Rough surface contact under creep conditions

Purpose – The purpose of this paper is to construct a continuous time series model to study the thermal creep of rough surfaces in contact.Design/methodology/approach – For normal loading, the contact between rough surfaces can often be modeled as the contact of an effective surface with a rigid fiat surface. A solution for the deformation of such equivalent surface, generated using fractal geometry, can be modified. However, in this study only the case of a single rough surface in contact with a rigid flat surface is considered. In the interface, the material is assumed to follow the idealized constitutive viscoelastic standard linear solid (SLS) model. Fractal geometry, through Cantor set theory, is utilized to model the roughness of the surface.Findings – An asymptotic time series power law is obtained, which associates the creep load, the buck temperature and the creep of the fractal surface.Originality/value – This law is only valid as long as the creep is of the size of the surface roughness. The mo...

Any engineering component possesses roughness on its surface when it is observed microscopically, including electrical connectors. Electrical connectors usually consist of a spring and a pin. In this study, the spring part is in the shape of a compliant curved beam whereas the pin one is of a flat form and these two parts are in contact during operation. This work presents a multi-physics (structural, electrical and thermal) finite element model of the bulk region of an electrical connector. The rough surfaces of the spring and pin parts are considered using a multi-scale sinusoidal rough surface (MSRS) contact model. The resulting coupled multi-physics connector model is used to analyze the performance of the connector while the applied current is incremented from 5 to 20 A. As expected, this produced a proportional rise in voltage drop and temperature across the bulk regions of the connector parts. The coupled multi-physics model together with the MSRS model should provide greater accuracy in the prediction of contact forces, electrical contact resistance (ECR) and thermal contact resistance (TCR). The present work also provides valuable information on stresses and strains distributions, current flow and temperature variations in the bulk regions of the electrical connector.

Ultrasonic determination of normal and shear interface stiffness and the effect of Poisson's ratio

Purpose – This work aims at constructing a continuous mathematical, linear elastic, model for the thermal contact conductance (TCC) of two rough surfaces in contact. Design/methodology/approach – The rough surfaces, known to be physical fractal, are modelled using a deterministic Cantor structure. Such structure shows several levels of imperfections and including, therefore, several scales in the constriction of the flux lines. The proposed model will study the effect of the deformation (approach) of the two rough surfaces on the TCC as a function of the remotely applied load. Findings – An asymptotic power law, derived using approximate iterative relations, is used to express the area of contact and, consequently, the thermal conductance as a function of the applied load. The model is valid only when the approach of the two surface in contact is of the order of the surface roughness. The results obtained using this model, which admits closed form solution, are displayed graphically for selected values of the system parameters; the fractal surface roughness and various material properties. The obtained results showed good agreement with published experimental results both in trend and the numerical values. Originality/value – The model obtained provides further insight into the effect that surface texture has on the heat conductance process. The proposed model could be used to conduct an analytical investigation of the thermal conductance of rough surfaces in contact. This model, although simple (composed of springs), nevertheless works well.

An improved mathematical elastic–plastic model for the contact of rough surfaces that is based on an accurate finite element solution of a deformable single asperity and a rigid flat surface is developed to provide dimensionless expressions for the contact area and contact load. This model differs from the existing models, in that it accounts for the level of interference beyond expected failure. The finite element solution is used to define the limits at which failure occurs. A fictitious ultimate‐stress asperity is introduced to facilitate the derivation of the contact model. This model considers a realistic picture of elastic–plastic deformation where elastic, plastic and failure behaviors can occur simultaneously for an asperity. Subsequent comparison of the results for estimating contact area and load using the present model and the earlier methods shows identical results for pure elastic contacts with plasticity index values at about 0.5 but substantial difference for the net elastic–plastic contacts having plasticity index values above 0.8. When plasticity index reaches 6 and beyond, the three models predict similar total contact area and load values and that the contact is purely plastic. Copyright © 2008 John Wiley & Sons, Ltd.

In previous work it was shown that some functionalized polymers used as viscosity index improvers are able to form thick boundary lubricating films. This behavior results from adsorption of the polymer on metal surfaces to form a layer of enhanced viscosity adjacent to the surface. In the current work the behavior of one such polymer in rough surface contact conditions is studied, using both model and real rough surfaces. It is found that the polymer is able to form a thick boundary film in rough surface contact, just as it does with smooth surfaces. It is also shown that the effect of this boundary film is to significantly reduce friction in rolling-sliding, rough surface, lubricated contact.

Contact of rough surfaces: A simple model for elasticity, conductivity and cross-property connections

A full-scale 3-D dynamic finite element (FE) model is created to solve the elastic-plastic wheel-rail rolling contact over rough surfaces under different friction forces. Both normal and tangential loads are applied properly. A bi-linear plastic material model is introduced and the real wheel and rail head geometries are simulated. The rolling of a drive wheel with full friction exploitation over a rough contact surface is analyzed in this paper. The stress distributions at the zone with rough surface are derived. From the results at a selected instant, it is found that roughness significantly increases the stress level of the surface layer. Furthermore, plasticity can greatly reduce stress peaks and change stress distributions. The maximum shear stress distribution at the rough surface is also analyzed to assess effects of roughness on fatigue crack initiation.

A numerical simulation technique is used to study contact between rough surfaces, allowing for the onset of plasticity at individual asperities. The model treats rough surfaces as anisotropic random processes, with Gaussian height distributions and Gaussian correlation functions. The simulation technique is combined with an iterative method for determining the final surface contact state for a specified applied load. This leads to the explicit calculation of all the contact areas for individual rough surfaces. From this, the authors obtain information on not only the average values for contact parameters such as the number of contact regions, surface separation and true contact area, but also on the fluctuations expected in these quantities because of the statistical nature of rough surface contact. Results from the model are compared with the predictions of a purely elastic model, showing how allowing for the onset of plasticity principally affects the number and size of the contact areas. The effects of strong surface anisotropy on contact parameters are also presented, showing the effects to be generally small in the mixed elastic-plastic regime, because of competing effects within plasticity. The conventional plasticity index is determined for the parameters used in the model calculations, confirming that the model predictions agree with this index as a definition of the average extent of elastic and plastic contact. The model may be used to calculate the friction coefficient for any contact state, assuming adhesion to be the only friction mechanism present. Sample results are compared with experimental friction measurements, showing that the incorporation of plasticity improves agreement between theory and experiment.

Functionally graded surface has been a domain of research interest due to its use in various technologically advanced applications. The work focuses on static and dynamic analysis of rough fractal surface with exponentially graded material properties. The rough fractal surface is modeled in ANSYS with the coordinate points generated using the two variable modified Weierstrass–Mandelbrot function. Material gradation is applied to the rough surface model in such a way that, for any value of the gradation or inhomogeneity parameter, material properties at the top of the rough surface always remain constant. Force–displacement behavior of the fractal surface in contact with a rigid flat surface is determined through finite element simulation. A parameter representing the nonlinearity of the system is extracted from the force–displacement plot. It is found that higher is the inhomogeneity parameter, higher is the nonlinearity of the system. Furthermore, for a certain change in inhomogeneity parameter, the change in nonlinearity is higher for rougher topography. The dynamic contact system is found to be softening in nature, and the softening nature increases with higher inhomogeneity parameter. The phase plot of the vibrating contact system becomes more asymmetric with respect to the velocity axis for higher value of inhomogeneity parameter.

A novel multiscale finite-element method to investigate the elastic contact of two-dimensional rough surfaces is presented. The aim of the method is to find the microscopic curve that describes the deformed shape of a solid with a smooth boundary surface in frictionless contact with a rigid rough surface. In addition, the real contact area is studied through the surface deformation. The contact traction on the contact surface and the maximum shear stress around the contact region are analyzed. This method is based on the variational inequality approach for solving the elastic frictionless contact problem. The strategy is to separate a small slice within the contact region and solve it as an independent system. Then the contact traction is obtained through iterations between the solution of the independent small slice and the solution of the total solid body. We observe a much higher pressure than the result of Hertz theory around the asperities. The main conclusions are (1)~the actual contact area and surface traction are dependent on the wavelength and amplitude of the surface roughness, (2) there is a much higher pressure around the asperities than predicted by Hertz theory, and (3) the location of maximum shear stress tends to be shifted toward the surface as compared with the case of smooth-surface contact. The method has the potential to be extended to solve three-dimensional rough contact problems.PACS Nos.: 03.40.D, 46.30.P, 62.20.P

In this paper simulation results of interaction between a biomimetic gecko adhesion array and rough contact surface are shown. First, the biomimetic gecko adhesion array with active control ability is proposed in brief. Then based on liner beam theory, the stress analysis of a single spatulae and the two dynamic procedures including dynamic contact and detached procedure are presented. And according to the height distribution of rough surface, theoretical models of two procedures are derived, which describes the interaction force between the biomimetic gecko adhesion array and rough surface. Finally based on proper choice of parameter, the simulation relational results of interaction force versus separation distance, preload, and separation angle in dynamic contact and detached procedure are shown and discussed in detail.

Persson’s theory of purely normal elastic rough surface contact: A tutorial based on stochastic process theory

Elastohydrodynamic lubrication is a type of lubrication which most machine elements such as bearings operate. Density changes, thermal and surface roughness effects are also key factors in bearings, working under heavy loads and high speeds. Previous research has focused on smooth surfaces where density and thermal effects have been neglected. The present study intends to model the effect of surface roughness and density on thermal elastohydrodynamic lubrication for sliding-rolling bearing using non-Newtonian lubricant. The surface roughness is incorporated into the film thickness equation while the non-Newtonian nature of the lubricant is incorporated into the Reynolds and energy equation by using the Eyring model. The changes in compressibility of the lubricant is given by the lubricant’s density equation. The energy equation is solved simultaneously with the Reynolds-Eyring equation, film thickness, density and viscosity of lubricant equations. The equations are then discretized using the finite difference numerical method and are solved simultaneously in Matlab together with their boundary conditions. It is noted that an increase in surface roughness results to a reduction in the film thickness and an increase in both temperature and pressure. Increase in temperature lowers the density of the lubricant while increase in pressure leads to an increase in density. It is also noted that an increase in the density of the lubricant leads to an increase in the film thickness. The temperature profile shows that as the load in the bearing is increased, the temperature of the lubricant also increases.

Phenomenological models reproducing the elasticity and acoustic properties of geomaterials and materials with damage have been successfully developed. These models yield macroscopic stress–strain constitutive equations featuring hysteresis with end-point memory, and predict the efficient generation of higher harmonics accompanying the propagation of monochromatic waves. The assumption common to these models is that the material’s microstructure is characterized by nonlinear compliant components of an unspecified nature which can exist in two states: “open” or “closed.” The density of the compliant units is defined on a mathematical continuum (the Preisach–Mayergoyz space) whose elements identify the dynamic behavior of the components. In this work, adhesion is shown to introduce hysteresis with end-point memory in the macroscopic behavior of an interface between two rough surfaces in contact, and, upon scattering, to generate higher harmonics bearing a striking similarity to those observed in wave propagation phenomena in media with distributed damage and in geomaterials. It appears, therefore, that two rough surfaces interacting via adhesion forces offer a meaningful example of macroscopic interface or bond with dynamics resembling that of the fictitious elements of the Preisach–Mayergoyz space, and acoustic nonlinear properties similar to those of rocks and damaged materials.