Loading–unloading contact analysis of a fractal rough surface with functional gradation

The present paper deals with a finite-element-based static loading–unloading analysis of a functionally graded rough surface contact with fractal characteristics. Two different gradation models, namely elastic and plastic gradations, are adopted. In these models, one out of yield strength and Young's modulus is varied spatially according to exponential functions, while the other is kept constant. In both these material models, separate inhomogeneity parameters control the variation of material properties. The gradation is such that throughout the top of the rough surface properties remain constant with variations in the depth direction being controlled by the above-mentioned parameters. Different fractal surfaces with different levels of roughness (governed by the values of fractal dimension and fractal roughness) have been analysed. The influence of the gradation parameters on the contact properties, viz. contact force, contact area, contact stress, etc., are investigated for both loading and unloading phases. It was found that for most of the loading phase, higher elastic, as well as plastic gradation parameter, causes higher contact force and contact area. However, in the case of the unloading of elastically graded surfaces, this trend is not maintained throughout. For the cases, where a substantial amount of yielding takes place during loading near the contact surface, the resulting contact area is found to be higher for the unloading phase in comparison with the same during the loading phase. The trend of plastic yielding at the vicinity of the contact surface is studied for varying gradation parameters. It is observed that the higher volume of yielded material is obtained for the higher value of elastic gradation parameter. On the other hand, the higher value of plastic gradation parameter causes more yielding to take place at the vicinity of the contact surface. Additionally, the effect of gradation on the energy dissipation due to plasticity after complete unloading is explored in detail.

Principles of discrete-event modeling of physical processes during technical surfaces contact interaction

The article discusses the advantages and disadvantages of computer modeling used in physical experiments field on rough surfaces contact interaction. Methods for constructing the software model are given. The description of a single irregularity in the form of revolution ellipsoid segment is presented and an algorithm for rough surface three-dimensional modeling based on it is proposed. Some assumptions made for generating surface topography do not significantly affect the simulation validity. Taking into account the individual parameters of each irregularity and the algorithm for their distribution make it possible to create inhomogeneous rough surfaces that are close to real ones relative to the physical experiments being carried out. The general principles of the software architecture and the data storage model of discrete-event modeling system of rough surface contact interaction are described. The developed software can be used for modeling the rough surfaces contact interaction, for researching of tribo-interface units’ parameters, predicting the characteristics of frictional interaction and tribotechnical tests computer simulation.

Evaluating Elastic-Plastic Wavy and Spherical Asperity-Based Statistical and Multi-Scale Rough Surface Contact Models with Deterministic Results

The solution to an elastic-plastic rough surface contact problem can be applied to phenomena such as friction and contact resistance. Many different types of models have therefore been developed to solve rough surface contact. A deterministic approach may accurately describe the entire surface, but the computing time is too long for practical use. Thus, mathematically abbreviated models have been developed to describe rough surface contact. Many popular models employ a statistical methodology to solve the contact problem, and they borrow the solution for spherical or parabolic contact to represent individual asperities. However, it is believed that a sinusoidal geometry may be a more realistic asperity representation. This has been applied to a newer version of the stacked multiscale model and statistical models. While no single model can accurately describe every contact problem better than any other, this work aims to help establish guidelines that determine the best model to solve a rough surface contact problem by applying mathematical and deterministic models to two reference surfaces in contact with a rigid flat. The discrepancies and similarities form the basis of those guidelines.

Elastic Rough Surface Contact and the Root Mean Square Slope of Measured Surfaces over Multiple Scales

This study investigates the predictions of the real contact area for perfectly elastic rough surfaces using a boundary element method (BEM). Sample surface measurements were used in the BEM to predict the real contact area as a function of load. The surfaces were normalized by the root-mean-square (RMS) slope to evaluate if contact area measurements would collapse onto one master curve. If so, this would confirm that the contact areas of manufactured, real measured surfaces are directly proportional to the root mean square slope and the applied load, which is predicted by fractal diffusion-based rough surface contact theory. The data predicts a complex response that deviates from this behavior. The variation in the RMS slope and the spectrum of the system related to the features in contact are further evaluated to illuminate why this property is seen in some types of surfaces and not others.

An Efficient Multi-Scale Modeling Method that Reveals Coupled Effects Between Surface Roughness and Roll-Stack Deformation in Cold Sheet Rolling

In thin-gauge cold rolling of metal sheet, the surface roughness of work-rolls is known to affect the rolled sheet surface morphology, the required rolling load, and the roll wear. While modeling of rough surfaces using statistical asperity theory has been widely applied to problems involving semi-infinite solids, the application of asperity distributions and their elastic-plastic behavior has not been considered in roll-stack models for cold sheet rolling. In this work, a simplified-mixed finite element method (SM-FEM) is combined with statistical elastic-plastic asperity theory to study contact interference and coupling effects between a rough work-roll surface and the roll-stack mechanics in cold sheet rolling. By mixing equivalent rough-surface contact foundations, Hertz foundations, and Timoshenko beam stiffness, an approach is created to efficiently model interactions between the micro-scale asperities and the macro-scale roll-stack deformation. Nonlinearities from elastic-plastic material behavior of the asperities and the sheet, as well as changing contact conditions along the roll length, are also accommodated. Performance of the multi-scale SM-FEM approach is made by comparison to a continuum finite element virtual material model. 3D studies for a 4-high mill reveal new multi-scale coupling behaviors, including non-uniform roughness transfer, and perturbations to the sheet thickness ‘crown’ and contact force profiles. The described multi-scale SM-FEM approach is general and applies to rough surface contact problems involving plates and shear-deformable beams having multiple contact interfaces and arbitrary surface profiles.

A stiffness model for bolted joints considering asperity interactions of rough surface contact

A revised fractal contact model considering asperity interactions is proposed. The displacement of mean of asperity heights is used to represent the effects of the asperity interactions. Then the critical contact area will be dependent on the contact load and the contact stiffness will be an integral whose integrand is an implicit expression. The fractal dimension and the fractal roughness are obtained by the measurement of surface profile to calculate the theoretical contact stiffness. The measurement of deformation is conducted to obtain the actual contact stiffness for verification, the results show that the proposed model is closer to the experimental results than other models without considering asperity interactions. Once the contact stiffness is determined, a new total normal stiffness model for bolted joints considering the contact of two rough surfaces is also proposed. Since the contact stiffness is dependent on the clamped force, the total normal stiffness for bolted joints is calculated iteratively at given initial preload and external separating force. Different from the classical model, the total normal stiffness for bolted joint decreases with the external separating force increases, and this stiffness loss will become larger with initial preload decreases. In this sense, the proposed total normal stiffness model is a way to determine the suitable initial preload for different sizes of bolts when the stiffness loss is restricted to a certain range.