Kyungmoon Jung, Gunhee Jang & Juho Kim

Transcription

1 Behavior of fluid lubricant and air oil interface of operating FDBs due to operating condition and seal design Kyungmoon Jung, Gunhee Jang & Juho Kim Microsystem Technologies Micro- and Nanosystems Information Storage and Processing Systems ISSN Volume 18 Combined 9-10 Microsyst Technol (2012) 18: DOI /s

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3 Microsyst Technol (2012) 18: DOI /s TECHNICAL PAPER Behavior of fluid lubricant and air oil interface of operating FDBs due to operating condition and seal design Kyungmoon Jung Gunhee Jang Juho Kim Received: 30 September 2011 / Accepted: 22 May 2012 / Published online: 8 June 2012 Ó Springer-Verlag 2012 Abstract This paper investigated the behavior of fluid lubricant and air oil interface of operating fluid dynamic bearings (FDBs) by using two-phase flow analysis of air and oil to describe the oil sealing mechanism of operating FDBs. The two-phase flow of fluid lubricant and air was analyzed by using the Navier Stokes equation and the volume of fluid method of a multi-phase flow. The proposed numerical method was verified by the numerical result of the Reynolds equation and the experimental result of the prior researcher. This research also discussed the effect on the oil leakage of the operating FDBs due to the existence of inward pumping groove, tapering angle and initial position of fluid. 1 Introduction Fluid dynamic bearings (FDBs) have been applied to the spindle motor of a computer hard disk drive (HDD) since FDBs provide better dynamical characteristics such as lower vibration and noise than ball bearings. Figure 1 shows one of the mechanical structures of a HDD with FDBs. The FDBs are composed of two grooved journal bearings and one grooved thrust bearing. One of the weaknesses of FBDs is the leakage of oil lubricant. Oil K. Jung G. Jang (&) Department of Mechanical Engineering, Hanyang University, 17 Haengdang-Dong, Seongdong-Gu, Seoul , Korea ghjang@hanyang.ac.kr K. Jung jkm0617@hanmail.net J. Kim Samsung Electro-Mechanics Co. Ltd., 314, Maetan 3-Dong, Yeongtong-Gu, Gyeonggi-Do, Suwon-Si , Korea hazel.kim@samsung.com particles coming out of the FDBs contaminate the air flow in the HDD, and they prevent a magnetic head from reading or writing the data when they sit on the magnetic disk as shown in Fig. 1. It also decreases the lifespan of FDBs because it decreases the amount of oil lubricant in the FDBs in addition to the normal evaporation. Several researchers have investigated the oil leakage from FDBs of the HDD. Bootsma and Tielemans (1977) investigated the leak-free operating conditions of herringbone grooved journal bearing experimentally. They also discussed the theories developed from the experimental results of leakfree operating conditions of herringbone grooved journal bearing. Kita et al. (2002) tried to predict oil leakage from operating FDBs by correlating the simulated pressure of FDBs with the experimentally measured oil leakage. Recently, the some researchers have made an effort to simulate the oil leakage from FDBs of the HDD by using the numerical method such as the finite volume method (FVM). Jung and Jang (2011) investigated the characteristics of oil leakage of non-operating FDBs due to the shock by solving the Navier Stokes equation and the volume of fluid (VOF) method of two-phase of air and oil. However, their research was limited to the oil leakage of non-operating FDBs due to shock. It still needs the numerical studies to describe the characteristics of the oil leakage of operating FDBs. We investigated the behavior of fluid lubricant and air oil interface of operating FDBs by using the two-phase flow analysis of air and oil numerically. The two-phase flow of fluid lubricant and air was analyzed by using the 3-D Navier Stoke equation with finite volume method, and the volume of fluid method. This research investigated the characteristics of oil leakage of FDBs due to operating speed and seal designs. And it also discussed the effect on the leak-free operating speed due to several seal designs.

4 1374 Microsyst Technol (2012) 18: Fig. 1 Contamination problem of the HDD due to the leaking oil of FDBs Leaking oil FDB Leakage Contamination 2 Method of analysis The flow of the fluid lubricant is calculated by using the Navier Stokes equation and the continuity equation. The Navier Stokes equation and the continuity equation can be written in the following Eqs. (1) and (2). o ðqvþþr: ðqvvþ ¼ rp þr: l rv þrv T ot þ qg þ F ð1þ oq þr: qv ot ð Þ ¼ S ð2þ where q, l and p are density, viscosity and pressure of fluid, respectively. And v, g, F and S are velocity vector, gravity acceleration vector, the surface tension force which arises from interaction with the multi-phase, and the mass flow which adds to the continuous phase from the dispersed second phase, respectively. The two phase flow of air and oil is calculated by using the VOF method which is known as an efficient numerical technique for tracking and locating the free surface or fluid fluid interface of multi phase flow. The VOF method defines the volume fraction of each phase in the control volume. The volume fraction a q of q-th phase fluid in a volume cell is described as follows: a q ¼ 0 : The cell is empty of the q-th fluid a q ¼ 1 : The cell is full of the q-th fluid ð3þ 0\a q \1 : The cell contains the interface between the q-th fluid Volume-averaged density and viscosity of fluid in volume cell are expressed as follows: q ¼ X2 q¼1 l ¼ X2 q¼1 a q q q a q l q ð4þ ð5þ The Navier Stokes equation of two phase flow is expressed by substituting Eqs. (4) and (5) into Eq. (1). And the interaction of each phase at air oil interface is calculated by the continuity equation of each phase. The continuity equation of the q-th phase which is also called the volume fraction equation can be written as follows: " # 1 o a q q q X 2 þr: a q q ot q v q ¼ _m pq _m pq ð6þ q q p¼1 where _m pq is the mass flow which moves from fluid of the q-th phase to fluid of the p-th phase. The Navier Stokes equation in application with volumeaveraged value and the continuity equation (6) are discretized by using the finite volume method to determine the pressure, velocity and volume fraction. Then, the unsteady motion of the air oil interface can be calculated by solving the discrete equations with constant time step. A commercial program named FLUENT is utilized in this research to perform the numerical calculation. 3 Analysis model and verification We developed a finite volume model for the FDBs of a commercial 2.5-in. HDD with the rated operating speed 7,200 rpm as shown in Fig. 2 to investigate the effect on the oil leakage of operating FDBs due to operating speed and seal design. It takes enormously long computation time to calculate the unsteady flow of whole FDBs due to the complexities of full 3-D Navier Stokes equation and bearing geometry. And the oil leakage of operating FDBs is dominantly determined by the outlet flow near the air oil interface. So we modeled the outlet field which is composed of grooved thrust bearing, plain journal bearing, and air oil interface to investigate the motion of fluid lubricant and air oil interface due to seal design. The coupled effect between the outlet field and internal field was assumed to be very small in the steady state of this simulation. The finite volume model and boundary conditions are shown in Fig. 3. The finite volume model of the FBDs has 547,018 four-node tetrahedron cells. Because the spiral thrust bearing in this model has 20 grooves which repeat the geometrical pattern in every 18, the periodic boundary condition was applied to both circumferential surfaces in order to reduce the computation time. Because the inlet of

5 Microsyst Technol (2012) 18: Internal field of FDBs Outlet field of FDBs Clamp Shaft Grooved thrust bearing Hub Spacer Disk Stator Magnet Sleeve Upper grooved journal bearing Lower grooved journal bearing Fig. 2 Mechanical structure of the HDD with FDBs Fig. 5 Experiment and simulation model of the Bootsma and Tielemans FDBs Table 1 Properties of fluid of the Bootsma and Tielemans experiment Property of fluid Value Fig. 3 Finite volume model and boundary conditions of the outlet field the model is connected to the plain journal bearing of internal field and the pressure difference of the plain journal bearing is very small at steady-state, the mass flow due to pressure effect and centrifugal effect from the plain journal bearing to the inlet of the simulation model is very Fig. 4 Comparison of pressure distributions between the Reynolds model and the Navier Stokes periodic model Viscosity of oil (Pa s) Surface tension of oil (N/m) Density of oil (Kg/m 3 ) 850 small. So, the boundary condition of the inlet was assumed to be no mass flow between internal field and outlet field. And the outlet of the model was assumed that the pressure of the air is in atmospheric pressure. The operating speed was applied to the rotating wall. The tapering angles of the rotating wall and the stationary sleeve are assumed to be 5 Periodic BC (a) Reynolds model (b) Navier-Stokes periodic model

6 1376 Microsyst Technol (2012) 18: Fig. 6 Simulated motion of fluid lubricant and air oil interface of the Bootsma and Tielemans FDBs due to the operating speed (white air, black oil) Fig. 7 Three different tapering angles in the outlet of the FDBs 15 degrees 10 degrees 10 degrees 5 degrees 5 degrees 0 degrees (a) Model with tapering (b) Model with tapering (c) Model with tapering angle of 10 degrees angle of 5 degrees(base model) angle of 0 degrees and 10, respectively, so that this model has enlarged tapering seal. This simulation used the densities and viscosities of the fluid lubricant and air, surface tension coefficient of fluid lubricant with respect to air, and static contact angle at a temperature of 20 C. We compared the steady-state solutions of the Navier Stokes periodic model with those of the Reynolds model (Jang et al. 2006) to verify the accuracy of the proposed model numerically. This simulation used the thrust grooved bearing area with small gap of the Navier Stokes periodic model as shown in Fig. 3 which satisfies the Reynolds assumption. The pressure boundary conditions at the inlet and outlet are typically used to solve the Reynolds model. The boundary condition of atmospheric pressure was applied to inlet and outlet of the Reynolds model and the Navier Stokes periodic model only for the purpose of numerical verification. The simulated pressure distribution and load capacity of the Navier Stokes periodic model match well with those of the Reynolds model as shown in Fig. 4. The axial load capacity of the Navier Stokes periodic model (7.8 mn) matches well with that of the Reynolds model (7.6 mn). We also compared the characteristics of oil leakage and leak free operating speed of the Navier Stokes periodic model with the Bootsma and Tielemans experimental results (Bootsma and Tielemans 1977). This example simulation used the Navier Stokes periodic model with the same seal design as the Bootsma and Tielemans experimental model. Figure 5a, b shows the Bootsma and Tielemans experiment and the simulation model of this research. The Bootsma and Tielemans FDBs are composed of the herringbone grooved journal bearing and the plain journal bearing. Because the geometry of the FDBs is symmetric and repeats every 30, the periodic boundary condition, the symmetric boundary condition and the atmospheric boundary condition were applied to the two circumferential sides, inlet and outlet of the simulation model. And the properties of fluid of this simulation used

7 Microsyst Technol (2012) 18: ,000 rad/s or over. Therefore, the characteristics of oil leakage and leak free operating speed of simulation model match well with those of the experiment. 4 Analysis result We calculated the unsteady motions of fluid lubricant and air oil interface to investigate the effect on the leak free operating speed due to seal design such as groove, tapering angle, and initial position of air oil interface. The operating speed increases from 7,200 to 28,800 rpm by the increment of 1,800 rpm in order to find the leak free operating speed. And the eccentricity of all cases in this simulation was assumed to zero. 4.1 Effect of the tapering angle on the leakage of operating FDBs Fig. 8 Velocity of the cross section of the models with tapering angle of 0,5, and 10 at the operating speed of 16,200 rpm and at the time of 0 s those in the reference paper as shown in Table 1. The Bootsma and Tielemans experiment showed that the oil leakage occurs at 1,800 rad/s by moving the air oil interface outwardly along the sleeve wall continuously due to the centrifugal effect of oil. Figure 6 shows the simulated unsteady motions of fluid lubricant and air oil interface of the simulation model due to the operating speed. The air oil interface of the simulation model does not move outward along sleeve wall at 1,500 rad/s or less. The air oil interface moves outward along sleeve wall continuously at Oil leakage was investigated due to tapering angle. Figure 7 shows three cases of the rotating wall of 0, 5 and 10 by increasing and decreasing tapering angle by 5. Figure 8 shows the velocity of the cross section of the models with tapering angle of 0, 5, and 10 at the operating speed of 16,200 rpm. The direction of oil flow due to the centrifugal effect of oil is radial direction. As the radial oil flow due to centrifugal effect meets the outer wall of hub, the radial oil flow is decomposed into the upward flow and downward flow. The downward flow along the hub at the corner of hub is generated by the centrifugal effect. And the tapering angle of journal bearing in this simulation model increases upward flow and decreases downward flow, so that the leak free operating speed increases with the increase of tapering angle. Figures 9 and 10 show the simulated unsteady motions of fluid lubricant and air oil interface due to the tapering angle at 16,200 and 18,000 rpm, respectively. The air oil interface of the model with tapering angle 0 breaks up at 16,200 rpm. The air oil interface of the model with tapering angle 5 doesn t break up at 16,200 rpm, but it breaks up at 18,000 rpm. The air oil interface of the model with tapering angle 10 doesn t break up at 18,000 rpm, but it breaks up at 19,800 rpm. Table 2 shows the simulated break-up speed of air oil interface due to three different tapering angles. 4.2 Effect of the thrust grooves on the leakage of operating FDBs Oil leakage was investigated due to the inward pumping effect of spiral groove on the thrust bearing. Figure 11 shows the geometries of the finite volume models with and without spiral grooves on the thrust bearing. Figures 12

8 1378 Microsyst Technol (2012) 18: (a) Model with tapering angle 0 degrees (b) Model with tapering angle 5 degrees (base model) Fig. 9 Simulated motion of fluid lubricant and air oil interface for the models with tapering angle of 0 and 5 at the operating speed of 16,200 rpm (a) Model with tapering angle 5 degrees (base model) (b) Model with tapering angle 10 degrees Fig. 10 Simulated motion of fluid lubricant and air oil interface for the models with tapering angle 5 and 10 at the operating speed of 18,000 rpm and 13 show the simulated unsteady motions of fluid lubricant and air oil interface due to the operating speed at 16,200 and 18,000 rpm. The air oil interfaces of both models do not break up at 16,200 rpm or less. The air oil interfaces of both models break up at 18,000 rpm and over. The oil moves downward along the hub and moves upward along the sleeve due to the centrifugal effect of oil. And the air oil interfaces finally breaks up along the corner of the hub. Figure 14 shows the velocity fields of cross section of the models with and without spiral grooves on the thrust

9 Microsyst Technol (2012) 18: Table 2 Simulated break-up speed of air oil interface of three different tapering angles due to operating speed Simulation model Operating speed (rpm) 14,400 16,200 18,000 19,800 21,600 Model with tapering angle 0 X O O O O Model with tapering angle 5 (base model) X X O O O Model with tapering angle 10 X X X O O O break-up of air oil interface, X no break-up of air oil interface Fig. 11 Models with and without spiral grooves on thrust bearing (a) Model with thrust grooves (base model) (b) Model without thrust grooves Fig. 12 Simulated motion of fluid lubricant and air oil interface of the models with and without spiral grooves on thrust bearing at the operating speed of 16,200 rpm (white air, black oil) bearing at the operating speed of 16,200 rpm. The downward flow along the hub and upward flow along the sleeve at the corner of hub are generated by the centrifugal effect in both models. And the inward-pumping flow occurs mostly at the groove area of the model with spiral grooves. The velocity magnitudes of downward flows of both models at the corner of hub are very similar, which indicates that the inward-pumping flow of thrust groove of this

10 1380 Microsyst Technol (2012) 18: (a) Model with thrust grooves (base model) (b) Model without thrust grooves Fig. 13 Simulated motion of fluid lubricant and air oil interface of the models with and without spiral grooves on thrust bearing at the operating speed of 18,000 rpm (white air, black oil) model is not effective to prevent the downward flow along the hub due to centrifugal effect. 4.3 Effect of the initial position of air oil interface on the leakage of operating FDBs The air oil interface of the base model was extended to the lower side of plain journal bearing as shown in Fig. 15b. The base model starts to break up at 18,000 rpm. However, the model with extended air oil interface doesn t break up at 18,000 rpm as shown in Fig. 15. And the air oil interface of the model with extended air oil interface still doesn t break up at 28,800 rpm as shown in Fig. 16. Because the radius of lower side of tapering angle is smaller than radius of upper side of tapering angle, the centrifugal effect decreases at the lower side of tapering angle. The air oil interface of the model with extended air oil interface is far from the corner of the hub along which the break-up of air oil interfaces occurs, so that the extended air oil interface makes it difficult to generate the break-up of the air oil interface. Therefore, the leak free operating speed increases as the initial position of air oil interface is in the lower side of tapering angle. 5 Conclusions Fig. 14 Velocity of the cross section of the models with and without spiral grooves on thrust bearing at the operating speed of 16,200 rpm We investigated the behavior of fluid lubricant and air oil interface of operating FDBs due to operating condition and

11 Microsyst Technol (2012) 18: (a) Base model (b) Model with extended air-oil interface Fig. 15 Simulated motion of fluid lubricant and air oil interface between the base model and the model with extended air oil interface at the operating speed of 18,000 rpm Fig. 16 Simulated motion of fluid lubricant and air oil interface of the model with extend air oil interface at the operating speed of 28,800 rpm seal design. We proposed the numerical method to describe the oil sealing mechanism of operating FDBs. The proposed numerical method takes account of the effect of centrifugal force of oil, and surface tension effect of air oil interface. And the proposed numerical method was verified by comparing with the numerical result and experimental result of prior researchers. The simulation results of this research shows that the oil leakage can occur mainly due to the centrifugal effect of oil at high operating speed. And it also shows that the oil leakage due to centrifugal effect is prevented by the tapering angle of bearing and the change of initial position of air oil interface. Our proposed numerical method can be utilized to develop a robust seal design of operating FDBs. Acknowledgments This work was supported by Samsung Electro- Mechanics Co. Ltd. and by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology ( ). References Bootsma J, Tielemans LPM (1977) Conditions of leakage-free operation of herringbone grooved journal bearings. J Lubr Technol 99: 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: 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: Kita H, Matsuoka K, Obata S, Noda H (2002) Prediction method of oil leakage of FDBs using numerical analysis. Microsyst Technol 8: