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Thermal contact conductance modeling of circular-arc contact surface with mutation area

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Abstract

A thermal contact conductance (TCC) analysis model between circular-arc contact surfaces with mutation area is established in view of multi-scale and multi factor effects. The fractal characteristics of contact surface is described by the W–M function. Contact area and contact pressure in four states are analyzed by considering elastic, first elastic–plastic, second elastic–plastic and complete plastic deformation processes when asperities contact. Therefore, a method for analyzing and calculating TCC is proposed. In addition, the calculation of TCC in the process of the experiment of circular-arc contact surfaces with mutation area is introduced. The TCC of circular-arc contact surfaces with mutation area is analyzed by the research object. It can be observed that local high temperature occurs between the contact surfaces with mutation area. In addition, the influence of temperature, material, roughness and contact pressure on TCC is mainly realized by changing the real contact area. The change of TCC on the contact surfaces with mutation area is affected by the internal heat transfer law of the contact object. The experimental results are in good agreement with the simulation results, which verifies the accuracy of the theoretical modeling.

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Abbreviations

D :

Fractal dimension

G :

Fractal-amplitude dimension

L :

Contour sample length

M :

The number of overlapping ridges

n :

Frequency level of the asperity

γ n :

Frequency of surface roughness spectrum

φ m ,n :

Random phase

z(x,y):

Amplitude function of 3D rough surface, m

x(t):

Fractal signal

k 1, 2 :

The thermal conductivity of the two materials, W/(m⋅K)

D m i :

Decomposition coefficient

w :

Width of the key on specimen A, mm

φ m i :

Wavelet function

σ 2 x :

The variance of fractal signal x(t)

α :

The slope of the fitting line

a, b :

Small simples

A, B :

Specimens

l :

Length of small simple a and b, mm

h :

Flattening height of small simple a and b, mm

d :

Width of small simple a and b, mm

A r :

Actual contact area of the whole contact surface, m2

R 3 :

Radius of specimen A, mm

R 4,5,6,7 :

Radius of temperature measuring point c, d, e, f, mm, the values are 30,50,70 and 90 respectively

δ e :

Critical deformation of the elastic and the first elastic–plastic deformations, m

δ e p :

Critical deformation of the first elastic–plastic and the second elastic–plastic deformations, m

δ p :

Critical deformation of the second elastic–plastic and complete plastic deformations, m

F ce :

Contact pressure of the elastic deformation, MPa

F cep1 :

Contact pressure of the first elastic–plastic deformation, MPa

F cep2 :

Contact pressure of the second elastic–plastic deformation, MPa

F cp :

Contact pressure of the complete plastic deformation, MPa

F e :

Contact pressure of the whole contact surface under elastic deformation, MPa

F ep1 :

Contact pressure of the whole contact surface under first elastic–plastic deformation, MPa

a :

Contact area of asperity, m2

n(a):

Contact points distribution

λ :

Effective contact coefficient

n′(a):

Improved contact points distribution

a L :

Area of the largest contact point, m2

A a(R):

Nominal contact area of the whole contact surface, m2

δ :

Deformation of the asperity, m

A * r(R):

Dimension actual contact area of the whole contact surface, m2

m :

scale number

k s :

The equivalent thermal conductivity, W/(m⋅K)

K :

The correlation coefficient

E :

The comprehensive elastic modulus

H :

Material hardness

r :

Radius of actual contact surface, m

r ′ :

Radius of the truncated area, m

r c :

Radius of curvature, m

T h :

Thickness of the specimen, m

h c :

TCC between asperities, W/(m2⋅K)

H c :

TCC between contact surfaces, W/(m2⋅K)

q ̋ r :

Radial heat flux density, W/m2

R 1 :

Outer radius of hollow specimen B, mm

R 2 :

Radius of the key on specimen A, mm

T 1,2,3,4 :

Temperature of temperature measuring point c, d, e, f, ℃

a e :

Critical contact area of the elastic and the first elastic–plastic deformations, m2

a ep :

Critical contact area of the first elastic–plastic and the second elastic-second deformations, m2

a p :

Critical contact area of the second elastic–plastic and complete plastic deformations, m2

a ce :

Average contact area of the elastic deformations, m2

a cep1 :

Average contact area of the first elastic–plastic deformations, m2

a cep2 :

Average contact area of the second elastic–plastic deformations, m2

a cp :

Average contact area of the complete plastic area deformations, m2

F p :

Contact pressure of the whole contact surface under complete plastic deformation, MPa

F ep2 :

Contact pressure of the whole contact surface under second elastic–plastic deformation, MPa

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Funding

This work is financially supported by the General Program of National Natural Science Foundation of China (Grant No.51875093, Grant No.51105065), the Fundamental Research Funds for the Central Universities from Ministry of Education of China (Grant No. N180304017, Grant No. N2103020) and the National Science Foundation for Postdoctoral Scientists of China (Grant No.2014M551105, 2015T80269).

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Authors and Affiliations

  1. School of Mechanical Engineering and Automation, Northeastern University, Shenyang, Liaoning, 110819, China

    Changcheng Sun, Yungao Chen, Yahui Zhao, Yang Liu & Kunpeng Feng

Authors
  1. Changcheng Sun
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  2. Yungao Chen
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  3. Yahui Zhao
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  4. Yang Liu
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Contributions

All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by Changcheng Sun, Yungao Chen, Yahui Zhao, Yang Liu, Kunpeng Feng. The first draft of the manuscript was written by Changcheng Sun and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Correspondence to Yang Liu.

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Sun, C., Chen, Y., Zhao, Y. et al. Thermal contact conductance modeling of circular-arc contact surface with mutation area. Heat Mass Transfer 59, 461–475 (2023). https://doi.org/10.1007/s00231-022-03232-z

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