Discrete Convolution And Fast Fourier Transform Research Articles

Analysis of adhesive contact of heterogeneous elastic materials

This paper reports a three-dimensional numerical model to solve adhesive elastic contact problem of heterogeneous materials with an engineered rough surface. This model integrates the Maugis-Dugdale (MD) adhesive contact model, the Boussinesq-Cerruti integral equations, the equivalent inclusion method (EIM), and the discrete convolution and fast Fourier transform (DC-FFT) algorithm, aiming at accurate determination of contact results for heterogeneous materials. An adhesive displacement-driven conjugate gradient method (CGM) was also developed to support rapid solutions of contact pressure and contact area. Four cases were analyzed to verify this model with satisfaction. This model was used to analyze the effects of inhomogeneity (location, size, and material properties) and adhesion on micro-adhesive-elastic contact, and the results lead to a curve-fitting equation for quick evaluation of the effects of inhomogeneity properties and adhesion characteristics on normal traction. It was also utilized to study the influence of the roughness level of a type of rough surface on the surface adhesion behavior.

Numerical method for quasi-static adhesive elastic contact subjected to tangential loading

This paper presents a three-dimensional (3D) numerical model for simulating the adhesive contact with linear isotropic elasticity considering the interaction between normal and tangential loads. The model is based on the Boussinesq-Cerruti integral equations for elasticity, the Maugis-Dugdale (MD) model for adhesion, and the friction/adhesion interaction theory in the McMeeking model; it uses the Coulomb's law of friction to identify the occurrence of local microslip. Efficient and accurate determination of the contact behavior, together with adhesive and stick/slip regions, uses the iterative conjugate gradient method (CGM) and the discrete convolution and fast Fourier transform (DC-FFT) algorithm. The model analyzes adhesive-contact pressure, shear traction, and subsurface stress fields. It is used to study the effects of increasing tangential loading on the variations of stick/slip zones and adhesive-energy dissipation, as well as the influence of sinusoidal roughness on surface adhesion behavior. Compared with most theoretical models, the proposed numerical model has no restrictions on surface geometry and roughness of contact bodies, and it should have a wider range of applications.

Modeling 3D sliding electrical contact considering fully coupled thermal-mechanical-electrical effects

The 3D sliding electrical contact model considering thermal-mechanical-electrical coupling is presented in this paper. The semi-analytical method (SAM) is used to solve this complex multi-physical contact model. Firstly, the frequency response functions (FRFs) for thermal-mechanical-electrical fields are derived. Then, with discrete convolution and fast Fourier transform (DC-FFT) speeding calculation, a solving procedure, including the conjugate gradient method for force balance and algorithms for electrical potential equilibrium and heat flux partition, is proposed for the first time to solve the fully coupled electrical contact problem. Last, the effects of multiple loadings including the current, normal force, and sliding velocity on electrical contact behaviors are systematically investigated.

Impact Contact mechanical Performance evaluation of coated medium by semi-analytical method

Mechanical components are often subject to impact loads during service. It has been proven that application of a solid coating effectively improves contact mechanical performance of the component and prolongs its service life. The present paper proposes a semi-analytical model for elastic solid coatings subjected to impact load, which is based on numerical solution of classical contact theory, combined with a novel step-by-step iterative strategy with respect to impact time and binary search method. A conjugate gradient method (CGM) and discrete-convolution and fast Fourier transform (DC-FFT) algorithm are employed for enhancing computation efficiency of the present model. Comparative studies between results obtained by the proposed model and finite element method (FEM) show the validity of the model. Influences of impact velocities and coating parameters on impact mechanical performance and elastic stress distribution of solid coated medium are further investigated as a step towards understanding the impact contact failure mechanism of coated material or component.

Effect of fluid inertia force on thermal elastohydrodynamic lubrication of elliptic contact

A non-Newtonian thermal elastohydrodynamic lubrication (TEHL) model for the elliptic contact is established, into which the inertia forces of the lubricant is incorporated. In doing so, the film pressure and film temperature are solved using the associated equations. Meanwhile, the elastic deformation is calculated with the discrete convolution and fast Fourier transform (DC-FFT) method. A film thickness experiment is conducted to validate the TEHL model considering the inertia forces. Further, effects of the inertia forces on the TEHL performances are studied at different operation conditions. The results show that when the inertia forces are considered, the central and minimum film thicknesses increase and film temperature near the inlet increases obviously. Moreover, the inertial solution of the central film thickness is closer to the experimental result compared with its inertialess value.

Modeling thermal-visco-elastohydrodynamic lubrication (TVEHL) interfaces of polymer-based materials

This paper reports a novel thermal-visco-elasohydrodynamic lubrication (TVEHL) model for analyzing the lubrication behavior of the interface formed by an elastic sphere and a polymer half-space. The temperature-dependent viscoelastic displacement of the polymer surface is calculated through the elastic-viscoelastic correspondence theory and frequency-temperature superposition. The discrete convolution and fast Fourier transform (DC-FFT) algorithm is used for efficient solution computation. The model is verified by comparing results from its degenerated forms with those from thermal-viscoelastic (TVE) contact and thermal-elastohydrodynamic lubrication (TEHL) theories. The results from the current model with and without considering temperature effect are also compared. The new TVEHL model is explored to study the viscoelastic material property, entraining speed, sliding-to-rolling ratio, and the coupled thermal-viscoelasticity effects.

Visco-elastohydrodynamic lubrication of layered materials with imperfect layer-substrate interfaces

This paper reports a novel visco-elastohydrodynamic lubrication (VEHL) model for the lubrication interface formed by a rigid sphere and a viscoelastic layer imperfectly coated on an elastic half-space, aiming to study the effects of layer viscoelasticity and imperfect layer-substrate interface on the lubrication behavior. The surface viscoelastic deformation is calculated based on a linear viscoelastic model and the correspondence principle. The contact solution is formulated with the discrete convolution and fast Fourier transform (DC-FFT) algorithm by using the influence coefficients (ICs) converted from frequency response functions (FRFs). The model is validated by using the results from its degenerated versions through comparisons with available published data. The new VEHL model is implemented to explore the effects of surface speed, layer thickness, and layer-substrate elastic modulus ratio, as well as the degree of displacement discontinuity or stiffness defect at the layer-substrate interface.

Three-dimensional rolling/sliding contact on a viscoelastic layered half-space

This paper proposes an efficient contact model for a viscoelastic layered half-space where coating and substrate have different creep functions (i.e. different viscoelastic behaviours). The problem is formulated in three dimensions for an imposed pressure and shear field. The influence coefficients are calculated with the Papkovich-Neuber potentials and computation performed using Discrete Convolution and Fast Fourier Transform (DC-FFT) algorithms. From there, an elastic/viscoelastic correspondence is applied to move the elastic solution to a viscoelastic one. The Generalized Maxwell viscoelastic model is used and presented in the form of Prony series. A validation is performed using not only results within the literature but also by comparison with a finite element analysis. Next, a parametric study is done to analyse the influence of different parameters such as the elastic modulus ratio, the relaxation time ratio, the coating thickness or the rolling velocity. The model allows the analysis of the transient regime for which most of the known models struggle. It allows also to calculate 3D stresses and so to extract the stresses at the interface between the coating and the substrate so one can estimate the risk of failure such as delamination.

Study on Logarithmic Crowning of Tapered Roller Profile Considering Angular Misalignment

Abstract The angular misalignment of the tapered roller contact pair aggravates the stress edge effect and the stress concentration effect at the contact field, which in turn would affect bearing capacity and fatigue life of the contact pair. In this paper, based on the angular misalignment, the geometric interference model of the tapered roller contact pair was established. And two types of logarithmic crowning models for the roller profile design were theoretically deduced, in which design redundancy was considered through the quadratic processing of the pre-pressure. Then, with the discrete convolution and fast Fourier transform (DC-FFT) method and the conjugate gradient method (CGM), contact characteristics of the tapered roller with these two logarithmic profiles were verified. The results show that two profiles can effectively prevent the stress edge/concentration effect, improve contact pressure distribution and stress field of the roller in misalignment state, and ensure that the contact condition in alignment state is not greatly affected. The logarithmic crowning scheme is also suitable for the profile design of heavy-duty tapered rollers and can provide a reference for the crowning of other finite-line contact pairs under angular misalignment.

Effect of imperfect coating on the elastohydrodynamic lubrication: Dislocation-like and force-like coating-substrate interfaces

Abstract The commonly existed imperfect coatings may cause the displacements and forces transmitting discontinuously at the coating-substrate interface. This paper reports an elastohydrodynamic lubrication (EHL) model of ball-coated half space with coupled dislocation-like and force-like coating-substrate interface. Reynolds equation is solved to obtain the pressure. The surface elastic deformation and subsurface stress are calculated with the discrete convolution and fast Fourier transform (DC-FFT) method with the influence coefficients (ICs) obtained through corresponding frequency response functions (FRFs). The model is validated by the available data, and then implemented to study the pressure, film thickness, and subsurface stress distributions under imperfect coating-substrate interfaces of dislocation-like, force-like, and the coupled conditions, with various displacements and stresses jumping coefficients.

Investigation of Contact Performance of Case-Hardened Gears Under Plasto-elastohydrodynamic Lubrication

Case-hardening is widely used to enhance gear loading capacity. Simulation of the material gradient properties and contact characteristics are the key issues in contact fatigue analysis of case-hardened gears. In this work, a plasto-elastohydrodynamic lubrication (PEHL) model incorporating the hardness gradient and surface roughness is developed to investigate the contact performance of case-hardened gears. The generalized Reynolds equation is solved to determine film thickness and contact pressure. The plastic deformation and residual stress are obtained via the half-space eigenstrain problem solving. The Dang Van multiaxial fatigue criterion and the Euler transformation are employed to evaluate the contact fatigue parameter based on the predetermined stress field. The discrete convolution and fast Fourier transform (DC-FFT) algorithm is used for accelerating the computation. The influences of effective case depth, surface hardness and surface roughness on the contact performance are investigated. Numerical results indicate that as the surface hardness increases, the probability of fatigue crack nucleation decreases, and the depth of the crack initiation site increases. For a lower surface roughness case, the maximum von Mises stress and equivalent plastic strain appear at a deeper layer. As the surface roughness increases, the maximum values of pressure and stress increase sharply and move closer to the surface.

Mixed elastohydrodynamic lubrication model for finite roller-coated half space interfaces

Abstract This paper presents a mixed elastohydrodynamic lubrication (EHL) model for finite roller-coated half space interfaces. The model is built with the unified mixed lubrication approach and the influence coefficients (ICs) relating the pressure on a contact surface to surface deformations and subsurface stresses, converted from the frequency response functions (FRFs). The elastic deformation is solved with the discrete convolution and fast Fourier transform (DC-FFT) algorithm. This model is used to explore the EHL performance of rollers subjected to a wide range of operating conditions. A parameters study is conducted to reveal the effects of coatings, macro geometry, and surface roughness on the lubrication of rollers.

Analysis of non-Hertz contact stress and bearing capacity on meshing pairs in a real-time non-clearance precision ball transmission

Considering the friction on meshing pairs in a real-time non-clearance precision ball transmission, a modified meshing mechanical analysis model was established, and the normal meshing force and tangential friction acting on each meshing pair were calculated accurately via the contact stiffness coefficient method. The ball–tooth contact was equivalent to the contact model of an ellipsoid and semi-infinite elastic solid according to non-Hertzian theory, and the contact stress of meshing pairs was analyzed by the discrete convolution and fast Fourier transform (DC-FFT) technique. Furthermore, the bearing-capacity estimation method for a transmission system was established based on the Mises yield criterion. The results show that the tangential distribution force has a significant effect on the contact stress field of a meshing pair, with the maximum Mises equivalent stress being approximately 0.621 times the central contact pressure at different meshing positions. Moreover, the bearing capacity of the planetary plate is weaker than that of the center plate; hence, the bearing capacity of a transmission system should be determined by the planetary plate.

Numerical Analysis of Transient Elastohydrodynamic Lubrication During Startup and Shutdown Processes

In this study, a numerical model is developed for the analysis of elastohydrodynamic lubrication (EHL) at transient conditions during startup and shutdown processes. The time-dependent solutions are derived from an iterative algorithm with surface roughness involved, and the initial value is specified as the solution of the dry contact for the startup or steady-state solution of the lubrication contact at the starting velocity for the shutdown. The technique of discrete convolution and fast Fourier transform (DC-FFT) is employed to improve the computational efficiency. Solutions for smooth surfaces are compared with those obtained numerically and experimentally, and good consistency can be found. Profiles of pressure and film thickness and contours of subsurface stresses are analyzed to reveal the effects of acceleration/deceleration on the lubrication evolution. An isotropic roughness is then taken into account for the analysis. It is concluded that the coupling effects of the lubricant cavitation and oriented roughness would result in complex profiles of pressure and film thickness due to their disturbances to the lubrication film. A machined rough surface is presented to demonstrate the generality of the model. The analysis may potentially provide guidance to estimate the behavior of mechanical elements.

A Fast Approximate Method for Heat Conduction in an Inhomogeneous Half-Space Subjected to Frictional Heating

This paper reports a new three-dimensional model for heat conduction in a half-space containing inhomogeneities, applicable to frictional heat transfer, together with a novel combined algorithm of the equivalent inclusion method (EIM) and the imaging inclusion approach for building this model. The influence coefficients (ICs) for temperature and heat flux are obtained via converting the frequency response function (FRF) and integrating Green's function. The model solution is based on the discrete convolution and fast Fourier transform (DC-FFT) algorithm using the ICs, convenient for solving problems involving multiple elliptical inhomogeneities with arbitrary orientations. A group of parametric studies are conducted for understanding the thermal fields in the inhomogeneous half-space due to surface frictional heating, influenced by the properties of the inhomogeneity, its depth, and orientation.

Simulation of Plasto-Elastohydrodynamic Lubrication in a Rolling Contact

Surface plastic deformation due to contact (lubricated or dry) widely exists in many mechanical components, as subsurface stress caused by high-pressure concentrated in the contact zone often exceeds the material yielding limit, and the plastic strain accumulates when the load is increased and/or repeatedly applied to the surface in a rolling contact. However, previous plasto-elastohydrodynamic lubrication (PEHL) studies were mainly for the preliminary case of having a rigid ball (or roller) rotating on a stationary elastic–plastic flat with a fixed contact center, for which the numerical simulation is relatively simple. This paper presents an efficient method for simulating PEHL in a rolling contact. The von Mises yield criteria are used for determining the plastic zone, and the total computation domain is discretized into a number of cuboidal elements underneath the contacting surface, each one is considered as a cuboid with uniform plastic strain inside. The residual stress and surface plastic deformation resulted from the plastic strain can be solved as a half-space eigenstrain–eigenstress problem. A combination of three-dimensional (3D) and two-dimensional (2D) discrete convolution and fast Fourier transform (DC-FFT) techniques is used for accelerating the computation. It is observed that if a rigid ball rolls on an elastic–plastic surface, the characteristics of PEHL lubricant film thickness and pressure distribution are different from those of PEHL in the preliminary cases previously investigated. It is also found that with the increase of rolling cycles, the increment of plastic strain accumulation gradually approaches a stable value or drops down to zero, determined by the applied load and the material hardening properties, eventually causing a groove along the rolling direction. Simulation results for different material hardening properties are also compared to reveal the effect of body materials on the PEHL behaviors.

Model for Elastohydrodynamic Lubrication of Multilayered Materials

A novel model is constructed for solving elastohydrodynamic lubrication (EHL) of multilayered materials. Because the film thickness equation needs the term of the deformation caused by pressure, the key problem for the EHL of elastic multilayered materials is to develop a method for calculating their surface deformations, or displacements, caused by pressure. The elastic displacements and stresses can be calculated by employing the discrete-convolution and fast Fourier transform (DC-FFT) method with influence coefficients. For the contact of layered materials, the frequency response functions (FRFs), relating pressure to surface displacements and stress components, derived from the Papkovich–Neuber potentials are applied. The influence coefficients can be obtained by employing FRFs. The EHL of functionally graded material (FGM) can also be well solved using a multilayer material system. The effects of material layers and property gradient on EHL film thickness and pressure are further investigated.

A Feature-Scale Greenwood–Williamson Model for Metal Chemical Mechanical Planarization

In this work, a new feature-scale model is proposed for investigating the interaction between the wafer pattern and individual pad asperities in the process of chemical mechanical planarization (CMP). Based on the contact mechanics equation and the modified Greenwood–Williamson (GW) model which captures the evolution of feature curvature and the modification of the pad asperity height distribution, the discrete convolution and fast Fourier transform (DC-FFT) technique is adopted and combined with the Picard iteration method to calculate the direct contact pressure distribution between the wafer surface and the polishing pad. The computed pressure is then used to determine the local removal rate of the underlying patterns and predict the evolution of the wafer surface profile. Furthermore, the method is extended to capture the metal dishing as the feature size changes. It is shown that the present model can avoid the false simulated results produced by directly applying the original GW model for CMP when the feature size approaches zero. Otherwise, the calculated surface profile and dishing values of pattern geometries are in good agreement with the experimental data. Therefore, this model can not only be used to simulate the evolution of the wafer surface for global planarization at lower technology nodes, but can also be applied to provide some basic design rules for improving the process parameters and reducing the time and cost for developing new architectures.

Three-Dimensional Local Yield Maps of Hard Coating Under Sliding Contact

The local yield maps for the identification of the yield initiation positions of hard coating on three-dimensional (3D) elastic half space under sliding contact were developed. In this study, the semi-analytical method (SAM), which is based on the conjugate gradient method (CGM) and the discrete convolution and fast Fourier transform (DC-FFT) technique, was employed to analyze the contact problem. By using this method, the von Mises stress distributions for various combinations of coating thicknesses, friction coefficients, and elastic moduli of the coating and substrate were calculated. Then, the positions of yield initiation were found with the calculated results by comparing the critical maximum contact pressure Pmax,c for von Mises yielding at or in the different positions (surface, coating, interface, and substrate), and the 3D-local yield maps were introduced in relation to the yield strength ratio of the coating to the substrate (Yf/Yb) and the ratio of the coating thickness to the Hertzian contact radius (t/a0). Finally, the effect of critical friction coefficient on the transition of yielding positions was discussed.

G010014 表面および界面の力学的特性を考慮した薄膜を有する半無限異方性弾性体の接触解析([G01001]計算力学部門一般セッション(1):固体力学の基礎的な数値解析)

In this paper, contact analysis for anisotropic elastic layered half-space is performed using surface Green function considering surface and interface property. The discrete convolution and fast Fourier transform (DC-FFT) method and conjugate gradient (CG) method were used for conducting the contact analysis. The contact analysis was conducted for investigating the effect of thickness of thin films and material of substrate on the penetration depth for the rigid spherical indenter.