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Optimum Design of Oil Lubricated Thrust Bearing for Hard Disk Drive with High Speed Spindle Motor

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Optimum Design of Oil Lubricated Thrust Bearing for Hard Disk Drive with High Speed Spindle Motor Hindawi Publishing Corporation International Journal of Rotating Machinery Volume 2013, Article ID 896148, 11 pages http://dx.doi.org/10.1155/2013/896148 Research Article Optimum Design of Oil Lubricated Thrust Bearing for Hard Disk Drive with High Speed Spindle Motor Yuta Sunami,1 Mohd Danial Ibrahim,2 and Hiromu Hashimoto1 1 Department of Mechanical Engineering, Tokai University, 4-1-1 Kitakaname, Hiratsuka-shi, Kanagawa-ken 259-1292, Japan 2 Department of Mechanical and Manufacturing Engineering, Faculty of Engineering, Universiti Malaysia Sarawak, 94300 Kota Samarahan, Sarawak, Malaysia Correspondence should be addressed to Yuta Sunami; [email protected] Received 29 July 2013; Accepted 15 October 2013 Academic Editor: Masaru Ishizuka Copyright © 2013 Yuta Sunami et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. This paper presents the application of optimization method developed by Hashimoto to design oil lubricated thrust bearings for 2.5 inch form factor hard disk drives (HDD). The designing involves optimization of groove geometry and dimensions. Calculations are carried out to maximize the dynamic stiffness of the thrust bearing spindle motor. Static and dynamic characteristics of the modeled thrust bearing are calculated using the divergence formulation method. Results show that, by using the proposed optimization method, dynamic stiffness values can be well improved with the bearing geometries not being fixed to conventional grooves. 1. Introduction spindlebyintroducingpermanentmagneticthrustplatesinto thebearingspindlestructure[6]orintroducingmagnetic HDD has been used as the main storage multimedia for fluid as lubricants [7]. However, there are very few attempts at electronics devices. Currently, HDD widely depends on oil finding an optimum design with a novel geometry to replace lubricated hydrodynamic bearings. Hydrodynamic bearing the conventional herringbone or spiral grooves for HDD. In is mainly supported by thrust and journal bearings. A the attempts at improving HDD performance, Arakawa et al. schematicviewofbearingsina2.5inchHDDisshownin [8] proposed a nonuniform spiral groove for journal bearings Figures 1 and 2. to expand the critical bearing number for higher revolution Hydrodynamic bearing gives better performance char- speed of HDD spindle. The approach indicated that the novel acteristics compared to conventional ball bearings as it nonuniform spiral grooves hydrodynamic bearings manage has high dynamic stiffness with additional much higher to increase the stability of rotation in high speeds. damping effects. These damping effect characteristics provide This suggests that there is a probability of a further smaller nonrepeatable run-out (NRRO). NRRO is the major improvement if the groove geometry is not being fixed to any contributor to the track misregistration in HDD read-write conventional grooves, either spiral or herringbone grooves. mechanism. Even though the repeatable run-out (RRO) of However, as far as authors know, there are no attempts at oil lubricated hydrodynamic bearing is higher than the ball drastically improving the bearing characteristics changing bearing spindle motor, the RRO can be corrected by a read- the geometry and dimensions for oil lubricated 2.5 inch write servo. Therefore, to reduce NRRO and increase spindle HDD spindle motor. Recently, HDD is being demanded to performance is to improve the bearing performance. be thinner. If the characteristic of thrust bearing can be Currently, groove geometries that are being widely used drastically improved, it is possible for HDD to be thinner. in HDD thrust bearings are mainly a spiral or a herringbone Therefore, in this paper, by adapting the optimization method grooved geometries. Several investigators have conducted initiated by Hashimoto, new optimum groove geometry and numerical analysis predictions of these grooves for HDD dimension to replace conventional grooves and increase the bearing performance [1–5]. There were also some attempts bearing performance of an oil lubricated 2.5 inch HDD had at improving the dynamic stiffness and damping of HDD been calculated. The groove geometry and dimension of the 2 International Journal of Rotating Machinery Thrust bearing Journal bearing Table 1: Initial 2.5 inch bearing parameters. Parameters Values 2.55 × 10−3 Outer radius out (m) 1.0 × 10−3 Inner radius in (m) Weight (N) 0.185 Revolution speed (rpm) 5000∼20,000 Figure 1: Bearings in spindle motor. Groove number 16 Seal ratio 0.58 −5 Groove depth ℎ (m) 1.0 × 10 Groove width ratio =(1/1 +2) 0.5 Geometry parameter 1 (deg) 0.0 Geometry parameter 2 (deg) 0.0 Geometry parameter 3 (deg) 0.0 Geometry parameter 4 (deg) 0.0 −3 Lubricant viscosity (Pa⋅s) 6.523 × 10 Shaft W s hr (a) hg rs =Rs/Rout R =b1/(b1 +b2) in Rs b1 b2 Land R out Groove Figure 3: Design parameters for thrust bearing. (b) method to obtain the optimum solutions for nonlinear Figure 2: Initial spiral thrust bearing groove geometry and pressure optimization problems. However, it sometimes can not find distribution; (a) groove geometry, (b) pressure distribution. the global optimum solution when the objective function has the multipeaks. Therefore, the direct search method is used first to roughly search for several local optimum solutions; thrust bearing for spindle motor are calculated using the then, SQP is used to find the local optimum solutions hybrid method [9, 10] with the improvement of dynamic when we set the initial values obtained by the direct search stiffness , being set as the objective function. method. The global optimum solution is finally obtained by The optimization results showed that the dynamic stiff- choosing the maximum or minimum value. Furthermore, the ness of oil lubricated thrust bearing can be improved by confirmation of the optimum solution is needed to clarify the introducing a new optimum geometry into the system. validity of the optimum solution. The validity of the optimum Vibration analyses were also presented to numerically verify solution is confirmed by comparing the value of the objective the applicability of the improved bearings. function calculated from the optimum design variables with those from randomly selected design variables. 2. Geometrical Optimization and Figure 3 shows the design parameters used in this opti- Analysis of Bearing Characteristics mization. The initial prescribed design parameters for thrust bearing in this paper, based on a commercialized 2.5 inch 2.1. Modification of Groove Geometry. The geometrical opti- form factor HDD design, are shown in Table 1.Takingthe mization process is carried out using the hybrid method spiral groove geometry as a threshold groove geometry, the [9, 10], a combination of direct search method and successive groove geometry parameters of angle variation 1 through 4 quadratic programming (SQP) method. SQP is a powerful are initially set to zero. International Journal of Rotating Machinery 3 From there, the groove geometry design parameters Δr Δr Δr Δr are changed arbitrarily using the cubic spline interpolation function [9]. The cubic spline interpolation function is a cubic O polynomial equation where each section connected to nodal points is a continuity of a second order derivative of the r4 function. Figure 4 shows the spiral groove geometry represented r as initial values in the feasible region for optimum design of O 2 r3 thrust bearing treated in this paper. Referring to the same figure,theinitiallinerepresentingthespiralgroovegeometry, r1 k th step is shown with the label initial groove geometry while the 1 4 3 new line of geometry after the spline interpolation function is r1 2 calculated step by step as shown with the label th step. The groove geometry parameter of 1 through 4 is set starting r2 r4 from inner region towards the outer region. The feasible r3 region for the groove geometry is divided equally into four regions in the radial direction as there were no significant effects on the optimization with regions over the divisions of Initial groove four. geometry With the most inner point of the initial spiral groove curve fixed at point , the angle variation of groove geometry is then evolved gradually from initial stage to the r final stage. Figure 4: Modifications of groove geometry. 2.2. Analysis of Bearing Characteristics. In this paper, apply- The spring coefficient and damping coefficient can be ing the boundary-fitted coordinate system to adjust the obtained, respectively, by integrating the real and imaginary geometrical optimization method derives the calculation partsofthedynamicpressurecomponents,, as follows: method of bearing characteristics. Moreover, in the process 2 of analyzing the static and dynamic characteristics of the 2 =∫ ∫ Re (−) bearings, the perturbation method is applied to the Reynolds 1 0 equivalent equation. The Reynolds equivalent equation can 2 (4) 1 2 be solved using the Newton-Raphson iteration method, and = ∫ ∫ (− ), Im the static component 0 and dynamic component of 1 0 pressure are obtained. This detailed calculation method is shown in the appendix. where isthesqueezefrequencyoftheshaft,whichis The load-carrying capacity is obtained by the following angular frequency of harmonic vibration when the bearing integration: is small vibrated in the axial direction under equilibrium condition, in the HDD obtained through the perturbation
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