Application of Fractal Contact Model in Dynamic Performance Analysis of Gas Face Seals
Hu et al. Chin. J. Mech. Eng.
Application of Fractal Contact Model in Dynamic Performance Analysis of Gas Face Seals
SongT‑ao Hu 0
Wei‑Feng Huang 0
Xiang‑Feng Liu 0
Yu‑Ming Wang 0
0 State Key Laboratory of Tribology, Tsinghua University , Beijing 100084 , China
Fractal theory provides scale‑ independent asperity contact loads and assumes variable curvature radii in the contact analyses of rough surfaces, the current research for which mainly focuses on the mechanism study. The present study introduces the fractal theory into the dynamic research of gas face seals under face‑ contacting conditions. StructureFunction method is adopted to handle the surface profiles of typical carbon‑ graphite rings, proving the fractal contact model can be used in the field of gas face seals. Using a numerical model established for the dynamic analyses of a spiral groove gas face seal with a flexibly mounted stator, a comparison of dynamic performance between the Majumdar‑ Bhushan (MB) fractal model and the Chang‑ Etsion‑ Bogy (CEB) statistical model is performed. The result shows that the two approaches induce differences in terms of the occurrence and the level of face contact. Although the approach distinctions in film thickness and leakage rate can be tiny, the distinctions in contact mechanism and end face damage are obvious. An investigation of fractal parameters D and G shows that a proper D (nearly 1.5) and a small G are helpful in raising the proportion of elastic deformation to weaken the adhesive wear in the sealing dynamic performance. The proposed research provides a fractal approach to design gas face seals.
Fractal theory; Asperity contact; Gas face seal; Dynamic performance
Face contact is an important physical reality in a
number of research fields [
]. In the field of face seals,
for contacting face seals, face contact is inevitable
during the opened operation. For non-contacting face seals
such as spiral groove gas face seals as shown in Figure 1,
they should possess a proper gas film thickness to avert
face contact during the opened operation. Even so, face
contact does occur during the startup and shutdown
], and is also a risk from disturbances
during the opened operation [
]. Therefore, it is imperative
to choose an adequate asperity contact model in the
analyses of face seals. With respect to asperity contact,
Greenwood and Williamson (GW model) [
] have done
a pioneering work, developing an elastic contact model
between rough surfaces. McCool [
] and Bhushan [
added asperity slope and curvature to capture rough
surfaces. Chang et al. [
] proposed the CEB elastic-plastic
contact model based on volume conservation during
plastic deformation to improve the GW model. Kogut
and Etsion (KE model) [
] developed a finite element
method to investigate the contact between a deformable
spherical asperity and a rigid flat, showing
dimensionless contact load and contact area over the increase in the
interference range from purely elastic through
elasticplastic to fully plastic contact.
However, Sayles and Thomas [
] revealed that many
engineered surfaces have the multi-scale
characteristic. Bhushan et al. [
] found that statistical parameters
depend strongly on the resolution of measuring
instruments, and are not unique for a surface because of the
multi-scale characteristic. It leads to the result that
measurements with different resolutions and scanning
lengths wouldn’t yield unique statistical parameters for
a surface. Moreover, statistical contact models overlook
the fact that the curvature radius of an asperity is a
function of asperity size, and surely assume a constant
curvature radius for all asperities. Majumdar and Bhushan
] used the Weierstrass-Mandelbrot (WM) function
to develop the first fractal contact model for real rough
surfaces where the assumption of variable curvature
radius was adopted. This fractal contact model has been
of interest to many researchers, and has been applied
to various applications. Wang and Komvopoulos [
] researched the interfacial temperature factor in the
fractal contact. Komvopoulos and Yan  generated a
three-dimensional fractal surface by the WM function
and introduced it into the contact model. Sahoo and
] analyzed the friction and the wear of
fractal surfaces. Ciavarella et al.  investigated the
elastic contact stiffness and the contact resistance of fractal
surfaces. Kogut and Jackson [
] used both statistical and
fractal approaches to characterize simulated surfaces,
and obtained substantial differences between the two.
Morag and Etsion (ME model) [
] argued that a
single asperity transferring from plastic to elastic when the
load increases and the contact area becomes larger in the
MB model is in contrast with classical contact
mechanics. They suggested the real deformation is an
independent parameter ranging from zero to full interference, and
thus developed a revised elastic-plastic contact model
with respect to a single fractal asperity.
Face contact can affect sealing performance, such as
dynamic behavior, thermodynamics, friction, wear. The
dynamics of face seals has been an active area since the
works by Etsion [
]. In the aspect of gas face seals,
direct numerical method [
] is detailed but
computationally intensive, whilst semi-analytical method
including perturbation method [
] and step jump
method , on the other hand, is a more practical and
efficient alternative but intensively depends on small
displacement precondition. Before the introduction of
asperity contact, stability and tracking have been used
to illustrate the potential menace of face contact.
Variables such as minimum film thickness, axial relative
displacement and angular transmissibility are regarded as
the indirect evaluation indexes of face contact. With the
development of simulation, asperity contact models have
been involved to directly gauge their influence on sealing
dynamic performance. Harp and Salant [
an axial dynamic model including the Abbott-Firestone
plastic asperity contact model. Green [
] researched the
transient performance of coned gas face seals during the
startup operation by using the CEB model. Ruan [
used the CEB model to investigate the transient
performance of spiral groove gas face seals during the startup
and shutdown operations.
The above dynamic works all used the statistical
contact models, while the fractal contact theory has not been
applied. The present study is an attempt to involve the
fractal theory in the dynamic research of gas face seals.
And a comparison of dynamic performance between
statistical and fractal approaches is performed. The widely
used, original contact models (i.e., the MB and the CEB
models) are selected, respectively, as the representatives
of fractal and statistical asperity contact models
accounting for excluding extra factors (such as the impact of
work hardening, the influence of neighboring asperities,
the introduction of new bi-Gaussian stratified surface
], the revision of contact mechanic
in ME model) involved in advanced statistical or fractal
2.1 MB Model
In the MB model, the surface profile z(x), as shown in
Figure 2, is random, multiscale and statistically
selfaffine. The WM function is used to describe the surface
profile. Its power spectrum is [
2 ln γ
· ω(5−2D) ,
where S is the power spectrum, ω is the frequency that
is the reciprocal of the wavelength of roughness, D is the
fractal dimension, G is the fractal roughness parameter,
γ determines the frequency spectrum of surface
roughness where γ = 1.5 is found to be a suitable value for high
spectral density and phase randomization [
]. In a
loglog plot of S(ω) ~ ω, the power law behavior of Eq. (1)
transforms into a straight line. The slope kp is related to
the fractal dimension D and the intercept Bp is related to
the fractal roughness parameter G. In practical
experiments, one needs to obtain the power spectrum of a real
surface profile in a log-log plot. If the relation is linear
and kp satisfies (− 3, − 1), it reveals the real surface profile
owns fractal characteristic. Then, D and G can be
calculated referring to kp and Bp.
The critical contact area of an asperity is [
where E is the Hertz elastic modulus, H is the hardness
of softer material, and the maximum contact pressure
coefficient K = 0.454 + 0.41υ (υ is the Poisson ratio). If the
area of a contact spot a < ac, the asperity is in plastic
contact; if a > ac, the asperity is in elastic contact. The total
contact load between a rough surface and a smooth plate
Pc is [
where the first term corresponds to elastic deformation
and the second term corresponds to plastic deformation.
al is the area of the largest contact spot. n(a) is the
sizedistribution of a [
n(a) = D2 · aaDlD//2 +21 .
The real contact area Ar is [
n(a)ada = 2 − D l
Are = 0,
Arp = Ar = 2 − D l
If al < ac, the elastic and plastic deformation can be
simply rendered as [
If al > ac, the elastic and plastic deformation can be
calculated as [
n(a)ada = 2 −D D (al − alD/ 2a(c2−D)/ 2),
D aD/ 2a(c2−D)/ 2.
n(a)ada = 2 − D l
2.2 Application of MB Model in Sealing Dynamics
The dynamic schematic of the two mated rings and the
geometry of the rotor are depicted in Figure 3. A total
of N spiral grooves are processed on the rotor at a depth
of δg. The ratio of groove width to the land width is
captured by λ = Wg/(Wg + Wl), and the ratio of groove length
to the dam length is characterized by β = (rg − ri)/(ro − ri).
α is the spiral angle varying from 0 to 180°. ro, ri and rg
are outer radius, inner radius and the boundary between
groove region and dam region. The gas film thickness
of any point (x, y) on the stator h(x, y) is given by h(x,
y) = c + <δg>, where c is the central gas film thickness
between the coupling rings, and <δg> indicates a δg-deep
groove in the groove region. Considering the stiffness
and damping properties of springs and the secondary
seal, the 1D axial dynamic equation is rendered by [
mc¨ + cszc˙ + kszc = −Fclosing + Fg + Fc,
where m is the stator mass. ksz is the stiffness of springs.
csz is the damping of flexible support. Fclosing is the total
load of the pressure-drop-generated fluid load and the
spring support load at equilibrium. Fclosing is applied on
the back of the stator, balancing the gas film opening
load Fg and the face contact load Fc. Fg can be obtained
by integrating the gas film pressure p over the nominal
sealing area An, rendered as Fg = An pdA. The gas
pressure distribution p is governed by the lubrication
equation. Assuming the gas flow is ideal and isothermal, and
Therefore, the value of Eq. (11) finally becomes
Ar 1 1
An = √π (1 − 1 + e−1.668h/ σ ).
The relation between h and al can be obtained from
Eqs. (5) and (14)
al = (2 D−√Dπ)An (1 − 1 + e−1.668h/ σ ).
Therefore, for a gas face seal, if h is known, al can be
calculated according to Eq. (15). Substituting n(a) from
Eq. (4) in Eq. (3), Pc finally becomes
4√π3E(D3G−D2−D1)alD/ 2 al3/ 2−D − ac3/ 2−D +
Pc = a
√πG1/ 2Eal3/ 4 ln acl + 3KHal3/ 4ac1/ 4,
2 − D
KHDalD/ 2 a1−D/ 2,
D = 1.5,
D = 1.5.
Then, the resulting Pc can be used in the sealing
dynamics to take the place of Fc in Eq. (8).
All in all, the calculation scheme can be summarized as
the effect of surface texture is ignored, the compressible
Reynolds equation is adopted as [
∇ · ph3∇p − 6μΩrphiθ − 12μ
where μ is the gas viscosity, r is the radius, iθ is the unit
vector in θ direction, and Ω is the shaft speed. The
boundary conditions to Eq. (9) are
p(r = ri) = pi, p(r = ro) = po.
For a given gas face seal, the film thickness h measured
from the mean plane of asperity height is easily obtained.
Majumdar and Bhushan [
] proposed that if the
asperity height of a surface follows a Gaussian distribution, h
respects the relation as below
Then Eq. (11) can be deduced as
Ar 1 ∞
An = √2π h/ σ
Ar 1 1
An = √π ( √2π
= √π (1 − √2π
∞ e−x2 2dx − √2π
The value of −h∞/σ e−x2 2dx
using an error function erf
√2π can be calculated by
e−x2 2dx ≈ erf( σ ) = 1 + e−1.668h/ σ .
Note the special condition that if al < ac, all the contact
spots are in plastic contact and Pc can be simplified as
Input of h
Calculation of al from
al > ac
D = 1.5
Calculation Pc from
lower part of Eq. (16)
Calculation Pc from
upper part of Eq. (16)
Calculation Pc from
3 Results and Discussion
3.1 Test of Fractal Characteristic in Gas Face Seals
As not all rough surfaces own fractal characteristic [
the precondition for using the MB model in gas face seals
is to determine whether the surface of sealing rings own
fractal characteristic. Ganti and Bhushan [
that for an isotropic fractal surface, the study of a section
provides complete information about the surface because
the fractal dimension D of the rough profile and that of
the surface Ds are related as D = Ds + 1, and the profile
and surface spectral densities are also related. Therefore,
a surface can be characterized by fractal parameters D
and G. Here, structure–function method [
] is adopted
to analyze the properties of surface profiles. In the
structure–function method, structure function S(τ) is defined
S(τ ) =
[z(x + τ ) − z(x)]2 =
S(ω)(ejωτ − 1)dω,
where τ is an increment of x, and <·> means the space
average. Substituting S(ω) from Eq. (1) in Eq. (18) and
integrating to yield
S(τ ) = CG2(D−1)τ 4−2D,
Γ (2D − 3) sin (2D − 3)π 2
(4 − 2D) ln γ
and Γ is the Gamma function. As the structure function
also follows a power law relation, Eq. (19) will transform
into a line in the log-log plot of S(τ) ~ τ. If its slope ks
satisfies the interval of (0, 2), it reveals that the real surface
owns fractal characteristic. Then, the fractal dimension D
and the fractal roughness parameter G can be calculated
ks = 4 − 2D,
Bs = lg CG2(D−1),
where Bs is the intercept.
The surface of an isotropic carbon-graphite ring,
serving in an industrial spiral gas-face-seal product, is tested
by the Talysuf surface topography measurement
system. Three rough profiles spaced 120° apart are tested
from inner radius to outer radius. The
corresponding log-log plot of S(τ) ~ τ is displayed in Figure 5. The
slopes of these three profiles are, respectively, 1.5933,
1.5905 and 1.5823, satisfying the interval of (0, 2) and
verifying that the measured surface owns fractal
characteristic. Therefore, the MB model can be used in this
typical gas face seal. Using Eqs. (20) and (21), the
fractal dimension D of the three profiles are, respectively,
1.2034, 1.2048 and 1.2089, and the fractal roughness
parameter G are 2.9961 × 10−13 m, 2.1073 × 10−13 m and
3.5568 × 10−13 m, respectively.
3.2 Comparison of Steady‑state and Transient Sealing
Since face contact occurs under low-speed
conditions such as the startup and shutdown operations, and
may take place during disturbances [
], the following
dynamic simulation is classified into two groups: the
steady-state response under low-speed conditions and
the transient response to disturbances. Here, the typical
operation condition parameter, pressure drop, is taken
as the variable. The organized simulation cases are listed
in Table 1. Table 2 illustrates the parameters of a spiral
groove gas face seal. Table 3 shows the parameters of the
CEB and the MB models with respect to the above three
profiles. The total contact load of the CEB model is
calculated by [
Pc = ηAnE 43 R1/ 2
(z − h + ys)3/ 2φ(z)dz
[2(z − h + ys) − ωc]φ(z)dz, (22)
m2 = avg[( dzd(xx) )2],
m4 = avg[( d2dzx(2x) )2].
where R is the mean summit radius, ys is the distance
between the mean of summit height and that of asperity
height, ωc is the critical elastic deformation of an asperity,
and φ is the distribution function of summit height which
is assumed to respect a Gaussian distribution. Note that
the surface parameters used in the CEB model, as shown
in Table 3 and Eq. (22), are calculated referring to Eqs.
(A4, A9–A13) in the appendix of Ref. [
] based on three
variables m0, m2 and m4. In Ref. [
], m0, m2 and m4 are,
respectively, defined as
Figure 6(a) displays the dimensionless contact area A*r
as a function of the dimensionless contact load P*c using
the MB and the CEB approaches, where Pc= Pc/(AnE)
and Ar = Ar/An. The contact area obtained by the CEB
model is greater than that obtained by the MB model at
the same contact load. The deviation between the two
is in the same order of magnitude with the results of
simulated surfaces in Figure 2 of Ref. [
]. It can be seen
that the results obtained by the CEB model have fine
distinctions, while those obtained by the MB model are
overlapped. It is because that the dimensionless
critical area of the asperity a*c (a*c= ac/An) in the MB model
is about 10−1 under current fractal parameters. When
P*c increases from 10−7 to 10−3, the dimensionless
largest area al* (al* = al/An) in the MB model increases from
about 10−6 to 10−2. In the MB model, it means that all the
contact spots are smaller than the critical contact area,
leading to full plastic contact. Thus, only the second term
of Eq. (16) for plastic contact is available, and the
distinction of G in Table 3 is not involved. One may wonder the
explanation about the full plastic deformation, yet this
phenomenon has also occurred in the case with D = 1.1
in Figure 10 of Ref. [
], and explained by Majumdar and
Bhushan that the load-area relation and the fraction of
the contact area in elastic and plastic deformation are
quite sensitive to fractal parameters [
]. This difference
between the MB and the CEB approaches shows that the
two approaches have distinctions in contact mechanism
and end face damage regardless of the degree of
distinctions in dynamic performance including film thickness,
leakage rate and face contact load. Figure 6(b) shows the
dimensionless gas film thickness h/σ as a function of the
dimensionless contact load P*c. It is obvious that the gas
film thickness of the CEB model is smaller than that of
the MB model at the same contact load. When P*c is about
10−7, the face contact load is too small to be
considered. By this, h/σ is about 4.0 in the CEB model and 6.6
in the MB model. It means that if h/σ was in the interval
of (4.0, 6.6), the MB model would provide a face contact
load in the dynamic analysis whilst the CEB model would
not. Therefore, it can be expected that there will be an
apparent difference between the two approaches in the
occurrence of face contact, which will be shown in the
subsequent simulation under low-speed conditions.
Profile 3 is selected to gauge the differences of sealing
performance between the MB and the CEB approaches.
A whole-ring numerical model is established for the
dynamic analyses of a spiral groove gas face seal with a
flexibly mounted stator using the finite element method.
In regards to the accuracy and stability of a complex
dynamic system, a very fine mesh and a very small time
step would be ideal. Yet, a balance should be struck
between accuracy and computing time. After
experiments, it is determined that a time step of 1 × 10−6 s with
a 3160-finite element mesh is adopted. The simulation is
carried out on a 2.3 GHz workstation.
Figure 7 shows the differences of steady-state
performance using the MB and the CEB approaches under
different pressure drops where the shaft speed Ω maintains
at 31.4 rad/s. The leakage rate Qi is r = (ri + rg)/2 referring
to the relationship
x2 + y2 + ∂y
x2 + y2
Mgas is the molar mass set to 29 g/mol, Rgas is the gas
constant set to 8.314 J mol−1 K−1, and Tgas is gas
temperature set to 293 K. There is no difference under the
nonpressure-drop condition (po = pi = 0.1 MPa) because the
gas film opening load Fg are able to balance the closing
load Fclosing at equilibrium and the face contact load Fc is
zero. When po increases in Figure 7(b), Fc transforms into
a non-zero value and its proportion in the total
opening load rises. The larger the proportion of Fc, the more
apparently the deviations display in the central film
thickness at equilibrium and face contact load. However, after
po reaching 5 MPa, the deviations of the two approaches
in the central film thickness at equilibrium and face
contact load start to decrease because the proportion of Fc
obtained by the MB model starts to decrease,
accounting for Fg becoming the dominant component of the
total opening load again. The deviation in leakage rate
still increases monotonically because the leakage rate is
related to not only the film thickness but also the
pressure drop. Moreover, it should be emphasized that before
po arriving at 1 MPa, Fc obtained by the MB model starts
to transform into a value of 40 N whilst Fc obtained by
the CEB model is still maintains at nearly zero, which is
in accordance with the prediction in Figure 6(b). It is
concluded that the two approaches will induce differences in
terms of the occurrence and the level of face contact.
Figure 8 illustrates the differences of transient
performance using the MB and the CEB approaches during a
fluctuation of pressure drop (i.e., po, instantaneously,
raises from 1 to 2 MPa at 0.01 s) where shaft speed Ω
maintains at 104.7 rad/s. The value of 104.7 rad/s is
large enough to guarantee the completely opened state
of the two mated rings. From the simulation case
without the contact model, it can be seen that the fluctuation
of pressure drop induces oscillations in the central film
thickness and leakage rate. After coupling the contact
model, face contact occurs. In Figure 8(b), the face
contact load obtained by the MB model is greater than that
obtained by the CEB model at the same film thickness
under current sealing parameters, which is in accordance
with Figure 6(b). When c decreases with an
instantaneous increase of po, Fc obtained by the MB model occurs
earlier and is greater at the same film thickness than that
obtained by the CEB model. These lead to a result that
the stator in the MB approach returns to a stable state
faster and its oscillation amplitude is smaller.
Moreover, though the distinctions of the two approaches about
the oscillation amplitude and oscillation time are tiny in
terms of film thickness and leakage rate, the distinction in
the face contact load is apparent. A greater face contact
load obtained by the MB model indicates that the surface
of the seal would undergo much more severe wear during
the fluctuation. Therefore, here, the dynamics using the
CEB model will offer a more optimistic consideration of
face wear than the dynamics using the MB model.
To sum up, the MB and the CEB approaches induce
different steady-state and transient performance in
the dynamic simulation. In particular, under current
sealing parameters, even if the distinctions of the two
approaches in film thickness and leakage rate are tiny,
the two approaches will induce apparent differences in
the occurrence and the level of face contact, which affect
contact mechanism and end face damage. In addition,
since not all surfaces own fractal characteristic, it should
be emphasized that the use of the MB model in other
types of seals or other fields has an extra limitation.
3.3 Investigation of Fractal Characteristic
Adhesive wear is a significant physical phenomenon in
the dynamic analyses of gas face seals for its effect on
the end face damage and service life. As adhesive wear
is more easily caused by plastic deformation, it is better
to raise the proportion of elastic deformation in the face
contact. In the MB model, a feasible approach to raise the
proportion of elastic deformation is to control the fractal
parameters D and G. Therefore, a parametric
investigation of D and G is performed. Note that the present study
focuses on the influence of D and G on the proportion of
elastic deformation. The detailed approach to realize the
control of D and G should be researched in the
The dimensionless form of total contact load in the MB
model is rendered as [
2 − D )(1−D)/ 2Ar∗(3−2D)/ 2
G∗D−1g1Ar∗D/ 2 (− aDc∗(3−2D)/ 2
KH g2Ar∗D/ 2ac∗(2−D)/ 2,
al > ac and D = 1.5,
√πG∗1/ 2( Ar∗ )3/ 4 ln Ar∗ 3KH ( Ar∗ )3/ 4ac∗1/ 4,
3 3ac∗ + 4E 3
al > ac and D = 1.5,
E Ar∗, al < ac,
G∗ = √An ,
ac∗ = (KH 2E)2/ (D−1) ,
g2 = (
g1 = 3 −D2D ( 2 −D D )D/ 2,
2 − D
Therefore, the proportion of elastic deformation can be
deduced from Eqs. (2), (5), (7), (24) and (25)
= 1 −
(2 − D)( K2HE )2/ (D−1)Ar∗
The values of D and G* are assumed within a common
range, and other material properties are still selected
from Table 2. Figure 9(a) shows the influence of D on the
asperity contact where G* maintains at 10−10. The case
with D = 1.5 has the greatest proportion of elastic contact
area at the same A*r. In the MB model, contact spots will
be in plastic deformation when a < ac. When D increases
from 1.3 to 1.5, ac decreases according to Eq. (2). It leads
to the result that more and more contact spots
transform from plastic deformation into elastic deformation.
However, after D reaching 1.5, the positive effect caused
by the decrease of ac is surpassed by the negative effect
caused by the refining of surface topography, leading to
more spots in plastic deformation. With respect to the
above negative effect, Majumdar and Bhushan [
that with the increase of D, the number of contact spots
below the critical size increases and the contribution of
these contact spots to the total contact area is significant.
Figure 9(b) shows the influence of G* on the asperity
contact when D maintains at 1.5. It can be seen that the
proportion of elastic contact area increases as G* decreases
because ac decreases with a decrease of G* according
to Eq. (2). Since ac decreases, a large amount of contact
spots transform from plastic deformation into elastic
deformation. It is concluded that a proper D (nearly 1.5)
and a small G are helpful for maximizing the proportion
of elastic deformation.
models in the attempt of incorporating the fractal
theory into the dynamic research of gas face seals.
(2) Structure-Function method is adopted to process
the surface profiles of a typical carbon-graphite
ring which is an industrial product, proving the MB
model can be utilized in the typical gas face seals.
(3) The CEB statistical model is selected to compare
with the MB model to gauge the differences of the
two approaches in dynamic performance. The MB
and the CEB approaches will induce differences in
terms of the occurrence and the level of face
contact. Although the distinctions in film thickness and
leakage rate may be tiny, the distinctions in contact
mechanism and end face damage are apparent. The
CEB approach offers a more optimistic
consideration of face contact.
(4) An investigation of fractal parameters D and G is
performed to explore a feasible approach to raise
the proportion of elastic deformation to weaken
adhesive wear in the sealing dynamic performance.
S‑ TH was in charge of the whole trial; S‑ TH wrote the manuscript; W‑FH, X ‑FL
and Y‑MW assisted with sampling and laboratory analyses. All authors have
read and approved the final manuscript.
1 State Key Laboratory of Tribology, Tsinghua University, Beijing 100084, China.
2 State Key Laboratory of Mechanical System and Vibration, Shanghai Jiao
Tong University, Shanghai 200240, China.
Song‑ Tao Hu, born in 1989, is currently a postdoctoral fellow at State Key
Laboratory of Mechanical System and Vibration, Shanghai Jiao Tong University,
China. He received his doctorate degree from State Key Laboratory of Tribology,
Tsinghua University, China, in 2017, and received his bachelor degree from
Northwestern Polytechnical University, China, in 2012. His research interests
include mechanical face seals. Tel: +86‑18221229658; E‑mail: hsttaotao@sjtu.
Wei‑Feng Huang, born in 1978, is currently an associate professor at State
Key Laboratory of Tribology, Tsinghua University, China. His research interests
include mechanical face seals. Tel: +86‑10‑62795124; E‑mail: huangwf@
Xiang‑Feng Liu, born in 1961, is currently a professor at State Key
Laboratory of Tribology, Tsinghua University, China. His research interests are machine
design and mechanical face seals. Tel: +86‑10‑62795122; E‑mail: liuxf@
Yu‑Ming Wang, born in 1941, is currently a professor at State Key
Laboratory of Tribology, Tsinghua University, China, and an academician of Chinese
Academy of Engineering. His research interest is fluid sealing technology. Tel:
+86‑10‑62771865; E‑mail: .
The authors declare no competing financial interests.
Ethics Approval and Consent to Participate
Supported by China Postdoctoral Science Foundation (Grant No.
2017M621458), National Science and Technology Support Plan Projects (Grant
No. 2015BAA08B02), National Natural Science Foundation of China (Grant
No. 11632011), and National Natural Science Foundation of China (Grant No.
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