Aerodynamically induced power loss in hard disk drives

Microsyst Technol (2005) 11: 741 746 DOI 10.1007/s00542-005-0575-8 TECHNICAL PAPER Sung-Oug Cho Æ Seung-Yop Lee Æ Yoon-Chul Rhim Aerodynamically induced power loss in hard disk drives Received: 30 June 2003 / Accepted: 20 January 2004 / Published online: 11 May 2005 Ó Springer-Verlag 2005 Abstract In this paper, the effects of rotational speed, form factor and enclosure conditions on power dissipation in hard disk drives are presented. The aerodynamically dissipated power losses by 3.5, 2.5 and 1 in. hard disks are experimentally measured using a vacuum chamber and compared to theoretical estimations. Experiments in open air without enclosure agree well with theoretical predictions; a 3.5-in. disk satisfies the turbulent model but 1 and 2.5-in. disks match the laminar one, which is inversely proportional to the half power of Reynolds number. Experiments using a single 3.5-in. disk in enclosure show that aerodynamic power loss is proportional to the second power of rotational speed and the fourth power of disk radius, which agrees with the laminar theory rather than turbulent one. It is also shown that the aerodynamic power loss is reduced as the axial gap and radial clearance of enclosure decrease. 1 Introduction Higher spindle speeds to increase data transfer rate in hard disk drives lead to increased power dissipation by disk rotation. In particular, the reduction of power consumption is one of the critical issues for the small form factor disk drives, which widely used for mobile S.-O. Cho Æ Y.-C. Rhim Department of Mechanical Engineering, Yonsei University, 134 Sinchon-dong, Seoudaemun-ku, Seoul, 120-749, Korea S.-Y. Lee (&) Department of Mechanical Engineering, Sogang University, Sinsu-dong, Mapo-ku, Seoul, 121-742, Korea E-mail: sylee@sogang.ac.kr Tel.: +82-2-7058638 Fax: +82-2-7120799 information devices. Aerodynamically induced friction loss that is one of the major contributors to power consumption, depends mainly on rotational speed and disk diameter. High spindle speed and power loss also leads to increased HDD temperatures for a given cooling condition. Thermal expansion of mechanical components of HDD can cause positioning error of read/ write heads over data tracks. Therefore, it is important to understand power loss and temperature distribution associated with rotational speed and design parameters (Schirle 1997). A lot of papers on power loss by rotating disks have been published since early 1960s. Daily and Nece (1960) studied power loss of a single rotating disk in a housing by introducing the non-dimensional torque coefficient as a function of Reynolds number. Schlichting (1979) summarized basic results on the issue in his famous book. Hudson and Eibeck (1991) performed experiments for a multiple corotating disk stack enclosed in an axisymmetirc shroud. Recently, many researchers have studied the aerodynamic power loss in commercial hard disk drives. Sato et al. (1990) presented temperature distribution and aerodynamic power loss in 5.25 in. hard disk drives. Imai et al. (1999) have studied the effect of radial clearance between disk and shroud gap to disk vibration and power loss using 2.5 and 3.5 in. disks. Shimizu et al. (2001) performed numerical simulation to evaluate the behavior of airflow and windage loss in hard disk drives. In general, aerodynamic power dissipated in hard disk drive is known to be proportional to 2.8th power of rotational speed and 4.6th power of disk diameter (Schirle and Lieu 1996). The relation on the effect of disk speed and diameter is originated from the theoretical analysis by Schlichting (1979). However, whether the power loss relation can be applicable to current disk drives with various form factors has not been verified yet. This paper presents the experimental results of aerodynamic power loss for various enclosure conditions. Experiments were performed using a vacuum chamber

742 and three disks of 3.5, 2.5 and 1 in. sizes, focusing on the effects of disk size, enclosure gap and radial shroud clearance on power dissipation. Finally, the experimental results are compared to theoretical ones. 2 Power dissipation in hard disk drives For a given form factor of HDD, increased spindle speed leads to increased power and temperature. Table 1 shows an example of the power dissipation distribution of a commercial 3.5-in. HDD with a single disk rotating at 5400 rpm. The largest contributor to power is the controller/channel IC, taking 47%. Power dissipated at VCM actuator coil is 23%. Power losses by motor copper/iron and the motor-driven circuit for running the spindle motor take 14 and 11%, respectively. Finally, the aerodynamic power loss induced by disk rotation takes 5%. In order to compare the power distribution at higher rotational speeds, we repeat the experiment for a 3.5-in. HDD rotating at 7200 rpm. Only the flow friction loss takes 10 with 5% increment, while the power percentiles of the other components are decreased. For the server or workstation computers with high rotational speeds from 7200 to 15,000 rpm, the aerodynamic power dissipation will be dramatically increased. It is reported that the windage loss of a 3.5-in. HDD with five disks rotating at 10,000 rpm has 62% of total power (Schirle 1997). Therefore, it is needed to understand the effect of spindle speed, disk size and enclosure conditions on power loss and modify design if necessary to avoid excessive power dissipation. 3 Theoretical power dissipation When a single disk rotates at a constant angular velocity in open air or enclosure, analytical expressions of aerodynamic power dissipation were derived by calculating flow-induced viscous force (Schlichting 1979). The frictional torque imposed on the one side of a disk is represented by T ¼ Z R 0 s w 2pr rdr ð1þ Table 1 Power loss distribution of 3.5 in. HDD at 5400 and 7200 rpm Parts 5400 rpm (%) Controller and channel 47 46 VCM coil 23 21 Motor loss 14 13 Motor drive 11 10 Aerodynamic loss 5 10 7200 rpm (%) Here s w denotes the circumferential component of shear stress and R is the disk radius. It is customary to introduce the following dimensionless torque coefficient C m ¼ 2T ð2þ 1 2 qx2 R 5 Here x is rotational speed. The torque coefficient for laminar flow is represented by C m ¼ p 3:87 ffiffiffiffiffiffi ; ð3þ Re as a function of Reynolds number Re= R 2 x /v. Here v is the kinematic viscosity. The airflow becomes turbulent at large Reynolds numbers, usually Re >3 10 5. For the turbulent regime, the friction coefficient is estimated by C m =0.146Re 1/5 using the 1/7 power law for the velocity distribution. When a disk rotates in enclosure, the frictional power dissipation can be calculated for two enclosure conditions of small and large gaps (Daily and Nece 1960; Hudson and Eibeck 1991). Table 2 summarizes the frictional coefficients for the enclosure conditions. In the small gap condition (case III), the axial gap H between the disk and enclosure wall is assumed to be smaller than the boundary layer thickness. The torque coefficient varies with Re 0.2, Re 0.25, Re 0.5 and Re 1 by changing the axial gap conditions and flow patterns. The frictional torque coefficient is converted into the aerodynamic power dissipation using P ¼ 2T x ¼ C m qx 3 R 5 : ð4þ For example, the power loss by turbulent flow in open case becomes P µ x 2.8 R 4.6. Table 3 summarizes power dissipation as functions of rotational speed and disk radius for the three cases. 4 Experiments and discussions 4.1 Experimental procedures The experimental apparatus, shown in Fig. 1, consists of the following components: spindle motor, vacuum chamber, motor drive, power analyzer, and vacuum pump. In order to measure aerodynamic power consumption in HDD, a vacuum chamber was built. The Table 2 Torque coefficients C m for different cases Case Laminar Turbulent I. Open air 3.87 Re 0.5 0.146 Re 0.2 II. Enclosure (large gap) 2.67 Re 0.5 0.0836 Re 0.2 or 2.83 Re 0.48 (H/R) 0.05 III. Enclosure (small gap) 2p (R/H) Re 1 0.0622 (Re H/R) 0.25

743 Table 3 Effects of rotation speed and disk radius on power loss Case Laminar Turbulent I. Open air x 2.5 R 4 x 2.8 R 4.6 II. Enclosure (large gap) x 2.5 R 4 x 2.8 R 4.6 III. Enclosure (small gap) x 2 R 4 /H x 2.5 R 4 /H chamber was designed to emulate basic disk drive feature, consisting of a stainless steel base and a transparent acryl cover. Experimental procedures to measure the aerodynamic power dissipation in open air are as following. First, a single hard disk is rotated in the chamber without chamber cover, and power analyzer measures the electrical power input between spindle motor and motor drive. The experiments are repeated in the speed range of 3000 10,200 rpm at intervals of 800 rpm by controlling the motor drive. The currents and voltages at three phases are measured simultaneously and integrated per unit time to obtain the spindle power consumption P k such as P k ¼ 1 T Z t 0 i k ðtþv k ðtþ dt; ð5þ where k =1,2,3.i k (t) and v k (t) are the instantaneous values of the current through and voltage across phase k, respectively. Second, the chamber cover is attached and we repeat the similar experiments by varying the disk-cover gap. Finally, the chamber is vacuumed by vacuum pump and the same experiments are implemented. The aerodynamic power dissipation can be easily obtained by calculating the difference between power inputs in air and vacuum. Then, the power loss is converted to dimensionless friction torque coefficient to compare the analytical estimations. 4.2 Power loss without enclosure Figure 2 shows the experimental results of aerodynamic power loss for 1, 2.5 and 3.5-in. hard disks rotating in open air without enclosure. It is shown that the power dissipation dramatically increases at high rotational speeds for 3.5 in. disk. The power loss of 3.5 in. disk is about 4.6 times larger than that of 2.5 in. disk. The windage loss for 1 in. disk is quite small and it is only 6.3 mw at 10,200 rpm. After converting power loss into the dimensionless torque coefficients of Eq. (2), we plot the coefficients as a function of Reynolds numbers in Fig. 3. For the 3.5-in. disk, Reynolds number is from 5 10 4 to 2 10 5, corresponding to a turbulence regime. The experimental result agrees well with the theoretical estimation at turbulence, which varies with Re 0.2. The Fig. 2 Aerodynamic power consumption versus rotational speeds for three types of hard disks Fig. 1 Experimental setup using vacuum chamber

744 Fig. 3 Torque coefficient as a function of Reynolds number for a single disk without enclosure 2.5-in. disk is operating from Re = 2.5 10 4 to 9 10 4, which is a transient regime from laminar to turbulence. Therefore, the torque coefficient is close to laminar theory (Re 0.5 ) at low rotational speeds, but it has a slope of Re 0.2 at high speeds. The 1-in. disk is operating from Reynolds number Re = 4 10 3 to 1.5 10 4 in a laminar flow regime, and the torque coefficient varies logarithmically with Re 0.5 of the laminar theory. 4.3 Power loss in enclosure In order to measure power dissipation of a disk rotating in enclosure, a housing apparatus was designed as shown in Fig. 4. It enables the change of the axial gap distance H between the disk and enclosure wall, and radial clearance s between the disk tip and shroud. The parameters are converted to dimensionless ones with respect to disk radius. Experiments are performed with variations of axial gap, H/R = 0.025, 0.05, 0.1 and 0.2, and with variations of radial shroud clearance, s/r = 0.021, 0.042 and 0.105. Shroud surface is produced as smooth as possible in order to reduce the surface roughness effect. A commercial 3.5-in. hard disk is used in the experiments in the speed range of 1500 10,500 rpm at intervals of 300 rpm. Figure 5 shows the experimental results for different axial gap conditions, with a fixed radial clearance between disk and shroud (s/r = 0.105). At low rotational speeds (Re <6 10 4 ), the friction loss has a minimum at H/R = 0.05. However, the frictional loss has a minimum at H/R = 0.025 (H = 1.125 mm) when rotational speed is larger than 3600 rpm (Re >6 10 4 ). Figure 6 shows the results in the logarithmic scale. At the region of small Reynolds numbers, the torque coefficient decreases with Re 0.5, which is equal to the expression of the laminar theory model with a large gap. However, the frictional loss is proportional to Re 1 of the small-gap laminar theory, at large Reynolds numbers (x > 3600 rpm). From the slope of Re 1, we can obtain that the associated power loss satisfies P / x 2 R 4 : ð6þ This relation for a single 3.5 in. hard disk rotating in enclosure is quite different from the conventional turbulent equation where the power loss is proportional to x 2.8 R 4.6, which is frequently mentioned in the previous researches (Schlichting 1979; Schirle and Lieu 1996;Sato et al. 1999). Based on the experiments of power loss, a 3.5-in. hard disk in enclosure without the actuator arm Fig. 4 Test apparatus of enclosure with circular shroud

745 Fig. 5 Torque coefficients for different axial gaps between disk and enclosure wall (E-block) satisfies the small-gap laminar theory rather than the turbulent model. In general, when the arm is inserted in the enclosure, the collision of airflow to the arm and turbulence around the arm increase power loss (Shimizu et al. 2001). Figure 7 shows the torque coefficients with respect to the change of s/r, with a fixed axial gap H/R = 0.05. When Reynolds number is less than 4 10 4, corresponding to x < 2400 rpm, the flow friction loss is minimal at s/r = 0.105. In the other cases, the friction loss has a minimum at s/r = 0.021. The power loss can be reduced by decreasing the radial clearance at high rotational speeds. The effect of the radial clearance on power loss agrees with the previous results using 2.5 in. HDD (Imai et al. 1999). 5 Conclusions In this paper, the effects of rotational speed, form factor and enclosure parameters on aerodynamic power loss are experimentally studied and compared to theoretical predictions. In open air, power loss by a 3.5-in. disk satisfies the turbulent model but power dissipations by 1 and 2.5-in. disks match the laminar one, which is inversely proportional to the half power of Reynolds number. Experiments using a single 3.5-in. disk in enclosure without arm show that aerodynamic power loss is proportional to the second power of rotational speed and the fourth power of disk radius, which agrees with the laminar theory rather than turbulent one. It is Fig. 6 Logarithmic plot of torque coefficients for different axial gap conditions

746 Fig. 7 Torque coefficients for different radial clearances between disk and shroud also shown that the aerodynamic power loss can be reduced with decreasing the axial gap and radial clearance. Acknowledgements The work was supported by Grant No. R11-1997-042-100002-0 of the Center for Information Storage Devices designated by the Korea Science and Engineering Foundation. References Daily JW, Nece RE (1960) Chamber dimension effects on induced flow and frictional resistance of enclosed rotating disks. J Basic Eng 82:648 653 Hudson AJ, Eibeck PA (1991) Torque measurements of corotating disks in an axisymmetric enclosure. J Fluid Eng 113:648 653 Imai S, Tokuyama M, Yamaguchi Y (1999) Reduction of disk flutter by decreasing disk-to-shroud spacing. IEEE Trans Magn 35(5):2301 2303 Lee S-Y, Yoon D-W, Park K (2003) Aerodynamic effect on natural frequency and flutter instability in rotating optical disks. Micro Technol 9:369 374 Sato I et al (1990) Characteristics of heat transfer in small disk enclosures at high speeds. IEEE Trans Magn 13(4):1006 1011 Schirle N (1997) Key mechanical technologies for hard disk drives. In: International conference on micromechatronics for information and precision equipment. pp 7 15 Schirle N, Lieu DK (1996) History and trends in the development of motorized spindles for hard disk drives. IEEE Trans Magn 32(3):1703 1708 Schlichting H (1979) Boundary layer theory, 7th edn. McGraw- Hill, New York, pp 102 107, 647 651 Shimizu H et al (2001) Study of aerodynamic characteristics in hard disk drives by numerical simulation. IEEE Trans Magn 37(2):831 836