Dynamic analysis of a HDD spindle system with FDBs due to the bearing width and asymmetric grooves of journal bearing

Transcription

1 Microsystem Technologies Micro- and Nanosystems Information Storage and Pro Springer-Verlag /s Technical paper Dynamic analysis of a HDD spindle system with FDBs due to the bearing width and asymmetric grooves of journal bearing G. H. 1 Jang, S. H. 1, H. LeeW. 1 and KimC. 2 S. Kim (1) PREM, Department of Mechanical Engineering, Hanyang University, 17 Haengdang-dong, Seongdong-gu, Seoul, , Republic of Korea (2) Sasmsung Advanced Institute of Technology, 111, Suwon, , Republic of Korea G. H. Jang ghjang@hanyang.ac.kr Phone: Fax: C. S. Kim kimcs@samsung.com Received: 29 June 2004 Accepted: 15 February 2005 Published online: 7 July 2005 Abstract This paper investigates the dynamic behav dynamic bearings (FDBs) by solving the Reynolds equ HDD spindle system in five degrees of freedom. FEM order to calculate the pressure distribution in flu obtained by integrating the pressure and shear stre behaviors of a HDD spindle system, such as the whir solving its nonlinear equations of motion with the two design methods to improve the dynamic character increasing friction torque, i.e., optimization of t bearings and the journal bearings with asymmetric g 1 Introduction Fluid dynamic bearings (FDBs) have replaced ball be rapidly. One of the reasons is that they provide be fluid lubricant prohibits the solid contact between because they provide the damping effect 1 shows in addition a rota shaft type of a HDD spindle system with FDBs, and t journal and two thrust bearings with herringbone or (1

2 increasing the memory capacity of a HDD. However, t friction torque, variable viscosity of the fluid lu stiffness and so on. In the viewpoint of a rotor dy one tenth of ball bearings, and it generates relati though non-repeatable run-out (NRRO) is very small. stiffness is to decrease the clearance of FDBs. But result in power or thermal problems. Fig. 1 Structure of a HDD spindle system with FDBs FDBs have been one of the oldest research areas for researchers have studied the FDBs used in a HDD ind topology such as the coupled journal and thrust bea Bootsma 1975) ( analyzed the load capacity, stability an lubricated spiral grooved bearing by using 1995), narrow Rahg and Leuthold 1996) ( and Zirkelback 1998) and San calculated Andres ( the dyn of the journal and thrust bearing used in a HDD. Ho coefficients, which are determined by the translati moment coefficients by the tilting 1999) proposed motions. a Jang metho an the dynamic coefficients of FDBs considering the fi bearing system. The prior researches only focused o rotor dynamics of a HDD spindle 2002a, b) system. investigated Jang and the Yo behavior of a HDD spindle system with FDBs under th nonlinear equations of motion in terms of three tra spindle system which is supported by FDBs is operat translational motions, it has to be described in ge dynamic behavior of system more accurately. This paper investigates the dynamic behavior of a H Reynolds equation and the equations of a motion of freedom. FEM is used to solve the Reynolds equation distribution in fluid film. Reaction forces and fri pressure and shear stress along the fluid film, res (2

3 system, such as the whirling and the tilting motion equations of motion with the Runge-Kutta method. Th to improve the dynamic characteristics of a HDD spi torque, i.e., optimization of the width of the lowe bearings with asymmetric grooves. 2 Method of analysis 2.1 Reynolds equation The Reynolds equations for journal and thrust beari cylindrical coordinates: (1) (2) where R, and h, are the radius of journal, film thickne HDD spindle system, respectively. Pressure in the f and 2 with FEM. For journal bearing, reaction force following equations 2002a): (Jang and Yoon (3) (4) (3

4 (5) For thrust bearing, reaction force and friction tor (6) (7) 2.2 Equations of motion As shown 1, in the Fig. HDD spindle system is supported by Figure 2 shows the free body diagram of the HDD spindl force, weight of a rotor and centrifugal force due motion of the HDD spindle system can be described b translational displacements in X, Y and Z direction and directions, so that the five nonlinear differential x y (8) (9) (4

5 (10) (11) (12) where x, y, F z, F x Mand are y M the reaction forces and moments u, u, e and u zare the mass unbalance of the HDD spindle syste unbalance from mass center G, respectively. Fig. 2 Free body diagram of a HDD spindle system (5

6 3 Simulation model and procedure 3.1 Simulation model A computer program was developed in order to analyz spindle system supported by a coupled journal 1 shows and t the major design parameters of a HDD spindle system composed of a rotating shaft, a hub, one disk, 1, and a it sp total mass is 50.6 g. The mass unbalance of the HDD g mm, which is the possible maximum value radius of the disk and the outer 2 shows radius the major of the desig hub. journal and thrust bearings. Because the clearance lower journal bearings is much larger than that of assumed to be negligible. Moreover, the pressure at journal and upper thrust bearing are also neglected conditions for a journal bearing are assumed to be direction and the ambient pressure in both sides an the ambient pressures at the inner and outer radius bearing are discretized by and elements respectively. Table 1 Major design variables of a HDD Design variable Mass, m (g) 27.6 Moment of inertia, I x, y (kg I ) m 4 Moment of inertia, I z (kg ) m Unbalance mass, u (g mm) m Rotating speed, (rpm) 10,000 Location of centers along z direction (mm) Mass center Upper journal Lower journal Upper thrust Lower thrust Table 2 Major design variables of FDBs (6

7 Design variable JournalThrust Radius of journal, R (mm) Groove type Herringbone Herringbone Number of grooves 8 12 Clearance m) ( Groove angle ( ) Viscosity, (Pa s) Inner radius (mm) 2.2 Outer radius (mm) Simulation procedure Figure 3 shows the simulation procedure used in this n of journal and thrust bearings, which support a HDD fluid film is calculated by solving the Reynolds eq friction torque are obtained by integrating the pre respectively, equations of motion in the five degre order Runge-Kutta method to calculate the new posit procedure is repeated until the orbit of a rotor co Fig. 3 Flow chart to calculate the dynamic behavior of a HDD spindle system (7

8 4 Results and discussion 4.1 Motion of a HDD spindle system due to journal bearing width The mass center of a HDD spindle 1 is system usually as located shown in span center so that it has a conical whirling motio bigger radius than the lower part. This conical mot capacity of a HDD. This can be achieved by proper s journal bearings. 4 shows Figure the loci of the mass center, th bearing centers due to the variation of the width o total width of the upper and the lower journal bear the models can be made within similar friction torq whirl radius. The whirl radius of mass center and t respectively, when the width of upper and lower jou 2.2 and 1.2 mm. Fig. 4 Whirling motion of a HDD spindle system due to the bearing width of journal bearing 4.2 Motion of a HDD spindle system due to asymmetrically grooved journal bearing Even though whirl radius and tilting angle can be r upper and lower journal bearing, a HDD spindle syst in small bearing reaction force or small stiffness proposes a journal bearing with asymmetric grooves (8

9 stiffness and damping coefficients without 5 shows changing the gr pattern of a conventional symmetrically grooved jou grooved journal bearing. Fig. 5 Symmetric and asymmetric grooves To compare the static and the dynamic characteristi groove pattern, only upper journal bearing of HDD s equation and the width of upper journal 6 bearing shows the is of journal center when the equations of motion of a translational motion in the X and Y directions with journal center is assumed to be the origin. It show grooves stays at the origin but the center of journ equilibrium point. It means that symmetric grooves motion of a rotor at the origin, but asymmetric gro eccentricity ratio 7 shows of the pressure Figure distribution bearing and the groove pattern along the circumfere 10,000 rpm. The pressure has local maximum and mini lubricant flows from groove to ridge and from ridge with asymmetric grooves generates the asymmetric pr eccentricity of 8 a and rotor. 9 show Figures the stiffness and damping bearings with symmetric and asymmetric grooves, res coefficients are calculated by the 1999). perturbation Most of met th coefficients due to asymmetric grooves are bigger t by 20 77%, xx but decreases K by 7% due to the asymmetric p reduction xx is of very K small compared with the increase o stiffness resulting from upper and lower journal be the asymmetric grooves in upper and lower journal b asymmetric grooves are bigger than those of the con respectively. The friction torque due to asymmetric symmetric bearing by 0.89%. (9

10 Fig. 6 Loci of journal center Fig. 7 Pressure distribution and groove location along the mid-plain of journal bearing (10

11 Fig. 8 Stiffness coefficients of journal bearing (11

12 Fig. 9 Damping coefficients of journal bearing Figure 10 shows the loci of the upper journal center, center with the asymmetrically and the symmetricall widths of upper and lower journal bearings are assu asymmetrically grooved journal bearings, the groove (12

13 shifted from that of lower journal bearing by 45. numerically analyzed in the five degrees 3. It shows of freedom that spindle system with symmetric grooves has a concent because there is no static load in this model. Howe bearings result in eccentric motion of the HDD spin because of the asymmetric pressure pattern generate spindle system with asymmetric grooves spins with b Average whirl radii of mass center due to the symme 38.9 nm, respectively, and the asymmetric grooves d center by 24.4%. 11 shows Figure the variation of tilting angl asymmetric grooves decrease the tilting angle by 24 Fig. 10 Loci of upper journal bearing, mass center and lower journal bearing (13

14 Fig. 11 Tilting angle of a HDD spindle system 5 Conclusion This paper investigates the dynamic behavior of a H Reynolds equation and the equations of a motion of freedom. It shows that the dynamics of a HDD spindl design variables of FDBs but also by the design var proposes two design methods to improve the dynamic without increasing friction torque, i.e., optimizat bearings and the journal bearings with asymmetric g bearing may have advantage in terms of small whirl proposed methods can be utilized to design a robust References Bootsma J (1975) Liquid-lubricated spiral-groove bearings. In: Phillips Research Report-Supplements, No. 7, The Netherlands Jang GH, Kim YJ (1999) Calculation of dynamic coefficients in a hydrodynamic bearing considering five degrees of freedom for a general rotor-bearing system. ASME J Tribol 121: Jang GH, Yoon JW (2002a) Nonlinear dynamic analysis of a hydrodynamic journal bearing considering the effect of a rotating or stationary herringbone groove. ASME J Tribol 124: (14

15 Jang GH, Yoon JW (2002b) Dynamic characteristics of a coupled journal and thrust hydrodynamic bearing in a HDD spindle system due to its groove location. Microsys Technol 8: Rahman M, Leuthold H (1996) Computer simulation of a coupled journal and thrust hydrodynamic bearing using a finite element method. In: Proceedings of 25th annual symposium incremental motion control systems& devices, pp Zang Y, Hatch MR (1995) Analysis of coupled journal and thrust hydrodynamic bearing using finite-volume method. ASME Adv Inf Storage Process Syst 1:71 79 Zirkelback L, San Andres L (1998) Finite element analysis of herringbone groove journal bearings : a parametric study. ASME J Tribol 120: (15