Page 76 - 《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 631

*
coefficient in fractal model of thermal contact conduc- shows the relationships between contact load F , real
tance are introduced by eq. (4) and eq. (10) respectively. contact area A and TCC H in the case of D=2.2, G=
∗
∗
r c
Based on the proposed model in this paper, the effects of 2 nm. The figure indicates that the TCC increases with
friction coefficient, fractal dimension, fractal roughness increasing contact load. As shown in Fig. 2(a), the TCC
and contact load on TCC are discussed. The calculation decreases with the increasing of friction coefficient
[30]
parameters are shown in Table 1 . μ under the same contact load. The reason for this phe-
nomenon is that the larger friction coefficient, the
Table 1 The calculation parameters.
rougher surface. Fig. 2(b) illustrates that the rougher
Parameter Specification
surface, the smaller real contact area, resulting in a less
Fractal dimension, D 2.2, 2.4, 2.6
Fractal roughness, G/nm 2,4,6 TCC under the same contact load. This finding is con-
Equivalent elastic modulus, E/GPa 192
sistent well with the experiment results in Ref [7, 10].
Harness, H/GPa 23.5
Scale parameters, γ 1.5 Therefore, the model of TCC proposed in this paper is
3
The length of the sample, L/nm 7.04×10 reasonable.
The cut-off length, L s /nm 5
4.2 Effect of fractal dimension
Friction coefficient, μ 0.3, 0.6, 0.9
In this section, the effect of fractal dimension D on
4.1 Effect of friction coefficient TCC is studied for μ=0.3, G=2 nm. As shown in Fig.
In this section, the effect of friction coefficient μ on 3(a), the TCC increases with the increasing of fractal
TCC is studied. The friction coefficient can indirectly dimension D under the same contact load. The reason for
affect the TCC by affecting the real contact area. Fig. 2 this phenomenon is that the larger fractal dimension, the

0.6 μ=0.3 4 μ=0.3
Thermal contact conductance, H * 0.4 Real contact area, A * /10 −3 r 3 2 1
c
μ=0.6
μ=0.6
μ=0.9
μ=0.9

0.2

0.0 0
0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0
*
*
Contact load, F /10 −4 Contact load, F /10 −4
* * * *
(a) F and H c (b) F and A r
Fig. 2 The effect of friction factor μ on real contact area A and TCC H ∗
∗
r c
4 3 μ=2.2 10.0 μ=2.2
Thermal contact conductance, H * 2 1 Real contact area, A * /10 −3 r 5.0
c
μ=2.4
μ=2.4
μ=2.6
μ=2.6
7.5

2.5

0 0.0
0.0 1.0 2.0 3.0 4.0 0.0 1.0 2.0 3.0 4.0
*
*
Contact load, F /10 −6 Contact load, F /10 −6
* * * *
(a) F and H c (b) F and A r
Fig. 3 The effect of fractal dimension D on real contact area A and TCC H ∗ c
∗
r