Reduction of windage loss of an optical disk drive utilizing air-flow analysis and response surface methodology. Y. H. Jung & G. H.

Transcription

1 Reduction of windage loss of an optical disk drive utilizing air-flow analysis and response surface methodology Y. H. Jung & G. H. Jang 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 Reduction of windage loss of an optical disk drive utilizing air-flow analysis and response surface methodology Y. H. Jung G. H. Jang Received: 30 September 2011 / Accepted: 4 June 2012 / Published online: 19 June 2012 Ó Springer-Verlag 2012 Abstract This research analyzes the source of the power consumption in an optical disk drive (ODD) of a laptop computer. It shows that approximately 70 % of electrical input power is dissipated through the windage loss in the ODD. The windage loss is calculated by simulating the air flow around the rotating disk, and the simulated windage loss is verified by comparing with the measured one. It investigates the windage loss according to the variation of the upper and lower gaps between the rotating disk and case, and the optimal upper and lower gaps are determined by using the response surface methodology to reduce the windage loss. Finally, it shows experimentally that the proposed optimal model reduces total power consumption by 6.5 %. 1 Introduction An optical disk drive (ODD) consumes the electrical input power to windage, bearing and electrical losses, and the windage loss is the biggest loss of all. It is originated from the shear stress between rotating disk and surrounding air. The shear stress is affected by eddy viscosity and velocity gradient which are dependent on the air flow and the internal structure of the ODD. Reduction of windage loss in an ODD is an important issue, especially in a mobile computer, to increase its operating time. It can be achieved Y. H. Jung G. H. Jang (&) PREM, Department of Mechanical Engineering, Hanyang University, 17 Haengdang-dong, Seongdong-gu, Seoul , Republic of Korea ghjang@hanyang.ac.kr URL: by optimizing the internal structure of the ODD in such a way to decrease the shear stress and velocity gradient between rotating disk and surrounding air. Many researchers have investigated the flow analysis in optical or hard disk drives in order to reduce the flowinduced vibration and the windage loss. Sato et al. (1990) studied the characteristics of the windage loss in a enclosure with 5.25-inch disks. They confirmed experimentally that total power loss increases in proportional to the number of disks and that windage loss dominates the total power loss with the increase of the rotating speeds. Imai et al. (1999) investigated various disk-to-shroud spacing in order to reduce disk flutter amplitudes. They showed experimentally that the flutter amplitudes are affected by changing the rotational speed and the shroud length. They investigated the power consumption due to disk-to-shroud spacing and rotational speed. Shimizu et al. (2001) performed aerodynamic simulation to evaluate the behavior of air flow and windage loss in hard disk drives. Cho et al. (2005) studied the effects of rotational speed, form factor and enclosure parameters on aerodynamic power loss and compared to theoretical predictions of power loss. They showed experimentally that the aerodynamic power loss can be reduced with the decrease of the axial gap and radial clearance. Cheng et al. (2009) designed the cover of an ODD that can effectively improve the flow-induced disk vibration. They showed numerically that altering the shape of disk top cover influences the rotating flow and the corresponding secondary recirculating vortex, and then the disk vibration. With a proper design of a disk cover, the flow-induced disk vibration was reduced substantially as compared to the original shape of the top cover. However, prior researchers did not investigate and classify the source of power loss of an ODD, and they did not propose the optimal design to decrease windage loss.

4 1446 Microsyst Technol (2012) 18: This research investigates and classifies the source of power loss in the slim ODD of a laptop computer which has the writing speed of 45 rpm and the reading speed of 5,500 rpm. It calculates the air flow around the rotating disk. Simulation result is verified by comparing with the measured windage loss. It identifies important design parameters of windage loss through the simulated flow around the rotating disk, and it formulates an optimal design problem to reduce the windage loss. The windage loss is proportional to the rotating speed, so that the optimization of the ODD to reduce the windage loss was performed at 5,500 rpm. Finally an optimized enclosure structure of the ODD is proposed and confirmed by experiment. 2 Classification of the power loss in an ODD 2.1 Electrical loss of the ODD The power losses of an ODD are classified into windage loss, the bearing loss, and the electrical loss which is composed of copper and iron loss. Figure 1 shows experimental setup for the measurement of current and voltage, and total input power is calculated by the multiplication of measured voltage and current for the spindle motor at various operating speed. Copper loss is determined by the multiplication of the square of current and resistance. Iron loss is determined by integrating the Bertotti equation (Bertotti et al. 1991) over the stator core as shown in Eq. (1). P iron ¼ K h B 2 m f þ p2 rd 2 ðb m f Þ 2 þ K e ðb m f Þ 3=2 ð1þ 6 where K h, K e, B m, r, d, and f are the coefficient of hysteresis loss, the coefficient of excess losses, the magnetic flux density, the conductivity of material, the thickness of the lamination and the frequency. This paper developed a three-dimensional finite element model to calculate the magnetic flux density of the stator of the ODD as shown in Fig. 2. The finite element model has 4 poles and 3 slots with 1/4 periodic boundary condition because the spindle motor of the ODD has 16 poles and 12 slots, and it has 1,200,000 tetrahedral elements. 2.2 Bearing loss of the ODD Bearing loss is determined by the Reynolds equation as shown in Eq. (2). o h 3 op þ o h 3 op ox 12l o ox oy 12l o oy ¼ 1 o ð 2 ox u xhþþ o oy u yh þ oh ð2þ ot where h, l o, u x, and u y are the film thickness, the fluid viscosity, the velocities in x and y direction, respectively. The plane journal bearing is used in the ODD spindle motor. And the bearing loss of the ODD spindle motor was calculated with the viscosity of oil at 25 C. Figure 3 shows a finite element model for the fluid dynamic bearings and pressure distribution. The finite element model has 4,000 quadrilateral elements. Pressure distribution is calculated by solving the Reynolds equation using FEM, and the friction torque of bearing can be determined by integrating the shear stress along the fluid film (Jang et al. 2006). 2.3 Windage loss of the ODD Windage loss is approximated as the subtraction of the copper loss, iron loss, and bearing loss as shown in Eq. (3). P windage ¼ VI P copper P iron P bearing ð3þ where V, I, P copper, P iron, and P bearing are the measured voltage, the measured current, the measured copper loss, the simulated iron loss, and the simulated bearing loss, respectively. When ODD spindle motor reaches the steadystate operating speed, the current and voltage measured Fig. 1 Experimental setup to measure current and voltage

5 Microsyst Technol (2012) 18: Fig. 2 Finite element model and calculated flux density of the stator of the ODD. a Finite element model, b flux density of stator Fig. 3 Finite element model and pressure distribution of the fluid dynamic bearings. a Finite element model, b pressure distribution instantly at the surrounding temperature of 25 C. Table 1 shows the measured current and voltage due to the rotating speed. To increase the reliability of the data, the same experiment was repeated five times and the measured current and voltages were averaged. Figure 4 shows the sources of the losses of the ODD system at 5,500 rpm by using the above method. Windage loss is approximately 70 % of total power consumption. Other loss of 3 % is the discrepancy between the simulation and the experiment, and it is suspected to be an error in experiment and simulation. In this classification, reduction of the windage loss is the most effective method to decrease the power consumption of the ODD. 3 Simulations of air flow 3.1 Simulation method and model The Navier Stokes and continuity equations to calculate the air flow and pressure inside the ODD can be written as shown in Eqs. (4 and 5): Table 1 Measured current and voltage due to rotating speed Rotating speed (rpm) ODD without disk Current (ma) Voltage (V) ODD with disk Current (ma) Voltage (V) 1, , , , , o ot ðqvþþrðqvvþ ¼ rpþr lðrvþrvt Þ þ F ð4þ oq þrðqvþ ¼0 ot ð5þ where q, l, p, v, g, and F are the density, the viscosity, the pressure of the air, the velocity vector, the gravity acceleration vector, and the external body force vector, respectively. The external body force vector F consists of

6 1448 Microsyst Technol (2012) 18: Table 2 Dimensions of the ODD and properties of the air flow Dimension (m) Value Property Value R c q (kg/m 3 ) R d l (kg/m 3 ) H d m (m 2 /s) H l X z (rpm) 5,500 H u H r Fig. 4 Loss sources of the ODD system at 5,500 rpm the Coriolis and the centrifugal force due to rotation as follows: F ¼ 2qX z v qx z ðx z RÞ ð6þ where X z is the rotating velocity vector and R is the position vector. We developed a finite volume model to analyze the flow in a slim ODD of a laptop computer. Figure 5 shows simplified axisymmetric finite volume model of the ODD. This research calculates the air flow around the rotating disk using the FLUENT. It is composed of a rotating part consisting of a disk and a rotor, and a stationary case, and air between the disk and the case. The dimensions of the ODD and properties of the air flow are shown in Table 2. It has 222,000 four-node quadrilateral cells, and we use two-dimensional axisymmetric swirl solver with the standard k x model to calculate the velocity and pressure of air. 3.2 Analysis of air flow The shear stress can be expressed in the following equation: s ¼ s la min ar þ s turbulence ¼ qðm þ e m Þ ou ð7þ oy where m and e m are the kinematic viscosity and the eddy viscosity, respectively. The friction torque can be determined by integrating the shear stress along the disk boundary: Z T friction ¼ r sda ð8þ r The windage loss of the ODD can be calculated in the following equation: P windage ¼ T friction x rpm ð9þ Figure 6 shows the simulated and measured windage losses at 1,500, 3,000, 4,500, and 6,000 rpm, respectively. It shows that overall trend of the simulated windage loss matches with that of the measured one. As the rotating speed increases, windage loss increases exponentially. Figure 7 shows the pressure distribution and velocity profile of the ODD. The pressure in the upper side of the disk is slightly different from that in the lower side, and one of the main causes is the different length of the gap. It also makes the different velocity gradient along upper and lower gap. The eddy viscosity can be defined by the Prandtl s mixing length theory shown in Eq. (10). e m ¼ ql 2 ou oy ð10þ where l is a mixing length. The eddy viscosity is directly proportional to the square of mixing length. Figure 8 shows the global value of the eddy viscosity due to the gap length, and it is calculated by integrating over the total area of air. The eddy viscosity decreases with the reduction of the upper and lower gap length. Vortex flow is formed around Fig. 5 Axisymmetric finite volume model of the ODD

7 Microsyst Technol (2012) 18: Fig. 6 Simulated and measured windage losses the outer rim of the disk. Since the density and kinematic viscosity are constant, the eddy viscosity and velocity gradient determine the shear stress in Eq. (7). Thus, the length of gap between rotating disk and case is a significant design variable. 4 Optimization of gap between rotating disk and case 4.1 Sensitivity analysis Optimization process is generally required to have long computation time due to many combinations of design variables. Therefore, it is important to determine major design variables which highly affect the friction torque through the sensitivity analysis of each design variable. The design variables are upper, lower and side gap lengths, respectively. Sensitivity analysis was performed for the upper and lower gaps. Figure 9 shows the sensitivity analysis of each design variable. Upper and lower gap lengths have large effect on friction torque. On the other hand, side gap length has little effect on friction torque. Thus, upper and lower gaps are chosen as the design Fig. 8 Eddy viscosity due to gap length. a Upper gap length, b lower gap length variables for the optimization problem. And the parametric study of upper and lower gaps due to gap length is performed. Figure 10 shows the friction torque due to the upper and lower gaps. In both gaps, the friction torque tends to decrease from 0.2 to 0.6 mm and to increase from 0.6 mm to end of boundary. 4.2 Optimization method A design optimization problem to minimize the windage loss can be formulated as follows: Fig. 7 Pressure and velocity distribution of the ODD at 5,500 rpm. a Pressure distribution, b velocity profile

8 1450 Microsyst Technol (2012) 18: Fig. 10 Friction torque due to the upper and lower gaps. a Upper gap length, b lower gap length Fig. 9 Sensitivity analysis of each design variable. a Upper gap, b lower gap, c side gap Minimize; PX ð i Þ ¼ P windage Subject toðx i Þ lower limit X i ðx i Þ upper limit where P(X i ) represents the windage loss of the ODD as an objective function. X i are upper and lower gap lengths as design variables, and their upper and lower limits are determined with the consideration of manufacturability. We improve computational efficiency in solving the design optimization problem by using the metamodel-based design optimization technique. Metamodel for windage loss is constructed by using the full factorial design method (FFD). FFD is an experiment which consists of two or more factors (Myers and Montgomery 1995). Design of experiments are constructed in such a way that the friction torque at 35 data points are calculated with the upper and lower gaps by the decrement of 0.2 mm. To find the optimal solution, the response surface method (RSM) is used as an optimization method. A cubic approximation function of the model is used to construct the fitted response surface. In general, the response model can be written as follows: Y ¼ b 0 þ Xk þ Xk i6¼j i¼1 b i x i þ Xk b ij x 2 i x j þ Xk i6¼j i¼1 b ii x 2 i þ Xk b ij x i x 2 j i¼1 b ii x 3 i þ Xk i6¼j b ij x i x j ð11þ where b is regression coefficients for design variable, and x i is i-th design variable. The coefficients of RSM can be written as follows: b _ ¼ðX 0 XÞ 1 X 0 Y ð12þ where X is the matrix of the level of the independent variables, X 0 is the transpose of the matrix, and b _ is the matrix of fitted coefficients (Box and Draper 1987). Table 3 shows the calculated regression coefficients. Figure 11 shows the response surface for the design variables of lower and upper gaps. Optimal upper and lower

9 Microsyst Technol (2012) 18: Table 3 Calculated regression coefficients Regression coefficients Value b b b b b b b b b b gaps of 0.59 and 0.57 mm are determined through this process, and the windage losses of the conventional and optimal design are and W, respectively. Figure 12 shows comparison of the velocity profile between conventional and optimal designs. Figure 13 shows the comparison of the velocity magnitude between conventional and optimal gaps at the radius of 20, 30, 40 and 50 mm. In the optimal design, the velocity of air flow linearly decreases from the disk to cover, and the back flow decreases at the outer rim of the disk. Table 4 shows the comparison of the absolute value of velocity gradient between conventional and optimal gaps over disk surface at the radius of 20, 30, 40 and 50 mm. The velocity gradient in the optimal gap changes linearly, and the optimal gap at Fig. 11 Response surface with respect to upper and lower gaps Fig. 12 Comparison of the velocity profile between conventional and optimal designs. a Conventional design, b optimal design

10 1452 Microsyst Technol (2012) 18: Fig. 13 Comparison of the velocity magnitude between conventional and optimal gaps over the disk at the radius of 20, 30, 40 and 50 mm Table 4 Comparison of the absolute value of velocity gradient between conventional and optimal gaps Radial position (mm) Absolute value of velocity gradient (1/s) Optimal upper gap Conventional upper gap Optimal lower gap Conventional lower gap E? E? E? E? E? E? E? E? E? E? E? E? E? E? E? E?04 Table 5 Comparison of the eddy viscosity between conventional and optimal gaps Model Conventional gap Eddy viscosity (kg m/s) 3.64E E-05 each radial position has smaller velocity gradient than that in the conventional gap. Table 5 shows the comparison of eddy viscosity between conventional and optimal gaps. Also, the optimal gap has smaller eddy viscosity than that in the conventional gap. Consequently, the friction torque decreases in the optimal gap due to the reduction of the velocity gradient at the disk surface and the eddy viscosity. 4.3 Power consumption measurement in the optimal gap Optimal upper (0.59 mm) and lower (0.57 mm) gaps To verify the simulated result of the optimal design, an ODD with optimal gap is constructed and the power consumption is measured. To obtain the exact experimental results, disk is attached and detached to the spindle Table 6 Comparison of simulated windage loss with measured one Model Simulated windage loss (W) Measured windage loss (W) Conventional gap Optimal upper and lower gaps Difference (%) motor 5 times, and measured currents are averaged to reduce the experimental error. Table 6 shows comparison of the simulated windage loss with measured one. Reduction of windage loss of 8 % in the simulation closely matches with that of 6.5 % in the experiment. The difference of windage loss may be originated from the fact that the axisymmetric model does not properly describe the flow inside the rectangular enclosure of the ODD. Figure 14 shows the comparison of the friction torque between the conventional and optimal models. Optimal model at 5,500 rpm has smaller windage loss at other speeds of 1,500, 3,000, 4,500, and 6,000 rpm than the conventional model by 6 8 %.

11 Microsyst Technol (2012) 18: Fig. 14 Comparison of the friction torque between conventional and optimal model 5 Conclusions This research measured and analyzed the source of total power loss in the ODD of a laptop computer. It investigates the windage loss due to the gap between the rotating disk and case by using flow analysis and response surface methodology. We propose the optimal gap between rotating disk and case to minimize the windage loss, and it shows experimentally that the optimal gap reduces windage loss. This research can be utilized to reduce the total power consumption by designing the optimal gap between disk and case. References Bertotti G, Boglietti A, Chiampi M, Chiarabaglio D, Fiorillo F, Lazzari M (1991) An improved estimation of iron losses in rotating electrical machines. IEEE Trans Magn 27(6): Box GEP, Draper NR (1987) Empirical model building and response surfaces. Wiley, New York Cheng CC, Wu FT, Ho KL (2009) Reduction of flow-induced vibration and noise of an optical disk drive. J Sound Vib 320(1 2):43 59 Cho SO, Lee SY, Rhim YC (2005) Aerodynamically induced power loss in hard disk drives. Microsys Technol Sens Actuators Syst Integr 11(8 10): Imai S, Tokuyama M, Yamaguchi Y (1999) Reduction of disk flutter by decreasing disk-to-shroud spacing. IEEE Trans Magn 35(5): 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(2): Myers RH, Montgomery DC (1995) Response surface methodology: process and product optimization using designed experiments. Wiley, New York Sato I, Otani K, Mizukami M, Oguchi S, Hoshiya K, Shimokura KI (1990) Characteristics of heat transfer in small disk enclosures at high rotation speeds. IEEE Trans Compon Hybrids Manuf Technol 13(4): Shimizu H, Tokuyama M, Imai S, Nakamura S, Sakai K (2001) Study of aerodynamic characteristic in hard disk drives by numerical simulation. IEEE Trans Magn 37(2):