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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
1 Introduction
Face contact is an important physical reality in a
number of research fields [
1–3
]. 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
operations [
4
], and is also a risk from disturbances
during the opened operation [
5
]. 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) [
6
] have done
a pioneering work, developing an elastic contact model
between rough surfaces. McCool [
7
] and Bhushan [
8
]
added asperity slope and curvature to capture rough
surfaces. Chang et al. [
9
] proposed the CEB elastic-plastic
contact model based on volume conservation during
plastic deformation to improve the GW model. Kogut
and Etsion (KE model) [
10, 11
] 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 [
12
] revealed that many
engineered surfaces have the multi-scale
characteristic. Bhushan et al. [
13
] 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
[
14
] 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 [
15,
16
] researched the interfacial temperature factor in the
fractal contact. Komvopoulos and Yan [17] generated a
three-dimensional fractal surface by the WM function
and introduced it into the contact model. Sahoo and
Chowdhury [
18, 19
] analyzed the friction and the wear of
fractal surfaces. Ciavarella et al. [20] investigated the
elastic contact stiffness and the contact resistance of fractal
surfaces. Kogut and Jackson [
21
] used both statistical and
fractal approaches to characterize simulated surfaces,
and obtained substantial differences between the two.
Morag and Etsion (ME model) [
22
] 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 ful (...truncated)