Page 75 - 《摩擦学学报》2020年第5期

630 摩 擦 学 学 报 第 40 卷

∫ ′ ∫ ′
a c1 D−1 a c1 contact materials respectively.
′
F ep = ∆F ep (a )n(a )da= a ′(D−1)/2 × a ′(1−D)/2
′
′
4 L
a ′ c2 a ′ c2 The TCC of a single micro-contact is given by
[ ]
( ′ )(D−2)/2
a c1 1 2k s r
′ ′ ′ ′
(1+ f(a ))× 1.1k µ σ y (1− f(a ))+ H f(a ) da h c = = (42)
a ′ r c [1−(A ) ]
∗ 1/2 3/2
(34) r
According to Eq. (6), (22), (25) and (42), the TCC
∫ ′
a c2 D−1
′
′
F p = ∆F p (a )n(a )da = Ha L × of a single asperity h , h and h at elastic, elastic-
′
′
3− D ce cep cp
a ′ s
(35)
( ) (3−D)/2 ( ) (3−D)/2  plastic and fully plastic deformation state can be
′ ′
 a c2 a s 
 
 
 −  expressed as
 
′ ′
a L a L
′ 1/2
2k s (a )
When D=2.5, h ce = √ ∗ 1/2 3/2 (43)
2π[1−(A ) ]
r
∫ ′
a L 3
1/2
′
F e = ∆F e (a )n(a )da = EG (lnγ) 1/2 2k s [a (1+ f(a ))] 1/2
′
′
′
′
2 h cep = √ (44)
a ′ c1 ∗ 1/2 3/2
(36) 2π[1−(A ) ]
( ) ( ) r
3π a L
′
−1/4 ′ 3/4
π a L 1− ln ′ 1/2
16 a c1 2k s (a )
′
h cp = √ (45)
∗ 1/2 3/2
π[1−(A ) ]
∫ ′ ∫ ′ r
a c1 3 a c1
′
′
′
′
F ep = ∆F ep (a )n(a )da= a ′3/4 × a ′−3/4 (1+ f(a ))×
8 L 3.2 TCC of the total contact asperities
a ′ c2 a ′ c2
[ ] According to Eq.(28), and Eq.(43~45), the TCC
( ′ )1/4
a c1
(1− f(a ))+ H f(a ) da ′
′
′
1.1k µ σ y
a ′ caused by the elastic contact area, the elastic-plastic con-
(37) tact area and the fully plastic contact area are given by
√
∫ ′ ( ) 1/4 ( ) 1/4  ∫ ′ ′ (D−1)/2
a c2  ′ a s ′  a L 2/π(D−1)k s a
′  a c2
′
F p = ∆F p (a )n(a )da = 3Ha L    −    H ce = h ce (a )n(a )da = L ×
′
′
′
′
′
′ ′  ∗ 1/2 3/2
a ′ s a L a L a ′ c1 (2− D)[1−(A ) ]
r
(38) ( )
a ′ (2−D)/2 −a ′ (2−D)/2
L
c1
Through the above analysis, the total contact load F
(46)
of the whole contact surfaces can be expressed as
∫ ′ ′ (D−1)/2
(D−1)k s a
a c1
 ′ ′ H cep = ′ ′ ′ L
F e + F ep + F p a c1 ⩽ a L h cep (a )n(a )da = √

 ∗ 1/2 3/2
 a ′ 2π[1−(A ) ]
 c2 r
 ′ ′ ′ (47)
F =  F ep +F p a c2 ⩽ a L < a c1 (39) ∫
′
 a c1

 ′−D/2
 ′ 1/2 ′
′ ′ a (1+ f(a )) da
F p 0 < a L < a c2
a ′ c2
3 Modeling for TCC ∫ a c2 2k s (D−1)a ′ (D−1)/2
′
′
′
H cp = h cp (a )n(a )da = L ×
′
√
∗ 1/2 3/2
a ′ s π(2− D)[1−(A ) ]
r
3.1 TCC of single contact asperity ( )
a ′ (2−D)/2 −a ′(2−D)/2
[20]
[16]
According to Ma et al and Zhao et al , thermal c2 s
(48)
contact resistance (TCR) of a single micro-contact can
Through the above analysis, the total TCC H of the
c
be expressed as
whole contact surfaces can be expressed as
∗ 1/2 3/2
ψ(c/b) [1−(c/b)] 3/2 [1−(A ) ]  ′ ′
r c = = = r (40) H ce + H cep + H cp a c1 ⩽ a L



2ck s 2rk s 2rk s  ′ ′ ′
H c =  H cep +H cp a c2 ⩽ a L < a c1 (49)



where A = A r /A a represents the non-dimensional real  ′ ′
∗
r H cp 0 < a L < a c2
contact area; A is the nominal contact area of the whole In order to make the results generalization, it is
a
contact surface; ψ(c/b)is the surface constriction necessary to carry out dimensionless treatment.
coefficient; k is the equivalent thermal conductance can F = F H = H c A = A r (50)
s
∗
∗
∗
A a E c 1/2 r A a
be expressed as k s A a
2 1 1
= + (41) 4 Results and discussion
k s k 1 k 2
where k and k are the thermal conductance of two In this paper, the asperity interaction and friction
2
1