Page 72 - 《摩擦学学报》2020年第5期

第 5 期 孙献光, 等: 考虑摩擦系数和微凸体相互作用的粗糙表面接触热导分形模型 627

[22]
properties and surface pressure were investigated. et al established a fractal model of thermal contact
[11]
Cooper et al firstly presented the thermal contact conductance between two cylinders’ joint surfaces, and
conductance model (CMY model), which laid a good the effects of cylinder curvature radius and contact type
foundation for subsequent researches. Based on the were analyzed.
[12]
CMY model, Jeng et al established a model of TCC Through the analysis of the above literature, it can
considering the elastic-plastic deformation of the be observed that most studies of TCC assume that the
asperity, which satisfied the continuous and smooth asperities of rough surfaces are independent. However,
conditions of the transition of asperity from elastic in fact, the asperities of rough surfaces are interactive.
deformation to full plastic deformation. In the aspect of Therefore, the above studies are not in line with the
TCC calculation, fractal theory has been widely used. engineering practice, in addition, most of them ignore
Based on the classical heat conduction theory and fractal friction coefficient. To make up for this deficiency, this
[13]
theory, Jiang and Zheng proposed a fractal model of study proposed a fractal model of thermal contact
TCC and studied the influences of contact load as well conductance of rough surfaces considering friction
as fractal parameters and material properties on the coefficient and asperity interaction based on the three-
[14]
TCC. Zou et al studied the effects of fractal dimension dimensional fractal theory. Subsequently, we investigate
and fractal roughness on the TCC. Zhang et al [15] the effects of friction coefficient, fractal dimension,
presented a model of thermal contact conductance based fractal roughness and contact load on TCC.
on Monte Carlo simulation and fractal theory. Ma et al [16] The structure of this paper is as follows. A model of
established a fractal model of TCC based on the two- contact mechanics considering friction coefficient and
dimensional fractal theory, and analyzed the influences asperity interaction is established in Section 2. In
of contact load, curvature radius of asperity and Section 3, the model for TCC is presented. In Section 4,
[17]
temperature on TCC. Liu et al established a fractal the effects of friction coefficient, fractal dimension and
model of TCC between two rough curved surfaces by fractal roughness and contact load on TCC were studied.
introducing the surface contact coefficient. The above Finally, some conclusions are given in Section 5.
researches are based on two-dimensional fractal theory,
2 Modeling for contact mechanics
however, it is unreasonable to use two-dimensional
fractal theory to describe three-dimensional rough 2.1 Asperity interaction model
surface. Thus, three-dimensional fractal theory has been Yan and Komvopoulous presented a function that
[23]
widely used in the prediction of TCC. Ji et al [18] can describe three-dimensional fractal surface
developed a fractal model for TCC of two rough topography by modifying the classic Weierstrass-
surfaces considering elastic-plastic deformation of the Mandelbrot (W-M) function. The modified W-M
asperity based on the three-dimensional fractal theory. function is given by
Considering base thermal resistance and constricted [ ( πx )]
′ (3−D)
1/2
z 0 (x) =G (D−2) (lnγ) (2r ) × cosϕ 1,n 0 −cos −ϕ 1,n 0
[19]
thermal resistance, Zhang et al proposed a fractal r ′
(1)
model of TCC based on three-dimensional fractal theory.
′
′
[20]
Zhao et al developed a fractal model considering where −r < x < r ; D (2<D<3) is the fractal dimension;
G is the fractal roughness; γ (γ>1) is a parameter that
thermal constriction conductance and air medium
controls the density of frequencies of profile; is
thermal conductance, then verified the utility of the ϕ 1,n 0
[21]
model by experiment. Li et al proposed a model of 3- random phase.
According to Eq.(1), the deformation δ of the single
D fractal thermal contact conductance based on three-
asperity after loading is equal to the amplitude difference
dimensional fractal theory, and the effects of normal
between the peak and valley of the cosine function. That
load, fractal dimension, fractal scale parameters and
( πx )
material characteristic parameters were investigated. Sun is, when cosϕ 1,n 0 = 1 and cos −ϕ 1,n 0 = −1, the defor-
r ′