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Microsyst Technol (2016) 22:1299–1305DOI 10.1007/s00542-016-2850-2

TECHNICAL PAPER

Robust shaft design to compensate deformation in the hub press‑fitting and disk clamping process of 2.5″ HDDs

Bumcho Kim1,2 · Minho Lee3 · Gunhee Jang3

Received: 16 September 2015 / Accepted: 19 January 2016 / Published online: 9 February 2016 © Springer-Verlag Berlin Heidelberg 2016

herringbone-grooved journal bearings and one spiral-grooved thrust bearing on the sleeve. The radial and axial clearances are approximately 2 and 30 μm, respectively, as shown in Fig. 1. A stopper is introduced to prevent separation of the rotating hub from the stationary parts and to form an oil interface with the sleeve. One of the most important design issues to be addressed with FDBs is to maintain a uniform radial gap between the shaft and sleeve within a range of several micrometers in order to reduce the non-repeatable runout (NRRO) at half speed whirl (HSW) frequency generated via the instability of FDBs.

Researchers have investigated various methods to improve the dynamic performance of the HDD spindle motor. Jang and Yoon (2003) studied the stability of a hydrodynamic journal bearing with rotating herringbone grooves in which pressure, stiffness, and damping coef-ficients vary with time. Yoon and Shen (2005) introduced a numerical model to predict the shock response of a rotating-shaft spindle system considering the effect of the nonlinear stiffness and damping coefficients originating from the FDBs. Lee et al. (2013) optimized FDB design in order to develop a robust disk-spindle system in a HDD utilizing modal analysis. However, their research was restricted to the analysis of ideal FDBs without common manufacturing errors such as imperfect shaft roundness and non-uniform clearance between the sleeve and shaft. Even minor manufacturing errors and assembly deforma-tion of the FDBs in a HDD spindle motor may affect the dynamic performance of an HDD spindle system. Several other researchers have investigated the dynamic perfor-mance due to manufacturing errors. Koak et al. (2009) studied the whirling, tilting, and axial motion of HDD spindle systems due to the imperfect cylindricity between the shaft and sleeve, and the imperfect perpendicularity

Abstract We investigated deformation of the outer diam-eter of a shaft due to the hub press-fitting and disk clamp-ing processes associated with a 2.5″ hard disk drive. We propose a new robust shaft design to minimize the effect of deformation on the outer diameter of the shaft. We numer-ically show the effect of deformation on the shaft due to the pressure, stiffness, and damping coefficients of fluid dynamic bearings (FDBs), and the critical mass and excita-tion response of the rotor-bearing system. We also experi-mentally measured the axial non-repeatable runout and the amplitude at the half speed whirl frequency of FDBs with both conventional and proposed designs. Through these tests we confirm that the proposed design improves the static and dynamic performance of the FDBs and rotor-bearing system.

1 Introduction

Fluid dynamic bearings (FDBs) in a hard disk drive (HDD) spindle motor support the rotating disk-spindle system using the pressure generated in the fluid lubri-cant. Most FDBs in 2.5″ HDDs are composed of two

* Gunhee Jang ghjang@hanyang.ac.kr

1 PREM, Department of Mechanical Engineering, Hanyang University, 17 Haengdang-Dong, Seongdong-Gu, Seoul 133-791, Republic of Korea

2 Samsung Electro-Mechanics Co. Ltd., 314, Maetan 3-Dong, Yeongtong-Gu, Suwon-Si, Gyeonggi-Do 443-743, Republic of Korea

3 PREM, Department of Mechanical Convergence Engineering, Hanyang University, 17 Haengdang-Dong, Seongdong-Gu, Seoul 133-791, Republic of Korea

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between the shaft and thrust plate of the FDBs. Kim et al. (2009) investigated the coupled journal and thrust FDBs with the imperfect roundness of a rotating shaft. Recently, Lee et al. (2014) investigated the characteristics of FDBs in an HDD spindle motor due to an hourglass-shaped sleeve generated through the ball-sizing process. How-ever, the shaft deformation generated through the assem-bly processes and its effect on the dynamic performance of the HDD spindle system have not been previously investigated.

The research presented here describes an investigation of shaft deformation caused by hub press-fitting and disk clamping processes in a 2.5″ HDD. We propose a robust shaft design to minimize the effect of shaft deformation in the assembly processes. We numerically analyzed the effect of a deformed shaft on the pressure, stiffness, and damp-ing coefficients of FDBs as well as the critical mass and excitation response of the rotor-bearing system. Finally, we experimentally validated the axial NRRO and the amplitude at the HSW frequency of FDBs with both conventional and proposed designs.

2 Shaft deformation due to the hub press‑fitting and disk clamping processes

Hub press-fitting and disk clamping processes in a 2.5″ HDD assembly process directly cause the shaft to deform through physical contact between the shaft and hub. In order to measure shaft deformation, the outer diameter of a shaft corresponding to the journal bearing is meas-ured using the stylus of a roughness measuring apparatus that moves from end to end, as shown in Fig. 2. Figure 3 shows the measured outer geometry of a shaft following the hub press-fitting and disk clamping processes. In the hub press-fitting process, compressive force exerted on the con-tacting area between the shaft and hub decreases the outer diameter of the shaft corresponding to the journal bearing. The shaft deformation occurs over 1.6 mm and the maxi-mum deformation is 1.9 μm at the top. When a top screw is tightened during the disk clamping process, the diameter of the shaft corresponding to the top screw is relieved and the disk clamping process restores the deformation of outer diameter of the shaft by 1.0 μm. Finally, the total shaft

Fig. 1 Cross section of a 2.5″ HDD spindle system

Fig. 2 Experimental set-up to measure the outer diameter of a shaft

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deformation occurs over 0.49 mm and the maximum defor-mation is 0.9 μm at the top. This deformation enlarges the radial clearance of the upper grooved journal bearing and changes the dynamic characteristics of the disk-spindle system.

3 Robust shaft design

In order to maintain a uniform radial gap between the shaft and sleeve following the hub press-fitting and disk clamping processes, we propose a robust shaft design. As shown in Fig. 4, the outer diameter of the shaft increases by 0.9 μm at the top and linearly decreases downward to 0.5 mm. In the hub press-fitting process, the shaft defor-mation occurs downward along 1.6 mm and the maximum deformation is 1.1 μm at the top, as shown in Fig. 5. The

top screw in the disk clamping process restores the outer diameter of the shaft by 1.2 μm. As a result, the total shaft deformation due to these assembly processes occurs down-ward along a length of 0.2 mm, and the maximum defor-mation is within 0.1 μm. We confirmed that the proposed robust shaft design decreases shaft deformation by approxi-mately 90 % when compared to conventional shaft designs.

4 Simulated verification

4.1 Verification through FDBs analysis

A computer program developed by Jang and Lee (2006) was used to calculate the dynamic coefficients of the FDBs. The governing equations of stationary grooved journal and thrust bearings can be written in the cylindrical coordinate system fixed to the sleeve, as shown in Eqs. (1) and (2), respectively:

where R, θ, hJ, hT, p, and μ are respectively the radius of the journal, rotating speed, film thickness of the journal and thrust bearings, pressure, and coefficient of viscosity of the FDBs. In addition r, θ, and z are the axes of the radial,

(1)

∂

R∂θ

(

h3J

12µ

∂p

R∂θ

)

+∂

∂z

(

h3J

12µ

∂p

∂z

)

=Rθ

2

∂hJ

R∂θ+

∂hJ

∂t,

(2)

1

r

∂

∂r

(

rh3T

12µ

∂p

∂r

)

+∂

r∂θ

(

h3T

12µ

∂p

r∂θ

)

=rθ

2

∂hT

r∂θ+

∂hT

∂t,

Fig. 3 Measured outer geometry of a shaft according to the assembly processes

Fig. 4 Proposed robust shaft design

Fig. 5 Measured outer geometry of the proposed shaft according to assembly processes

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circumferential, and axial directions, respectively. The pressure in the coupled bearings is calculated by applying the Reynolds boundary condition. The film thickness of the journal bearing including deformed shaft geometry can be written as follows (Lee et al. 2014):

where cg, cr, er, θ, and φ are the groove depth, radial clear-ance of the journal bearing, translational motion eccentric-ity, angular coordinate measured from the fixed negative x-axis, and attitude angle, respectively. Δc represents the variation in the radial clearance of the journal bearing, and

(3)hJ = cg + cr − er cos(θ − ϕ)+�c,

is used to describe the deformed shaft geometry along the z-axis, as shown in Fig. 6.

Table 1 shows the major design parameters of the FDBs used in this research. Figure 7a shows the pressure distribu-tion of the journal bearing with a conventional shaft design. The rotational speed and eccentricity ratio are 5400 rpm and 0.1, respectively. The maximum pressure of the upper and lower grooved journal bearings and the plain journal bearing that exists between the upper and lower grooved journal bearings are 0.75, 1.10, and 0.03 MPa, respectively. The upper grooved journal bearing has a smaller maxi-mum pressure than the lower grooved journal bearing due to the enlarged upper radial gap. The pressure distribution of the FDBs with the proposed shaft design is calculated as shown in Fig. 7b. The maximum pressure of the upper, lower grooved journal bearings and the plain journal bear-ing are 1.60, 1.27, and 0.32 MPa, respectively. We con-firmed that the upper grooved journal bearing has a larger maximum pressure than the lower grooved journal bearing, and that the maximum pressure of the plain journal bear-ing increases approximately 10 times when compared with conventional shaft design. Figure 8 shows the effect of eccentricity ratio on the stiffness and damping coefficients of FDBs with both conventional and proposed designs. The radial stiffness and damping coefficients also increase with increased eccentricity ratios, and the stiffness and damping coefficients of FDBs with the proposed design are larger than those of FDBs with a conventional design. The axial stiffness and damping coefficients show no significant change in value, because the increased or decreased radial

Fig. 6 Journal bearing with deformed outer geometry of a shaft

Table 1 Major design parameters of FDBs

Design variable Design value

Grooved journal bearing Journal radius (mm) 1.5

Radial clearance (μm) 1.9

Upper bearing width (mm) 1.15

Lower bearing width (mm) 0.95

Number of groove (EA) 9

Groove depth (μm) 3

Groove angle (°) 20

Groove ratio (–) 0.3

Grooved thrust bearing Axial clearance (μm) 30

Bearing width (mm) 0.89

Number of groove (EA) 12

Groove depth (μm) 15

Groove angle (°) 20

Groove ratio (–) 0.5

Fig. 7 Pressure distribution of the journal bearing in FDBs with a the conventional shaft design and b the proposed shaft design

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gap corresponding to the upper end of the upper grooved journal bearing does not significantly affect the pressure distribution of the thrust bearing.

4.2 Verification through critical mass

The critical mass, which is the solution of the equations of motion of the rigid disk-spindle system supported by the

FDBs, can be represented with five degrees of freedom as follows (Kim et al. 2010):

where M, G, C, and K are the mass, gyroscopic, damping, and stiffness matrices, respectively. M includes the mass and mass moments of inertia of the rotor, and G includes the mass moments of inertia of the rotor and the rotor speed. Once the radius of gyration is introduced to express the mass moment of inertia with respect to the mass, Eq. (4) can be represented as a single variable, i.e., the mass of the rotor. The solution of Eq. (4) is assumed to be an exponen-tial function, as follows:

Substituting Eq. (5) into (4) yields the following equation:

The eigenvalue of Eq. (6) can be generally expressed as � = −�real + i�img. The motion of the rotor is stable if �real is greater than zero and is unstable if �real is less than zero. Therefore, the critical condition exists when �real is equal to zero. The solutions of the characteristic determinant of Eq. (6) are the critical mass (ma)c and the corresponding frequency �img. The behavior of the disk-spindle system supported by coupled journal and thrust bearings can be regarded as stable if the mass, ma, is less than the critical mass (ma)c, and unstable if ma is greater than (ma)c . Lee et al. (2012) proposed a method to design a robust HDD disk-spindle system using the critical mass. They showed that FDBs with large critical mass have small RRO and NRRO.

The critical mass of the rotors supported by FDBs with both conventional and proposed designs is calculated using a method developed by Kim et al. (2011). Figure 9 shows the stability of the HDD spindle system sup-ported by the FDBs according to eccentricity ratio. Criti-cal mass increases with increasing eccentricity ratio due to the increased stiffness and damping coefficients of the

(4)Mx + (C+G)x +Kx = 0,

(5)x = xhexp(�t).

(6){−�2M+�(C+G)+K}xhexp(�t) = 0.

Fig. 8 Stiffness and damping coefficients of FDBs a Kxx, b Kzz, c Cxx, d Czz

Fig. 9 Stability of an HDD spindle system according to the eccen-tricity ratio

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journal bearing. The critical mass of FDBs with the pro-posed design is larger than that of FDBs with a conven-tional design.

4.3 Verification through modal analysis

The NRRO of a rotating rigid disk-spindle system sup-ported by the FDBs in five degrees of freedom can be esti-mated by solving the equations of motion with centrifugal force due to unbalanced mass or external shock, as shown in Eq. (7) (Kim et al. 2011):

where Δc is the force vector of the external excitation. NRRO is usually generated by manufacturing errors, insta-bility of FDBs, and external shock. Based on this research, we estimate NRRO due to HSW by applying the swept sine excitation, which has an amplitude of 5 G from 0 to 200 Hz over 5 s. This is applied in addition to the centrifugal force in a force vector, as follows:

where a, T, ωs, and ωe are the sweep rate, sweep period, and starting and ending frequencies, respectively. Figure 10 shows the swept sine excitation in the time domain.

Figure 11 shows the numerically-simulated frequency spectra of the radial displacement of the center of mass excited by the x-directional swept sine. The solid and dot-ted lines show the frequency spectra from 0 to 200 Hz of FDBs with conventional and proposed shaft designs, respectively. The maximum amplitude at the HSW fre-quency of FDBs with conventional and proposed shaft designs are 0.94 nm at 49.4 Hz and 0.41 nm at 50.6 Hz, respectively. The amplitude at the HSW frequency of FDBs with the proposed shaft design is smaller than that of FDBs with conventional shaft design by approximately 56.4 %.

5 Experimental verification

We experimentally measured the axial NRRO and ampli-tude at the HSW frequency. Figure 12 shows the experi-mental set-up used to measure the axial NRRO of the HDD spindle system. The input voltage applied to the motor is 5 V and the axial NRRO is measured on the disk at a radius of 13 mm via a capacitance probe. The frequency spectra of the axial NRRO were monitored at the signal analyzer from

(7)Mx+ (C+G)x + kx = F(t),

(8)F = p0 sin(a

2t2 + ωst

)

,

(9)a =ωe − ωs

T,

0 to 200 Hz. The measured overall axial NRRO with the proposed shaft design is approximately 0.096 μm, which is smaller than with a conventional shaft by 14.3 %. Also, the maximum amplitude at the HSW frequency with the proposed shaft design is smaller than with the conventional shaft by 63.7 % as shown in Fig. 13.

0 1 2 3 4 5-6

-4

-2

0

2

4

6

Time [sec]

Am

plitu

de [N

]

Fig. 10 Swept sine excitation in time domain

Fig. 11 Simulated frequency spectra of the radial displacement of the mass center excited by the x-directional swept sine

Fig. 12 Experimental set-up to measure the axial NRRO of an HDD spindle motor

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6 Conclusions

We investigated shaft deformation caused by hub press-fit-ting and disk clamping processes in a 2.5″ HDD. In order to obtain a uniform radial gap in the journal bearing following the assembly processes, a robust shaft design is proposed. We numerically demonstrated the effects of an enlarged radial gap resulting from shaft deformation on the pressure, stiffness, and damping coefficients of FDBs, as well as the critical mass and excitation response of the rotor-bearing system. We also experimentally validated the axial NRRO and amplitude at the HSW frequency of FDBs with both

conventional and proposed designs. We confirmed that the proposed robust shaft design improves the performance of FDBs and the HDD disk-spindle system.

Acknowledgments This research was performed at Samsung-Han-yang Research Center for Precision Motors, and was sponsored by Samsung Electro-Mechanics Co. Ltd.

References

Jang GH, Lee SH (2006) Determination of the dynamic coefficients of the coupled journal and thrust bearings by the perturbation method. Tribol Lett 22(3):239–246

Jang GH, Yoon JW (2003) Stability analysis of a hydrodynamic journal bearing with rotating herringbone grooves. J Tribol 125:291–300

Kim HW, Jung KM, Jang GH (2009) Dynamic characteristics of a hard disk drive spindle system due to imperfect shaft roundness. IEEE Trans Magn 45:5148–5151

Kim MG, Jang GH, Kim HW (2010) Stability analysis of a disk-spin-dle system supported by coupled journal and thrust bearings con-sidering five degrees of freedom. Tribol Int 43:1479–1490

Kim MG, Jang GH, Lee JH (2011) Robust design of a HDD spindle system supported by fluid dynamic bearings utilizing the stabil-ity analysis of five degrees of freedom of a general rotor-bearing system. Microsyst Technol 17:761–770

Koak KY, Jang GH, Kim HW (2009) Whirling, tilting and axial motions of a HDD spindle system due to the manufacturing errors of FDBs. Microsyst Technol 15:1701–1709

Lee JH, Jang GH, Ha HJ (2012) Robust optimal design of the FDBs in a HDD to reduce NRRO and RRO. Microsyst Technol 18:1335–1342

Lee JH, Jang GH, Jung KM (2013) Optimal design of fluid dynamic bearings to develop a robust disk-spindle system in a hard disk drive utilizing modal analysis. Microsyst Technol 19:1495–1504

Lee JH, Lee MH, Jang GH (2014) Effect of an hourglass-shaped sleeve on the performance of the fluid dynamic bearings of a HDD spindle motor. Microsyst Technol 20:1435–1445

Yoon JK, Shen IY (2005) A numerical study on rotating-shaft spin-dles with nonlinear fluid-dynamic bearings. IEEE Trans Magn 41:756–762

Fig. 13 Measured frequency spectra of axial NRRO with a the con-ventional shaft design and b the proposed shaft design