Zhanjiang Wang

An Efficient Numerical Method With a Parallel Computational Strategy for Solving Arbitrarily Shaped Inclusions in Elastoplastic Contact Problems

The plastic zone developed during elastoplastic contact may be effectively modeled as an inclusion in an isotropic half space. This paper proposes a simple but efficient computational method to analyze the stresses caused by near surface inclusions of arbitrary shape. The solution starts by solving a corresponding full space inclusion problem and proceeds to annul the stresses acting normal and tangential to the surface, where the numerical computations are processed by taking advantage of the fast Fourier transform techniques with a parallel computing strategy. The extreme case of a cuboidal inclusion with one facet on the surface of the half space is chosen to validate the method. When the surface truncation domain is extended sufficiently and the grids are dense enough, the results based on the new approach are in good agreement with the exact solutions. When solving a typical elastoplastic contact problem, the present analysis is roughly two times faster than the image inclusion approach and six times faster than the direct method. In addition, the present work demonstrates that a significant enhancement in the computational efficiency can be achieved through the introduction of parallel computation.

Novel Model for Partial-Slip Contact Involving a Material With Inhomogeneity

Contacts involving partial slip are commonly found at the interfaces formed by mechanical components. However, most theoretical investigations of partial slip are limited to homogeneous materials. This work proposes a novel and fast method for partial-slip contact involving a material with an inhomogeneity based on the equivalent inclusion method, where the inhomogeneity is replaced by an inclusion with properly chosen eigenstrains. The stress and displacement fields due to eigenstrains are formulated based on the half-space inclusion solutions recently derived by the authors and solved with a three-dimensional fast Fourier transform algorithm. The effectiveness and accuracy of the proposed method is demonstrated by comparing its solutions with those from the finite element method. The partial slip contact between an elastic ball and an elastic half space containing a cuboidal inhomogeneity is further investigated. A number of in-depth parametric studies are performed for the cuboidal inhomogeneity with different sizes and at different locations. The results reveal that the contact behavior of the inhomogeneous material is more strongly influenced by the inhomogeneity when it is closer to the contact center and when its size is larger.

Exploration on a Fast EHL Computing Technology for Analyzing Journal Bearings with Engineered Surface Textures

Solving elastohydrodynamic lubrication (EHL) problems is a complex and time-consuming process due to the interactive solutions of the Reynolds equation and contact elasticity. Analyzing journal bearing EHL problems is even more difficult due to the scale difference in the structural and surface features, which may span four orders of magnitude. This article presents a fast EHL computing technology utilizing a parallel numerical iterative method (the red–black successive overrelaxation method) and multithreaded computing scheme conducted by OpenMP directives. The fast computational approaches allow the construction of high-density EHL meshes for effective descriptions of important texture features of journal bearing surfaces.

Effects of Shaft Axial Motion and Misalignment on the Lubrication Performance of Journal Bearings Via a Fast Mixed EHL Computing Technology

A mixed elastohydrodrynamic (EHL) model for journal bearings considering an axial flow due to shaft axial motion and misalignment is developed for lubrication performance evaluation. A new, faster mixed EHL computing technology utilizing the odd–even successive overrelaxation (OESOR) parallel numerical iterative method is proposed based on the red–black successive overrelaxation (RBSOR) method to minimize the execution time prolonged by the complexity caused by the axial flow and misalignments. The multithreaded computing scheme conducted by the OpenMP directive using different meshes and threads suggests that the OESOR method exhibits better efficiency. A series of transient analyses was conducted to solve the mixed EHL model with the parallel OESOR method. The results show that the axial flow and misalignments significantly affect the average pressure, hydrodynamic and asperity contact pressure, elastic deformation, and other characteristics of the journal bearings.

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 Numerical Approach for Analyzing Three-Dimensional Steady-State Rolling Contact Including Creep Using a Fast Semi-Analytical Method

This article presents a new rolling contact solver using a semi-analytical method (SAM) to analyze three-dimensional steady-state rolling contacts, including the effects of creep. This new solver includes both the normal and tangential contact issues for the pressure and shear tractions, respectively. The accuracy and efficiency of the present method are demonstrated by comparison to existing analytical and numerical solutions. Rolling contact problems for a smooth infinite roller pressed against a half space with either a single asperity or a sinusoidal wave are investigated. The results show the complexity of pressure and shear traction. Asperities produce higher localized pressures, which demand larger local shear tractions to produce slip in such regions. Stick regions are also observed at the trailing edge of the contact.

Investigation on the effect of coating properties on lubrication of a coated spur gear pair

A thermal elastohydrodynamic lubrication model is proposed for a coated gear pair in which the influence coefficients for the elastic deformation and the subsurface stress components are obtained through the frequency response functions. The generalized Reynolds equation is utilized to represent the non-Newtonian effect. Energy equations of the contacting solids and the oil film are derived and solved based upon the marching method. The discrete convolute, fast Fourier transform method is used for fast calculation of the tooth surface displacement and the stress components underneath the surface. Variations of the slide-to-roll ratio, rolling speed, and the tooth load during gear meshing are considered and the film squeeze effect is taken into account. Effects of the coating thickness on the tribological performance, i.e. the film thickness, the pressure, the frictional behavior as well as the stress components are investigated under both the smooth and rough surface assumptions. Effects of the root mean square value of the tooth surface roughness on the pressure and stresses are discussed.

Numerical analysis of the influence of distributed inhomogeneities on tangential fretting

The tangential fretting is explored in the present study when one of the contacting bodies distributed with multiple inhomogeneities. The tangential fretting contact of an elastic sphere with an inhomogeneous material is considered. A new numerical model based on a semi-analytical method is developed by using Eshelby’s equivalent inclusion method and fast Fourier transform algorithms. The coupling between the contact loading and inhomogeneities is fully considered. The influence of multiple inhomogeneities on tangential contact is investigated. Parametric studies are conducted for the effects of randomly distributed inhomogeneities on the contact pressure, tangential displacement, subsurface stress, etc., revealing the significance of the influences of inhomogeneity distribution parameters on tangential fretting performance.

Effect of Surface Hardening Technique and Case Depth on Rolling Contact Fatigue Behavior of Alloy Steels

Surface hardening techniques are widely used to improve the rolling contact fatigue (RCF) resistance of materials. This study investigated the RCF resistance of hardened, ground steel rods made from three different aircraft-quality alloy steels (AISI 8620, 9310, and 4140) and hardened using different techniques (atmosphere carburizing, vacuum carburizing, and induction hardening) at different case depths. The RCF life of the rods was determined using a three ball-on-rod rolling contact fatigue test machine. After testing, the microstructures of the rods were examined using metallographic techniques. The stress distributions and plastic deformation zones for the specimens under RCF were calculated using an elastoplastic model for plastically graded materials. Relationships between surface hardness, case depth, and RCF life were investigated. The longest lives were observed for the vacuum-carburized AISI 9310 specimens, and the shortest lives were observed for the induction-hardened AISI 4140 specimens. It is concluded that the most important factors in determining the RCF lives of high-cleanliness surface-hardened alloy steels are (1) the hardness in the region of highest octahedral shear stress (in this case, ∼0.13 mm beneath the surface) and (2) the depth of high hardness (>613 HV), which determines the plastic deformation zone size.

Numerical Modeling of Partial Slip Contact Involving Inhomogeneous Materials

When solving the problems involving inhomogeneous materials, the influence of the inhomogeneity upon contact behavior should be properly considered. This research proposes a fast and novel method, based on the equivalent inclusion method where inhomogeneity is replaced by an inclusion with properly chosen eigenstrains, to simulate contact partial slip of the interface involving inhomogeneous materials. The total stress and displacement fields represent the superposition of homogeneous solutions and perturbed solutions due to the chosen eigenstrains. In the present numerical simulation, the half space is meshed into a number of cuboids of the same size, where each cuboid is has a uniform eigenstrain. The stress and displacement fields due to eigenstrains are formulated by employing the recent half-space inclusion solutions derived by the authors and solved using a three-dimensional fast Fourier transform algorithm. The partial slip contact between an elastic ball and an elastic half space containing a cuboidal inhomogeneity was investigated.Copyright