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Research Papers: Hydrodynamic Lubrication

Tangential Damping and its Dissipation Factor Models of Joint Interfaces Based on Fractal Theory With Simulations

[+] Author and Article Information
Xueliang Zhang

e-mail: zhang_xue_l@sina.com

Nanshan Wang

e-mail: tyus2012@163.com

Guosheng Lan

e-mail: yjsxylgs@163.com

Shuhua Wen

e-mail: kd_wsh@sina.com

Yonghui Chen

e-mail: cyh9672@sohu.com
School of Mechanical Engineering,
Taiyuan University of Science and Technology,
Taiyuan, Shanxi 030024, China

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received October 26, 2012; final manuscript received August 24, 2013; published online November 7, 2013. Assoc. Editor: Dong Zhu.

J. Tribol 136(1), 011704 (Nov 07, 2013) (10 pages) Paper No: TRIB-12-1190; doi: 10.1115/1.4025548 History: Received October 26, 2012; Revised August 24, 2013

Based on contact fractal theory, a modified MB fractal model, and from the energy dissipation point and considering the mechanism of energy dissipation of joint interfaces, tangential damping and its dissipation factor models of joint interfaces are proposed. Numerical simulations reveal the varying relations of tangential damping and its dissipation factor versus corresponding parameters such as fractal dimension, fractal roughness, friction factor, and plastic index. A micro convex nonlinear relation (when fractal dimension is between 1.1 and 1.4) or near linear relation(when fractal dimension is between 1.4 and 1.9) between dimensionless tangential damping and dimensionless normal contact force over the joint interfaces varies with the fractal dimension of the surface profiles, dimensionless tangential damping increases(when fractal dimension is between 1.1 and 1.7) or decreases (when fractal dimension is between 1.7 and 1.9) with the increment of fractal dimension, and decreases with the increase of dimensionless fractal roughness. While the influences of plastic index, the ratio of hardness to yield strength, and the ratio of total tangential force to total normal force on dimensionless tangential damping are similar, and a concave nonlinear relation between tangential damping dissipation factor and the normal contact force over the joint interfaces, the tangential damping dissipation factor, meanwhile, decreases with the increment of the friction factor. In addition, the validation of the tangential contact damping model is implemented in indirect ways, which make comparison between the proposed tangential stiffness model and the literature.

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Figures

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Fig. 1

Three states of an equivalent spherical asperity in contact with a rigid flat surface: (a) inception of equivalent spherical asperity in contact with flat rigid surface but not subjected to any forces, (b) equivalent spherical asperity is only subjected to a normal force p, and (c) equivalent spherical asperity is subjected to a normal force p and a tangential force t

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Fig. 2

Qualitative description of statistical self-affinity for a surface profile

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Fig. 3

A rough surface 1 with spherical asperities in contact with a rigid flat surface 2

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Fig. 4

Change of dimensionless total tangential damping Ct* with dimensionless total force P* and the influence of fractal Dimension D on dimensionless total tangential damping Ct* over the whole joint interface for different fractal dimension D ((a) D = 1.1 ∼ 1.4, (b) D = 1.4 ∼ 1.9) on the condition of the given parameters of parentheses (k = 1.0,φ = 1.0,G* = 1.0 × 10-10,T/P = 1.0 × 10-5,μ = 0.25)

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Fig. 5

Influence of dimensionless roughness G* on dimensionless total tangential damping Ct* on the condition of the given parameters of parentheses (k = 1.0,φ = 1.5,T/P = 1.0 × 10-5,μ = 0.25) and the representative fractal dimension D ((a) D = 1.3 and (b) D = 1.7)

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Fig. 6

Influence of parameter k on dimensionless total tangential damping Ct* on the condition of the given parameters of parentheses (φ = 1.0,G* = 1.0×10-10,T/P = 1.0×10-5,μ = 0.25) and the representative fractal dimension D ((a) D = 1.3 and (b) D = 1.7)

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Fig. 7

Influence of plastic index φ on dimensionless total tangential damping Ct* on the condition of the given parameters of parentheses (k = 1.0,G* = 1.0 × 10-10,T/P = 1.0 × 10-5,μ = 0.25) and the representative fractal dimension D ((a) D = 1.3 and (b) D = 1.7)

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Fig. 8

Influence of the ratio of total tangential force T to total normal force P on dimensionless total tangential damping Ct* on the condition of the given parameters of parentheses (k = 1.0,φ = 1.5,G* = 1.0 × 10-10,μ = 0.25) and the representative fractal dimension D ((a) D = 1.3 and (b) D = 1.7)

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Fig. 9

Change of tangential contact damping dissipation factor η with total normal force P over the whole joint interfaces on the condition of the given parameters of parentheses (k = 1.0,φ = 1.5,G* = 1.0 × 10-10,T = 2.0×10-5N,μ = 0.25)

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Fig. 10

Influence of different tangential force T on tangential contact damping dissipation factor η on the condition of the given parameters of parentheses (k = 1.0,φ = 1.5,G* = 1.0 × 10-10,μ = 0.25)

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Fig. 11

Influence of different friction factor μ on tangential contact damping dissipation factor η on the condition of the given parameters of parentheses (k = 1.0,φ = 1.5,G* = 1.0 × 10-10,T = 2.0 × 10-5N)

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Fig. 12

Change of dimensionless total tangential stiffness Kt* with dimensionless total force P* over the whole joint interface for different fractal dimension D ((a) D = 1.2∼1.4, (b) D = 1.6∼1.8) between our model and the one given in the literature [36] on the condition of the given parameters of parentheses (k = 1.0,φ = 1.0,G* = 1.0 × 10-10,T/P = 1.0 × 10-5,μ = 0.25)

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