for the decrease of static and dynamic FDB performance associated with an hourglass-shaped sleeve. 2 Effect of hourglass shaped sleeves on power, RRO, and NRRO We measured the power consumption, RRO, and NRRO of HDD samples in order to investigate the effect of hourglass-shaped sleeves on the performance variation of HDD spindle motors supported by FDBs. Figure 2 illustrates the experimental setup used to measure power consumption, RRO, and NRRO. We chose two HDD spindle motor samples. Sample 1 exhibits average power consumption, RRO, and NRRO; sample 2 has less power consumption and larger RRO and NRRO than the other samples. Table 1 shows the comparison of measured power consumption, RRO, and NRRO between sample 1 and 2. It shows that sample 1 has greater power consumption and smaller RRO and NRRO than those of sample 2. Samples 1 and 2 were disassembled and the sleeves of each were cut in half to measure the shape of the grooved area. Figure 3 shows the cross-sectional view of the sleeve, and Fig. 4a and b show the straight sleeve of sample 1 and the hourglass-shaped sleeve of sample 2, respectively. The hourglass-shaped sleeve of sample 2 increases the average clearance between the grooved sleeve and the rotating shaft, consequently decreasing friction torque and power consumption. Friction torque of FDBs in a 2.5 HDD consumes roughly 30 % of input power, and power reduction of 3 % means that the friction torque of FDBs is decreased by 10 % in the journal bearing with hourglass-shaped sleeve (Lee et al. 2013a). As shown in Table 1, an increase in the average clearance

3 1437 Fig. 2 Experimental setup for measuring the power consumption, RRO and NRRO Table 1 Power consumption, RRO and NRRO between the FDBs with straight and with hourglass-shaped sleeves FDBs with straight sleeves FDBs with hourglassshaped sleeves Power consumption (mw) RRO (μm) NRRO (μm) Difference (%) 3 Method of analysis 3.1 Governing equations The Reynolds equations of journal and thrust bearings can be represented as follows: ( hj 3 R θ 12µ ) ( p + R θ z h 3 J 12µ ( ) ( r h3 T p + ht 3 r r 12µ r r θ 12µ ) p = θ z h J z 2 θ + h J t ) p r θ = θ z h T 2 r θ + h T t (1) (2) where R, r,p, h J, h T, θ z, and µ are the radius of journal and thrust, pressure, film thickness of journal and thrust bearings, rotating speed and viscosity, respectively. The film thickness of the journal bearing including the hourglass-shaped sleeve can be written as follows: Fig. 3 Cross-sectional view of the sleeve of the FDBs of hourglass-shaped sleeve also decreases the stiffness and damping coefficients, which increases RRO and NRRO. h J = c g + c r e r cos(θ ϕ) + f (z) where c g, c r, e r, φ, and θ are the groove depth, radial journal bearing clearance, translational motion eccentricity, attitude angle, and angular coordinate measured from the fixed negative x-axis, respectively. f (z) is the variation of radial clearance of the journal bearing to describe the hourglass-shaped sleeve along the z-axis as shown in Fig. 5. This research developed a finite element program to solve Eqs. (1) to (3) to calculate pressure, load capacity, and friction torque. It also developed a finite element program (3)

4 1438 Fig. 4 Measured inner surface of sleeves, a straight sleeve, b hourglass-shaped tapered sleeve where M, G, C, and K are the mass, gyroscopic, damping, and stiffness matrices, respectively. M includes the mass and the mass moments of inertia of the rotor and G includes the mass moments of inertia of the rotor and the rotor speed. Once the radius of gyration is introduced to express the mass moment of inertia with respect to the mass, Eq. (4) can be represented as a single variable, i.e., the mass of the rotor. The solution of Eq. (4) can be assumed to be an exponential function as follows: x = x h exp(ωt), Substituting Eq. (5) into Eq. (4) yields the following equation: (5) Fig. 5 Journal bearing with an hourglass-shaped sleeve to solve the perturbed equations of Eqs. (1) and (2) in order to calculate the stiffness and damping coefficients. 3.2 evaluation of dynamic performance of HDD spindle motor The critical mass, which is the solution of the equations of motion of the rigid disk-spindle system supported by the FDBs, can be represented with five degrees of freedom as follows (Kim et al. 2011): Mẍ + (C + G)ẋ + Kx = 0 (4) { Ω 2 M + Ω(C + G) + K}x h exp(ωt) = 0. The eigenvalue of Eq. (6) can be generally expressed as = real + i img. The motion of the rotor is stable if Ω real is >0 and is unstable if Ω real is <0. Therefore, the critical condition exists when Ω real is equal to 0. The solutions of the characteristic determinant of Eq. (6) are the critical mass (m a ) c and the corresponding frequency Ω img. The behavior of the disk-spindle system supported by coupled journal and thrust bearings can be regarded as stable if the mass m a is less than the critical mass (m a ) c, and unstable if m a is greater than (m a ) c. Lee et al. (2012) proposed a method to design a robust HDD disk-spindle system using the critical mass. They showed that FDBs with large critical mass have small RRO and NRRO. Repeatable runout and NRRO of a rotating rigid diskspindle system supported by the FDBs in five degrees of freedom can be estimated by solving the equations of motion with the centrifugal force due to unbalanced mass or external shock, respectively, as follows (Lee et al. 2012): Mẍ + (C + G)ẋ + Kx = F(t) (6) (7)

5 1439 Fig. 6 Finite element model and pressure distribution of FDBs, a FEM model, b pressure distribution where F(t) is the force vector of the centrifugal force or external shock. At steady-state, the centrifugal force due to an unbalanced mass is a major factor in determining whirl radius or RRO. Non-repeatable runout is generated by various sources such as manufacturing errors, instability of FDBs and external shocks. This research estimates NRRO due to half-speed whirl (HSW) by applying the swept sine excitation in addition to the centrifugal force in force vector, as follows: a t 2 + ωs t, F = p0 sin (8) 2 ωe ω s, a= T Table 2 Lower, upper and optimal values of design variables Design variable Grooved journal bearing Grooved thrust bearing Bearing width (mm) Radial clearance (μm) Axial total clearance (μm) Groove pattern Number of grooves (EA) Upper: 1.95 Lower: Herringbone 8 Groove depth (μm) 5 Upper: Lower: Spiral Upper: 10 Lower: 20 Upper: 8 Lower: 15 (9) where a, T, ωs, and ωe are sweep rate, sweep period, and starting and ending frequencies, respectively. 3.3 Simulation model We developed a finite element model of FDBs to numerically investigate the effect of hourglass-shaped sleeves. The finite element model of a 2.5 HDD spindle motor rotating at 7,200 rpm was developed with 3,380 isoparametric bilinear elements in four nodes. Figure 6a and b show the finite element model and its pressure distribution, respectively; Table 2 shows the major design variables. The FDB performance is investigated for an hourglass-shaped sleeve in which upper taper length ( cu) of the upper grooved journal bearing and the lower taper length ( cl) of the lower grooved journal bearing increases from 0 to 1 μm by 0.2 μm increments. The lower taper length of the upper grooved journal bearing and the upper taper length of the lower journal grooved bearing are assumed to be zero. A quadratic function is applied to describe the tapered shape of the upper and lower grooved journal bearings, as shown in Fig Performance of FDBs due to hourglass shaped sleeves Figure 7a shows the pressure distribution in the journal bearing of FDBs with a straight sleeve. The speed of rotation and eccentricity ratio are 7,200 rpm and 0.1, respectively. The maximum pressure of the upper and lower grooved journal bearing are 2.70 and 1.98 MPa, 13

6 1440 Fig. 7 Pressure distribution of the journal bearing due to the effect of straight and hourglassshaped sleeves, a pressure distribution in the journal bearing of the FDBs with straight sleeves, b pressure distribution in the journal bearing of the FDBs with hourglass-shaped sleeves (taper length = 1 μm) respectively. Figure 7b shows the pressure distribution in the FDB journal bearing with an hourglass-shaped sleeve with a 1 μm taper length. The maximum pressures on the upper and lower grooved journal bearings are 2.03 and 1.41 MPa, respectively, lower than those found on the straight-sleeved FDB by 24.8 and 28.8 %, respectively. Figure 8 shows the friction torque due to variation of taper length and eccentricity. Friction torque decreases with increasing taper length and decreasing eccentricity ratio because the shear stress also decreases due to pressure reduction in the journal bearing with hourglass-shaped sleeves. Figure 9 shows the stiffness and damping coefficients due to taper length and eccentricity. The radial stiffness and damping coefficients decrease with increasing taper length and decreasing eccentricity ratio; this is because of the reduced pressure in hourglass-shaped sleeves. However, axial stiffness and damping coefficients decrease with increasing eccentricity ratio, but are not affected by taper length. Figure 10 shows the stability of the HDD spindle system supported by FDBs according to taper length and eccentricity ratio. Critical mass decreases with increasing taper Fig. 8 Friction torque due to taper length and eccentricity ratio length because the hourglass-shaped sleeve decreases the stiffness and damping coefficients of the overall journal bearing. An hourglass-shaped sleeve with taper lengths of 0.4 and 1 μm decrease the stability by 5 and 10 %, respectively, in comparison with the straight sleeve, respectively. Figure 11 shows the rotating motion of a HDD spindle motor and its whirl radius. The mass imbalance in the

7 1441 Fig. 9 Stiffness and damping coefficients due to taper length and eccentricity ratio, a Kxx, b Kzz, c Cxx, d Czz Fig. 10 Stability of a HDD disk-spindle system due to taper length and eccentricity ratio HDD spindle system is assumed to be 0.2 g mm. Whirl radius increases with increasing taper length because increasing taper length decreases stiffness and damping coefficients. When taper length increases from 0 to 1 μm, whirl radius in the top shaft in turn increases from 51.8 to 66.4 nm. This research applies a swept sine excitation to the mass center of the HDD spindle in the positive x direction to estimate RRO and NRRO. The swept sine excitation has an amplitude of 5 G from 0 to 300 Hz over 5 s. It is able to excite all frequencies under 300 Hz, including the HSW and rotating frequencies. Figures 12a and b show the frequency spectra of the mass center radial displacement the excited by the x-directional swept sine for the FDBs with Fig. 11 Whirling motion and whirl radius of a HDD spindle system due to taper length and eccentricity ratio, a whirling motion of a HDD spindle system, b whirl radius of a HDD spindle system straight sleeve and hourglass-shaped sleeve with 1 μm taper length, respectively. The rotating frequency amplitude of the FDBs with hourglass-shaped sleeve is larger

8 1442 Fig. 13 Proposed design of a FDB with hourglass-shaped groove Fig. 12 Frequency spectra of the radial displacement of the mass center excited by the x-directional swept sine for the FDBs with straight and hourglass-shaped sleeves, a straight sleeve, b hourglassshaped sleeve than that of the FDBs with straight sleeve by approximately 28.6 %, and the amplitudes of HSW frequency of the FDBs with hourglass groove sleeve is larger than that of FDBs with straight sleeves by approximately 25.0 %. 5 Robust design of the FDBs with hourglass shaped sleeve Figure 13 shows a proposed robust sleeve design to compensate for the reduction of the static and dynamic characteristics in FDBs with hourglass-shaped sleeve. Sleeve groove depths of the journal bearing are inscribed with an hourglass-shape, as shown in Fig. 13. The groove depths of the lower part of the upper journal bearing ( d u ) and upper part of the lower journal bearing ( d l ) decrease to compensate for the pressure reduction in the upper and lower portions of the hourglass sleeve. In this analysis, we assume that d u and d l are 1 μm. We investigate the performance of the proposed hourglass-shaped groove depth in two cases: case 1 is a straight sleeve with hourglass-shaped groove depth as in Fig. 5, and case 2 is an hourglass-shaped sleeve with hourglass-shaped groove depth, as in Fig. 13. Figure 14a shows the pressure distribution of FDBs with straight sleeves and hourglass-shaped groove depths (case 1). The rotating speed and eccentricity ratio are 7,200 rpm and 0.1, respectively. The maximum pressure of the upper and lower grooved journal bearing are 2.82 and 2.04 MPa, respectively. These are greater than those of FDBs with straight sleeves and straight groove depths (Fig. 7a) by 4.4 and 3.0 %, respectively. Figure 14b shows the pressure distribution of FDBs with hourglass-shaped sleeves and hourglass-shaped groove depths (case 2). The maximum pressures of upper grooved journal bearing and lower grooved journal bearing are 2.08 and 1.43 MPa, respectively. These are larger than those of FDBs with straight sleeves and straight groove depths (Fig. 7b) by 2.5 and 1.4 %, respectively. In both cases, hourglass-shaped groove depth in journal bearing increases the maximum pressure. Figure 15 shows the effect of taper length on the friction torque of FDBs with straight and hourglass-shaped groove depths. The friction torque decreases with increasing taper length, but the friction torque of the FDBs with straight groove depth is nearly the same as that of FDBs with hourglass-shaped groove depth. Figure 16 shows the effect of taper length on the stiffness and damping coefficients of FDBs with straight and hourglass-shaped groove depths. The radial stiffness and damping coefficients decrease with increasing taper length, but the stiffness and damping coefficients of FDBs with hourglass-shaped groove depths are always larger than those of FDBs with straight groove

9 1443 Fig. 14 Pressure distribution of the proposed journal bearing (eccentricity ratio = 0.1), a pressure distribution of the FDBs with straight sleeve and hourglass-shaped groove depth (case 1), b pressure distribution of FDBs with hourglass-shaped sleeve and hourglass-shaped groove depth (case 2) Fig. 15 Friction torque of FDBs with straight and hourglass-shaped groove depths (eccentricity ratio = 0.1) depths. The axial stiffness and damping coefficients maintain the same value because hourglass-shaped groove depth does not affect the pressure distribution of thrust bearing in this FDB model. Figure 17 shows the effect of taper length on the stability of FDBs with straight and hourglass-shaped groove depths. Critical mass decreases with increasing taper length, but the critical mass of FDBs with hourglass-shaped groove depth is always approximately 10 % larger than that of FDBs with straight groove. Figure 18 shows the effect of taper length on FDB whirl radius with straight and hourglass-shaped groove depths. The mass unbalance of the HDD spindle system is assumed to be 0.2 g mm. Whirl radius increases with increasing taper length, but the whirl radius of FDBs with hourglassshaped groove depths is always smaller at any position of the rotating shaft than that of FDBs with straight groove depths because an hourglass-shaped groove depth increases the stiffness and damping coefficients. Figure 19 shows the effect of taper length on x-directional amplitudes of HSW and rotation frequency for FDBs with straight and hourglass-shaped groove depths, respectively. The amplitudes of the rotation frequency of FDBs with hourglass-shaped groove depths are smaller than those of the FDBs with straight groove depths by approximately 5 to 10 %. The amplitude of HSW frequency of FDBs with hourglass groove depths is smaller than that of FDBs with straight groove depths by approximately 10 %.

10 1444 Fig. 16 Stiffness and damping coefficients of FDBs with straight and hourglass-shaped groove depths (eccentricity ratio = 0.1), a Kxx, b Kzz, c Cxx, d Czz Fig. 17 Stability chart of FDBs with straight and hourglass-shaped groove depths due to taper length (eccentricity ratio = 0.1) Fig. 19 X-directional amplitude of half-speed whirl and rotating frequencies for the FDBs with straight and hourglass-shaped groove depths (eccentricity ratio = 0.1) 6 Conclusions Fig. 18 Whirl radius of the FDBs with straight and hourglass-shaped groove depths (eccentricity ratio = 0.1) This research investigated the characteristics of FDBs of an HDD spindle motor due to hourglass-shaped sleeve. We demonstrated experimentally that an hourglass-shaped sleeve generated through the ball-sizing process is a major source of large RRO and NRRO. We also numerically proved the negative effect of hourglass-shaped sleeves on pressure, friction torque, stiffness and damping coefficients, critical mass, and shock response. Finally, we proposed a robust design of FDBs with hourglass-shaped groove depth to compensate for the decrease of static and dynamic performance of FDBs with hourglass-shaped sleeves. This research can be utilized to develop a more robust design of FDBs and the HDD disk-spindle system.

11 Acknowledgments This research was performed at the Samsung- Hanyang Research Center for Precision Motors, sponsored by Samsung Electro-Mechanics Co. Ltd. and by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology ( ). References Jang GH, Lee SH (2006) Determination of the dynamic coefficients of the coupled journal and thrust bearings by the perturbation method. Tribol Lett 22: Jang GH, Yoon JW (2003) Stability analysis of a hydrodynamic journal bearing with rotating herringbone grooves. J Tribol 125: Jang GH, Lee SH, Kim HW (2006) Finite element analysis of the coupled journal and thrust bearing in a computer hard disk drive. J Tribol 128: Kim MG, Jang GH, Kim HW (2010) Stability analysis of a disk-spindle system supported by coupled journal and thrust bearings considering five degrees of freedom. Tribol Int 43: Kim MG, Jang GH, Lee JH (2011) Robust design of a HDD spindle system supported by fluid dynamic bearings utilizing the stability analysis. Microsyst Technol 17: Koak KY, Jang GH, Kim HW (2009a) Whirling, tilting and axial motions of a HDD spindle system due to the manufacturing errors of FDBs. Microsyst Technol 15: Koak KY, Kim HW, Jung KM, Jang GH (2009b) Dynamic characteristics of a HDD spindle system due to imperfect shaft roundness. IEEE Trans Magn 45: Lee JH, Jang GH, Ha HJ (2012) Robust optimal design of the FDBs in a HDD to reduce NRRO and RRO. Microsyst Technol 18: Lee JH, Lee MH, Jang GH (2013a) Experimental verification of the optimal FDBs in a HDD spindle motor to minimize power loss. IEEE Trans Magn 49: Lee JH, Jang GH, Jung KM (2013b) Optimal design of fluid dynamic bearings to develop a robust disk-spindle system in a hard disk drive utilizing modal analysis. Microsyst Technol 19: Yoon JK, Shen IY (2005) A numerical study on rotating-shaft spindles with nonlinear fluid-dynamic bearings. IEEE Trans Magn 41: Zhang XQ, Wang XL, Liu R (2012) Effects of microfabrication defects on the performance of gas bearings with high aspect ratio in microengine. Tribol Int 48: