DOI 10.1007/s00542-015-2537-0 TECHNICAL PAPER Effect of the cross sectional shape of the recirculation channel on expulsion of air bubbles from FDBs used in HDD spindle motors Yeonha Jung 1 Gunhee Jang 1 Chiho Kang 1 Hyunho Shin 2 Jongyeop Jeong 2 Received: 30 September 2014 / Accepted: 11 April 2015 Springer-Verlag Berlin Heidelberg 2015 Abstract This paper experimentally and numerically investigated the behavior of air bubbles in the oil lubricant of operating fluid dynamic bearings (FDBs) with a crosssectional recirculation channel (RC). Experiments were performed to visually observe the behavior of trapped air bubbles in operating FDBs with crescent and circular cross-sectional RCs, respectively. Furthermore, a numerical study was carried out to investigate the phenomenon of air bubble expulsion from the FDB. The flow field of a FDB was calculated by the Navier Stokes equation, continuity equation and volume of fluid (VOF) method. Results indicated that a crescent cross-sectional RC generates a larger pressure difference between the upper and lower regions of the RC and a faster flow velocity along the RC than a circular cross-sectional RC, because the former has larger wall shear stress than the latter, mainly due to a longer perimeter. Finally, we designed a novel RC that efficiently expels air bubbles. 1 Introduction Fluid dynamic bearings (FDBs) are used in the spindle motors of computer hard disk drives (HDDs). Figure 1 shows the mechanical structure of a HDD with FDBs. FDBs in a HDD are composed of coupled journal and thrust bearings, and they generate pressure through the fluid lubricant in the micron-level clearance with pumping * Gunhee Jang ghjang@hanyang.ac.kr 1 2 Department of Mechanical Engineering, Hanyang University, 17 Haengdang Dong, Seongdong Gu, Seoul 133 791, Korea Samsung Electro-Mechanics Co. Ltd., 314, Maetan 3 Dong, Yeongtong Gu, Suwon Si, Gyeonggi Do 443 743, Korea and wedge effect. The FDBs provide both the stiffness and damping effect and they prohibit solid contact between the shaft and sleeve, which have lower vibration and noise than ball bearings. However, one of the weaknesses of FDBs is instability due to air bubbles in the oil lubricant of FDBs. Air bubbles are formed and trapped in the oil lubricant by an improper oil injection process or external shock. Trapped air bubbles decrease the rotational accuracy and stability of a rotor-bearing system in a manner that generates non-repeatable run-out (NRRO) and decreases the stiffness and damping coefficients of FDBs. One possible solution to expel trapped air bubbles from FDBs is to include a recirculation channel (RC). The RC is designed to balance the pressures between the upper and lower parts of the FDB and to circulate the oil lubricant as well as to expel air bubbles out of the FDB. However, it has not been verified experimentally or numerically whether the RC expels air bubbles out of the FDB. Several researchers have studied the behavior of air bubbles in the FDBs of HDDs. Asada et al. (2002) experimentally investigated the ingestion of air bubbles in journal bearings at both low and high rotating speeds. They also examined the effect of groove angle on air bubbles ingestion. In 2005, this group experimentally studied the oil circulation mechanism that results in expulsion of air bubbles trapped in FDBs by calculating the pressure, flow rate, and capillary force of each part of a FDB. Jung et al. (2013) numerically investigated the motion of air bubbles trapped in grooved and plane journal bearings of an operating FDB. They proposed a novel FDB design to expel air bubbles trapped in grooved journal and plane journal bearings to the outside air. However, none of these prior studies investigated the effect of a RC on air bubble expulsion. Several researchers have investigated flow field characteristics induced by passage of fluid through the
flow field of a FDB was calculated by the Navier Stokes equation and the continuity equation. Finally, we designed a RC that expels air bubbles efficiently from a FDB. 2 Experiment 2.1 Experimental setup and model Fig. 1 Mechanical structure of a HDD with a FDB Figure 2 shows the experimental setup we used to investigate the behavior of air bubbles in a FDB. Two FDBs one with a crescent cross-sectional RC and the other with a Fig. 2 Experimental setup to observe the behavior of air bubbles cross-section of a RC. Bahrami et al. (2007) numerically studied the pressure difference in micro channels with an arbitrary cross-section and experimentally verified numerical models. They proposed a novel approximate solution for determining the pressure difference in micro channels with an arbitrary cross-section. Metz et al. (2010) numerically and experimentally investigated the movement of gas bubbles in tapered structures. They showed that the gas bubble in the narrow end of the tapered channel moves towards the wider opening of the channel to minimize its surface energy. However, they only studied the motion of bubbles in channel systems. No prior study investigated the effect of a RC on expelling air bubbles from FDBs used in the spindle motor of a HDD. This paper experimentally and numerically investigates the behavior of air bubbles in the oil lubricant of operating FDBs according to the cross-sectional shape of the RC. Experiments were performed to visually observe the behavior of trapped air bubbles in operating FDBs with crescent and circular cross-sectional RCs, respectively. Furthermore, a numerical study was carried out to investigate the phenomenon of expulsion of air bubbles from FDBs. The Fig. 3 Observed behavior of air bubbles in FDBs with a crescent cross-sectional RC. a Behavior of air bubbles during operation. b Behavior of air bubbles under non-operating conditions. c Behavior of air bubbles at re-operating condition
After air bubbles were generated, the rotor was operated at 5400 rpm, and the behavior of the air bubbles at the bottom of the FDB was recorded using a high-speed camera with 3.260 fps (frames-per-second) and 1280 800 pixel. 2.2 Experimental results Figures 3 and 4 show the behavior of air bubbles in FDBs with crescent and circular cross-sectional RCs, respectively. As the rotor rotated, the air bubbles spread circumferentially and moved in the circumferential direction. When the rotor stopped, the moving air bubbles stopped and were trapped at the lower region of the RC, because the lower region of the RC had more space than the axial clearance of the thrust bearing and air bubbles at the lower region of the RC minimized their surface to reduce surface tension. After the rotor rotated again, the air bubbles in the crescent cross-sectional RC were sucked into the RC and finally discharged outside of the FDB because the upper region of the RC was exposed to the atmosphere. However, the air bubbles in the circular crosssectional RC remained trapped in the lower region of the RC. These results indicated that the cross-section of the RC had a significant effect on air bubble expulsion from the FDB. 3 Analysis of oil flow 3.1 Analysis method Flow of an oil lubricant was calculated using FLUENT (2006). Navier Stokes and continuity equations are shown in Eqs. (1) and (2), respectively: ( (ρv) + (ρvv) = p + [ )] µ v + v T + ρg + F t (1) Fig. 4 Observed behavior of air bubbles in FDBs with a circular cross-sectional RC. a Behavior of air bubbles during operation. b Behavior of air bubbles under non-operating conditions. c Behavior of air bubbles at re-operating condition circular cross-sectional RC were prototyped. The covers of the FDBs comprised a transparent acrylic panel to allow visual observation of the motion of air bubbles. And two light sources were arranged at the bottom of the FDBs to easily observe the air bubbles. The area of the crescent cross-section was the same as that of the circular cross-section. Generally, air bubbles were generated by negative pressure. The negative pressure can be occurred by rotating the FDB in the opposite direction due to the herringbone groove of journal bearing. Fig. 5 Geometry and boundary conditions of FDB
Fig. 6 Finite volume model of FDBs with crescent and circular cross-sectional RCs Table 1 Properties of oil lubricant at 20 C Property of fluid Value Viscosity (Pa s) 0.0129 Density (kg/m 3 ) 920.4 Surface tension coefficient (N/m) 0.0315 Static contact angle at wall ( ) 6 Table 2 Calculated maximum and minimum pressures in FDBs with crescent and circular cross-sectional RCs Crescent cross-sectional RC Circular crosssectional RC Maximum pressure (Pa) 1,187,542 1,187,523 Minimum pressure (Pa) 61,421 61,481 ρ t + (ρv) = S where ρ, µ, and p are the density, viscosity, and pressure, respectively, and v, g, F and S are the velocity vector and gravity acceleration vector, the surface tension force that arises from interaction between air and oil, and the mass flow, which adds to the continuous phase from the dispersed second phase, respectively. In the steady laminar flow of the oil lubricant, F and S are assume to be zero. Equation (2) is the general form (2) of the continuity equation and is valid for incompressible as well as compressible flows. The boundary condition for velocity is a no-slip condition on the wall. The two-phase flow of the air and oil is calculated using the VOF method, which is known to be an efficient numerical technique for tracking and locating the free surface or the fluid fluid interface of multi-phase flows. The VOF method defines the volume fraction of each phase in the control volume. The volume fraction α q of the q-th phase fluid in a volume cell is described as follows: Fig. 7 Pressure distributions of FDBs with crescent and circular cross-sectional RCs. a Crescent cross-sectional RC. b Circular cross-sectional RC
Fig. 8 Pressure distributions of models with crescent and circular cross-sectional RCs. a Crescent cross-sectional RC. b Circular cross-sectional RC Table 3 Calculated mean wall shear stress in crescent and circular cross-sectional RCs Mean wall shear stress (Pa m 2 ) Crescent cross-sectional RC 7.64E 06 α q = 0 : The cell is empty of the q-th fluid α q = 1 : The cell is full of the q-th fluid 0 <α q < 1 : The cell partially contains the q-th fluid The volume-averaged density and viscosity of the fluid in a cell are expressed as follows: Fig. 9 Axial velocity distributions of models with crescent and circular cross-sectional RCs. a Crescent cross-sectional RC. b Circular crosssectional RC Circular cross-sectional RC 2.50E 06 (3) ρ = µ = 2 α q ρ q q=1 2 α q µ q q=1 The Navier Stokes equation of two-phase flow is expressed by substituting Eqs. (4) and (5) into Eq. (1). The interaction of each phase at the air-oil interface is calculated by the continuity equation of each phase. The continuity equation of the q-th phase, which is also known as the volume fraction equation, can be written as follows: α q t + (α q v q ) = 1 ρ q 2 ) (ṁpq ṁ qp q=1 (4) (5) (6)
Fig. 10 Finite volume model of the proposed tapered crescent and circular cross-sectional RCs Fig. 11 Pressure distributions of the conventional and proposed tapered models with a crescent cross-sectional RC. a Conventional model. b Proposed tapered model where ṁ pq is the mass flow that moves from the fluid of the q-th phase to the fluid of the p-th phase. The Navier Stokes equation in application with the volume-averaged value and the continuity Eq. (6) are discretized by using the finite volume method to determine the pressure, velocity, and volume fraction. The unsteady motion of the air-oil interface can then be calculated by solving the discrete equations with a constant time step. 3.2 Analysis model A finite volume model for FDBs used in commercial 2.5 HDD was developed to investigate the effect of the crosssectional shape of the RC on expulsion of air bubbles out of a FDB. Figure 5 shows the geometry and boundary conditions of the FDB. It consisted of a hub, sleeve, shaft, cover, recirculation channel, two grooved thrust bearings, and two grooved journal bearings. Figure 6 shows the finite volume model of FDBs with crescent and circular cross-sectional RCs. A diameter of the circular cross-sectional RC was 400 μm. The crescent cross-sectional RC had the same crosssectional area as the circular cross-sectional RC. The length of crescent and circular cross-sectional RC was 2.45 mm. We compared the steady-state solutions of the crescent and circular cross-sectional RCs used in the experiment. In this calculation the fluid is assumed to be fully filled in the clearance of FDBs without air. The finite volume model of the FBDs had about 2,600,000 cells, comprising hexahedron, tetrahedron, and wedge cells. Table 1 shows the properties of oil lubricant at 20 C. The viscosity and density of the oil lubricant at 20 C were assumed to be 0.0129 Pa s and 920.4 kg/m 3, respectively. The pressure along the outlet boundary was assumed to be atmospheric. An operating speed of 5400 rpm was applied to the rotating wall.
Fig. 12 Pressure distributions of the conventional and proposed tapered model with a circular cross-sectional RC. a Conventional model, b proposed tapered model Table 4 Calculated pressure differences in the conventional and proposed tapered models Pressure difference (Pa) Conventional model Proposed tapered model Difference (%) Crescent cross-sectional RC 84 195 132 Circular cross-sectional RC 18 31 72 Fig. 13 Axial velocity distributions of the conventional and proposed tapered model with a crescent cross-sectional RC. a Conventional model. b Proposed tapered model 3.3 Analysis results The steady-state solution of the model with a crescent crosssectional RC was compared with that of the model with a circular cross-sectional RC. Figure 7 shows the pressure distribution in FDBs with crescent and circular cross-sectional RCs. The pressure is coupled between the upper and lower parts of the FDB by the RC. Table 2 shows the calculated maximum and minimum pressure in FDBs with crescent and circular cross-sectional RCs. Maximum pressure was generated at the center of the upper grooved journal bearing and minimum pressure was generated at the end of the upper
Fig. 14 Axial velocity distributions of the conventional and proposed tapered model with a circular cross-sectional RC. a Conventional model. b Proposed tapered model Table 5 Calculated average axial velocities of the conventional and proposed tapered models Average axial velocity (m/s) Conventional model Proposed tapered model Difference (%) Crescent cross-sectional RC 3.1E 03 4.3E 03 38 Circular cross-sectional RC 2.1E 03 2.9E 03 38 grooved journal bearing. Maximum and minimum pressures of the model with a crescent cross-sectional RC were similar to those of the model with a circular cross-sectional RC, indicating that the maximum and minimum pressures were not affected by the cross-sectional shape of the RC. Figure 8 shows the pressure distribution along the RC for models with crescent and circular cross-sectional RCs. The pressure differences along the RC for the crescent and circular crosssectional RCs were 84 and 18 Pa, respectively. The crescent cross-sectional RC had a larger pressure difference than the circular cross-sectional RC. This pressure difference can be expressed as shown in Eq. (7), and mean wall shear stress can be expressed as shown in Eq. (8) (2007): p = τwl A τ = 1 A L A L τda L where w, L, A, A L, and τ are the perimeter of the RC, length of the RC, cross-sectional area of the RC, lateral surface area, and wall shear stress, respectively. Pressure difference is proportional to mean wall shear stress. Table 3 shows the calculated mean wall shear stress in the crescent and circular cross-sectional RCs. The mean wall shear stress in the crescent cross-sectional RC was (7) (8) larger than that in the circular cross-sectional RC. Figure 9 shows the axial velocity distribution of the models with crescent and circular cross-sectional RCs. Average velocities of the models with crescent and circular cross-sectional RCs were 3.1 and 2.1 mm/s, respectively. Crescent crosssectional RC had a larger average velocity than the circular cross-sectional RC. Even though these two RCs had the same cross-sectional area, the pressure difference and average velocity were greater in the crescent cross-sectional RC than the circular cross-sectional RC due to increased wall shear stress in the former. These results indicated that the pressure difference and velocity in a RC are affected by the cross-sectional shape of the RC. In the experiment, air bubbles in the circular cross-sectional RC were not sucked into the RC because the pressure difference and velocity were not sufficient. Therefore, a sufficient velocity and pressure difference in the RC are required to expel air bubbles from a FDB. 4 Proposed design of a FDB with a tapered RC 4.1 Proposed FDB design to expel air bubbles We designed a FDB with a tapered RC to expel air bubbles efficiently. Air bubbles can be expelled through the RC if
Fig. 15 Simulated RC models and boundary conditions Fig. 16 Simulated unsteady motion of an air bubble in the conventional model with a crescent cross-sectional RC (blue air bubble). a 0.0 ms, b 0.2 ms, c 0.4 ms, d 0.6 ms a sufficient pressure difference and flow velocity are generated. Furthermore, an air bubble tends to move from the narrow region to the wide region of a RC to minimize its surface energy (2010). It always tends to maintain a circular shape to reduce surface energy. Figure 10 shows our proposed tapered crescent and circular cross-sectional RCs. The hub, sleeve, shaft, cover, two grooved thrust bearings, and two grooved journal bearings used in the FDB are the same as those used in the conventional model. The proposed model with circular cross-sectional RC was modeled in such a way that the diameter of upper and lower region had 400 and 280 μm, respectively. The proposed RC with crescent cross-sectional RC was modeled in such a way that the upper region of the RC had the same area as the model with circular cross-sectional RC, while the lower region of the RC had one half area of the conventional model. 4.2 Simulation of the proposed FDB with a tapered RC Pressure and velocity in steady-state solutions were calculated for the proposed FDB models with a tapered RC, and compared with those of the conventional model. Figure 11 shows the pressure distribution of the conventional and proposed tapered models with a crescent cross-sectional
Fig. 17 Simulated unsteady motion of an air bubble in the conventional model with a circular cross-sectional RC (blue air bubble). a 0.0 ms, b 0.2 ms, c 0.4 ms, d 0.6 ms Fig. 18 Simulated unsteady motion of an air bubble in the proposed tapered model with a crescent cross-sectional RC (blue air bubble). a 0.0 ms, b 0.2 ms, c 0.4 ms, d 0.6 ms RC. Figure 12 shows the pressure distribution of the conventional and proposed tapered models with a circular cross-sectional RC. In Figs. 11 and 12, the pressure differences in both of the proposed tapered RCs were larger than that in the conventional RC. Table 4 shows the calculated pressure difference in conventional and proposed RCs. In the crescent cross-sectional RC, the proposed tapered RC increased the pressure difference by 132 %, and in the circular cross-sectional RC, the proposed tapered RC increased the pressure difference by 72 % compared with the conventional model. Figure 13 shows the axial velocity distribution of the conventional and proposed tapered models with a crescent cross-sectional RC. Figure 14 shows the axial velocity distribution of the conventional and proposed tapered models with a circular cross-sectional RC. It is clear from Figs. 13 and 14 that axial velocity in the
Fig. 19 Simulated unsteady motion of an air bubble in the proposed tapered model with a circular cross-sectional RC (blue air bubble). a 0.0 ms, b 0.2 ms, c 0.4 ms, d 0.6 ms Table 6 Calculated expulsion time of the air bubble from the conventional and proposed tapered RCs Expulsion time (s) Conventional model Proposed tapered model Difference (%) Crescent cross-sectional RC 0.9E 03 0.6E 03 33 Circular cross-sectional RC 1.5E 03 1.0E 03 33 Fig. 20 Pressure distributions of the conventional and proposed tapered models with crescent and circular crosssectional RCs at 0.4 ms proposed tapered RCs was faster than that in the conventional RC because the lower region of proposed tapered RCs had smaller area than the conventional RCs. The velocity is inversely proportional to the area. Table 5 shows that both of the proposed FDBs with tapered RCs had a 38 % higher average axial velocity than the conventional RCs. 4.3 Unsteady motion of the air bubbles in the RC We calculated the unsteady motion of the air bubble in the RC and compared the expulsion time of the air bubbles in the conventional and proposed tapered model with crescent and circular cross-sectional RCs. Because the simulation of the unsteady motion of air bubbles in the whole FDB
Fig. 21 Axial velocity distributions of the conventional and proposed tapered models with crescent and circular crosssectional RCs at 0.4 ms requires a long computational time due to the complexities of the full three-dimensional Navier Stokes equation and the bearing geometry, we modeled only the RC to investigate the motion of the air bubbles along RC. Figure 15 shows the RC models and boundary conditions. Velocity of the lubricant along the inlet boundary was assumed to be 1 m/s in order to reduce the computational time. This simulation used the densities and viscosities of the oil lubricant and air, the surface tension coefficient of oil lubricant with respect to air, and the static contact angle at 20 C as shown in Table 1. The air bubble was located at the lower region of RC in this simulation models. The diameter of the air bubble was assumed to be 400 μm. Figures 16 and 17 show the simulated unsteady motion of an air bubble in the conventional model with crescent and circular cross-sectional RCs. The air bubble moved from lower region of the RC to upper region of the RC. And the air bubble was expelled through central region of the RC due to the fast velocity. The air bubble in the model with a crescent cross-sectional RC moved faster than the model with circular cross-sectional RC. Figures 18 and 19 show the simulated unsteady motion of an air bubble in the proposed tapered model with crescent and circular cross-sectional RCs. Moving speed of the air bubble in the crescent cross-sectional RC were faster than that in the circular cross-sectional RC. And moving speeds of air bubbles in the both proposed tapered models were faster than those in the conventional models. Table 6 shows the calculated expulsion time of the air bubble in the conventional and proposed tapered RCs. Both the proposed tapered RCs decreased expulsion time of the air bubbles from the RC by 33 % compared with the conventional RCs. Figures 20 and 21 show the pressure and axial velocity distributions of the conventional and proposed tapered models with crescent and circular cross-sectional RCs at 0.4 ms. The pressure difference and axial velocity were larger in the crescent cross-sectional RC than the circular cross-sectional RC due to increased wall shear stress in the former as explained in 3.3. Also, the pressure difference and axial velocity in the proposed tapered RCs were larger than those in the conventional RCs because the lower region of proposed tapered RCs had smaller area than the conventional RCs. Therefore, the proposed FDBs can easily expel air bubbles because of larger pressure difference and faster velocity of fluid flow in the proposed tapered RCs than the conventional RC. 5 Conclusions We experimentally and numerically investigated the behavior of air bubbles in the oil lubricant of operating FDBs according to the crescent and circular cross-sectional shape of the RC. The pressure differences of the crescent and circular cross-sectional RCs were 84 and 18 Pa, respectively. Average axial velocities of the models with crescent and circular cross-sectional RCs were 3.1 and 2.1 mm/s, respectively. Expulsion of air bubbles was significantly affected by the cross-sectional shape of the RC, and a large pressure difference between the upper and lower regions of the RC and fast flow velocity along the RC resulted in efficient expulsion of air bubbles out of the FDB. Finally, we proposed tapered RCs with a larger upper region than lower region to increase the pressure difference and velocity of oil fluid flow. The proposed tapered models with a crescent and circular cross-sectional RCs increased the pressure difference by 132 and 72 % compared with the conventional models. Both of the proposed FDBs with tapered RCs increased the average axial velocity by 38 % compared with the conventional models. The unsteady motion of air bubble in the proposed RCs had shorter expulsion time than the conventional RCs from the two phase analysis using the VOF method. Both of the proposed tapered RCs
decreased expulsion time of the air bubbles from the RC by 33 % compared with the conventional RCs. Our design can be utilized to develop robust FDBs that expel air bubbles effectively. 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 (2010 0021919). Asada T, Saito H, Itou D (2005) Design of hydrodynamic bearing for mobile hard disk drives. IEEE Trans Magn 41:741 743 Bahrami M, Yovanovich M, Culham J (2007) A novel solution for pressure drop in singly connected microchannels of arbitrary cross-section. Int J Heat Mass Transf 50:2492 2502 FLUENT 6.3 User s Guide (2006) Jung KM, Jung YH, Lee JH, Jang HK, Jang GH (2013) Motions of air bubbles trapped in grooved and plane journal bearings of operating fluid dynamic bearings. IEEE Trans Magn 49:2433 2436 Metz T, Paust N, Zengerle R (2010) Capillary driven movement of gas bubbles in tapered structures. Microfluid Nanofluid 9(2 3):341 355 References Asada T, Saito H, Asaida Y, Itoh K (2002) Design of hydrodynamic bearings for high-speed HDD. Microsyst Technol 8:220 226