Real Contact Area of Fractal-Regular Surfaces and Its Implications in the Law of Friction

2004 ◽  
Vol 126 (1) ◽  
pp. 1-8 ◽  
Author(s):  
Shao Wang
Keyword(s):  
Fractal Dimension ◽  
Contact Area ◽  
Hertzian Contact ◽  
Real Contact Area ◽  
Contact Ratio ◽  
Regular Surface ◽  
Fractal Surfaces ◽  
Linear Friction ◽  
Fractal Domains ◽  
Macroscopic Shape

The concept of a fractal-regular surface, with a dual-section power spectrum, has been implemented in an elastic-plastic contact analysis. Under certain assumptions, the analysis of individual fractal domains can be decoupled from that of the macroscopic shape. Due to the increase in the number of contacting fractal domains associated with a macroscopic contact expansion, the contact area-load relationship for fractal-regular surfaces is nearly linear, with a load exponent of 1-1.11, in contrast to 1-1.33 for fractal surfaces. Thus, the Amontons law of friction can be reasonably explained with fractal-regular surfaces under the assumption of a linear friction-area relationship. The distribution of the local real-to-apparent contact ratio in a nominally Hertzian contact was found to vary with the fractal dimension. The plastic contact ratio tends to be more uniformly distributed as the fractal dimension approaches unity.

A Microcontact Model Developed for Asperity Heights with a Variable Profile Fractal Dimension, A Surface Fractal Dimension, Topothesy, and Non-Gaussian Distribution

2009 ◽  
Vol 25 (1) ◽  
pp. 103-115
Author(s):  
J. L. Liou ◽  
J. F. Lin
Keyword(s):  
Fractal Dimension ◽  
Contact Area ◽  
Distribution Functions ◽  
Real Contact Area ◽  
Contact Deformation ◽  
Surface Fractal Dimension ◽  
Surface Fractal ◽  
Deformation Regime ◽  
The Mean ◽  
Non Gaussian

AbstractThe cross sections formed by the contact asperities of two rough surfaces at an interference are islandshaped, rather than having the commonly assumed circular contour. These island-shaped contact surface contours show fractal behavior with a profile fractal dimension Ds. The surface fractal dimension for the asperity heights is defined as D and the topothesy is defined as G. In the study of Mandelbrot, the relationship between D and Ds was given as D = Ds + 1 if these two fractal dimensions are obtained before contact deformation. In the present study, D, G, and Ds are considered to be varying with the mean separation (or the interference at the rough surface) between two contact surfaces. The D-Ds relationships for the contacts at the elastic, elastoplastic, and fully plastic deformations are derived and the inceptions of the elastoplastic deformation regime and the fully plastic deformation regime are redefined using the equality of two expressions established in two different ways for the number of contact spots (N). The contact parameters, including the total contact force and the real contact area, were evaluated when the size distribution functions (n) for the three deformation regimes were available. The results indicate that both the D and Ds parameters in these deformation regimes increased with increasing the mean separation (d*). The initial plasticity index before contact deformation (ψ)0 is also a factor of importance to the predictions of the contact load (F*t) and contact area (At*) between the model of variable D and G, non-Gaussian asperity heights and circular contact area and the present model of variable D and G, non-Gaussian asperity heights and fractal contact area.

scholarly journals Elastic-contact-based tool-path planning for free-form surface in belt grinding

2019 ◽  
Vol 11 (1) ◽  
pp. 168781401881992 ◽  
Author(s):  
Junde Qi ◽  
Bing Chen
Keyword(s):  
Path Planning ◽  
Contact Area ◽  
Tool Path ◽  
Hertzian Contact ◽  
Free Form ◽  
Real Contact Area ◽  
Elastic Contact ◽  
Tool Path Planning ◽  
Belt Grinding ◽  
Free Form Surface

As for the fact that the majority of current researches take the technology of tool-path planning for free-form surface only as a geometrical problem, which is not suitable for belt grinding because of the elastic deformation of the grinding belt that leads to a variable contact, in this article, the tool-path planning method for belt grinding is developed from the elastic contact point of view. Based on the Hertzian contact theory and taking the grinding force into consideration, a calculation method of the contact area between the belt and the workpiece is presented. Then, a tool-path planning model is presented based on the real contact area to meet the full coverage. In addition, an optimization model based on the constant scallop-height is further developed to meet the high form accuracy of the workpiece. First, a modified model for the material removal depth is developed based on the Preston equation. Then, according to the curvature of the contact surface, three situations are analyzed and the calculation methods of the tool-path interval are given. Finally, experiments on the simulation blade are conducted, and the experimental results show the effectiveness of the method in this article.

A Fractal Theory of the Temperature Distribution at Elastic Contacts of Fast Sliding Surfaces

1995 ◽  
Vol 117 (2) ◽  
pp. 203-214 ◽  
Author(s):  
S. Wang ◽  
K. Komvopoulos
Keyword(s):  
Fractal Dimension ◽  
Temperature Distribution ◽  
Contact Area ◽  
Temperature Rise ◽  
Maximum Temperature ◽  
Real Contact Area ◽  
The Real ◽  
Sliding Surfaces ◽  
Real Contact ◽  
Maximum Temperature Rise

The statistical temperature distribution at fast sliding interfaces is studied by characterizing the surfaces as fractals and considering elastic deformation of the asperities. The fractions of the real contact area in the slow, transitional, and fast sliding regimes are determined based on the microcontact size distribution. For a smooth surface in contact with a rough surface, the temperature rises at the real contact area are determined under the assumption that most of the frictional heat is transferred to one of the surfaces. The interfacial temperature rises are bounded by the maximum temperature rise at the largest microcontact when the fractal dimension is 1.5 or less, and are unbounded when it is greater than 1.5. Higher temperature rises occur at larger microcontacts when the fractal dimension is less than 1.5, and at smaller microcontacts when it is greater than 1.5. For a fractal dimension of 1.5, the maximum temperature rise at a microcontact is independent of its size. The maximum temperature rise at the largest microcontact is expressed as a function of the friction coefficient, sliding speed, elastic and thermal properties, real and apparent contact areas, and fractal parameters. The closed-form solutions for the distribution density function of the temperature rise can be used to calculate the fraction of the real contact area of fast sliding surfaces subjected to temperature rises in any given range. The present theory is applied to boundary-lubricated and dry sliding contacts to determine the fractions of the real contact area where lubricant degradation and thermal surface failure may occur.

Wear Mechanism of Ceramic Materials in Dry Rolling Friction

1986 ◽  
Vol 108 (4) ◽  
pp. 522-526 ◽  
Author(s):  
S. S. Kim ◽  
K. Kato ◽  
K. Hokkirigawa ◽  
H. Abe´
Keyword(s):  
Silicon Nitride ◽  
Wear Rate ◽  
Contact Area ◽  
Ceramic Materials ◽  
Rolling Friction ◽  
Bearing Steel ◽  
Rolling Contact ◽  
Hertzian Contact ◽  
Real Contact Area ◽  
Wear Process

Wear tests in dry rolling contact were carried out at room temperature on five ceramic materials, such as silicon nitride, silicon carbide, cermet, titania, and alumina. The results showed that wear rate of silicon nitride was smaller than any of the other ceramic materials and bearing steel. Observations of worn surface and wear debris revealed that ceramic materials have two types of wear, one related to real contact area and another related to Hertzian contact area. It was also found that brittle fracture dominates the wear process of ceramic materials in dry rolling contact. Based on the experimental results, wear rate of ceramic materials was expressed with a new nondimensional parameter.

Multiscale Simulation to Determine Rubber Friction on Asphalt Surfaces

2016 ◽  
Vol 44 (4) ◽  
pp. 226-247 ◽  
Author(s):  
Korbinian Falk ◽  
Ronny Lang ◽  
Michael Kaliske
Keyword(s):  
Contact Pressure ◽  
Contact Area ◽  
Bulk Material ◽  
Multiscale Simulation ◽  
Real Contact Area ◽  
The Road ◽  
Real Contact ◽  
Rubber Friction ◽  
Linear Friction ◽  
Mechanical Approach

ABSTRACT The interaction between rubber and asphalt pavement depends on the roughness characteristics of the road surface, as well as the contact pressure, slip velocity, and temperature. A homogenization procedure of rubber friction, based on the finite element method, is presented, in order to gain surface dependent friction properties by numerical simulation. Furthermore, the method allows a deep insight into microscale phenomena, like real contact area, microscopic contact pressure, or flash temperature. Rubber undergoes large deformations in contact with rough surfaces. Therefore, the material characteristics of rubber need to be modeled by hyperelasticity and viscoelasticity at finite deformations and dependent on temperature. Thus, hysteresis friction, originating in energy dissipation of the bulk material, i.e., the viscoelastic properties, is evaluated. Adhesion friction is a phenomenon associated with the real contact area and is included in the proposed methodology by a physically motivated, fracture mechanical approach. The resulting macroscopic friction features are validated by experiments based on a linear friction tester. Analytical state of the art solutions are compared with the numerical results.

scholarly journals Modeling of the Loading–Unloading Contact of Two Cylindrical Rough Surfaces with Friction

2020 ◽  
Vol 10 (3) ◽  
pp. 742 ◽  
Author(s):  
Honghai Wang ◽  
Peng Jia ◽  
Liquan Wang ◽  
Feihong Yun ◽  
Gang Wang ◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Contact Area ◽  
Fractal Model ◽  
Contact Load ◽  
Real Contact Area ◽  
Curvature Radius ◽  
Real Contact ◽  
Deformation Stages ◽  
Nonlinear Relation ◽  
Loading And Unloading

The first fractal model for the loading–unloading process between two cylindrical surfaces with friction is presented. The nonlinear relation between the real contact area and the contact load in different deformation stages are deduced for a load–unload cycle. The impacts of parameters in the model are discussed. The numerical results show that for a given dimensionless contact load, the dimensionless real contact area of the loading–unloading process of cylindrical contact surface with friction, as well as the differences of the dimensionless real contact area between the loading and unloading processes, increase with the increase of the loading interference and fractal dimension, decrease of the profile scaling parameter and curvature radius, or the substitution of external contact for internal contact.

Effect of normal load on the frictional and wear behaviour of carbon fiber in tow-on-tool contact during three-dimensional weaving process

2020 ◽  
pp. 152808372094461
Author(s):  
Ning Wu ◽  
Ximing Xie ◽  
Jie Yang ◽  
Yajie Feng ◽  
Yanan Jiao ◽  
...  
Keyword(s):  
Carbon Fiber ◽  
Contact Area ◽  
Normal Load ◽  
Three Dimensional ◽  
Hertzian Contact ◽  
Wear Behaviour ◽  
Real Contact Area ◽  
The Real ◽  
Real Contact ◽  
Fracture Damage

The effect of normal load on the frictional and wear behaviour of carbon fiber is investigated by simulating the tow-on-tool friction relevant to the beating-up motion of three-dimensional (3 D) weaving process. The true number of contact filaments over a range of normal loads is calculated by characterizing the cross-section parameters of carbon tow. The real contact area is calculated on the basis of the filaments amount by Hertzian contact model. The friction force values obtained from multiplying the real contact area with shear strength are closely with the measured results. The coefficient of friction increases with the increase of normal loads. When the normal load is 250, 400 and 600 mN, the tensile loss rate of the carbon tow after friction test is 6.3%, 23.2% and 42.4% respectively. The filaments reveal multiple fracture damage patterns which are caused by stretching, shearing and compression during the weaving process.

Measurement of real contact area under Hertzian contact using sputtered thin film

2019 ◽  
Vol 2019.27 (0) ◽  
pp. 711
Author(s):  
Yoshiki Shionoya ◽  
Takahisa kawaguchi ◽  
Yoshimasa Takayama
Keyword(s):  
Thin Film ◽  
Contact Area ◽  
Hertzian Contact ◽  
Real Contact Area ◽  
Real Contact

An Analytical Thermodynamic Approach to Friction of Rubber on Ice

2012 ◽  
Vol 40 (2) ◽  
pp. 124-150
Author(s):  
Klaus Wiese ◽  
Thiemo M. Kessel ◽  
Reinhard Mundl ◽  
Burkhard Wies
Keyword(s):  
Coefficient Of Friction ◽  
Liquid Layer ◽  
Contact Area ◽  
Leading Edge ◽  
Viscous Friction ◽  
Analytical Approximation ◽  
Real Contact Area ◽  
Length Scales ◽  
Real Contact ◽  
Ice Surface

ABSTRACT The presented investigation is motivated by the need for performance improvement in winter tires, based on the idea of innovative “functional” surfaces. Current tread design features focus on macroscopic length scales. The potential of microscopic surface effects for friction on wintery roads has not been considered extensively yet. We limit our considerations to length scales for which rubber is rough, in contrast to a perfectly smooth ice surface. Therefore we assume that the only source of frictional forces is the viscosity of a sheared intermediate thin liquid layer of melted ice. Rubber hysteresis and adhesion effects are considered to be negligible. The height of the liquid layer is driven by an equilibrium between the heat built up by viscous friction, energy consumption for phase transition between ice and water, and heat flow into the cold underlying ice. In addition, the microscopic “squeeze-out” phenomena of melted water resulting from rubber asperities are also taken into consideration. The size and microscopic real contact area of these asperities are derived from roughness parameters of the free rubber surface using Greenwood-Williamson contact theory and compared with the measured real contact area. The derived one-dimensional differential equation for the height of an averaged liquid layer is solved for stationary sliding by a piecewise analytical approximation. The frictional shear forces are deduced and integrated over the whole macroscopic contact area to result in a global coefficient of friction. The boundary condition at the leading edge of the contact area is prescribed by the height of a “quasi-liquid layer,” which already exists on the “free” ice surface. It turns out that this approach meets the measured coefficient of friction in the laboratory. More precisely, the calculated dependencies of the friction coefficient on ice temperature, sliding speed, and contact pressure are confirmed by measurements of a simple rubber block sample on artificial ice in the laboratory.

scholarly journals Improved design criterion for frictionally engaged contacts in overrunning clutches

2021 ◽  
Author(s):  
Nadine Nagler ◽  
Armin Lohrengel
Keyword(s):  
Design Process ◽  
Contact Area ◽  
Axial Load ◽  
State Of The Art ◽  
Tangential Force ◽  
Design Criterion ◽  
Hertzian Contact ◽  
Loss Of Function ◽  
Axial Loads ◽  
Improved Design

AbstractOverrunning clutches, also known as freewheel clutches, are frictionally engaged, directional clutches; they transmit torque depending on the Freewheel clutch rings’ rotation directions. The torque causes a tangential force in the Hertzian contact area. The hitherto “state-of-the-art design criterion” bases on this load situation. In practice, axial loads additionally act on the frictionally engaged Hertzian contact area. This additional axial load can cause the loss of the friction connection and so the freewheel clutch slips. This publication presents an improved design criterion for frictionally engaged contacts in freewheel clutches. It allows to consider tangential as well as axial loads during the design process. Additionally, it offers the possibility to estimate the probability of frictional engagement loss and gross slip based on the freewheel clutch’s application scenario. This publication points out how to use the improved design criterion to design freewheel clutches that are more robust against a loss of function.

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