TECHNICAL PAPER

Height analysis of the air-oil interfaces in the non-operatingand operating FDBs in a tied shaft of HDDs

Minho Lee1 • Jihoon Lee1 • Kyobong Kim1• Gunhee Jang1

Received: 15 November 2017 / Accepted: 29 March 2018 / Published online: 3 April 2018� Springer-Verlag GmbH Germany, part of Springer Nature 2018

AbstractWe proposed a method to predict the heights of upper and lower air-oil interfaces of the non-operating and operating fluid

dynamic bearings (FDBs) in the tied shaft of hard disk drives. To predict the height of upper and lower air-oil interfaces,

we formulated the linear pressure and volume equations in both cases of non-operating and operating conditions,

respectively. The initial heights of upper and lower air-oil interfaces are determined by pressure and volume equations

during non-operating condition. Pressure equation consists of capillary pressure, atmospheric pressure, hydrostatic pressure

and applied pressure, and volume equation consists of the volumes of the clearance and the injected oil. In case of

operating condition, hydrodynamic pressure generated by grooved bearings is additionally considered in the pressure

equation, because heights of air-oil interfaces vary due to hydrodynamic pressure during operating condition. The linear

pressure and volume equations were solved simultaneously to calculate the heights of upper and lower air-oil interfaces

both in non-operating and operating conditions. In case of non-operating conditions, the height of upper air-oil interface

increases with the increase of pressure difference because pressure of lower air-oil interface is higher than that of upper air-

oil interface. Since the volume of injected oil is constant, height of lower air-oil interface decreases due to pressure

difference. In case of operating conditions, the height of upper air-oil interface decreases according to rotating speed

because more oil flows inside the FDBs and recirculation channel than upper seal. On the other hand, the height of the

lower air-oil interface increases because volume variation of the oil due to the increase of the flying height is smaller than

that due to the decrease of the height of the upper air-oil interface. Finally, we verified the proposed method by measuring

the height of upper air-oil interface both in the non-operating and operating conditions.

1 Introduction

Figure 1 shows the mechanical structure of hard disk drives

(HDDs) supported by fluid dynamic bearings (FDBs) in a

rotating shaft and tied shaft. As shown in Fig. 1, the FDBs

in the rotating shaft have a seal which is located to upward

part of upper thrust bearing and the shaft combined with

rotating parts of HDD rotates during operation. On the

other hand, the FDBs in the tied shaft have double seals

which are upper and lower seals and the sleeve combined

with rotating parts of HDD rotates during operation. HDDs

with the tied shaft are more robust under external shock

than those with the rotating shaft because both top and

bottom of the shaft are fixed to cover and base of HDDs,

respectively. They have been mainly applied in the HDDs

applied to computer servers requiring high memory den-

sity. However, the FDBs in the tied shaft are more vul-

nerable to oil leakage than those in the rotating shaft

because the FDBs in the tied shaft have double seals

located both at the upper and lower air-oil interfaces.

Oil injection of the FDBs in the tied shaft is mainly

achieved by hydrostatic pressure and capillary pressure

difference. After the oil injection, heights of the upper and

lower air-oil interfaces during non-operating condition are

determined by the pressure equilibrium and the volume

occupied by oil. Heights of air-oil interfaces of FDBs in the

tied shaft during operating condition are determined by the

initial heights of air-oil interfaces in non-operating condi-

tion and the pressure generated by grooved bearings. Oil

which is in equilibrium during non-operating condition

may leak out in operating conditions if excessive oil is

injected or air-oil interface is broken due to external shock.

& Gunhee Jang

ghjang@hanyang.ac.kr

1 PREM, Department of Mechanical Convergence

Engineering, Hanyang University, 222, Wangsimni-ro

Seongdong-gu, Seoul 04763, Republic of Korea

123

Microsystem Technologies (2018) 24:4613–4620https://doi.org/10.1007/s00542-018-3876-4(0123456789().,-volV)(0123456789().,-volV)

Also, air-oil interface of FDBs in the tied shaft can be

easily broken during operating condition according to

increasing the height of the air-oil interface due to rotating

speed. Therefore, prediction of the heights of air-oil

interfaces of the FDBs in the tied shaft is important during

non-operating and operating conditions because they are

important variables to determine oil leakage as well as

robustness against external pressure and shock.

Many researchers have investigated the seal of FDBs or

oil leakage due to shock. Roger Ku and Shumway (1998)

investigated experimentally shock responses during oper-

ating conditions. They measured radial displacement of

disk due to amplitude and duration of shock. Kita et al.

(2002) studied oil leakage according to flow pressure on

upper groove-less area in herringbone grooved journal

bearings and they measured amount of oil leakage to verify

their analysis. Hishida et al. (2010) analyzed the funda-

mental characteristics of a taper seal used to prevent oil

leakage from fluid bearings and investigated experimen-

tally oil meniscus by using a micro-focus laser microscope.

Jung and Jang (2011) studied the axial shock-induced

motion of the air-oil interface in non-operating FDBs by

experiment and simulation. They reported the effects of the

magnitude of the shock and oil viscosity on the break-up of

the air-oil interface. Wei et al. (2011) studied the charac-

teristics of leakage of rotary seal by using hydraulic

resistance network. Leakage characteristics of rotary seal

were investigated according to rotating speed, temperature

and structural parameters. Andres and Delgado (2012)

studied the oil flow in grooved oil seals with hydro static

bearings operating eccentrically. They also predicted the

stiffness and damping coefficients according to static

journal eccentricity ratio. Jung et al. (2012) investigated the

behavior of fluid lubricant and air-oil interface of the FDBs

according to operating condition and seal design. They

calculated two-phase flows of air and oil according to

tapering angle and initial position of fluid by using volume

of fluid (VOF) method. Jung et al. (2013) studied the

behavior of air bubbles and the air-oil interface in FDBs at

low speeds by using the VOF method and their research

was verified by the experimental results. Feng and Li

(2013) studied the oil leakage of the FDBs with radial and

axial seals. They analyzed the deformed interface accord-

ing to amplitude of shock and rotating speed. However,

Kita et al. did not consider seal structure of their journal

bearing and other researchers studied FDBs in a rotating

shaft with one seal structure. No previous researchers have

studied to predict height of air-oil interface of FDBs.

Several researchers have studied the FDBs in the tied

shaft with double seals Lee et al. (2016) investigated oil

injection process to predict the oil injection time of FDBs

in the tied shaft by using the Kirchhoff’s pressure law.

They proposed an algorithm to calculate the oil injection

time and calculated the oil injection time according to

temperature, clearance of upper seal and radius of recir-

culation channel. They also verified the proposed method

by measuring oil injection time. Injected oil is located to

specific height by the pressure equilibrium and the volume

occupied by oil and can be broken by external pressure or

shock. So, the height of air-oil interfaces should be pre-

dicted to prevent oil leakage due to external pressure or

shock. However, their research was restricted to predict oil

injection time of the FDBs in a tied shaft. They did not

study the air-oil interfaces of the FDBs in the tied shaft and

did not consider location of the air-oil interfaces. Kang

et al. (2016) investigated the dynamic behavior of air-oil

interface of the FDBs in the tied shaft due to non-operating

axial shock. They conducted a drop test of the HDDs to

measure oil leakage, and simulated the air-oil interface due

to non-operating axial shock. However, they did not study

the variation of the heights of air-oil interfaces of FDBs.

Park et al. (2016) investigated the air-oil interface in tied-

shaft type FDBs according to chamfer location and incli-

nation angle of circulation hole. They analyzed the

Fig. 1 Mechanical structure of HDDs supported by FDBs in the tied shaft in a the rotating shaft and b tied shaft

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hydrodynamic pressure by using commercial software

ANSYS and calculated the height of air-oil interfaces in the

tied shaft. When disks are installed to the HDD spindle

motor, external pressure may be applied to upper or lower

seals and air-oil interfaces can be broken due to applied

external pressure. Air-oil interfaces can also be broken

when the rotating speed changes. Therefore, applied pres-

sure and rotating speed should be considered to calculate

the height of air-oil interfaces of FDBs in the tied shaft.

However, they did not include the effect of the difference

of applied pressures of upper and lower air-oil interfaces

and the rotating speed of the FDBs. They also did not

verify their simulated results with experiments.

In this research, we proposed a method to predict the

heights of upper and lower air-oil interfaces of the FDBs in

the tied shaft of HDDs. We formulated a pressure equation

during non-operating conditions according to capillary

pressure, atmospheric pressure, hydrostatic pressure and

applied pressure, and a volume equation according to the

volumes of the clearance and the injected oil. We also

formulated the pressure equation due to the effect of

hydrodynamic pressure generated by grooved bearings. We

solved the linear equations of pressure and volume simul-

taneously to calculate the heights of upper and lower air-oil

interfaces both in non-operating and operating conditions.

In case of operating conditions, we calculated the hydro-

dynamic pressure generated by grooved bearings, and

solved the linear equations repeatedly with hydrodynamic

pressure to calculate the heights of upper and lower air-oil

interfaces. Finally, we verified the proposed method by

measuring the height of upper air-oil interface.

2 Method of analysis

2.1 Prediction of the heights during non-operating condition

Since the FDBs in the tied shaft have double seals which

are upper and lower seals as shown in Fig. 1a, they are

vulnerable to oil leakage. Oil in the FDBs in the tied shaft

is injected by capillary pressure (Lee et al. 2016), and the

initial heights of upper and lower air-oil interfaces are

determined by pressure equation and volume equation in

non-operating condition. Figure 2 shows the pressures and

volumes and heights of the air-oil interfaces of the FDBs in

a tied shaft. Pressure equation and volume equation can be

written as follows (White 1999).

P2 h2ð Þ � P1 h1ð Þ ¼ qgH ð1ÞVInjection ¼ V1 h1ð Þ þ V2 h2ð Þ þ VFDB ð2Þ

where P1(h1), P2(h2), q, g and H are pressures at upper and

lower air-oil interfaces, density, gravitational acceleration

and height between upper and lower air-oil interfaces,

respectively. VInjection is the volume of injected oil in upper

and lower seals, and V1(h1) and V2(h2) are volumes of

upper and lower seals of the FDBs, respectively. h1 and h2are the initial heights of upper and lower air-oil interfaces

of the FDBs in the tied shaft in non-operating condition,

respectively. VFDB is volume of the inside of the FDBs and

recirculation channel except volumes of the upper and

lower seals.

P1(h1) and P2(h2) in Eq. (1) can be written in the fol-

lowing Eqs. (3) and (4).

P1ðh1Þ ¼ Patm þ Pap1 � Pc1 h1ð Þ � qgh1 ð3Þ

P2ðh2Þ ¼ Patm þ Pap2 � Pc2 h2ð Þ � qgh2 ð4Þ

where Patm, Pap1, Pap2, Pc1(h1) and Pc2(h2) are atmospheric

pressure, applied external pressures of upper and lower air-

oil interfaces, and capillary pressures of upper and lower

air-oil interfaces, respectively. It is required to consider

pressure difference between upper and lower air-oil inter-

faces to predict the height of air-oil interfaces because

external pressure may be applied to upper or lower inter-

faces in the process of disk installation. Equation (1) can be

rewritten by substituting Eqs. (3) and (4) into Eq. (1) as

follows.

Pc1 h1ð Þ � Pc2 h2ð Þ ¼ qg H � h1 þ h2ð Þ þ Pap1 � Pap2

� �

ð5Þ

Capillary pressures (Pc1(h1) and Pc2(h2)) can be written

as follows (Lee et al. 2016).

Fig. 2 Reference line and heights of the air-oil interfaces in non-

operating condition

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Pc1 h1ð Þ ¼ r1

ru1þ 1

ru2

� �ð6Þ

Pc2 h2ð Þ ¼ r1

rl1þ 1

rl2

� �ð7Þ

where r, ru1, rl1, ru2 and rl2 are surface tension, radii of

curvature of film thickness direction of upper and lower

air-oil interfaces and radii of curvature of radial direction

of upper and lower air-oil interfaces, respectively. The radii

of curvature of film thickness direction can be written as

follows.

ru1 ¼d1=2

cos hc þ hg1� � ð8Þ

rl1 ¼d2=2

cos hc þ hg2� � ð9Þ

where d1, d2, hc, hg1 and hg2 are clearances of upper and

lower air-oil interfaces, contact angle and geometric angles

of upper and lower air-oil interfaces, respectively. The radii

of curvature of radial direction (ru2 and rl2) are radii of the

bearings. Equation (5) can be rewritten by substituting

Eqs. (6)–(9) into Eq. (5) as follows.

2 cos hc þ hg1� �

d1�2 cos hc þ hg2

� �

d2

¼ qgr

H � h1 þ h2ð Þ þ 1

rPap1 � Pap2

� �þ 1

rl2� 1

ru2

� �

ð10Þ

Volume equations of the FDBs in this research can be

written as follows.

V1 ¼1

2r2u2 � ru2 � g1ð Þ2� ru2 � g1 � h1tanhg1a

� �2h

þ ru2 � h1tanhg1b� �2i

ph1 ð11Þ

V2 ¼ r2l2 �1

2rl2 � g2ð Þ2þ rl2 � g2 � h2tanhg2

� �2n o� �ph2

ð12ÞVðh1; h2Þ ¼ V1ðh1Þ þ V2ðh2Þ ð13Þ

where V1, V2, g1, g2, hg1a, hg1b and hg2 are volumes in

upper and lower seals of FDBs, clearances of upper and

lower seals and tapered angles of upper and lower seals,

respectively. g1, g2, hg1a, hg1b and hg2 are described as

shown in Fig. 3.

Finally, we can determine the initial heights of upper

and lower air-oil interfaces of the FDBs in the tied shaft by

solving the linear simultaneous equations of Eqs. (10) and

(13) in non-operating condition.

2.2 Prediction of the heights during operatingcondition

Figure 4 shows the hydrodynamic pressure and the heights

of the upper and lower air-oil interfaces in operating con-

dition. Since hydrodynamic pressure is generated by

grooved bearings in operating condition, hydrodynamic

pressure should be considered to calculate the heights of

the air-oil interfaces of the FDBs in the tied shaft during

operating condition. Pressure generated by grooved bear-

ings can be obtained by solving Reynolds equation of the

journal and thrust bearings. Reynolds equations of the

journal and thrust bearings can be written in the following

Eqs. (14) and (15) (Bernard et al. 1994).

Fig. 3 Design variables of the upper and lower seals

Fig. 4 Reference line and heights of the air-oil interfaces in operating

condition

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o

Rohh3

12lop

Roh

� �þ o

oz

h3

12lop

oz

� �¼ R _h

2

oh

Rohþ oh

otð14Þ

1

r

o

orrh3

12lop

or

� �þ o

rohh3

12lop

roh

� �¼ r _h

2

oh

rohþ oh

otð15Þ

where R, _h, h, p and l are the radius, rotating speed, film

thickness, pressure and coefficient of viscosity, respec-

tively. r, h and z are the radial, circumferential and axial

coordinates, respectively.

The heights of the air-oil interfaces of the FDBs in the

tied shaft in operating condition can be calculated by

pressure equation and volume equation during operating

condition. Pressure equation in dynamic equilibrium con-

dition and volume equation during operating condition can

be written as follows.

P�1 ¼ Patm � Pc1 h�1

� �þ qgh�1 ð16Þ

P�2 ¼ Patm � Pc2 h�2

� �þ qgh�2 ð17Þ

P�2 � P�

1 ¼ Pc1 h�1� �

� Pc2 h�2� �

þ qg h�2 � h�1� �

ð18Þ

VInjection ¼ V h�1; h�2

� �ð19Þ

where P�1; P

�2; h

�1 and h�2 are hydrodynamic pressures, and

the heights of the upper and lower air-oil interfaces in

operating condition, respectively. P�1 and P�

2 can be

obtained by solving the Reynolds equations in Eqs. (14)

and (15). h�1 and h�2 are calculated repeatedly by the algo-

rithm as shown in Fig. 5. First, initial heights of upper and

lower air-oil interfaces (h1 and h2) are calculated in non-

operating condition. A finite element model is developed

with the consideration of h1 and h2 to solve the Reynolds

equation and to determine P�1 and P�

2. Then, h�1 and h�2 are

determined by solving the linear simultaneous equations of

Eqs. (18) and (19). We repeat this process until the solution

of h�1 and h�2 is converged.

3 Results and discussion

3.1 Calculation and measurement of the heightin non-operating condition

Table 1 shows the oil properties of the FDBs in the tied

shaft. Figure 6 shows the calculated heights of upper and

lower air-oil interfaces according to pressure difference

between upper and lower air-oil interfaces. As shown in

Fig. 2, oil meniscus height of upper air-oil interface is

measured and calculated from the reference line located

upward from the bottom of upper seal by 1.113 mm and oil

meniscus height of lower air-oil interface is calculated

from the reference line located upward from the bottom of

lower seal by 1.429 mm. Height of upper air-oil interface

increases with the increase of pressure difference because

pressure of lower air-oil interface is higher than pressure of

upper air-oil interface. The pressure difference is 469 Pa

when height of upper air-oil interface is - 0.25 mm. Since

the volume of injected oil is constant, height of lower air-

oil interface decreases with the increase of pressure

difference.

We verified the proposed method by measuring the

height of upper air-oil interface. Figure 7 shows the mea-

sured height of upper air-oil interfaces of the FDBs in the

tied shaft according to pressure difference. We measured

only the height of upper air-oil interface of five samples

Fig. 5 Algorithm to calculate the heights of air-oil interfaces of the

FDBs in the tied shaft

Table 1 Oil properties of the

FDBs in the tied shaftProperties Value

Density (kg/m3) 920

Contact angle (�) 5

Surface tension (N/m) 0.0315

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because the rotor structure hides the lower air-oil interface.

Results of five samples were presented as lines #1 to #5 in

Fig. 7. Measured height of upper air-oil interfaces of the

FDBs is very close to the simulated one in Fig. 6a. As

predicted in the simulation, the height of upper air-oil

interface increases with the increase of pressure difference

because pressure of lower air-oil interface was higher than

pressure of upper air-oil interface. The pressure difference

of 470 Pa is applied when average height of upper air-oil

interface is measured to be - 0.25 mm.

3.2 Calculation and measurement of the heightin operating condition

Table 2 shows the design variables of the grooved journal

and thrust bearings. The volume variation of the oil in the

upper and lower seals should be considered with increase

of rotating speed because rotor is moving up by pressure

due to grooved thrust bearings and the flying height

increases with the increase of rotating speed. So we con-

sidered the volume variation of the oil in the upper and

lower seals according to rotating speed. In this research,

mass and volume of the injected oil are 7.3 mg and

7.935e-9 m3 and initial height of the upper air-oil inter-

face in non-operating condition is - 641.1 lm. However,

the heights of the upper air-oil interface of samples 1 and 2

which is used for experiment are - 882 and - 820 lm.

The heights of the air-oil interfaces may be lower than

design value because the injected oil evaporates or the oil

is injected less than required amount of the oil. Thus, we

adjusted the volume of the injected oil from 7.935e-9 m3

(7.3 mg) to 7.233e-9 m3 (6.7 mg) in simulation to match

the experimental measurements. In this condition, the

simulated height of the upper air-oil interface was

- 823 lm.

The height of the upper air-oil interface was calculated

and measured with the increase of rotating speed from

3600 to 7200 rpm with the intervals of 1800 rpm. Figure 8

shows the calculated and measured heights of the upper air-

oil interface of the FDBs in the tied shaft according to

rotating speed. Table 3 shows the measured and simulated

heights and the errors according to rotating speed. We

measured the height of upper air-oil interface of two dif-

ferent samples (#1 and #2) during operating conditions

which were represented as #1 and #2 in Fig. 8 with solid

lines. Simulation results are shown as dotted line in Fig. 8.

When rotating speed increases, the height of the upper air-

oil interface decreases. The oil flows inside of the FDBs

because pumping direction of the upper grooved thrust

bearing is inward. And more oil flows into the recirculation

channel than upper seal because the diameter of the

recirculation channel is relatively lager than clearance of

the upper seal (flow resistance of recirculation channel is

smaller than that of clearance). For these reasons, the

height of the upper air-oil interface decreases with the

increase of rotating speed. As shown in Fig. 8 and Table 3,

the simulated height of the upper seal relatively well

matches with the measured height of upper seal according

to rotating speed even though the finite element model

Fig. 6 Simulated heights of a upper and b lower air-oil interfaces

according to pressure difference during non-operating condition

Fig. 7 Measured heights of upper air-oil interface according to

pressure difference during non-operating condition

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cannot describe perfectly real shape of FDBs such as

chamfer of recirculation channel and curved corner of

thrust bearings. Nevertheless, the trend in the measured and

simulated results, which decreases with increasing rotating

speed, is similar and there exist the average errors of 4.45%

in sample #1 and 10.46% in sample #2 between the mea-

sured and simulated results. The height of the lower air-oil

interface was also calculated according to rotating speed as

shown in Fig. 9. The height of the lower air-oil interface

increases with the increase of the rotating speed because

volume variation occupying the oil due to the increase of

the flying height from 7.08 to 9.03 lm is smaller than that

due to the decrease of the height of the upper air-oil

interface from - 989 to - 1051 lm.

4 Conclusions

We proposed a method to predict the heights of upper and

lower air-oil interfaces of the FDBs in the tied shaft of

HDDs. We formulated a pressure equation during non-

operating conditions according to capillary pressure,

atmospheric pressure, hydrostatic pressure and applied

pressure, and a volume equation according to the volumes

of the clearance and the injected oil. We also formulated

the pressure equation including the effect of hydrodynamic

pressure generated by grooved bearings during operating

condition. We solved the linear equations of pressure and

volume simultaneously to calculate the heights of upper

and lower air-oil interfaces both in non-operating and

operating conditions. In case of non-operating conditions,

height of upper air-oil interface increases with the increase

of pressure difference because pressure of lower air-oil

interface is higher than that of upper air-oil interface. Since

Table 2 Major design variables

of grooved journal and thrust

bearings

Design variable Journal bearing Thrust bearing

Groove type (-) Herringbone Spiral

Groove depth (lm) 5 15

Groove angle (�) 20 20

Number of grooves (EA) 6 10

Ratio of groove to groove and ridge (-) 0.4 0.5

Total length of grooved journal bearings (mm) Upper: 1.0

Lower: 1.1

–

Total axial gap of thrust bearing (lm) – 20

Fig. 8 Simulated and measured heights of upper air-oil interface

according to rotating speed during operating condition

Table 3 Values and errors of

the measured and simulated

results according to rotating

speed

Rotating speeds (rpm) Heights of the upper seal (mm) Error #1 (%) Error #2 (%)

Sample #1 Sample #2 Simulation

3600 - 0.948 - 0.870 - 0.989 4.32 13.68

5400 - 0.992 - 0.921 - 1.018 2.62 10.53

7200 - 1.230 - 1.074 - 1.151 6.42 7.17

Fig. 9 Simulated heights of lower air-oil interface according to

rotating speed during operating condition

Microsystem Technologies (2018) 24:4613–4620 4619

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the volume of injected oil is constant, height of lower air-

oil interface decreases with the increase of pressure dif-

ference. In case of operating conditions, height of upper

air-oil interface decreases with rotating speed because

more oil flows inside of the FDBs and recirculation channel

than upper seal. The height of the lower air-oil interface

increases with the increase of the rotating speed because

volume variation of the oil due to the increase of the flying

height is smaller than that due to the decrease of the height

of the upper air-oil interface. Finally, we verified the pro-

posed method by measuring the height of upper air-oil

interface both in non-operating and operating conditions.

The proposed method can be effectively applied to predict

the air-oil interfaces of the FDBs in the tied shaft and this

research contribute to developing a robust design of FDBs.

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