A Contact Mechanics Model for Rough Surfaces Based on a New Fractal Characterization Method

Abstract

There are mainly two kinds of contact mechanics models for rough surfaces. One is based on the statistical characteristic parameters and depends on the measurement scale of rough surface topography. The other is based on the fractal parameters, which is independent of the measurement scale. However, most of the contact models for rough surfaces based on fractal theory use the size that is corresponding to the contact area of an asperity or the sample length as the base diameter of an asperity to describe the initial profile of asperities. As a result, the obtained deformation mechanism of asperities is not correct. To solve this problem, a new fractal characterization method for rough surfaces based on the fractal dimension [Formula: see text], fractal roughness [Formula: see text] and the highest asperity height is proposed, and then a fractal contact model independent of the measurement scale is established. The contact mechanism of asperities and variation trends of the real contact area and contact stiffness are discussed. When the contact pressure of the rough surface is less than its yield strength, its normal contact stiffness can be expressed as the first derivative of the contact pressure versus the normal compression, regardless of the deformation forms of asperities.

Review about the Application of Fractal Theory in the Research of Packaging Materials

“…Mandelbrot proposed the concept of fractal in 1975, which refers to the graph, phenomenon, or process with self-similarity [ 1 ]. Fractal objects generally exist in nature, such as curved coastline, rough surface, and so on [ 2 , 3 ]. At present, fractal theory has been extensively used in natural science, engineering technology, social culture, and other fields [ 4 , 5 , 6 , 7 ].…”

Normal fractal contact stiffness model among three disks of rod-fastening rotor system with considering friction and the asperities interaction

“…Morag and Etsion (2007) provided a revised MB model which showed the critical contact area of an asperity is scale dependent and related to the length scale (base diameter) of an asperity, and this modification makes the transition from elastic to plastic mode coincide with classical contact mechanics for an asperity. Sun et al (2018) presented a contact mechanics model and normal stiffness model which are related to the base diameter of each asperity and the elastoplastic contact regime is also considered. Yuan et al (2017) and Xu et al (2019) presented the size distribution of each level asperity and developed a revised elastoplastic contact stiffness model of rough surfaces based on MB model.…”

“…Most of their contact stiffness models are based mainly on the mechanisms of elastic deformation. Actually, the mechanisms of elastic deformation, plastic deformation and elastoplastic transition deformation exist at the same time (Kogut and Etsion, 2002;Jackson and Green, 2005;Lin and Lin, 2005;Zhao et al, 2007;Yuan et al, 2017;Sun et al, 2018;Wei et al, 2020).…”

“…It can be known that some of them, such as Morag and Etsion (2007), Sun et al (2018) and Chen et al (2016), improved the original fractal model by reflecting the scale dependence of contact parameters with the length of base diameter of asperities. Some of them, such as Liu et al (2015), Chen et al (2016) and Guan et al (2018a), considered the effects of friction coefficient on the normal fractal contact stiffness model.…”

“…Some of them (Zhao and Chang, 2001;Ciavarella et al, 2008;Buczkowski, 2014;Wang et al, 2017) considered the effects of asperities interactions. Some of them (Kogut and Etsion, 2002;Jackson and Green, 2005;Lin and Lin, 2005;Zhao et al, 2007;Yuan et al, 2017;Sun et al, 2018) considered the elastoplastic contact stage besides the elastic contact regime. Some of them (Yang et al, 2019) considered both elastoplastic contact regime and friction effects.…”