Shuangbiao Liu

A versatile method of discrete convolution and FFT (DC-FFT) for contact analyses

The fast Fourier transform (FFT) technology has been introduced into the process of contact analyses. However, a problem may occur at the borders of the domain due to a periodic error involved. In order to obtain reasonable results, an expedient treatment requires a computational physical domain much larger than the target domain at the cost of calculation efficiency. This paper studies the source of the error and investigates the methods that can help avoid this error and improve the efficiency. Discrete convolution and FFT (DC-FFT) is first adopted instead of the method of continuous convolution and Fourier transform for the contact problems. A few approaches based on the DC-FFT method are presented and numerical results are compared.

Studying Contact Stress Fields Caused by Surface Tractions With a Discrete Convolution and Fast Fourier Transform Algorithm

The knowledge of contact stresses is critical to the design of a tribological element. It is necessary to keep improving contact models and develop efficient numerical methods for contact studies, particularly for the analysis involving coated bodies with rough surfaces. The fast Fourier Transform technique is likely to play an important role in contact analyses. It has been shown that the accuracy in an algorithm with the fast Fourier Transform is closely related to the convolution theorem employed. The algorithm of the discrete convolution and fast Fourier Transform, named the DC-FFT algorithm includes two routes of problem solving: DC-FFT/Influence coefficients/Greens, function for the cases with known Greens functions and DC-FFT/Influence coefficient/conversion, if frequency response functions are known. This paper explores the method for the accurate conversion for influence coefficients from frequency response functions, further improves the DC- FFT algorithm, and applies this algorithm to analyze the contact stresses in an elastic body under pressure and shear tractions for high efficiency and accuracy. A set of general formulas of the frequency response function for the elastic field is derived and verified. Application examples are presented and discussed.

A Three-Dimensional Thermomechanical Model of Contact Between Non-Conforming Rough Surfaces

A necessary step in understanding failure problems of tribological elements is to investigate the contact performance of rough surfaces subjected to frictional heating. It is essential that the interfacial variables are obtained through solving the interactive thermomechanical contact problem. This paper studies the three dimensional thermomechanical contact of non-conforming rough surfaces, the model of which includes the normal surface displacements caused by the contact pressure, frictional shear, and frictional heating. Influence coefficients and frequency response functions for elastic and thermoelastic displacements, as well as those for temperature rises, are investigated for model construction. In order to develop an accurate and efficient solver, the numerical algorithms with the discrete convolution and fast Fourier transform techniques and the single-loop conjugated gradient method are used. The model modules are numerically verified and the thermomechanical performance of the rough surfaces in a point contact is studied.

Contact analyses for bodies with frictional heating and plastic behavior

The stress field within machine components is an important indicator for contact failures. Since both thermal stresses due to frictional heating and plasticity are significant in engineering application, it is critical to predict the total stress field. In this work, the steady-state thermal effect is considered and a thermo-elastic-plastic contact model is developed. The model is applicable for rolling and/or sliding contact problem, as far as small equivalent plastic strain hypothesis is respected. Influence coefficients for surface normal displacement, temperature, and strain and stress tensors are used with the discrete convolution and fast Fourier transform algorithm. The single-loop conjugate gradient iteration scheme is also applied to achieve fast convergence speed. Simulations are presented for several academic examples ranging from elastic to thermo-elastic-plastic. The thermo-elastic-plastic analyses show that the heat factor in a contact situation has significant effect not only on the critical Hertzian pressure and on the pressure distribution, but also on the magnitude and depth of the maximum von Mises stress during loading and the residual ones found after unloading.

Fast Fourier Transform Based Numerical Methods for Elasto-Plastic Contacts of Nominally Flat Surfaces

This paper presents a three-dimensional numerical elasto-plastic model for the contact of nominally flat surfaces based on the periodic expandability of surface topography. This model is built on two algorithms: the continuous convolution and Fourier transform (CC-FT) and discrete convolution and fast Fourier transform (DC-FFT), modified with duplicated padding. This model considers the effect of asperity interactions and gives a detailed description of subsurface stress and strain fields caused by the contact of elasto-plastic solids with rough surfaces. Formulas of the frequency response functions (FRF) for elastic/plastic stresses and residual displacement are given in this paper. The model is verified by comparing the numerical results to several analytical solutions. The model is utilized to simulate the contacts involving a two-dimensional wavy surface and an engineering rough surface in order to examine its capability of evaluating the elasto-plastic contact behaviors of nominally flat surfaces.

Elastic Fields due to Eigenstrains in a Half-Space

Engineering components inevitably encounter various eigenstrains, such as thermal expansion strains, residual strains, and plastic strains. In this paper, a set of formulas for the analytical solutions to cases of uniform eigenstrains in a cuboidal region-influence coefficients, is presented in terms of derivatives of four key integrals. The linear elastic field caused by arbitrarily distributed eigenstrains in a half-space is thus evaluated by the discrete correlation and fast Fourier transform algorithm, along with the discrete convolution and fast Fourier transform algorithm. By taking advantage of both the convolution and correlation characteristics of the problem, the formulas of influence coefficients and the numerical algorithms are expected to enable efficient and accurate numerical analyses for problems having nonuniform distribution of eigenstrains and for contact problems.

Mixed Lubrication Analyses by a Macro-Micro Approach and a Full-Scale Mixed EHL Model

This paper presents an improvement of a simplified approach, namely, the macro-micro approach, used to model the mixed elastohydrodynamic lubrication problems in counter-formal contacts, and its comparison with Zhu and Hus full-scale mixed-EHL model. In this approach, Patir and Cheng average flow model is employed to obtain the distribution of piecewise average pressure. A contact-embedment method that incorporates the detail of asperity contact pressure into the overall pressure distribution is utilized to reveal the severity of surface interaction. Numerical experiments are conducted, and the results are compared with those obtained by means of the full-scale mixed-EHL. The regime of the application of this macro-micro approach is explored.

A Three-Dimensional Thermal-Mechanical Asperity Contact Model for Two Nominally Flat Surfaces in Contact

The rough surface contact in a tribological process involves frictional heating and thermoelastic deformations. A three-dimensional thermal-mechanical asperity contact model has been developed, which takes into account steady-state heat transfer, asperity distortion due to thermal and elastic deformations, and material yield. The finite-element method (FEM), fast Fourier transform (FFT), and conjugate gradient method (CGM) are employed as the solution methods. The model is used to analyze the thermal-mechanical contact of typical rough surfaces and investigate the importance of thermal effects on the contact performance of surface asperities.

Transient Thermoelastic Stress Fields in a Half-Space

Computing the thermoelastic stress field of a material subjected to frictional heating is essential for component failure prevention and life prediction. However the analysis for three-dimensional thermoelastic stress field for tribological problems is not well developed. Furthermore, the pressure distribution due to rough surface contact is irregular; hence the frictional heating can hardly be described by an analytical expression. This paper presents a novel set of frequency-domain expressions (frequency response functions) of the thermoelastic stress field of a uniformly moving three-dimensional elastic half-space subjected to arbitrary transient frictional heating, where the velocity of the half-space, its magnitude and direction, can be an arbitrary function of time. General formulas are expressed in the form of time integrals, and important expressions for constant velocities are given for the transient-instantaneous, transient-continuous, and steady-state cases. The thermoelastic stress field inside a translating half-space with constant velocities are illustrated and discussed by using the discrete convolution and fast Fourier transform method when a parabolic type or an irregularly distributed heat source is applied.

An efficient method of analyzing the effect of roughness on fatigue life in mixed-ehl contact

An efficient and comprehensive Macro-Micro-Fatigue approach for analyzing the effect of roughness on fatigue life in mixed elastohydrodynamic lubrication contact is presented. It involves two macro-micro approaches, one for mixed lubrication analysis and the other for contact stress evaluation. The macro-micro approaches make it possible to efficiently model pressure and film thickness distribution over the entire area of contact, at the same time allowing a detailed account of asperity interaction effects. The three-stage process comprises a dry rough contact solver, a simplified mixed elastohydrodynamic lubrication solver, and a hydrostatic rough contact solver, all of which are presented. Subsurface stresses are calculated and fatigue life is estimated using the Zaretsky fatigue model. Numerical simulations are performed for several cases of point contacts of rough surfaces and results are presented on a comparative basis.