Simulations of Particle Trajectories in Hard Disk Drives ... - IEEE Xplore

IEEE TRANSACTIONS ON MAGNETICS, VOL. 52, NO. 8, AUGUST 2016

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Simulations of Particle Trajectories in Hard Disk Drives Considering the Trapping Criterion Guoqing Zhang, Yuwen Zhu, Hui Li, Shengnan Shen, Yun Yang, Sen Liu, Xiao Lei, and Shijing Wu School of Power and Mechanical Engineering, Wuhan University, Wuhan 430072, China The presence of particles, which can intrude into the air bearing, is one of the most common factors in the failure of hard disk drives (HDDs). Previous studies have investigated particles trajectories with the assumption of ideal trapping or reflecting boundary conditions in air-filled drives. However, only the colliding particle with insufficient energy to escape the potential well will be trapped by the surface. In this paper, considering the particle-surface energy during the collision, the trapping criterion of the ∗ ) for Al O particles is developed as the boundary conditions for different colliding surfaces incident normal critical velocity (Vni 2 3 inside a 2.5 in drive. Then, trapping status for Al2 O3 particles and particles trajectories inside the drive are simulated by using the commercial computational fluid dynamics solver FLUENT with user-defined functions. The results reveal that the particles will travel longer distances until trapped by HDD components when considering the trapping criterion. In addition, smaller particles will more likely degrade the head–disk interface reliability, since they easily stick on the disk surface. Index Terms— Computational fluid dynamics simulations, hard disk drive (HDD), particle trajectory, trapping criterion, trapping status.

I. I NTRODUCTION

I

N RECENT years, the areal recording density of hard disk drives (HDDs) has increased rapidly for the continual demand of mass storage, which requires ultralow flying height, more accurate seeking positions, and higher disk rotation speeds. Meanwhile, the reliability and the stability of HDDs are becoming more important for high-performance HDDs. However, an ultralow flying height can increase the possibility of contact between the head and the disk, which results in surface damage of the disk and generates wear particles. The presence of these particles, which can intrude into the air bearing, is one of the most common factors in the failure of HDDs [1]. Particle trajectory and final trapping status have been the subject of considerable interest and intensive research. Some previous studies have focused on particle transport in the head– disk interface (HDI) [2]–[8], including the studies of particle motion and contamination. For example, Shen et al. [5] investigated the particle flow in an air bearing and the contamination of particles. Based on their numerical results, particles are likely to contaminate slider surfaces in the transition regions on the rails. The density of the particles and the pitch angle of the slider were also found to significantly affect the flying path of the particles. On the other hand, several studies have been conducted about the issue of particle trajectory and generation in the whole HDD [9]–[12], including experiments and numerical simulations. For example, Liu et al. [12] investigated the particle trajectory in a turbulent flow field and the trapping status of particles in a 2.5 in air-filled HDD. Their results revealed that the filter on the left side was more efficient at trapping particles. In addition, the majority of particles were trapped by the cover with the assumption of the cover set as an ideal trapping boundary. Manuscript received January 11, 2016; revised March 16, 2016; accepted April 6, 2016. Date of publication April 11, 2016; date of current version July 18, 2016. Corresponding author: H. Li (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMAG.2016.2552505

Previous studies have provided useful insights into the characteristics of particle motion and the mechanism of particle contamination. However, there exist obvious deficiencies in the simulations of particle trajectory inside the whole HDD model mentioned earlier. Due to the assumption of ideal trapping and reflecting boundary conditions of surfaces regardless of particle velocity, such simulations are unable to reveal the true process of collisions between the particle and the surface. Actually, only the colliding particle with insufficient energy to escape the potential well will be trapped by the surface [13]. Unlike the ideal boundary conditions in the previous studies, this paper, however, more systematically and comprehensively investigate particles trajectories by considering the trapping criterion inside an air-filled HDD. A geometrical model of a 2.5 in HDD with the head gimbal assembly (HGA) positioned at the middle diameter (MD) of the disk is built. Considering the particle-surface energy during the collision [13], the trapping criterion of the incident normal critical velocity (Vni∗ ) for Al2 O3 particles is developed as the boundary conditions for different colliding surfaces inside the drive. Particle trapped occurs when the particle’s incident normal velocity (Vni ) is smaller than Vni∗ in collision. Trapping status for Al2 O3 particles and particle trajectories inside drives are simulated by using the commercial computational fluid dynamics solver ANSYS FLUENT 15.0 [14] with user-defined functions (UDFs). II. M ETHODOLOGY The equation for particle motion is described by Newton’s second law m

d Vp = F gravit y + F drag + F saffman dt

(1)

where m is the particle mass, V p is the particle velocity, and t is the time. Three forces acting on particle are considered, F gravity, F drag , and F saffman are the gravity force, drag force, and Saffman force, respectively. Other forces, such as the

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Fig. 1.


Schematic of the collision process. TABLE I H AMAKER C ONSTANTS B ETWEEN Al2 O 3 PARTICLES AND D IFFERENT C OMPONENTS [15], [19] Fig. 2.

Geometrical model of a 2.5 in HDD.

TABLE II D ENSITY AND S IZE OF Al2 O 3 PARTICLES [12]

Magnus force, virtual mass force, pressure gradient force, Basset force, and Brownian force, are neglected [12]. The collision of a particle and a surface can be characterized in terms of the energy of the particle-surface system, as shown in Fig. 1. The particle’s incident normal critical velocity Vni∗ can be expressed as [13] 1/2 A132 (1 − e2 ) dp (2) Vni∗ = π z 0 ρ p e2 where A132 is the Hamaker constant between materials 1 and 2 separated with material 3, e is the normal coefficient of restitution and equals to 0.98 for hard particle [13], z 0 is the equilibrium separation between the particle and the surface (typically equals to 4 Å), and d p and ρ p denote the particle’s diameter and density, respectively. The Hamaker constant A132 can be estimated by the following equation [15]: A132 2 n 1 − n 23 n 22 − n 23 3νe = √ 8 2 n 21 +n 23 1/2 n 22 +n 23 1/2 n 21 +n 23 1/2 + n 22 +n 23 1/2 (3) where n i is the refractive index of material i , is the Planck constant, and v e = 3×1015 s−1 . In this paper, materials 1 and 2 refer to the particle’s material and HDD components materials, respectively. Material 3 denotes the air. The calculated Hamaker constants A132 between Al2 O3 particles and HDD components in the air are shown in Table I. A geometrical model of a 2.5 in HDD built in our previous work [16] is shown in Fig. 2. The model consists of HGA, actuator arm, voice coil motor (VCM), bobbin, magnet, spindle motor, disk, filter, cover, and base. The x-, y-, and z-directions are defined along the length, width, and height of the HDD base, respectively. The rotational speeds of the disk

are 5400 and 15 000 r/min, which form a rotating turbulent flow with the Reynolds number of approximate 4.3 × 104 and 8 × 104 , respectively. In this paper, a convergent time-averaged turbulent airflow field is obtained by using ANSYS FLUENT 15.0 with the renormalization group k-ε turbulent model [14]. The simulation of Al2 O3 particle trajectory is performed using the Lagrangian tracking method in discrete phase model (DPM), which was commonly applied for the calculation of various transports and depositions in complex geometries [17]. In the DPM, particle tracking in the flow field is stochastic, and particle–particle interactions are negligible, since the discrete phase (particles) is sufficiently dilute [18]. The density and the diameter of Al2 O3 particles are shown in Table II. The surfaces of HDD components are assumed to be polished. In this paper, two types of boundary conditions are applied separately. The boundary condition without trapping criterion is the same as the previous ideal boundary condition used in Liu’s work [12], where only the cover and the filter are set as ideal trapping boundary conditions regardless of the particle velocity. New proposed boundary condition with the trapping criterion (2) is applied for all inner surfaces of the investigated HDD except that the filter is set as the ideal trapping boundary. The UDF DEFINE_DPM_BC is used to specify user-defined boundary conditions with the trapping criterion for particles. The DEFINE_DPM_BC function is executed every time when a particle touches a surface inside the HDD. The particle is trapped by the surface at a velocity condition of Vni < Vni∗ . The critical velocities Vni∗ for Al2 O3 particles colliding with different HDD components are calculated, as shown in Fig. 3. It can be clearly seen that Vni∗ decreases as the particle diameter increases. Vni∗ for the investigated particles in this paper are shown in Table III. The UDF PARTICLE_STATISTICS is used to determine their final trapping positions.

ZHANG et al.: SIMULATIONS OF PARTICLE TRAJECTORIES IN HDDs CONSIDERING THE TRAPPING CRITERION

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TABLE IV T RAPPING AND R EBOUNDING B EHAVIORS FOR THE

PARTICLES IN F IG . 5

Fig. 3. Al2 O3 particle critical velocity versus particle diameter (d p ) for different colliding surfaces of the HDD. TABLE III C RITICAL V ELOCITY Vni∗ FOR Al2 O 3 PARTICLES C OLLIDING W ITH D IFFERENT C OMPONENTS

Fig. 5. Fig. 4.

Z -coordinate value of the particle trajectory versus time in Fig. 4.

Visualization of the particle trajectory inside the HDD.

III. R ESULTS AND D ISCUSSION A. Particle Trajectory Inside HDD Fig. 4 shows the particle trajectory behaviors. A particle with d p = 1.0 μm is released from the tip of the HGA located above the MD of the disk. It can be obviously seen that there is a partial overlap of two trajectories. The centrifugal effects on particle trajectories increase with the traveling distance. Then, the particles move toward the outside diameter (OD) of the disk. The particle is trapped as soon as contacting with the cover inner surface when the trapping criterion is not considered. However, when considering the trapping criterion, the particle is finally trapped by the magnet surface.

Based on Table IV, the critical velocities Vni∗ of the cover and magnet surfaces are 0.0334 and 0.0950 m/s, respectively. The collision processes between particles and various surfaces both with and without considering the trapping criterion are shown in Fig. 5. In the absence of the trapping criterion, the particle sticks on the cover in spite of Vni = 0.9372 > 0.0334 m/s as shown at the colliding point B. However, considering the trapping criterion, the particle first rebounds at the colliding point A at the time of 32.86 ms due to Vni = 0.9844 > 0.0334 m/s. Then, the particle velocity decreases and the particle rebounds at the colliding point C at the time of 33.63 ms due to Vni = 0.3487 > 0.0334 m/s again. From Fig. 5(b), the particle is finally trapped at the colliding point D on the magnet surface at time of 56.36 ms due to Vni = 0.0930 < 0.0950 m/s.

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Fig. 6. Trapping status for Al2 O3 particles released from different positions without/with the trapping criterion at 5400 r/min. (a) Without criterion. (b) With criterion. TABLE V PARTICLE T RAPPING R ATE FOR VARIOUS R ELEASE P OSITIONS AT 5400 r/min

B. Effects of Particle Release Position The 50 Al2 O3 particles with d p = 0.3 μm are released from the eight release positions, as shown in Fig. 6. The eight big symbols represent the eight release positions. Four of them are located at the inner diameter (ID) on the disk surface. The remaining four release positions are at the tip of the HGA (above the MD of the disk), center of the arm (above the OD of the disk), and the VCM region, respectively. The small symbols correspond to the final positions of the particles, where the particles are trapped. Fig. 6(a) shows the trapping status for Al2 O3 particles without the trapping criterion at a disk rotational speed of 5400 r/min. As shown in Table V, all of the particles are trapped by the cover and the filter when the trapping criterion is not applied, since it only sets the cover and filter as ideal trapping boundaries [12]. Moreover, almost all of the particles are trapped by the cover wherever they are released. This can be explained by that the cover has a large surface area and can easily trap particles which are accelerated by the airflow. In addition, a lot of particles are trapped on the right-up side

Fig. 7. Trapping status for Al2 O3 particles released from different positions without/with the trapping criterion at 15 000 r/min. (a) Without criterion. (b) With criterion.

of the cover, since the airflow is obstructed by the arm and has a strong turbulent intensity and high velocity perturbation. Fig. 6(b) shows the trapping status for Al2 O3 particles considering the trapping criterion at 5400 r/min. Obviously, significantly fewer particles are trapped by the cover than in Fig. 6(a). All of the HDD components trap different numbers of particles. From Table V, it can be seen that approximate one third of the particles are trapped by the inner edge of the disk when the particles are released from the ID. This is because the airflow circulates inward toward the spindle and its velocity above the center of the spindle is low. The velocity of the particles involved in the flow is lower than the critical velocity of the disk surface, so the particles are trapped immediately after being released. However, 17%∼22% particles are trapped by the disk when the particles are released from the MD, OD, and VCM region. Comparing the trapping status of particles under the two boundary conditions, it can be concluded that the HDI is more likely to suffer reliability issues, such as contact and even crash, due to more particles being trapped on the disk surface when considering the trapping criterion. Moreover, the filter cannot provide the expected filtration efficiency for the particles with a size of 0.3 μm at 5400 r/min under both boundary conditions. Fig. 7 shows the trapping status of Al2 O3 particles under the two boundary conditions as the disk rotational speed increases to 15 000 r/min. Fig. 7(a) shows that the particles are more scattered on the cover than that in Fig. 6(a). It is because the airflow velocity and the turbulence intensity increase with the disk rotational speed compared Fig. 7(a) with Fig. 6(a). The rotary flow with a higher speed becomes more oscillated when it is obstructed by the HDD inner walls, especially by the actuator arm. Then, the particles involved in the airflow tend to exhibit more dispersed trajectories. From Fig. 7(b) and Table VI, it can be clearly seen that 42% particles are trapped by the disk when particles are released from the ID. However, when particles are released from the MD, OD, and VCM region, the number of particles

ZHANG et al.: SIMULATIONS OF PARTICLE TRAJECTORIES IN HDDs CONSIDERING THE TRAPPING CRITERION

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TABLE VI PARTICLE T RAPPING R ATE FOR VARIOUS R ELEASE P OSITIONS AT 15 000 r/min

Fig. 9. Particle trapping rate for various particle sizes with the criterion at 5400 r/min.

Fig. 8. Trapping status for Al2 O3 particles of various sizes at 5400 r/min. (a) Without criterion. (b) With criterion.

trapped by the disk significantly reduces, and the particle trapping rate by the disk is 13%, 12%, and 10%, respectively. The reason should be that the particles are easily accelerated by the higher speed rotary airflow, and more particles move into the VCM cavity, where they then decelerate and become trapped. For the same reason, the number of particles trapped by the filter also increases. C. Effects of Particle Size In Fig. 8, 50 Al2 O3 particles (d p = 0.3, 1, 5, and 10 μm) are released from the tip of the HGA (above the MD of the disk) at a disk rotational speed of 5400 r/min. Fig. 8(a) shows that most of the particles with d p = 10μm are easily trapped by the cover area above the filter when the trapping criterion is not considered. That is to say, the particles with d p = 10 μm move toward the cover area above the filter easily even when the disk rotational speed is 5400 r/min. This can be explained by the unobvious following behaviors of big particles in the airflow field. However, only a small amount of other particles (d p = 0.3∼5 μm) are trapped by the same area. When considering the trapping criterion, small particles (d p = 0.3∼5 μm) easily enter the VCM region, as shown

Fig. 10. Trapping status for Al2 O3 particles with various sizes at 15 000 r/min. (a) Without criterion. (b) With criterion.

in Fig. 8(b). The particle trapping rate is tabulated, as shown in Fig. 9. With an increase in particle sizes, the number of particles trapped by the filter increases, but the number of particles trapped by the disk decreases. When the particle diameter exceeds 5 μm, there are no particles trapped by the disk, but more than 85% of particles are trapped by the filter. It indicates that smaller particles will more likely degrade the HDI reliability, since they easily attach onto the disk surface. For a disk rotational speed of 15 000 r/min, the results of the particle trapping status are shown in Fig. 10. When the trapping criterion is not considered, the particles with the sizes of 5 and 10 μm are more likely to be trapped by the filter instead of the cover, as shown in Fig. 10(a). Similar to the results of Fig. 9, Fig. 11 shows that big particles are likely trapped by the filter. Especially, 100% of the particles with a size of 10 μm are trapped by the filter. The reason should be that big particles have a large inertia after being accelerated by the high rotational speed airflow, and then overcome centripetal force and fly to the filter. It becomes more obvious when the disk rotational speed is increased comparing Fig. 9 with Fig. 11.

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ACKNOWLEDGMENT This work was supported in part by the National Natural Science Foundation of China under Grant 51505342, and in part by the Fundamental Research Funds for the Central Universities of China under Grant 2042015kf0193. R EFERENCES

Fig. 11. Particle trapping rate for various particle sizes with the criterion at 15 000 r/min.

IV. C ONCLUSION In this paper, a geometrical model of a 2.5 in HDD with HGA positioned at the MD of the disk is built. Considering the particle-surface energy during the collision, a trapping criterion for Al2 O3 particles is developed for different colliding surfaces inside the drive. Then, the trapping status and the trajectories of Al2 O3 particles inside the drive are simulated. The results observed are as follows. 1) Without considering the trapping criterion, most of particles will be trapped by the cover in a very short time after being released. 2) With considering the trapping criterion, particle will travel longer distances until being trapped by HDD components inside the drive due to the low critical velocity. Therefore, the particle has more chance to scratch the components. 3) Smaller particles will more likely degrade the HDI reliability, since they easily attach on the disk surface. Although there is a great improvement in this paper compared with the previous work and a new trapping criterion for particle is proposed, the viscosity of the lubricant film on the disk surface has not been considered. In addition, it also ignores the collisions among particles as well as the secondary movement of the particles induced by the shear flow inside the drive. In the next work, more comprehensive factors will be considered to study the particle trapping status and trajectory.

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