n -Point Asperity Model for Contact Between Nominally Flat Surfaces

Abstract

For several decades, asperities of nominally flat rough surfaces were considered to be points higher than their immediate neighbors. Recently, it has been recognized that this model is incorrect. To address the issue, a new multiple-point asperity model, called the n-point asperity model, is introduced in this paper. In the new model, asperities are composed of n neighboring sampled points with n-2 middle points being above a certain level. When the separation between two surfaces decreases, new asperities with higher number of sample points, n, will come into existence. Based on the above model, the height and curvature of n-point asperities are defined and their distributions are found. The model is developed for Gaussian surfaces and for the general case of an autocorrelation function (ACF). As a case study, the exponential ACF is applied to the new model, which is shown to produce remarkably good agreement with measurements from real and simulated surfaces.

Adhesive Friction Based on Accurate Elastic-Plastic Finite Element Analysis and n-Point Asperity Concept

“…Measured or practical values of standard deviation of height ordinates, correlation length, and correlation coefficient can be incorporated in the pdf and ACF to predict existence of n-point asperity topography on the surface. The concept of existence of an n-point asperity can be clearly understood from As per the definition (Hariri, Zu, and Ben Mrad [17]), an n-point asperity is said to exist above a certain level from the mean line of surface profile when out of total 'n' consecutive peak ordinates, middle (n-2) ordinates are above the level and end two ordinates are below the level. As can be seen in the figure 2, the rigid smooth surface is at a level of ' 'h from the mean line of rough surface profile and is interfering with the part of rough surface profile.…”

“…For the simplification of the problem, it is considered that each height ordinate follows Gaussian distribution. So the resultant joint pdf will also follow Gaussian distribution and as given by Hariri et al [17], for exponential autocorrelation function with correlation coefficient ) ( , it is given as …”

“…They suggested considering asperities as protuberances on protuberances on protuberances which was originally proposed by Archard [25]. Hariri, Zu, and Ben Mrad [17] used Archard's concept for definition of their asperity but with some modification. They used straight line segments to connect the consecutive height ordinates and obtained rough surface profile.…”

“…So it necessitates assigning equivalent single height and curvature to each n-point asperity. For this purpose, Hariri, Zu, and Ben Mrad [17] replaced the poly line form of an n-point asperity with an equivalent parabolic form which is shown as dotted line curve in the figure 2. The equivalent parabolic curve passes through the first and the last points and also through a middle imaginary point whose ordinate is given by 0 z (called equivalent asperity height).…”

“…[24], Archard [25], and Hariri et al [17]. In conventional model like GW, the asperities are defined as peaks having hemispherical tips.…”