Height analysis of the air-oil interfaces in the non-operating and operating FDBs in a tied shaft of HDDs

Transcription

1 ( ().,-volV)( ().,-volV) TECHNICAL PAPER Height analysis of the air-oil interfaces in the non-operating and operating FDBs in a tied shaft of HDDs Minho Lee 1 Jihoon Lee 1 Kyobong Kim 1 Gunhee Jang 1 Received: 15 November 2017 / Accepted: 29 March 2018 Ó Springer-Verlag GmbH Germany, part of Springer Nature 2018 Abstract We proposed a method to predict the heights of upper and lower air-oil interfaces of the non-operating and operating fluid dynamic bearings (FDBs) in the tied shaft of hard disk drives. To predict the height of upper and lower air-oil interfaces, we formulated the linear pressure and volume equations in both cases of non-operating and operating conditions, respectively. The initial heights of upper and lower air-oil interfaces are determined by pressure and volume equations during non-operating condition. Pressure equation consists of capillary pressure, atmospheric pressure, hydrostatic pressure and applied pressure, and volume equation consists of the volumes of the clearance and the injected oil. In case of operating condition, hydrodynamic pressure generated by grooved bearings is additionally considered in the pressure equation, because heights of air-oil interfaces vary due to hydrodynamic pressure during operating condition. The linear pressure and volume equations were solved simultaneously to calculate the heights of upper and lower air-oil interfaces both in non-operating and operating conditions. In case of non-operating conditions, the height of upper air-oil interface increases with the increase of pressure difference because pressure of lower air-oil interface is higher than that of upper airoil interface. Since the volume of injected oil is constant, height of lower air-oil interface decreases due to pressure difference. In case of operating conditions, the height of upper air-oil interface decreases according to rotating speed because more oil flows inside the FDBs and recirculation channel than upper seal. On the other hand, the height of the lower air-oil interface increases because volume variation of the oil due to the increase of the flying height is smaller than that due to the decrease of the height of the upper air-oil interface. Finally, we verified the proposed method by measuring the height of upper air-oil interface both in the non-operating and operating conditions. 1 Introduction Figure 1 shows the mechanical structure of hard disk drives (HDDs) supported by fluid dynamic bearings (FDBs) in a rotating shaft and tied shaft. As shown in Fig. 1, the FDBs in the rotating shaft have a seal which is located to upward part of upper thrust bearing and the shaft combined with rotating parts of HDD rotates during operation. On the other hand, the FDBs in the tied shaft have double seals which are upper and lower seals and the sleeve combined with rotating parts of HDD rotates during operation. HDDs with the tied shaft are more robust under external shock than those with the rotating shaft because both top and & Gunhee Jang ghjang@hanyang.ac.kr 1 PREM, Department of Mechanical Convergence Engineering, Hanyang University, 222, Wangsimni-ro Seongdong-gu, Seoul 04763, Republic of Korea bottom of the shaft are fixed to cover and base of HDDs, respectively. They have been mainly applied in the HDDs applied to computer servers requiring high memory density. However, the FDBs in the tied shaft are more vulnerable to oil leakage than those in the rotating shaft because the FDBs in the tied shaft have double seals located both at the upper and lower air-oil interfaces. Oil injection of the FDBs in the tied shaft is mainly achieved by hydrostatic pressure and capillary pressure difference. After the oil injection, heights of the upper and lower air-oil interfaces during non-operating condition are determined by the pressure equilibrium and the volume occupied by oil. Heights of air-oil interfaces of FDBs in the tied shaft during operating condition are determined by the initial heights of air-oil interfaces in non-operating condition and the pressure generated by grooved bearings. Oil which is in equilibrium during non-operating condition may leak out in operating conditions if excessive oil is injected or air-oil interface is broken due to external shock.

2 Fig. 1 Mechanical structure of HDDs supported by FDBs in the tied shaft in a the rotating shaft and b tied shaft Also, air-oil interface of FDBs in the tied shaft can be easily broken during operating condition according to increasing the height of the air-oil interface due to rotating speed. Therefore, prediction of the heights of air-oil interfaces of the FDBs in the tied shaft is important during non-operating and operating conditions because they are important variables to determine oil leakage as well as robustness against external pressure and shock. Many researchers have investigated the seal of FDBs or oil leakage due to shock. Roger Ku and Shumway (1998) investigated experimentally shock responses during operating conditions. They measured radial displacement of disk due to amplitude and duration of shock. Kita et al. (2002) studied oil leakage according to flow pressure on upper groove-less area in herringbone grooved journal bearings and they measured amount of oil leakage to verify their analysis. Hishida et al. (2010) analyzed the fundamental characteristics of a taper seal used to prevent oil leakage from fluid bearings and investigated experimentally oil meniscus by using a micro-focus laser microscope. Jung and Jang (2011) studied the axial shock-induced motion of the air-oil interface in non-operating FDBs by experiment and simulation. They reported the effects of the magnitude of the shock and oil viscosity on the break-up of the air-oil interface. Wei et al. (2011) studied the characteristics of leakage of rotary seal by using hydraulic resistance network. Leakage characteristics of rotary seal were investigated according to rotating speed, temperature and structural parameters. Andres and Delgado (2012) studied the oil flow in grooved oil seals with hydro static bearings operating eccentrically. They also predicted the stiffness and damping coefficients according to static journal eccentricity ratio. Jung et al. (2012) investigated the behavior of fluid lubricant and air-oil interface of the FDBs according to operating condition and seal design. They calculated two-phase flows of air and oil according to tapering angle and initial position of fluid by using volume of fluid (VOF) method. Jung et al. (2013) studied the behavior of air bubbles and the air-oil interface in FDBs at low speeds by using the VOF method and their research was verified by the experimental results. Feng and Li (2013) studied the oil leakage of the FDBs with radial and axial seals. They analyzed the deformed interface according to amplitude of shock and rotating speed. However, Kita et al. did not consider seal structure of their journal bearing and other researchers studied FDBs in a rotating shaft with one seal structure. No previous researchers have studied to predict height of air-oil interface of FDBs. Several researchers have studied the FDBs in the tied shaft with double seals Lee et al. (2016) investigated oil injection process to predict the oil injection time of FDBs in the tied shaft by using the Kirchhoff s pressure law. They proposed an algorithm to calculate the oil injection time and calculated the oil injection time according to temperature, clearance of upper seal and radius of recirculation channel. They also verified the proposed method by measuring oil injection time. Injected oil is located to specific height by the pressure equilibrium and the volume occupied by oil and can be broken by external pressure or shock. So, the height of air-oil interfaces should be predicted to prevent oil leakage due to external pressure or shock. However, their research was restricted to predict oil injection time of the FDBs in a tied shaft. They did not study the air-oil interfaces of the FDBs in the tied shaft and did not consider location of the air-oil interfaces. Kang et al. (2016) investigated the dynamic behavior of air-oil interface of the FDBs in the tied shaft due to non-operating axial shock. They conducted a drop test of the HDDs to measure oil leakage, and simulated the air-oil interface due to non-operating axial shock. However, they did not study the variation of the heights of air-oil interfaces of FDBs. Park et al. (2016) investigated the air-oil interface in tiedshaft type FDBs according to chamfer location and inclination angle of circulation hole. They analyzed the

3 hydrodynamic pressure by using commercial software ANSYS and calculated the height of air-oil interfaces in the tied shaft. When disks are installed to the HDD spindle motor, external pressure may be applied to upper or lower seals and air-oil interfaces can be broken due to applied external pressure. Air-oil interfaces can also be broken when the rotating speed changes. Therefore, applied pressure and rotating speed should be considered to calculate the height of air-oil interfaces of FDBs in the tied shaft. However, they did not include the effect of the difference of applied pressures of upper and lower air-oil interfaces and the rotating speed of the FDBs. They also did not verify their simulated results with experiments. In this research, we proposed a method to predict the heights of upper and lower air-oil interfaces of the FDBs in the tied shaft of HDDs. We formulated a pressure equation during non-operating conditions according to capillary pressure, atmospheric pressure, hydrostatic pressure and applied pressure, and a volume equation according to the volumes of the clearance and the injected oil. We also formulated the pressure equation due to the effect of hydrodynamic pressure generated by grooved bearings. We solved the linear equations of pressure and volume simultaneously to calculate the heights of upper and lower air-oil interfaces both in non-operating and operating conditions. In case of operating conditions, we calculated the hydrodynamic pressure generated by grooved bearings, and solved the linear equations repeatedly with hydrodynamic pressure to calculate the heights of upper and lower air-oil interfaces. Finally, we verified the proposed method by measuring the height of upper air-oil interface. 2 Method of analysis 2.1 Prediction of the heights during nonoperating condition Since the FDBs in the tied shaft have double seals which are upper and lower seals as shown in Fig. 1a, they are vulnerable to oil leakage. Oil in the FDBs in the tied shaft is injected by capillary pressure (Lee et al. 2016), and the initial heights of upper and lower air-oil interfaces are determined by pressure equation and volume equation in non-operating condition. Figure 2 shows the pressures and volumes and heights of the air-oil interfaces of the FDBs in a tied shaft. Pressure equation and volume equation can be written as follows (White 1999). P 2 ðh 2 ÞP 1 ðh 1 Þ ¼ qgh ð1þ V Injection ¼ V 1 ðh 1 ÞþV 2 ðh 2 ÞþV FDB ð2þ Fig. 2 Reference line and heights of the air-oil interfaces in nonoperating condition where P 1 (h 1 ), P 2 (h 2 ), q, g and H are pressures at upper and lower air-oil interfaces, density, gravitational acceleration and height between upper and lower air-oil interfaces, respectively. V Injection is the volume of injected oil in upper and lower seals, and V 1 (h 1 ) and V 2 (h 2 ) are volumes of upper and lower seals of the FDBs, respectively. h 1 and h 2 are the initial heights of upper and lower air-oil interfaces of the FDBs in the tied shaft in non-operating condition, respectively. V FDB is volume of the inside of the FDBs and recirculation channel except volumes of the upper and lower seals. P 1 (h 1 ) and P 2 (h 2 ) in Eq. (1) can be written in the following Eqs. (3) and (4). P 1 ðh 1 Þ¼P atm þ P ap1 P c1 ðh 1 Þqgh 1 ð3þ P 2 ðh 2 Þ¼P atm þ P ap2 P c2 ðh 2 Þqgh 2 ð4þ where P atm, P ap1, P ap2, P c1 (h 1 ) and P c2 (h 2 ) are atmospheric pressure, applied external pressures of upper and lower airoil interfaces, and capillary pressures of upper and lower air-oil interfaces, respectively. It is required to consider pressure difference between upper and lower air-oil interfaces to predict the height of air-oil interfaces because external pressure may be applied to upper or lower interfaces in the process of disk installation. Equation (1) can be rewritten by substituting Eqs. (3) and (4) into Eq. (1) as follows. P c1 ðh 1 ÞP c2 ðh 2 Þ ¼ qgðh h 1 þ h 2 Þþ P ap1 P ap2 ð5þ Capillary pressures (P c1 (h 1 ) and P c2 (h 2 )) can be written as follows (Lee et al. 2016).

4 P c1 ðh 1 Þ ¼ r 1 þ 1 ð6þ r u1 r u2 P c2 ðh 2 Þ ¼ r 1 þ 1 ð7þ r l1 r l2 where r, r u1,r l1,r u2 and r l2 are surface tension, radii of curvature of film thickness direction of upper and lower air-oil interfaces and radii of curvature of radial direction of upper and lower air-oil interfaces, respectively. The radii of curvature of film thickness direction can be written as follows. d 1 =2 r u1 ¼ ð8þ cos h c þ h g1 d 2 =2 r l1 ¼ ð9þ cos h c þ h g2 where d 1,d 2, h c, h g1 and h g2 are clearances of upper and lower air-oil interfaces, contact angle and geometric angles of upper and lower air-oil interfaces, respectively. The radii of curvature of radial direction (r u2 and r l2 ) are radii of the bearings. Equation (5) can be rewritten by substituting Eqs. (6) (9) into Eq. (5) as follows. 2 cos h c þ h g1 2 cos h c þ h g2 d 1 d 2 ¼ qg ð r H h 1 þ h 2 Þþ 1 r P 1 ap1 P ap2 þ 1 r l2 r u2 ð10þ Volume equations of the FDBs in this research can be written as follows. V 1 ¼ 1 h 2 r2 u2 ð r u2 g 1 Þ 2 2 r u2 g 1 h 1 tanh g1a i 2 þ r u2 h 1 tanh g1b ph 1 ð11þ V 2 ¼ rl2 2 1 n ðr l2 g 2 Þ 2 o 2 þ r l2 g 2 h 2 tanh g2 ph 2 2 Vðh 1 ; h 2 Þ¼V 1 ðh 1 ÞþV 2 ðh 2 Þ ð12þ ð13þ where V 1,V 2,g 1,g 2, h g1a, h g1b and h g2 are volumes in upper and lower seals of FDBs, clearances of upper and lower seals and tapered angles of upper and lower seals, respectively. g 1,g 2, h g1a, h g1b and h g2 are described as shown in Fig. 3. Finally, we can determine the initial heights of upper and lower air-oil interfaces of the FDBs in the tied shaft by solving the linear simultaneous equations of Eqs. (10) and (13) in non-operating condition. Fig. 3 Design variables of the upper and lower seals 2.2 Prediction of the heights during operating condition Figure 4 shows the hydrodynamic pressure and the heights of the upper and lower air-oil interfaces in operating condition. Since hydrodynamic pressure is generated by grooved bearings in operating condition, hydrodynamic pressure should be considered to calculate the heights of the air-oil interfaces of the FDBs in the tied shaft during operating condition. Pressure generated by grooved bearings can be obtained by solving Reynolds equation of the journal and thrust bearings. Reynolds equations of the journal and thrust bearings can be written in the following Eqs. (14) and (15) (Bernard et al. 1994). Fig. 4 Reference line and heights of the air-oil interfaces in operating condition

5 o h 3 op þ o h 3 op ¼ R h _ oh Roh 12l Roh oz 12l oz 2 Roh þ oh ð14þ ot 1 o r h3 op þ o h 3 op ¼ r h _ oh r or 12l or roh 12l roh 2 roh þ oh ð15þ ot where R, h, _ h, p and l are the radius, rotating speed, film thickness, pressure and coefficient of viscosity, respectively. r, h and z are the radial, circumferential and axial coordinates, respectively. The heights of the air-oil interfaces of the FDBs in the tied shaft in operating condition can be calculated by pressure equation and volume equation during operating condition. Pressure equation in dynamic equilibrium condition and volume equation during operating condition can be written as follows. P 1 ¼ P atm P c1 h 1 þ qgh 1 ð16þ P 2 ¼ P atm P c2 h 2 þ qgh 2 ð17þ P 2 P 1 ¼ P c1 h 1 Pc2 h 2 þ qg h 2 h 1 ð18þ V Injection ¼ V h 1 ; h 2 ð19þ where P 1 ; P 2 ; h 1 and h 2 are hydrodynamic pressures, and the heights of the upper and lower air-oil interfaces in operating condition, respectively. P 1 and P 2 can be obtained by solving the Reynolds equations in Eqs. (14) and (15). h 1 and h 2 are calculated repeatedly by the algorithm as shown in Fig. 5. First, initial heights of upper and lower air-oil interfaces (h 1 and h 2 ) are calculated in nonoperating condition. A finite element model is developed with the consideration of h 1 and h 2 to solve the Reynolds equation and to determine P 1 and P 2. Then, h 1 and h 2 are determined by solving the linear simultaneous equations of Eqs. (18) and (19). We repeat this process until the solution of h 1 and h 2 is converged. 3 Results and discussion 3.1 Calculation and measurement of the height in non-operating condition Table 1 shows the oil properties of the FDBs in the tied shaft. Figure 6 shows the calculated heights of upper and lower air-oil interfaces according to pressure difference between upper and lower air-oil interfaces. As shown in Fig. 2, oil meniscus height of upper air-oil interface is measured and calculated from the reference line located upward from the bottom of upper seal by mm and oil meniscus height of lower air-oil interface is calculated from the reference line located upward from the bottom of Fig. 5 Algorithm to calculate the heights of air-oil interfaces of the FDBs in the tied shaft Table 1 Oil properties of the FDBs in the tied shaft Properties Value Density (kg/m 3 ) 920 Contact angle ( ) 5 Surface tension (N/m) lower seal by mm. Height of upper air-oil interface increases with the increase of pressure difference because pressure of lower air-oil interface is higher than pressure of upper air-oil interface. The pressure difference is 469 Pa when height of upper air-oil interface is mm. Since the volume of injected oil is constant, height of lower airoil interface decreases with the increase of pressure difference. We verified the proposed method by measuring the height of upper air-oil interface. Figure 7 shows the measured height of upper air-oil interfaces of the FDBs in the tied shaft according to pressure difference. We measured only the height of upper air-oil interface of five samples

6 because pressure of lower air-oil interface was higher than pressure of upper air-oil interface. The pressure difference of 470 Pa is applied when average height of upper air-oil interface is measured to be mm. 3.2 Calculation and measurement of the height in operating condition Fig. 6 Simulated heights of a upper and b lower air-oil interfaces according to pressure difference during non-operating condition Fig. 7 Measured heights of upper air-oil interface according to pressure difference during non-operating condition because the rotor structure hides the lower air-oil interface. Results of five samples were presented as lines #1 to #5 in Fig. 7. Measured height of upper air-oil interfaces of the FDBs is very close to the simulated one in Fig. 6a. As predicted in the simulation, the height of upper air-oil interface increases with the increase of pressure difference Table 2 shows the design variables of the grooved journal and thrust bearings. The volume variation of the oil in the upper and lower seals should be considered with increase of rotating speed because rotor is moving up by pressure due to grooved thrust bearings and the flying height increases with the increase of rotating speed. So we considered the volume variation of the oil in the upper and lower seals according to rotating speed. In this research, mass and volume of the injected oil are 7.3 mg and 7.935e-9 m 3 and initial height of the upper air-oil interface in non-operating condition is lm. However, the heights of the upper air-oil interface of samples 1 and 2 which is used for experiment are and lm. The heights of the air-oil interfaces may be lower than design value because the injected oil evaporates or the oil is injected less than required amount of the oil. Thus, we adjusted the volume of the injected oil from 7.935e-9 m 3 (7.3 mg) to 7.233e-9 m 3 (6.7 mg) in simulation to match the experimental measurements. In this condition, the simulated height of the upper air-oil interface was lm. The height of the upper air-oil interface was calculated and measured with the increase of rotating speed from 3600 to 7200 rpm with the intervals of 1800 rpm. Figure 8 shows the calculated and measured heights of the upper airoil interface of the FDBs in the tied shaft according to rotating speed. Table 3 shows the measured and simulated heights and the errors according to rotating speed. We measured the height of upper air-oil interface of two different samples (#1 and #2) during operating conditions which were represented as #1 and #2 in Fig. 8 with solid lines. Simulation results are shown as dotted line in Fig. 8. When rotating speed increases, the height of the upper airoil interface decreases. The oil flows inside of the FDBs because pumping direction of the upper grooved thrust bearing is inward. And more oil flows into the recirculation channel than upper seal because the diameter of the recirculation channel is relatively lager than clearance of the upper seal (flow resistance of recirculation channel is smaller than that of clearance). For these reasons, the height of the upper air-oil interface decreases with the increase of rotating speed. As shown in Fig. 8 and Table 3, the simulated height of the upper seal relatively well matches with the measured height of upper seal according to rotating speed even though the finite element model

7 Table 2 Major design variables of grooved journal and thrust bearings Design variable Journal bearing Thrust bearing Groove type (-) Herringbone Spiral Groove depth (lm) 5 15 Groove angle ( ) Number of grooves (EA) 6 10 Ratio of groove to groove and ridge (-) Total length of grooved journal bearings (mm) Upper: 1.0 Lower: 1.1 Total axial gap of thrust bearing (lm) 20 Fig. 8 Simulated and measured heights of upper air-oil interface according to rotating speed during operating condition cannot describe perfectly real shape of FDBs such as chamfer of recirculation channel and curved corner of thrust bearings. Nevertheless, the trend in the measured and simulated results, which decreases with increasing rotating speed, is similar and there exist the average errors of 4.45% in sample #1 and 10.46% in sample #2 between the measured and simulated results. The height of the lower air-oil interface was also calculated according to rotating speed as shown in Fig. 9. The height of the lower air-oil interface increases with the increase of the rotating speed because volume variation occupying the oil due to the increase of the flying height from 7.08 to 9.03 lm is smaller than that due to the decrease of the height of the upper air-oil interface from to lm. Fig. 9 Simulated heights of lower air-oil interface according to rotating speed during operating condition 4 Conclusions We proposed a method to predict the heights of upper and lower air-oil interfaces of the FDBs in the tied shaft of HDDs. We formulated a pressure equation during nonoperating conditions according to capillary pressure, atmospheric pressure, hydrostatic pressure and applied pressure, and a volume equation according to the volumes of the clearance and the injected oil. We also formulated the pressure equation including the effect of hydrodynamic pressure generated by grooved bearings during operating condition. We solved the linear equations of pressure and volume simultaneously to calculate the heights of upper and lower air-oil interfaces both in non-operating and operating conditions. In case of non-operating conditions, height of upper air-oil interface increases with the increase of pressure difference because pressure of lower air-oil interface is higher than that of upper air-oil interface. Since Table 3 Values and errors of the measured and simulated results according to rotating speed Rotating speeds (rpm) Heights of the upper seal (mm) Error #1 (%) Error #2 (%) Sample #1 Sample #2 Simulation

8 the volume of injected oil is constant, height of lower airoil interface decreases with the increase of pressure difference. In case of operating conditions, height of upper air-oil interface decreases with rotating speed because more oil flows inside of the FDBs and recirculation channel than upper seal. The height of the lower air-oil interface increases with the increase of the rotating speed because volume variation of the oil due to the increase of the flying height is smaller than that due to the decrease of the height of the upper air-oil interface. Finally, we verified the proposed method by measuring the height of upper air-oil interface both in non-operating and operating conditions. The proposed method can be effectively applied to predict the air-oil interfaces of the FDBs in the tied shaft and this research contribute to developing a robust design of FDBs. References Andres LS, Delgado A (2012) A novel bulk-flow model for improved predictions of force coefficients in grooved oil seals operating eccentrically. J Eng Gas Turbines Power 134: Bernard JH, Steven RS, Bo OJ (1994) Fundamentals of fluid film lubrication. McGraw-Hill, Inc., New York Feng M, Li C (2013) Characteristics of axial and radial surface tension sealing structures for HDD FDB spindles. IEEE Trans Magn 49: Hishida N, Hirayama T, Hashimoto M, Matsuoka T (2010) Analysis and experimental study on oil leakage from fluid bearing. Int J Surf Sci Eng 4: Jung KM, Jang GH (2011) Axial shock-induced motion of the air-oil interface of fluid dynamic bearings of a non-operating hard disk drive. IEEE Trans Magn 47: Jung KM, Jang GH, Kim JH (2012) Behavior of fluid lubricant and air oil interface of operating FDBs due to operating condition and seal design. Microsyst Technol 18: Jung KM, Lee JH, Jung YH, Jang HK, Jang GH (2013) Behavior analysis of air bubbles in the oil lubricant of FDBs at low speed operating conditions. Microsyst Technol 19: Kang CH, Jung YH, Lee JH, Lee MH, Kim BC, Kang GH (2016) Dynamic behavior of air-oil interface in fluid dynamic bearings with a double sealing structure in a hard disk drive due to non-operating axial shock. Tribol Int 98: Kita H, Matsuoka K, Obata S, Noda H (2002) Prediction method of oil leakage of FDBs using numerical analysis. Microsyst Technol 8: Lee MH, Lee JH, Kang CH, Kim KB, Jang HK, Kim BC, Kang GH (2016) Prediction of the oil injection time of FDBs in an HDD spindle motor with a tied shaft by utilizing Kirchhoff s pressure law. Microsyst Technol 22: Park CH, Lee DH, Jung IY, Jun SO (2016) Prediction of air-oil interface location in tied-shaft type fluid dynamic bearings. J Mech Sci Technol 30: Roger Ku CP, Shumway M (1998) Experimental investigation of shock responses of cantilever-shaft design hydrodynamic bearing spindle motors. IEEE Trans Magn 34: Wei C, Hong JH, Hu J (2011) Analysis and experimental study on the characteristics of leakage of rotary seal using sealing ring. Adv Materials Res : White FM (1999) Fluid mechanics. McGraw-Hill, Inc., New Delhi