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Research Papers

# A Microcontact Non-Gaussian Surface Roughness Model Accounting for Elastic Recovery

[+] Author and Article Information
Jeng Luen Liou

Department of Aircraft Engineering, Air Force Institute of Technology, Kaohsiung, 820, Taiwan ROC

Jen Fin Lin1

Department of Mechanical Engineering, National Cheng Kung University, Tainan, 701, Taiwan ROCjflin@mail.ncku.edu.tw

1

Corresponding author.

J. Appl. Mech 75(3), 031015 (May 01, 2008) (13 pages) doi:10.1115/1.2840043 History: Received October 15, 2006; Revised August 09, 2007; Published May 01, 2008

## Abstract

Most statistical contact analyses assume that asperity height distributions $(g(z*))$ follow a Gaussian distribution. However, engineered surfaces are frequently non-Gaussian with the type dependent on the material and surface state being evaluated. When two rough surfaces experience contact deformations, the original topography of the surfaces varies with different loads, and the deformed topography of the surfaces after unloading and elastic recovery is quite different from surface contacts under a constant load. A theoretical method is proposed in the present study to discuss the variations of the topography of the surfaces for two contact conditions. The first kind of topography is obtained during the contact of two surfaces under a normal load. The second kind of topography is obtained from a rough contact surface after elastic recovery. The profile of the probability density function is quite sharp and has a large peak value if it is obtained from the surface contacts under a normal load. The profile of the probability density function defined for the contact surface after elastic recovery is quite close to the profile before experiencing contact deformations if the plasticity index is a small value. However, the probability density function for the contact surface after elastic recovery is closer to that shown in the contacts under a normal load if a large initial plasticity index is assumed. How skewness (Sk) and kurtosis (Kt), which are the parameters in the probability density function, are affected by a change in the dimensionless contact load, the initial skewness (the initial kurtosis is fixed in this study) or the initial plasticity index of the rough surface is also discussed on the basis of the topography models mentioned above. The behavior of the contact parameters exhibited in the model of the invariant probability density function is different from the behavior exhibited in the present model.

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## Figures

Figure 8

Variations of the dimensionless total contact area with the dimensionless contact load. They are presented based on different skewness and kurtosis values before the roughness surface contacts. (a) Probability density functions g(z*) are invariant. (b) Probability density functions g(z*) are varied with dimensionless mean separation d*.

Figure 7

Variations of the dimensionless contact load with the dimensionless mean surface separation. They are presented based on different skewness and kurtosis values before the roughness surface contacts. (a) Probability density functions g(z*) are invariant. (b) Probability density functions g(z*) are varied with dimensionless mean separation d*. The initial plasticity indices used in the evaluation were 0.5 and 2.0, respectively.

Figure 6

Variations of (a) the skewness (Sk) and (b) the kurtosis (Kt) with the dimensionless contact load for the contact surfaces after completing the elastic recovery. These data were evaluated by changing the initial skewness (Sk0) only; the initial kurtosis (Kt0) was fixed at 3, and the initial plasticity indices used in the evaluation were 0.5 and 2.0, respectively.

Figure 5

Variations of (a) the skewness (Sk) and (b) the kurtosis (Kt) with the dimensionless contact load for the contact surfaces under a constant normal load. These data were evaluated by changing the initial skewness (Sk0) only; the initial kurtosis (Kt0) was fixed at 3.

Figure 4

The probability density functions evaluated at different mean separations for (a) the surface contacts under a normal load; (b) the rough contact surface with a plasticity index of 0.5, which is obtained after elastic recovery; and (c) the rough contact surface with a plasticity index of 2.0, which is obtained after elastic recovery

Figure 3

(a) The probability density functions of surface asperities before contact deformation. The initial plasticity indices are ψ0=0.5 and ψ0=2.0, respectively. The filled-in areas indicate the “strain energy” available for the elastic recovery of the rough surface after finishing the unloading process. (b) Variations of the probability density function for the surface contacts under a normal load and the rough contact surface after elastic recovery. The initial plasticity indices are also 0.5 and 2.0, respectively.

Figure 2

Flowchart for the numerical analyses of Sku and Ktu

Figure 1

The schematic diagram of two contact surfaces with deformations

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