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The temperature effects of gas physical properties, such as the dynamic viscosity and mean free path on the gas bearing force and flying attitude of a slider, were studied based on a generalized lubrication equation derived from the Boltzmann equation. The simulation studies showed that these variations with the environmental temperature are relatively small in an unsealed disk drive, but they are significant in a fully sealed one. By evaluating temperature effects in a sealed drive filled with various gases, we present an acceptable lubricating gas selection criterion for the future ultra-thin film bearings from the viewpoint of head-disk interface properties.
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IEEE TRANSACTIONS ON MAGNETICS, VOL. 46, NO. 6, JUNE 2010 1389
Effects of Gas Physical Properties on Flying Performance
of Air Bearing Slider
Weidong Zhou, Bo Liu, Shengkai Yu, Wei Hua, and Leonard Gonzaga
Data Storage Institute, (A*STAR) Agency for Science, Technology and Research, 117608 Singapore
The temperature effects of gas physical properties, such as the dynamic viscosity and mean free path on the gas bearing force and
flying attitude of a slider, were studied based on a generalized lubrication equation derived from the Boltzmann equation. The simulation
studies showed that these variations with the environmental temperature are relatively small in an unsealed disk drive, but they are
significant in a fully sealed one. By evaluating temperature effects in a sealed drive filled with various gases, we present an acceptable
lubricating gas selection criterion for the future ultra-thin film bearings from the viewpoint of head-disk interface properties.
Index Terms—Air bearing slider, disk drives, flying height, head-disk interface, magnetic recording.
I. INTRODUCTION
IN modern magnetic storage devices, air bearing sliders are
normally used to house the magnetic head at the target track
over the surface of the magnetic media. Between the surfaces of
magnetic head and disk is a thin layer of air film to form high
stiffness air-bearing cushion and support the head float over the
disk, which constitutes a successful application of gas lubrica-
tion. The minimum thickness of air film, or called the slider-disk
mechanical spacing or flying height (FH), is limited by the sur-
face roughness of the disk and slider. Currently, the magnetic
spacing, defined as the gap between the magnetic head and the
magnetic media, is about 10–12 nm in the hard disk drives,
which corresponds to the areal density of 250 Gb/in . Pushing
technology to 5–10 Tb/in areal densities requires a magnetic
spacing to be only 2–4 nm [1]. However, at such a low magnetic
spacing, the magnetic materials in the media and head will easily
corrode in the air, especially in the presence of high humidity
and high temperature. The lower flying height also increases the
possibility of head-disk contacts and risk of head and media cor-
rosions. In the meantime, any further reduction in the thickness
of overcoat and lubricant layers will degrade the corrosion-re-
sistant property of these layers and affect the reliability of the
disk drives. Therefore, it is a big challenge of pushing the mag-
netic spacing below 4 nm.
One possible approach to reduce the overcoat and lubricant
thickness effectively is to use the other gas, such as argon and
helium, instead of air as the lubricating gas at the head-disk in-
terface. The gas should have much better anti-corrosion capa-
bility than the air so that the concern of the possible corrosion
of the magnetic layer can be eased and the function of the over-
coat and lubricant can be limited to the mechanical protection
only. In such a case, it is expected that thinner overcoat and lu-
bricant layers could be used to reduce the magnetic spacing for
ultra-high recording areal density.
Manuscript received October 27, 2009; revised December 11, 2009; accepted
December 25, 2009. Current version published May 19, 2010. Corresponding
author: W. Zhou (e-mail: zhou_weidong@dsi.a-star.edu.sg).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TMAG.2009.2039854
There were some efforts to study the effects of gas composi-
tion on the slider flying height [2] and also to develop helium
filled disk drives [3], [4]. Besides, it was found that there are
some other advantages to use the gas in the disk drives, such as
less positioning errors caused by the flow induced vibrations,
lower power consumption and smoother temperature distribu-
tion in the drive [4]. However, which gas is an ideal one is still
unclear. In this article, we will focus our attention on the phys-
ical properties of various gases and their effects on the slider’s
flying attitudes in a completely sealed drive, especially when the
disk drives operate in a wide temperature range. By evaluating
the variation of flying attitude at various temperatures, we will
provide an acceptable criterion for the lubricating gas selection.
II. NUMERICAL METHOD AND MODELS
The generalized lubrication equation based on the Boltzmann
equation can be expressed as
(1)
where and are normalized air bearing pressure and FH
between the slider and the disk, and are the bearing number
and the Poiseuille flow factor respectively, which are defined as
[5]
(2)
(3)
where is the Knudsen number, is the mean free
path of the gas, is the slider’s nominal FH, is slider’s
length, is ambient pressure, is the slider’s velocity vector
and is the viscosity of the gas.
The first term and second terms in (1) represent the flow
rates of the Poiseuille flow and the Couette flow respectively.
When the parameters for the gas film configuration are fixed, we
can see that only two parameters, bearing number and Knudsen
number, will affect the pressure distribution and loading car-
rying capacities of gas-lubricated slider bearings. In a sealed
0018-9464/$26.00 © 2010 IEEE
1390 IEEE TRANSACTIONS ON MAGNETICS, VOL. 46, NO. 6, JUNE 2010
Fig. 1. Air bearing slider design used in the study (a) 2D view; (b) 3D view.
Fig. 2. (a) Steady gap FH and (b) pitch angle in various gases.
TABLE I
PROPERTIES OF AIR,ARGON,H
ELIUM,NEON AND HYDROGEN
drive filled with some gas other than the air, the physical prop-
erties of the gas, such as viscosity and mean free path, should
be considered carefully because these properties will affect both
bearing number and Knudsen number as shown in (2) and (3).
Another consideration is the environmental temperature, as the
disk drive always operates in a wide temperature range and
sometimes the temperature in the head-disk interface may be
significantly different from that in normal condition.
The parameters varying with the gas temperature include the
viscosity and mean free path of the gas. For routine calculations
Fig. 3. Gap FH changes with environmental temperature in sealed and unsealed
disk drives.
with dilute gases, the power-law formula can be used for the
viscosity of the gas
(4)
ZHOU et al.: EFFECTS OF GAS PHYSICAL PROPERTIES ON FLYING PERFORMANCE OF AIR BEARING SLIDER 1391
Fig. 4. Bearing force changes with environmental temperature in (a) an unsealed drive and (b) a sealed drive.
where is the gas viscosity at reference temperature is
temperature exponent of the viscosity.
We also proposed a generalized formulation [6] for the mean
free path of the gas which incorporates various molecular dy-
namics models and considers temperature effects as
(5)
where is the mean free path of the gas at atmospheric pres-
sure and reference temperature based on hard sphere (HS)
model, is a factor to describe a generalized mean free path for
various molecular dynamic models. This factor is unity for the
HS model, which is used in the simulations for simplicity.
In our simulation, the pressures on the boundaries of an un-
sealed drive are set as one atmosphere pressure, whereas they
are varying with the temperature in a sealed drive by following
ideal gas law.
III. SIMULATION RESULTS AND DISCUSSIONS
A. Steady Flying Attitudes in Various Gases
A femto-sized slider, as shown in Fig. 1, is used to study the
temperature effects on the slider’s bearing force and flying atti-
tude. The slider flies over the disk with a radius of 27.9 mm, a
skew of 7.25 and a disk rotation speed of 10000 rpm. The gas
bearing pressure distribution is calculated by using our self-de-
veloped air bearing simulator, ABSolution. Then it is integrated
for gas bearing force. The simulator will compare this force
and other forces with the external load force and force center
to check if the current flying attitude is in a slider balanced po-
sition. If not, the quasi-Newton algorithm is applied to search
for a balancing flying attitude.
The gas physical properties under standard conditions (101
325 Pa and 0 C), which are used in the simulation, are listed in
TableI. By setting the physical properties of various gases in the
simulator, we calculated the steady flying heights in air, argon,
helium, neon and hydrogen filled disk drive as 9.29 nm, 10.94
nm, 6.20 nm, 10.34 nm and 6.49 nm respectively, as shown
in Fig. 2, when the environmental temperature is at 20 C. We
can see that flying attitudes in air, argon and neon are similar,
but they are quite different in helium and hydrogen which have
much lower gap FH and pitch angle. This is because the densi-
ties of these gases are much smaller than those of air, argon and
neon, so the bearing forces generated across the head-disk inter-
face are not strong enough to sustain the slider flying at higher
flying height.
B. Temperature Effects on FH Change in Air
Next, we compared the temperature effect of physical prop-
erties of air on the gap FH change in sealed and unsealed disk
drives. The result is shown in Fig. 3. We can see that the gap
FH will slightly decrease as the environmental temperature in-
crease in an unsealed drive. However, it will increase with the
temperature in a fully sealed drive. This is because the mech-
anisms of temperature effect in unsealed and sealed drives are
different, which can be seen clearly by comparing gas bearing
force between Fig. 4(a) and (b). In an unsealed drive, the tem-
perature effect of the mean free path (MFP), which increases
the Knudsen number in (3) and thus reduces the load carrying
capacity of gas bearing, will be offset by the temperature ef-
fect of viscosity, which increase the bearing number as shown
in (2) and enhance the slider’s load carrying capacity as the air
viscosity increase with the environmental temperature. There-
fore, the total effect of these two parameters will result in small
change of bearing force with the temperature. In a fully sealed
drive, however, the gap bearing force increases significantly as
the environmental temperature changes from Cto70 C.
This is because both the dynamic viscosity and ambient pres-
sure increase with the environmental temperature, but the mean
free path of the gas keeps almost the same due to the assumption
that there is no volume change in a fully sealed drive.
C. Temperature Effects on FH Change in Various Gases
We further used our air bearing simulator to obtain the steady
flying attitude at various environmental temperatures in an un-
sealed drive and sealed drive respectively. The results are shown
in Figs. 5 and 6. We can see that the gap FH changes for various
gases in an unsealed drive are only in the range of 0.2–0.5 nm
as the environmental temperature changes from Cto70 C.
1392 IEEE TRANSACTIONS ON MAGNETICS, VOL. 46, NO. 6, JUNE 2010
Fig. 5. Gap FH changes with environmental temperature in an unsealed drive.
Fig. 6. Gap FH changes with environmental temperature in a sealed drive.
However, if the slider-disk spacing is reduced to 3 nm or below
in the future disk drives, this small FH variation still needs to be
considered carefully in the slider design. On the other hand, the
gap FH changes due to the environmental temperature effect in
a sealed drive are found to be much different in various gases.
The variations of gap FH are about 0.44 nm in helium, 0.45 nm
in hydrogen, 0.96 nm in neon, 1.12 nm in air and 1.38 nm in
argon as the environmental temperature increases from C
to 70 C in a fully sealed drive. Therefore, we can conclude that
hydrogen or helium could be an ideal alternative to the air in
the future hard disk drives. For an Al O -TiC head with carbon
coating, hydrogen may not be very suitable because hydrogen
bonding interaction occurs and may cause high friction at the
interface. Another major concern on using helium is still the
sealing related problems because this gas has smaller molecular
size compared with the other gases and thus is more easily to
leak out of the drives. The possible solutions are to use mixed
gases and/or lower gas pressure in the drives. And these will be
addressed in the future study.
IV. CONCLUSION
In summary, the effects of gas physical properties on the gas
bearing force and flying attitudes of air bearing slider are studied
based on a generalized lubrication equation derived from the
Boltzmann equation. It is found the gap FH changes for various
gases in a sealed drive could be much higher than those in an
unsealed drive as the environmental temperature changes from
10 Cto70 C. By evaluating the gap FH variations at the same
environmental temperature range for various gases, we conclude
that helium could be an ideal alternative to the air in the future
extremely high density magnetic recording from the viewpoint
of head-disk interface properties.
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... 。基于气膜润滑方程,Zhou 等[9]研究了气体物理特性对磁头滑块飞行高度和气膜承载力的影响, 并指出了硬盘内部填充气体的选择标准。 通过 Ansys/CFX,Kil 等[10] ...
... The particle velocity V can be expressed as a function of the slip parameter β and the distance between the particle and the solid surface X, with the initial conditions of V = V 0 at X = X 0 (Barnocky and Davis 1988) where β = 6λ/X 0 , λ is the air mean free path, μ is the air viscosity, and d is the particle diameter. The values of air physical properties under standard conditions (101,325 Pa and 273.15 K) are used in the simulation (Zhou et al. 2010). The initial conditions of V 0 and X 0 are derived from the results of the particle trajectory in the far-field region. ...
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